electrical sensors for chemical processes: …snsm/group/dissertations/... · separation and the...
TRANSCRIPT
ELECTRICAL SENSORS FOR CHEMICAL PROCESSES: CAPACITIVE
SENSING OF PHOTOINDUCED INTRAMOLECULAR CHARGE
TRANSFER REACTIONS AND UNIVERSAL BIOAFFINITY
SENSOR BASED ON CONDUCTANCE VARIATION
THROUGH NANOPORES
BY
IVAN VALER’EVICH VLASSIOUK, B.S.
A dissertation submitted to the Graduate School
in partial fulfillment of the requirements
for the degree
Doctor of Philosophy
Major Subject: Chemistry
New Mexico State University
Las Cruces, New Mexico
December 2005
ii
“Electrical sensors for chemical processes: capacitive sensing of photoinduced
intramolecular charge transfer reactions and universal bioaffinity sensor based on
conductance variation through nanopores,” a dissertation prepared by Ivan
Valer’evich Vlassiouk in partial fulfillment of the requirements for the degree, Doctor
of Philosophy, has been approved and accepted by the following:
Linda Lacey Dean of the Graduate School Sergei Smirnov Chair of the Examining Commitee Date
Committee in charge:
Dr. Sergei Smirnov, Chair
Dr. Igor Sevostianov
Dr. Jeremy Smith
Dr. Haobin Wang
iii
ACKNOWLEDGEMENTS
First of all I would like to express my gratitude to my parents. Without their
unobtrusive guiding thorough almost every step in my life I would not even start to
think of getting my PhD. It was them who tried to make me think by introducing to
me math problems when I was very young. It was them who paid unexpected visit to
the Novosibirsk when I was about to drop off from the university and convinced me
to get a bachelor degree. I hope they are glad that I have got a PhD.
I would like to thank my adviser Dr. Sergei Smirnov for everything. It is
impossible to enumerate every thing that he did for me. I am grateful for introducing
to me the exciting field of electron transfer and thrilling biosensors subject. He was
the generator of ideas; he had explanations for every single experiment data that I got.
He was very supportive not only in the lab, but in the life behind lab doors.
Also I am thankful to the members of my committee: Dr. H. Wang, Dr. J.
Smith and Dr. I. Sevostianov for reading my project, listening countless presentations
(at least number of those presentations seems to me to be countless) and making
valuable comments and suggestions. I acknowledge all the professors at the
Department of Chemistry and Biochemistry as well.
I want to acknowledge our collaborators: Dr. Devens Gust (Arizona State
University), Dr. Franz-Peter Montforts (Universität Bremen) and Dr. Piotr Piotrowiak
(Rutgers University) for providing us with extraordinary molecules and for the
memorable conversations and discussions.
iv
Present and former graduate students of our group: Alexey Krasnoslobodtsev,
Pavel Takmakov and Kirill Velizhanin for all fun and terrific time at “High Desert”
brewery.
The last but not least I would like to thank the closest people to me – my wife
and my daughter. I think it was their ~95% “fault” of getting me into all this PhD
work. I am grateful to my wife, Natasha, for almost all of those truly unforgettable
moments that she presented to me. I believe she did her best to support me. I want to
thank my daughter, Marina, for making my life meaningful, for cheering me up and
for trying to be good at math.
v
VITA
January 13 1979 Born in Khabarovsk, Far East region, Russia
June 1995 Graduated from Gymnasium N 3, Khabarovsk
1995-2000 Student at Novosibirsk State University
1998-2000 Research assistant at Institute of Chemical Kinetics and Combustion, Novosibirsk
2000 B.S. degree in chemistry, Novosibirsk State University
2000-2005 Research and Teaching Assistant, Department of Chemistry and Biochemistry, New Mexico State University
Major publications
1) I. Vlassiouk, S. Smirnov, D. Gust “Photovalve: Light Induced Switch of Hydrophobicity in Nanopores” Nano Lett., submitted, 2005
2) V. Szczepanski, I. Vlassiouk, S. Smirnov “Stability of chemically modified alumina nanopores” Langmuir, in preparation, 2005.
3) P. Takmakov, I. Vlassiouk, S. Smirnov “Nanoporous Alumina as a Matrix for Fluorescence Based Detection of The Biological Species” Biosensors & Bioelectronics, 2005, submitted
4) I. Vlassiouk, P.Takmakov, S.Smirnov,, “Sensing DNA hybridization via ionic conductance through a nanoporous electrode” Langmuir, 2005, v. 21, no. 11, pp. 4776-4778.
vi
5) Vlassiouk, I; Krasnoslobodtsev, A; Smirnov, S; Germann, M, “"Direct" detection and separation of DNA using nanoporous alumina filters” Langmuir; 2004; v. 20, no. 23, pp. 9913-9915
6) Vlassiouk, I; Smirnov, S, “Electric polarization of dilute polar solutions: Revised treatment for arbitrary shaped molecules” J. Phys. Chem.; 2003; v. 107, no. 38, pp. 7561-7566.
7) Montforts, FP; Vlassiouk, I; Smirnov, S; Wedel, M, “Long-lived photoinduced charge transfer state of synthetically affable porphyrin-fullerene dyads” J. Porph. Phthal., 2003; v. 7, no. 9-10, pp. 651-666.
8) Smirnov, SN; Liddell, PA; Vlassiouk, IV; Teslja, A; Kuciauskas, D; Braun, CL; Moore, AL; Moore, TA; Gust, D “Characterization of the giant transient dipole generated by photoinduced electron transfer in a carotene-porphyrin-fullerene molecular triad” J. Phys. Chem., 2003; v. 107, no. 38, pp. 7567-7573
9) Smirnov, S; Vlassiouk, I; Kutzki, O; Wedel, M; Montforts, FP, “Unusual role of oxygen in electron-transfer processes” JACS; 2002; v. 124, no. 16, pp. 4212-4213
10) Vlassiouk, I; Smirnov, S; Kutzki, O; Wedel, M; Montforts, FP, “Radical induced impeding of charge recombination” J. Phys. Chem; 2002; v. 106, no. 34, pp. 8657-8666.
11) Vlasyuk, IV; Bagryansky, VA; Gritsan, NP; Molin, YN; Makarov, AY; Gatilov, YV; Shcherbukhin, VV; Zibarev, AV, “1,2,3-Benzodithiazolyl radicals formed by thermolysis and photolysis of 1,3,2,4-benzodithiadiazines” Phys. Chem. Chem. Phys; 2001; v. 3, no. 3, pp. 409-415
12) Gritsan, NP; Bagryansky, VA; Vlasyuk, IV; Molin, YN; Makarov, AY; Platz, MS; Zibarev, AV, “Intermediates of photolysis of 1,3,2,4-benzodithiadiazines studied by matrix isolation spectroscopy and quantum chemistry” Russ. Chem. Bull., 2001; v. 50, no. 11, pp. 2064-2070
13) Bagryansky, VA; Vlasyuk, IV; Gatilov, YV; Makarov, AY; Molin, YN; Shcherbukhin, VV; Zibarev, AV, “Formation of stable 1,2,3-benzodithiazolyl
vii
radicals by thermolysis of 1,3,2,4-benzodithiadiazines” Mend. Comm., 2000; no. 1, pp. 5-6A
viii
Field of study
Major field: Chemistry
Physical chemistry
ix
ABSTRACT
ELECTRICAL SENSORS FOR CHEMICAL PROCESSES: CAPACITIVE
SENSING OF PHOTOINDUCES INTRAMOLECULAR CHARGE
TRANSFER REACTIONS AND UNIVERSAL BIOAFFINITY
SENSOR BASED ON CONDUCTANCE VARIATION
THROUGH NANOPORES
BY
IVAN VALER’EVICH VLASSIOUK
Doctor of Philosophy
New Mexico State University
Las Cruces, New Mexico, 2005
Dr. Sergei Smirnov, Chair
Development of two types of electrical sensors for detecting photochemical
and biochemical processes are described. The photoinduced transient displacement
current technique (PTDC) is used for studying light induced charge transfer processes
in solutions and ionic conductance sensors based on nanoporous alumina membranes
are applied for studying DNA binding.
Both, theoretical and experimental development of PTDC technique is
provided. In theory, a revised treatment for deducing dipole moments of solute
molecules from the light induced electric polarization change is given, that allows
x
application to arbitrarily shaped molecules. A simplified approach for data evaluation
is suggested and compared with the analytical solution for an ellipsoidal cavity and
with a numerical solution for two spherical ions.
The theoretical results are applied to porphynoid-fullerene dyads and
carotenoid (C) porphyrin (P) fullerene (C60) triad. For the dyads, optical and PTDC
study demonstrate efficient intramolecular electron transfer from porphyrin to
fullerene with the lifetime of the charge transfer state on the order of a few
nanoseconds in low polarity solvents. Solvent polarity effect on the yield of charge
separation and the conformations in the charge transfer state are investigated in detail.
Excitation of a carotenoid (C) porphyrin (P) fullerene (C60) molecular triad yields ,
via a sequential two-step photoinduced electron transfer process, a charge-separated
state, C•+-P-C60•−, with a lifetime of 340 ns in 2-methyltetrahydrofuran solution.
PTDC investigation of the dipole moment of the charge-separated state in
tetrahydrofuran and 2-methyltetrahydrofuran confirm the formation of a giant dipole
with a moment in excess of 150 D, corresponding to separated charges located on the
fullerene and carotene moieties of the triad. Detailed comparison corroborates the
hypothesis of insignificant conformational changes in the molecule upon charge
transfer.
We also show that stable radicals, such as molecular oxygen and TEMPO, can
inhibit or accelerate back electron transfer in the charge transfer state by enhancing
intersystem crossing of the singlet radical ion pair into its triplet state. The
phenomenon is demonstrated on a series of porphynoid-fullerene dyads. The
xi
discrimination is linked with the energy of the charge separated state relative to that
of the locally excited triplet states. Due to the spin statistics, the reverse intersystem
crossing is less efficient, allowing use of oxygen and other paramagnetic species for
impeding charge recombination in various electron transfer systems. The
interpretation is also confirmed by measurements of singlet oxygen yield and (lack
of) magnetic field effects.
A new concept for using alumina nanoporous membranes (AAO) modified
with DNA for “label-free” detection and separation/purification of the target ss-DNA
is demonstrated. A high surface density of DNA (4×1012 cm-2) and high efficiency of
hybridization (ca. 70%) in combination with increased effective surface area, make
this system very attractive for development of various ss-DNA (or RNA) detection
methods. Moderate transparency of AAO in the UV and IR regions allows direct
detection of DNA hybridization by optical and IR absorption, as well as electrical
detection. The application of such membranes for DNA purification is also
demonstrated. Electrical detection of DNA hybridization with label-free approach is
demonstrated using impedance variation resulted from blocking the pores by bound
the DNA to ionic flow. Using cyclic voltammetry, dc conductance, and impedance
spectroscopy we confirm the importance of pore size – the effect is observed with 20
nm diameter pores and is absent for 200 nm pores.
This concept can be applied to detecting a broad range of biological species
that possess strong enough bioaffinity interactions.
xii
TABLE OF CONTENTS
1 INTRODUCTION ................................................................................ 1
1.1 The dissertation overview ..................................................................... 3
1.2 References............................................................................................. 5
2 ELECTRIC POLARIZATION OF DILUTE POLAR SOLUTIONS. REVISED TREATMENT FOR ARBITRARY SHAPED MOLECULES....................................................................................... 7
2.1 Introduction........................................................................................... 7
2.2 Theory ................................................................................................... 10
2.3 Theoretical Examples............................................................................ 17
2.3.1 Ellipsoidal cavity .................................................................................. 17
2.3.2 Two spheres .......................................................................................... 21
2.4 Experimental Examples ........................................................................ 25
2.4.1 Almost spherical molecules .................................................................. 25
2.4.2 Almost ellipsoidal molecules ................................................................ 26
2.4.3 Very large molecules ............................................................................ 27
xiii
2.5 Conclusions........................................................................................... 30
2.6 References............................................................................................. 30
3 LONG-LIVED PHOTOINDUCED CHARGE TRANSFER STATE OF SYNTHETICALLY AFFABLE PORPHYRIN – FULLERENE DYADS................................................................................................. 33
3.1 Introduction........................................................................................... 33
3.2 Experimental Section ............................................................................ 33
3.3 Results................................................................................................... 36
3.3.1 Spectroscopic investigations ................................................................. 36
3.3.2 Transient displacement current measurements ..................................... 42
3.3.3 Chemical instability .............................................................................. 47
3.4 Discussion ............................................................................................. 49
3.4.1 Ground state geometry .......................................................................... 49
3.4.2 Charge-separated state geometry .......................................................... 52
3.4.3 Dipole moments .................................................................................... 55
3.4.4 Electron transfer rates ........................................................................... 57
xiv
3.5. Conclusions........................................................................................... 63
3.6 References............................................................................................. 64
4 CHARACTERIZATION OF THE GIANT TRANSIENT DIPOLE GENERATED BY PHOTOINDUCED ELECTRON TRANSFER IN A CAROTENE-PORPHYRIN-FULLERENE MOLECULAR TRIAD................................................................................................... 69
4.1 Introduction........................................................................................... 69
4.2 Results................................................................................................... 71
4.2.1 Transient absorption measurements...................................................... 71
4.2.2 Molecular modeling .............................................................................. 72
4.2.3 Transient DC photocurrent measurements............................................ 72
4.2.4 Photoinduced voltage curves ................................................................ 74
4.2.5 Analysis of the data............................................................................... 75
4.3 Discussion ............................................................................................. 79
4.3.1 Magnitude of the dipole moment .......................................................... 79
4.3.1.1 Molecular shape .................................................................................... 80
4.3.1.2 Effect of mutual polarizability .............................................................. 81
xv
4.3.1.3 Quantum yield....................................................................................... 83
4.3.1.4 Molecular conformation........................................................................ 83
4.3.2 Rotation times ....................................................................................... 85
4.3.3 Lifetime of the charge-separated state .................................................. 87
4.4 Conclusions........................................................................................... 87
4.5 References............................................................................................. 88
5 RADICAL INDUCED IMPEDING OF CHARGE RECOMBINATION ............................................................................. 94
5.1 Introduction........................................................................................... 94
5.2 Experimental Section ............................................................................ 98
5.3 Results and Discussion.......................................................................... 101
5.3.1 Dipole measurements with O2 ............................................................................................... 101
5.3.2 Singlet oxygen measurements............................................................... 111
5.3.3 Dipole measurements with TEMPO and heavy atoms ......................... 114
5.3.4 Intersystem crossing rates at high radical concentrations..................... 117
5.3.5 Effects of heavy atoms and magnetic field ........................................... 122
xvi
5.3.6 Discussion ............................................................................................. 122 5.4 Conclusions........................................................................................... 126
5.5 References............................................................................................. 127
6 OPTICAL AND ELECTRIC SENSING OF THE DNA HYBRIDIZATION INSIDE ALUMINA NANOPORES .................... 131
6.1 “Direct” detection and separation of DNA using nanoporous alumina filters ..................................................................................................... 131
6.1.1 Introduction........................................................................................... 131
6.1.2 Results and discussion .......................................................................... 132
6.2 Sensing DNA hybridization via ionic conductance through nanoporous electrode. ........................................................................... 139
6.2.1 Results and discussion .......................................................................... 141
6.3 Conclusions........................................................................................... 149
6.4 References............................................................................................. 150
APPENDICES
A DERIVATION OF EQUATIONS (5.12) AND (5.13) ......................... 154 B SUPPORTING INFORMATION FOR 6.1 SECTION “DIRECT”
DETECTION AND SEPARATION OF DNA USING NANOPOROUS ALUMINA FILTERS............................................... 158
xvii
C SUPPORTING INFORMATION FOR 6.2 SECTION SENSING DNA HYBRIDIZATION VIA IONIC CONDUCTANCE THROUGH NANOPOROUS ELECTRODES .................................... 168
D ELECTRIC POLARIZATION CALCULATION OF DILUTE POLAR SOLUTIONS. FOR ARBITRARY SHAPED MOLECULES....................................................................................... 180
xviii
LIST OF TABLES
2.1 Parameters for scaling using ellipsoidal approximation and the dipole moments. ............................................................................................... 27
3.1 The energies of the local singlet (ES), the local triplet (ET), and the charge separated (GCS) states for the dyads and fullerene. ............................... 40
3.2 Experimental fitting parameters for the dipole signals of dyads in different solvents.................................................................................................. 45
3.3 Reorganization energy for the charge transfer reactions from porphyrin to fullerene in different solvents................................................................ 59
3.4 Franck –Condon factors for charge separation rates from different excited states (in eV-1) in three solvents calculated using equation (3.12)........ 61
5.1 Dipole moments, µ, and the energies of the local triplet (ET) and the charge transfer states (ECT) for the four dyads along with the singlet charge recombination rates in toluene (kCRS).................................................... 101
5.2 Rate constants of “oxygen quenching” for the four dyads and fullerene in toluene. .................................................................................................. 103
5.3 Rate constants of “TEMPO quenching” for the four dyads in toluene. 124
6.1 Effect of the immobilized DNA surface density inside AAO on its impedance change at 0.01 Hz at 20nm side upon DNA hybridization.................... 147
xix
LIST OF FIGURES
2.1 Illustration of solvent induced dipole moment for different molecular cavity shapes. ........................................................................................ 13
2.2 Two-dimensional projection of the 3-D isopotential surfaces normalized by the dielectric constant, ε, for two point charges of opposite sign placed at the foci of a spheroid with the aspect ratio a/b = 3.5....................................................................................................... 19
2.3 Integrated solvent induced dipole moment dependence on the dielectric constant ε for the case of Fig. 2.2.......................................... 20
2.4 Two-dimensional projection of 3-D isopotential surfaces normalized by the dielectric constant, ε, for two point charges of opposite sign placed inside the two spheres of equal radii that are positioned at close contact .......................................................................................... 22
2.5 Integrated solvent induced dipole moment dependence on the dielectric constant ε for the case of Fig. 2.2.......................................... 23
2.6 Integrated solvent induced dipole moment dependence on the dielectric constant ε for the case when two point charges of opposite sign are placed inside the two spheres of equal radii that are positioned at a distance three times their radii. ..................................... 24
2.7 Transient displacement current signals for two molecules in toluene solution observed after absorbing 38 µJ at 396 nm in a cell with 0.56 mm gap and using 1 MΩ load resistor. ................................................. 28
3.1 Molecular structures for the molecules under study ............................. 34
3.2 Optical absorption spectra of the dyads in different solvents and their comparison with the convoluted sums of the absorption spectra of C60 and a corresponding porphyrin........................................................ 38
xx
3.3 Steady state fluorescence spectra for the dyads ZnP-C60 and P-C60
and the corresponding porphyrins, ZnP and P. ..................................... 39
3.4 Approximate energy levels for different states of the dyads in toluene and the labels of the rate constants........................................................ 40
3.5 Steady state fluorescence spectra of C60(COOEt)2 in toluene and THF with excitation at 330 nm. ............................................................ 41
3.6 Transient displacement current signals for ZnP-C60 and P-C60 in toluene and THF for 20 µJ absorbed energy at 396 nm and 600 V of external voltage ..................................................................................... 44
3.7 Transient displacement current signal from P-C60 in CH2Cl2 for 20 µJ absorbed energy at 396 nm and 600 V.................................................. 48
3.8 Calculations for ZnP-C60 and P-C60 dyads at different center-to-center separations. ................................................................................. 51
3.9 Illustration of two isoenergetic (from calculation using AM1) geometries of the dyads......................................................................... 52
3.10 Calculations for ZnP-C60 and P-C60 dyads at different center-to-center separations in THF ..................................................................... 54
4.1 Structure and the lowest-energy conformation for triad as calculated using MM+ molecular mechanics methods........................................... 73
4.2 Photoresponse of C-P-C60 triad in THF as measured in the displacement current mode.................................................................... 76
4.3 Photoresponse of C-P-C60 triad in 2-MTHF as measured in the displacement current mode and the charge displacement mode. .......... 77
xxi
5.1 Molecular structures for the four molecules under study. .................... 95
5.2 Transient displacement charge signals for ZnPor – C60 dyad in toluene with varying oxygen concentrations......................................... 104
5.3 Transient displacement charge signals for ZnChl – C60 dyad in toluene at different oxygen concentrations. .......................................... 105
5.4 Schematic energy diagram for the two chlorin-C60 dyads. ................... 106
5.5 Transient displacement charge signal for ZnChl – C60 dyad in toluene with 8.35 mM of oxygen .......................................................... 110
5.6 Kinetic of singlet oxygen luminescence at 1270 nm for solution of C60 in toluene and 1 atm of O2. ............................................................. 113
5.7 Reverse intersystem crossing rate for ZnChl-C60 dyad in toluene induced by O2 and TEMPO................................................................... 116
5.8 Kinetic scheme for multiple collisions with TEMPO........................... 118
5.9 Kinetic scheme for multiple collisions with oxygen............................. 121
6.1 Immobilization scheme......................................................................... 133
6.2 UV absorption spectra of a 200 nm AAO filter (60 µm thick) with: A – ss-DNA 21-mer immobilized inside the pores and B - after hybridization with a complementary 21-mer. ....................................... 134
6.3 IR absorption of a 200 nm filter with immobilized 21-mer and after its hybridization with a complementary 41-mer ................................... 135
xxii
6.4 Normalized temperature variation of the UV absorption at 260 nm for the immobilized hybrid between the 21-mer and the 41-mer.......... 136
6.5 Schematic representation of the DNA purification using developed technique ............................................................................................... 137
6.6 Absorption spectra of 1 mL solution originally with 185 nM of Cy5-tagged ss-DNA (21-mer) before and after a single pass through the AAO affinity filter. Spectrum of the filter with hybridized Cy5 tagged complementary ss-DNA. ........................................................... 138
6.7 Proposed sensor .................................................................................... 140
6.8 Experimental electrochemical cell ........................................................ 141
6.9 CV in the region for Fe(CN)63-/4- oxidation/reduction: (A) at the 20
nm side of a modified membrane and (B) 200nm side. ........................ 142
6.10 Chronocoulometric plot for charge passed through the modified nanoporous membrane modified with 21-mer ss-DNA immobilized inside pores filter before and after hybridization with complementary 21-mer. .................................................................................................. 144
6.11 Nyquist plot for impedance at 20 nm side of a membrane and 200 nm side ........................................................................................................ 145
6.12 Impedance increase at 0.01 Hz upon complete DNA hybridization as a function of surface density of initial ss-DNA..................................... 148
B1 Stoichiometric solution of the 21-mer with its complementary 21-mer shows ca. 20% hypochromism at 260 nm in 1 M NaCl with Tm = 79oC and ca.18% in 0.1 M NaCl with Tm = 67oC.............................. 166
xxiii
B2 UV absorption spectra of a 200 nm AAO filter (60 mm thick) with ss-DNA 21-mer immobilized inside the pores and after hybridization by a complementary 41-mer.................................................................. 164
B3 Stoichiometric solution of the 21-mer and the 41-mer (1.8 µM of
each) shows ca.12% hypochromism at 260 nm in 0.2 M NaCl with Tm = 67oC .............................................................................................. 165
B4 UV absorption of the target ss-DNA 21-mer solution before and passing through the modified filter. ...................................................... 166
C1 UV Absorbance spectra of immobilized ssDNA at nanoporous 20nm membrane .............................................................................................. 170
C2 UV absorbance change upon hybridization of immobilized ssDNA by complementary 21-mer. ................................................................... 171
C3 Low frequency portion of the Bode plot for two orientations of the filter. ...................................................................................................... 172
C4 SEM image of the 200 nm side and 20 nm side of the “20nm” Whatman filter ...................................................................................... 173
C5 SEM image of gold nanowires prepared by electroreduction of gold from solution into nanoporous alumina filter from the 20 nm side ...... 174
C6 Diffusion of Fe(CN)6-3/-4 through 200 nm membrane........................... 176
C7 CV in the region for Ru(NH3)62+ /3+ oxidation/reduction at the 20 nm
side of a modified membrane and 200nm side...................................... 177
C8 Anisotropy factor in CV (ratio of the amplitudes on 20nm side to that at 200 nm............................................................................................... 178
1
1 INTRODUCTION
Photosynthesis, responsible for production of organic matter from carbon
dioxide and transformation of sunlight into chemical energy,1 is the most
important biological process on earth. The initial key step of photosynthesis is
light induced electron transfer from a chlorin dimer donor to a quinone acceptor
in the photosynthetic reaction centre. Numerous artificial photosynthetic systems
constituting porphinoid donors and quinone acceptors have been designed to
investigate photoinduced energy and electron transfer.2 The systems, synthesized
to mimic natural photosynthesis, range from simple dyads to very complex
molecular arrangements assembled from several subunits. Since their discovery,
fullerenes,3 especially C60, have become attractive as acceptor subunits for
molecular dyads (and larger systems), in which light induced electron transfer
proceeds from a porphinoid donor to the fullerene.4 Studying of these systems is
driven by a desire to optimize high yield and a long lifetime of charge transfer
states.
The most widely used technique for investigating photoinduced electron
transfer is the transient optical absorption technique. This powerful technique
allows accurate measurement of kinetics with high time resolution and the ability
to identify anion and cation moieties as well as excited state species. However,
this technique does not provide information about the charge distribution in the
charge transfer state that can alter as a result of conformational changes.
2
In this work we used the photoinduced transient displacement current
technique5 (PTDC) to offer unambiguous measure of the separation distance
between charges formed as a result of photoexcitation. The technique allows
measurement of the distance between charges directly and thus provides
information complementary to that from transient absorption. Even though PTDC
has a limited time resolution, ca. 0.5ns, which is not sufficient to monitor the
kinetics of charge separation in many cases, a slower charge recombination can
be easily evaluated. Due to intrinsic limitations, electrolytes and high polarity
solvents are restricted from being used in this technique, but studies in relatively
polar solvents such as THF and methylene chloride, can be easily performed.
Photosynthesis is not the only key biological process that can be
investigated using electrical measurements. The amazing selectivity of many
biological reactions such as antibody/antigen interaction or DNA hybridization
can be applied for electrical biosensors construction. Numerous physical
phenomena are applied for constructing the biosensors.6 Fluorescence detection is
the method of choice for the majority of commercially successful biosensor
microarrays due to the high sensitivity. However, the procedure of modifying the
analyte with a fluorescence probe is expensive and time-consuming. We
developed a new universal biosensor based on nanoporous alumina membranes
where the detection relies on either the ionic conductance variation due to volume
exclusion, or UV and IR direct absorption change. Neither of these methods
requires modification of the target molecule.
3
1.1 The dissertation overview
The dissertation consists of five individual chapters that address different
issues summarized below. They have separate introductions and conclusions.
Chapter 2 is dedicated to the theoretical development of the photoinduced
transient displacement current technique. In particular, we address the issue of
solvent contribution to the dipole signal of arbitrary shaped molecules. The
solution of the Poisson equation for bulky molecules is not easy to obtain because
of the demanding calculations. The developed theory shows how the solution of
the Poisson equation can be realized for an arbitrary shaped molecule by first
obtaining an analytical solution for the charge distribution in the molecule in
vacuum and then calculating the solvent polarization by integrating the resulting
electric field with the solvent dielectric constant.
Chapter 3 describes the PTDC (and optical) studies of photoinduced
electron transfer processes for four porhinoid-fullerene dyads synthesized in Dr.
P. Montforts group. Questions related to the molecular conformations,
photoinduced dipole moment magnitude, lifetime of the charge transfer states in
different solvents is addressed.
Chapter 4 discusses various properties of a molecular triad synthesized in
Dr. D. Gust group. The triad consists of three subunits: carotene-porphyrin-
fullerene . The largest reported dipole is measured for this triad upon
photoexcitation. Effects of the molecular shape, mutual polarizability, as well as
4
of the quantum yield and the rotation time under the external electric field are
discussed. The lack of conformational changes in the photoinduced charge
transfer state is confirmed. Importance of the solvent polarization contribution
developed in Chapter 2 for treating such large molecules is demonstrated.
Chapter 5 addresses the question of the lifetime of charge transfer (CT)
states and its dependence on intersystem crossing caused by collisions with
radicals. The effect of O2 and TEMPO on the intersystem crossing rate is shown.
The lifetime of the generated triplet CT state is much longer then that for the
singlet state. We show that, depending on the energy of the CT state with respect
to that of the locally excited triplet state, the lifetime of the CT state can be either
prolonged or shortened as a result of intersystem crossing. The lifetime of the
transition state is estimated to be small and close to that of a transient encounter
complex.
Chapter 6 details the new proposed biosensor based on nanoporous
alumina membranes. The emphasis is given to the method based on changing
ionic conductivity through the nanopore. The immobilization technique inside the
alumina nanopores is described. The immobilization and hybridization efficiency
of DNA in nanopores (and the temperature dependence for the latter) are
measured by UV and IR absorbance. Application of such nanoporous membranes
as convenient bioaffinity filters is demonstrated. Cyclic voltammetry,
chronocoulometry and impedance spectroscopy are applied to measure the
nanopore blockage upon hybridization.
5
1.2 References
1 a) The Photosynthetic Reaction Center (Eds.: J. Deisenhofer, J. R. Norris), Academic Press, San Diego, 1993; b) Huber R, Angew. Chem. 1989, 101, 849; Angew. Chem. Int. Ed. Engl. 1989, 28, 848; c) Deisenhofer J, Michel H, Angew. Chem. 1989, 101, 872; and Angew. Chem. Int. Ed. Engl. 1989, 28, 829.
2. a) Gust D, Moore TA in Topics in Current Chemistry, vol. 159, Photoinduced Electron Transfer III (Ed.: J. Mattay), Springer, Berlin, 1991; b) Wasielewski MR, Chem. Rev. 1992, 92, 435; c) Gust D, Moore TA, Moore AL, Acc. Chem. Res. 1993, 26, 198; d) Kurreck H, Huber M, Angew. Chem. 1995, 107, 929; Angew. Chem. Int. Ed. Engl. 1995, 34, 849; e) Tauber AY, Kostiainen RK, Hynninen PH, Tetrahedron 1994, 50, 4723; f) Borovkov VV, Gribkov AA, Kozyrev AN, Brandis AS, Ishida A, Sakata Y, Bull. Chem. Soc. Jpn. 1992, 65, 1533; g) Maruyama K, Yamada H, Osuka A, Chem. Lett. 1989, 5, 833; h) Tauber AY, Helaja J, Kilpeläinen I, Hynninen PH, Acta Chem. Scand. 1997, 51, 88.
3. Hirsch A, The Chemistry of the Fullerenes, Thieme, Stuttgart, 1994.
4. a) Imahori H, Sakata Y, Adv. Mater. 1997, 9, 537; b) Gust D, Moore TA, Moore AL, Res. Chem. Intermed. 1997, 23, 621; c) Martín N, Sánchez L, Illescas B, Pérez I, Chem. Rev. 1998, 98, 2527; d) Diederich F, Kessinger R, Acc. Chem. Res. 1999, 32, 537; e) Imahori H, Sakata Y, Eur. J. Org. Chem. 1999, 2445-2457; f) Linssen TG, Dürr K, Hanack M, Hirsch A, J. Chem. Soc., Chem. Commun. 1995, 103; g) Drovetskaya T, Reed CA, Boyd P, Tetrahedron Lett. 1995, 36, 7971; h) Kuciauskas D, Lin S, Seely GR, Moore AL, Moore TA, Gust D, Drovetskaya T, Reed CA, Boyd PDW, J. Phys. Chem. 1996, 100, 15926; i) Dietel E, Hirsch A, Eichhorn E, Rieker A, Hackbarth S, Röder B, J. Chem. Soc., Chem. Commun. 1998, 1981; j) Tomé AC, Enes RF, Tomé JPC, Rocha J, Neves MGPMS, Cavaleiro JAS, Elguero J, Tetrahedron 1998, 54, 11141; k) Cheng P, Wilson SR, Schuster DI, J. Chem. Soc., Chem. Commun. 1999, 89; l) Bourgeois JP, Diederich F, Echegoyen L, Nierengarten JF, Helv. Chim. Acta 1998, 81, 1835; m) Helaja J, Tauber AY, Abel Y, Tkachenko NV, Lemmetyinen H, Kilpeläinen I, Hynninen PH, J. Chem. Soc., Perkin Trans. 1 1999, 2402; n) Tkachenko NV, Rantala L, Tauber AY, Helaja J, Hynninen PH, Lemmetyinen H, J. Am. Chem. Soc. 1999, 121, 9378; o) Zheng G, Dougherty TJ, Pandey RK, J. Chem. Soc., Chem. Commun. 1999, 2469; p) Kräutler B, Sheehan CS, Rieder A, Helv. Chim. Acta 2000, 83, 583; q) Kräutler B, Rieder A, J. Am. Chem. Soc. 2000, 122, 9050; r)
6
Montforts F-P, Kutzki O, Angew. Chem. 2000, 112, 612; s) Kutzki O, Walter A, Montforts F-P, Helv. Chim. Acta 2000, 83, 2231.
5. Smirnov, S. N.; Braun, C. L. Rev. Sci. Instrum. 1998, 69, 2875-2887.
6. “Principles of Chemical and Biological Sensors” Ed. Dermot Diamond, Wiley-Interscience, 1998
7
2 ELECTRIC POLARIZATION OF DILUTE POLAR SOLUTIONS. REVISED
TREATMENT FOR ARBITRARY SHAPED MOLECULES
2.1 Introduction
Onsager’s semicontinuum model1 is widely used for treating solvent effects in
various phenomena2 ranging from the calculation of the reorganization and solvation
energies to the evaluation of dielectric properties of solutions. In this model, a
molecule is represented as a point dipole that is placed in the center of a spherical
cavity of radius a (representing the molecule) and surrounded by a dielectric
continuum with the dielectric constant of a solvent, ε. Solvent polarization by the
dipole leads to a reaction field, R:
( ) µεεµ
12121
3 +−
==a
fR (2.1)
that in turn polarizes the molecule. This results in an enhanced molecular dipole
moment, µ':
( )121211
'
3 +−
−=
−=
εεα
µα
µµ
af
gg (2.2)
where µg is the molecule’s gas phase dipole moment and α is its polarizability. The
electric polarization of a solution can be calculated using the angular distribution
function, W(θ), for both, the solute and the solvent molecule dipole moments. The
8
functions W(θ) (for each type of dipoles) are related to a Boltzmann distribution of
the dipole energy, U(θ), in the external field:
W(θ) = e-U(θ)/kT, (2.3)
where the angle θ is given with respect to the direction of the electric field. In the
Onsager model, the energy U(θ) is calculated for the molecules’ point dipole
moment and the elecric field inside the cavity, Ec:
( ) ( ) θµµθ cos'' cc EEU ⋅−=⋅−=rr (2.4)
For a spherical cavity, Ec is equal to:
( ) 00123 EEE sphsphericalc
rrrξ
εε
=+
= (2.5)
In the Onsager model, interaction of the dipole with other surrounding dipoles is
neglected apart from the effect of changing the cavity field. The average dipole
moment will have a nonzero projection along the external field, which, in the limit of
small external fields, can be calculated from expansion as a sum of the orientational
part:
( )
cBB
cTkU ETk
dTkE
de Br
rrrrr
3''
1''2
/)( µµµµµ θ =Ω
⋅+=Ω>=< ∫∫ − (2.6)
and the polarizability part, α'Ec. The total electric polarization, P, which is a measure
of the average dipole moment per unit volume of the solution, is equal to:
( ) ( )
++
+=
TknE
TknEP
B
ssssc
B
ooooc 3
''
3'
'22 µ
αµ
α , (2.7)
9
where no and ns are the solvent and solute number densities, respectively. Imposing a
constraint that the total volume is a sum of the volumes of the components, allows to
derive3-6 the expression for the electric polarization of a dilute solution in the external
electric field E0:
0
2
3'
'' ETk
nPPB
sssso ∑
++=
µαϕ , (2.8)
Here P’o is the polarization of the neat solvent scaled for the change in volume due to
the dissolved solutes. The factor ϕs:
)2(3
)2(12
342
222
D
Ds n
n+
+
+=
εε
εεϕ , (2.9)
depends not only on the solvent dielectric constant but also on its refractive index, nD.
The summation in Eq. (2.8) is extended over all types of solutes with their number
densities, ns, dipole moments, µ’s, and polarizabilities, α’s.
Since the reaction field (2.1) is much stronger than a typical external electric
field, the dipole moment µ’ in Eq. (2.2) can be interpreted as the dipole moment of
the solute in a particular solvent. With such an interpretation, the measurement of the
solution’s dielectric constant provides a straightforward method for obtaining an
“unambiguous” dipole moment value for the solute. Moreover, when measuring the
dipole moment change due to photoexcitation (as is in the photoinduced transient
displacement current technique4-6) the change of the electric polarization shows no
dependence on the molecule’s radius, a. Independence of the result on the molecule’s
radius makes the technique attractive for analyses of photoinduced electron transfer
processes as a “direct” method for measuring the dipole moment change.
10
Following Böttcher,2 previous attempts4-6 to extend this analysis to a broader
class of nonspherical molecules by treating them as ellipsoids and scaling
appropriately the local field factor did not take into account the effect of solvent
polarization. Here we correct this shortcoming and suggest an approximate method
for treating generic molecular shapes.
2.2 Theory
Onsager’s model prescribes that the potential energy U(θ) in Eq. (2.3) can be
reduced to that of a point dipole interacting with the external field that is modified by
surface charges on the interface between the cavity and the surrounding solvent. The
resulting description can be simplified by introducing a new cavity field, Ec, on the
solute’s point dipole inside the cavity, with the total energy of that dipole in the
external field given by the same Eq. (2.4). Kirkwood7 pointed out that the assumption
of treating the solvent as a continuum in the vicinity of the cavity surface is
oversimplifying and could fail when correlations similar to hydrogen bonding exist
between molecules. Nevertheless, in many cases, especially when solutes are larger
than solvent molecules and no specific interactions are present, this correlation can
probably be neglected. One should note that, in the case of a spherical cavity,
Onsager’s assumption of zero contribution of the solute-solvent interaction to the
distribution function in Eq. (2.4) is consistent with a zero net polarization induced in
11
the solvent by the solute. Indeed, the integral of the field from a point dipole, Eµ, over
the region outside a spherical cavity is exactly zero due to the spherical symmetry:
( ) 0==∫ ∫> R RVV S
e SdRdVErr
ϕµ , (2.10)
The situation changes when the cavity is nonspherical. First of all, the field
inside the cavity is different. For example, in an ellipsoidal cavity with its axis “a”
oriented parallel to the external field, the field inside equals:
( ) 00)1(EE
AE a
aac
rrrξ
εεε
=−+
= (2.11)
where the “depolarization factor”, Aa, is given by the integral:2-4
∫∞
+++=
02/122/122/32 )()()(2 csbsas
dsabcAa (2.12)
Obviously, Eqs. (2.11-2.12) reduce to the spherical case given by Eq. (2.5)
when three semiaxes, a, b and c, become equal and when Aa = 1/3. Böttcher had
extended Onsager’s model to a nonspherical case2 via substituting the cavity field in
Eq. (2.7) by its nonspherical analog given in Eq. (2.11). Previous derivation of the
transient displacement current data that followed the same approach4-6 was
inconsistent. Because of a nonspherical geometry, the integral in Eq. (2.10) is no
longer zero, i.e. one cannot presume that a dipole moment in an ellipsoidal cavity has
zero effect on orientation of surrounding solvent dipoles.
We will try to resolve this problem by enclosing the solute molecule in a
spherical cavity in which the remaining part of the cavity is filled with a continuum
dielectric matching properties of the solvent. This approach is similar to the
12
Kirkwood model7 but is much simpler since any short-range specific interactions in
the vicinity of the solute molecule are neglected. This should be an acceptable
simplification for large solutes and can be cautiously applied to small molecules as
well. We will consider exact solutions to simple molecular cavity shapes and then
propose a simplified treatment for arbitrary shaped molecules.
In our model, we describe a total dipole moment from a solute molecule as a
superposition of its own dipole moment, µ'cs, and the induced dipole moment in the
solvent, Ms:
Mcs = µ'cs + Ms, (2.13)
where µ'cs has the same meaning as in Eq. (2.2), i.e. the dipole moment in a particular
solution (not the gas phase value). In this new interpretation, Eq. (2.8) for the electric
polarization of the solution becomes:
0
2
3' E
TkM
nPPB
cssso ∑
+= ϕ , (2.14)
where ϕs is given by Eq. (2.9) and the polarizability term is omitted. Note that Eq.
(2.9) was obtained with an assumption that both solute and solvent molecules were
spheres. For simplicity, we will continue treating solvent molecules as spheres while
nonsphericity of solutes will be incorporated through the solvent contribution to Mcs
in Eq. (2.13).
In order to calculate the solvent contribution, Ms, the molecule is enclosed in a
spherical cavity of a larger size, as in Fig. 2.1. This divides the solvent into two
regions, one external to the cavity and one internal to the cavity yet outside the solute
13
cavity, i.e. the shaded regions in Fig. 2.1. The radius of the spherical cavity, R, should
be large enough that, from the external solvent perspective, the charge distribution is
well represented as a point dipole. In this limit, the integral over the external volume,
VR, equals zero:
+
-
-+
+-
-+
-+
-+
+
-
-+
-+
-+
A B C D
+-
-+
-+
-+
-+
Figure 2.1. Illustration of solvent induced dipole moment for different molecular cavity shapes. The molecular cavity is identified by the white region, while the gray area outside it shows solvent enclosed into a larger sized spherical cavity together with the molecule. In the case A of a spherical molecular cavity, the solute dipole moment, µcs, shown by the large plus and minus signs and thick arrow, polarizes solvent in such a way that net dipole moment induced in the solvent, Ms, is zero. Cases B and C represent the prolate and oblate cavity shapes, respectively. Solute dipole of a prolate shape induces dipole moment in the surrounding solvent, Ms, (small pluses and minuses and thin arrows) that partially cancels the solute dipole moment, while in the oblate case the solvent induced complements the solute dipole. In a concave molecule (case D) the dipole moment induced in the solvent, Ms, might counteract the solute dipole to an even greater extent than in the prolate case B.
14
( ) 0==∫ ∫> R RVV S
e SdRdVErr
ϕµ , (2.15)
as it was in Eq. (2.10). The solvent contribution, Ms, to the total dipole moment, Mcs,
can then be calculated through integration of the electric polarization, )(rP r , outside
the molecular cavity:
∫>>
=sR VVV
s dVrPM )(r (2.16)
where the integration takes places over the interior solvent region.
The electric polarization can be found by solving the Poisson’s equation
for the electric field:
( ) 0)( =⋅∇ rE rε (2.17)
with appropriate boundary conditions for potential at the molecular surface, Se. These
are:
( ) ( )
∇⋅=∇⋅
=
ee
ee
ee
SoSSiS
SoSi
nn ϕεϕ
ϕϕrrrr (2.18)
where ϕi is the electric potential inside the molecular cavity, ϕo is the potential
exterior to the molecule, and nSe is a unit vector normal to the surface. Knowing the
electric field distribution, one can calculate the electric polarization via:
( ) )(4
1)( rErP rr
πε −
= (2.19)
and use Eq. (2.16) to calculate Ms. An effective solute cavity can be constructed by
“rolling” a sphere with hydrogen’s van der Waals radius over the molecular surface.
The molecule is represented by a superposition of overlapping spheres with
15
appropriate atomic van der Waals radii.8 This is a standard procedure used in
molecular modeling software packages for calculation of such properties as molecular
volume; it also eliminates singularities in Poisson’s equation.
The procedure described here allows for calculation of the electric polarization
P of a dilute solution of molecules with known shape and charge distribution. In
reality we usually solve the inverse problem, i.e. extracting information about the
charge distribution in a molecule from the measurements of P (or its change as in the
dipole technique) in solutions of that molecule. In Onsager’s formulation, this
inversion is unambiguous because the charge distribution is represented by a point
dipole placed in the center of a spherical cavity. When attempting to determine a
distribution of charges within a molecule, however, there is inevitably a greater
degree of both complexity and ambiguity in the data interpretation process. Indeed,
the polarization, P, only contains information about the first moment of the charge
distribution. Given this situation, an appropriate goal is to mimic a charge distribution
for the solute and then calculate consecutively µ'cs, Ms, and Mcs, comparing the last
quantity with the experimentally determined value. While the unique solution to this
problem is not always possible, it should work well in cases with 100% charge
transfer between well recognizable moieties.
In the following, we consider the procedure in detail and evaluate possible
approximations. The procedure starts by distributing charges inside a molecular
cavity and surrounding that cavity by a continuous dielectric representing the solvent.
Based on the charge distribution, Poisson’s equation can be solved numerically. This
16
is quite a demanding approach for an arbitrary shaped molecule. The first
simplification can be achieved by reducing the charge distribution on the molecule to
a simpler representation by placing a few point charges at appropriate locations.
Calculations show that results of this approximation are sensitive mostly to where the
centers of positive and negative charges are placed, contribution of finer details is
insignificant. A second simplification imposed on how Poisson’s equation is solved.
It is based on the fact that the electric field from a point charge in a continuum
dielectric differs from the field calculated in vacuum only by a factor of ε. The
electric field in vacuum, Evac, from a set of point charges qi located at the points ri, is
easily calculated without integration:
( ) ( )∑ −−
=i
i
i
ivac rr
rr
qrE 3 (2.20)
Approximating the electric field in a dielectric continuum by Evac/ε leads to a
relatively simple equation for calculating the solvent contribution to the dipole
moment, Ms, that can be realized without numerical solution of Poisson’s equation:
∫∫>>
−≈
−=
ss VVvac
VVs dVrEdVrEM )(
41)(
41 rrrrr
πεε
πε , (2.21)
Here Evac )(rr is calculated according to Eq. (2.20) and the integration excludes the
molecule’s cavity volume, Vs. The integration in (2.21) can be limited from above by
a spherical cavity of a large enough radius.
17
In the following part we will compare analytically and numerically solvable
cases with this approximation. If both sides of Eq. (2.21) are multiplied by (1-1/ε)-1,
the resulting relationship:
∫>
≈−
sVVvacs dVrEM )(
41
1rrr
πεε (2.22)
not only reflects the accuracy of the described approximation, but also provides a
simple mechanism for evaluating the applicability of the concept. According to this
equation, the exact value of Ms multiplied by (1-1/ε)-1, should be equal Ms in a
vacuum, independent of ε.
2.3 Theoretical Examples
2.3.1 Ellipsoidal cavity
An ellipsoidal cavity represents a first complication beyond the spherical
cavity model. This cavity can be characterized by three semiaxes: a, b, and c.
Poisson’s equation in this case can be solved analytically, which is also useful here
because it allows for evaluation of the approximations in Eq. (2.22). Fig. 2.2
represents plots of equipotential surfaces obtained by numerical solution of Poisson’s
equation using the FEMLAB program.9 The comparison illustrates that the exact
solution looks very similar to the “vacuum solution” of Eq. (2.20) normalized by the
dielectric constant. Quantitative assessment of the accuracy of our approximations is
18
given in Fig. 2.3, where the exact solution for Ms is shown as a function of dielectric
constant for the ellipsoid of Fig. 2.2. The numerical solutions, given by points, are in
essentially exact agreement with the analytical solution:
( )( )
( ) 31131 µ
εεε
a
as A
AM
−+−−
−= , (2.23)
where the depolarization factor Aa is given by Eq. (2.12). From the analytic solution
in Eq. (2.23) it is apparent that the solvent contribution is negative for prolate
molecules (Aa < 1/3) and becomes positive for oblates (Aa > 1/3). As Fig. 2.3
indicates, the Evac/ε approximation works well for a prolate ellipsoid. The maximum
error can be characterized by the spread between the maximum and minimum values
in Fig. 2.3. Taking advantage of the analytic solution, we can evaluate that error as:
( )
−
−=
−
∆∞
a
aas A
AAM
131
1 1
µε
ε (2.24)
which is negative for oblate spheroids (or any ellipsoid with dipole moment oriented
along short axis) and can be quite large. For prolate spheroids the error is positive
(overestimate in the resulting µcs) and quite small--the largest error for Aa < 1/3 is less
than 3.4 % and is realized for Aa = 0.1835. A negative and plausibly large error for
molecules with dipole moment oriented along a short axis, such as oblate spheroids,
has to be noted too. However, molecules of this type are rare and using an ellipsoidal
approximation for them would be a better choice, as compared with the use of
approximation (2.21).
19
Figure 2.2. Two-dimensional projection of the 3-D isopotential surfaces normalized by the dielectric constant, ε, for two point charges of opposite sign placed at the foci of a spheroid with the aspect ratio a/b = 3.5. The dielectric constant outside the ellipse equals ε =1 and ε =10 for cases A and B, respectively, but inside the spheres is unity in both cases. Note that if scaled by ε, the two solutions are very similar. Regions with potentials 0.05, 0.1, 0.15 (in units charge/distance) are shown in three different colors.
A B
20
1 100.239
0.245
0.252
0.259
0.265
0.272
(M
s/µcs
)ε/(ε
-1)
log(ε)
Figure 2.3. Integrated solvent induced dipole moment dependence on the dielectric constant ε for the case of Fig. 2.2. Points are calculated numerically using Femlab program (see text for details). Solid line represents the analytic solution of Eq. (2.23) with Aa = 0.08965.
Combination of Eqs. (2.13), (2.14) and (2.23) simplifies into a more compact
form:
0
2
3'
' ETk
nPPB
cssco ∑
+=
µϕ , (2.25)
21
with a new factor ϕc:
( ) )2(3)2(
)2(3)2(
1 42
222
42
222
D
Da
D
D
ac n
nn
nA +
+=
++
−+
=εε
ξεε
εεεϕ (2.26)
This compact form offers a more straightforward interpretation – the dipole
moment ξaµ'cs is the “external dipole moment” introduced by Onsager and now
extended for a nonspherical cavity. Alternatively, one may relate the two dipole
moments, µ'cs and Mcs, as a measure of solute nonsphericity, ηa, given by:
( )
a
spha
cs
csa
AM ξ
ξε
εεµη =
+−+
==12
13
' (2.27)
2.3.2 Two spheres
This model is a natural approximation for intermolecular charge separation.
The two-sphere case is relatively easy to solve numerically using the FEMLAB
program.9 In Fig. 2.4, isopotential surfaces normalized by the dielectric constant, ε,
for two point charges of opposite sign placed inside two spheres of equal radii in
contact are shown. The dielectric constant outside the spheres equals ε =1 and ε = 10
for cases A and B, respectively, but inside the spheres is unity in both cases. Visually
it is difficult to recognize a difference between the two graphs. Qualitative
comparison is given in Fig. 2.5 for spheres in contact, and for two identical spheres
separated by one radius – in Fig. 2.6. As before for a spheroid, a weak dependence on
ε in the Figs. 2.5 and 2.6 supports the validity of the estimate in Eq. (2.21). The
22
spread of Ms is smaller when the ions are further separated, as is expected from the
model, but even for a close contact the spread is less than 2.6%.
Figure 2.4. Two-dimensional projection of 3-D isopotential surfaces normalized by the dielectric constant, ε, for two point charges of opposite sign placed inside the two spheres of equal radii that are positioned at close contact. The dielectric constant outside the spheres equals ε =1 and ε =10 for cases A and B, respectively, but inside the spheres is unity in both cases. Note that if scaled by ε, the two solutions are very similar. Regions with potentials 0.05, 0.1, 0.15 (in units charge/distance) are shown in three different colors.
Thus we see that in cases where analytic and numeric solutions allow
comparison of exact values for solvent contribution to the dipole moment, Ms, with
that approximated using Eq. (2.21), the agreement is acceptable given the enormous
simplification of numerical solution. Prolate molecules are treated exceptionally well
in this model while oblate molecules and molecules where dipole moments oriented
23
along short axes have to be approached more cautiously. It helps to realize that the
latter cases are very rare or typically of low interest. It is also worth noting that
extremely prolate molecules (Aa ~ 0) or any other case where the distance between
separated charges defines a sphere with the volume much larger than molecule’s
volume, Eqs.(2.25,2.26) reduce to a much simpler form for the coefficient ϕc:
1 10
0.249
0.252
0.255
0.257
0.260
0.263
0.265
(M
s/µcs
)ε/(ε
-1)
log(ε)
Figure 2.5. Integrated solvent induced dipole moment dependence on the dielectric constant ε for the case of Fig. 2.2. Points are calculated numerically using Femlab program (see text for details).
24
)2(3
)2(42
22
D
Dc n
n+
+=
εε
ϕ (2.28)
This simplification might be very useful for large molecules where ellipsoidal
approximation is difficult to apply.
1 10
0.3082
0.3085
0.3088
0.3090
(M
s/µcs
)ε/(ε
-1)
log(ε)
Figure 2.6. Integrated solvent induced dipole moment dependence on the dielectric constant ε for the case when two point charges of opposite sign are placed inside the two spheres of equal radii that are positioned at a distance three times their radii. Points are calculated numerically using Femlab program (see text for details). Note that the dependence is weaker than that in Fig. 2.5 for charges in close proximity.
25
2.4 Experimental Examples
This chapter is dedicated primarily to establishing an improved theoretical
treatment for analysis of dielectric polarization data and the transient displacement
current data in particular. Below we give a few examples as a demonstration of
consequence for the revised treatment. The measurements were performed using our
standard setup for the transient displacement current measurement, the details of
which can be found elsewhere.6
2.4.1 Almost spherical molecules
Bianthryl is an interesting symmetric molecule, which gains a dipole moment
upon photoexcitation by “breaking” its ground state D2d symmetry. Nevertheless, the
excited state D2 distortion is not very dramatic. The excited state of this molecule
possesses dipole moment even in nonpolar solvents such as toluene. Even though the
spherical model was used to evaluate its dipole moment,12 neither a spherical nor an
ellipsoidal approximation describes well the molecule’s shape. As a result, the
approximate method of Eqs.(2.20-2.21) is appropriate. For this purpose, a program
was written in FORTRAN 90 which calculates the solvent contribution to the dipole
moment, Ms, from Eq. (2.21). Charges in the dipolar state of bianthryl were
distributed according to charge densities in the cation and anion radicals of the two
anthracene moieties, respectively. This distribution corresponds to the dipole moment
26
µ'cs = 20.6 D. Using van der Waals radii from Bondi8 we calculated Ms = -3.86(1-1/ε)
D. This leads to a 10% to 20% reduction of the dipole moment, depending on the
solvent polarity.
2.4.2 Almost ellipsoidal molecules
DMANS- 4-dimethylamino 4’-nitrostilbene is a molecule that has been
frequently used for calibration and comparison using different methods.4,6,11
Previously we reported that in the spherical approximation, DMANS dipole moment
in toluene equals Mcs = 31.0 ± 1.5 D.6 Due to the elongated and rigid shape of this
molecule, the ellipsoidal approximation seems appropriate for DMANS. Using the
ground state geometry obtained by semiempirical AM1 optimization the following
semiaxes were calculated:10 a = 11.8 Å, b = 4.1 Å, c = 4.1 Å with the dipole moment
oriented along the a-axis. The depolarization factor along this axis equals Aa = 0.092
and the dipole calculated from Eq. (2.27) is µ'cs = 36.4 ± 1.7 D.
Two “new” molecules, PANT-(para-amino-nitroterphenyl) and PANB-(para-
amino-nitrobiphenyl) sketched in Fig. 2.7 along with their dipole signals, also have
elongated and rigid shapes, justifying the use of the ellipsoidal approximation for
them. The dipole signals shown were measured in the displacement charge mode and
have a fast and a slow component: the former being from the short lived singlet
charge transfer state and the slow one from the triplet charge transfer state populated
via intersystem crossing from the singlet state. Dipole moments and the rates of
27
recombination and intersystem crossing were obtained from independently measured
fluorescence lifetimes of the singlet states and by presuming that the dipole moments
are the same for the singlet and triplet states. Approximating the molecular shapes by
ellipsoids, as shown in Table 2.1, the appropriate scaling factors for the dipole
moments were calculated using Eq. (2.27).
Table 2.1. Parameters for scaling using ellipsoidal approximation and the dipole moments. Molecule Ellipsoidal parameters0 Mcs, D Aa* ηa** µcs= ηaMcs ,D
DMANS a = 8.8 Å, b = 3.4 Å, c = 2.0 Å 31.0 0.092 1.174 36.4
PANB a = 6.9 Å, b = 3.4 Å, c = 2.0 Å 17.8 0.124 1.151 20.5
PANT a = 9.1 Å, b = 3.4 Å, c = 2.0 Å 29.3 0.088 1.176 34.5
*- values are calculated for toluene solvent, ε = 2.38
**-from Eq. (2.7)
2.4.3 Very large molecules
Two triad molecules for which we have measured dipole moments in their
photoexcited states can be described as very large molecules. They are
methoxyaniline-aminonaphthalimide-dimethylphenyl-naphthalenediimide-octyl (MA-
ANI-NI)5 synthesized by the M. Wasielewski group now at Northwesten Univeristy,
and carotene-porhyrin-fullerene triad13,14 – synthesized in Arizona State University.
28
Figure 2.7. Transient displacement current signals for two molecules in toluene solution observed after absorbing 38 µJ at 396 nm in a cell with 0.56 mm gap and using 1 MΩ load resistor. The experimental traces are shown by solid lines and the fitting curves by points; dashed lines depict laser pulse. A: PANB. Simulation was done with the following parameters: Mcs = 18.5 D, the lifetime of a singlet charge transfer excited state τCRS = 0.7 ns and the intersystem to a long-lived triplet charge transfer state τisc = 0.6 ns. B: PANT. Simulation parameters: Mcs = 29.3 D, τCRS = 1.7 ns, τisc = 8.3 ns.
0 5 10 15 20
0
2
4
6
8
10
Time (ns)
Phot
ores
pons
e (m
V)
B0
1
2
3
4
Pho
tore
spon
se (m
V)
A
NNH2
O
O2
NNH2
O
O3
29
The former was reported5 to have 16.3 Å charge separation if the spherical
approximation was used. Reevaluation of its dipole moment can be done by using the
ellipsoidal approximation10 since the molecule is fairly straight and rigid. Using
values of V = 679 Å3 and 2a = 32.1 Å, we find b = 3.2 Å and Aa = 0.068. This results
in avalue of µ'cs = 93 ± 7 D or 19.4 Å of charge separation, in remarkable agreement
with the expected charge separation distance based on the center to center distances
for the donor (MA) and acceptor (NI) moieties. Another triad from ASU has the
largest dipole moment ever experimentally measured.14 The distance between the
centers of the donor and acceptor (carotenoid and fullerene) based on molecular
modelling is 34 Å, which corresponds to a dipole moment of 163 D. This would be in
poor agreement with the experimental value in the spherical approximation Mcs = 110
± 5 D. The ellipsoidal model is inappropriate in this case due to a bow-like contour of
the molecule, but because of its extended shape, the reduced form for the scaling
factor given in Eq. (2.28) can be applied. The resulting value of the dipole moment
µ'cs = 154 ± 6 D is in good agreement with the value obtained by direct numerical
approximation for solvent contribution using Eqs. (2.20-2.21), µ'cs =156 ± 6 D. The
latter was calculated using van der Waals radii from Ref. 8, yielding Ms = -46 ± 1 D,
and the total dipole moment of the charge transfer state to µ'cs = Mcs - Ms = 110 + 46 =
156 ± 6 D. In either approach, the dipole moment demonstrates a remarkable
agreement with the value estimated from the expected positions of charges in the
charge transfer state of this triad. More extensive discussion on the large molecules
dipole moments can be found in chapters 3 and 5.
30
2.5 Conclusions
The problem of dielectric polarization for dilute polar solutions was revisited
and a new treatment based on calculating the solvent contribution to the total dipole
moment for solute molecules has been suggested. An analytic solution for ellipsoidal
molecular cavities and a simplified approximation for arbitrary shaped molecules,
based on mimicking the electric field as a solution in vacuum normalized by the
dielectric constant (Eq. (2.20)), have been derived and analyzed. Experimental
examples with photoinduced electron transfer show remarkable agreement between
the measured dipole moments and those expected based on the distance between
donor/acceptor moieties.
2.6 References
1. Onsager, L. J. Am. Chem. Soc., 1936, 58, 1486
2. Böttcher, C.J.F. Theory of Electric Polarization; Elsevier, Amsterdam, London, New York, 1973.
3. Liptay W., Dipole Moments and Polarizabilities of Molecules in Excited Electronic States, in Excited States, Lim E.C., Ed; Academic Press: New York, Vol. I, 1974, p.129
4. Smirnov, S.N; Braun, C.L., J. Phys. Chem., 1994 (98) 1953-1961.
31
5. Smirnov, S.N.; Braun, C.L., Greenfield, S. R.; Svec, W.A.; Wasielewski, M.R., J. Phys. Chem., 1996 (100) 12329 -12336.
6. Smirnov, S.N.; Braun, C.L., Rev. Sci. Instr., 1998, 69, 2875-2887.
7. Kirkwood, J., J. Chem. Phys., 1939, 7, 911
8. Bondi, A., J. Phys. Chem., 1964, 68, 441
9. FEMLAB is a commercial MATLAB-based electromagnetic modeling tool, which employs the finite element method to solve partial differential equations. The linear stationary 3D electrostatics module was used for solving Laplace equation. Meshing was performed using the default settings for “finer” mesh option. In order to avoid singularities, point sources were introduced to the system via internal FEMLAB function - V_test.
10. The longitudinal axis 2a is usually easier to identify as the molecule’s length, i.e. the distance between the remote atoms plus their van der Waals radii. The equatorial axis, 2b, can then be calculated from the van der Waals molecular volume, V = 4πab2/3, the value for which is usually available from molecular modeling software packages, such as HyperChem, Spartan or Gaussian. Alternatively, for planar conjugated molecules the shortest semiaxis can be taken c = 2.0 Å and the b value calculated, based on a and c, from the volume: V = 4πabc/3.
11. Smirnov, S.N.; Braun, C.L., Chem. Phys. Lett., 1994, 217, 167-172.
12. Smirnov, S.N.; Braun, C.L., Ankner-Mylon, S.E.; Grzeskowiak, K.N.; Greenfield, S. R.; Wasielewski, M.R., Mol. Crys. & Liq. Crys.,1996, 283, 243-248.
13. Kuciauskas, D.; Liddell, P. A.; Lin, S.; Stone, S.; Moore, A. L.; Moore, T. A.;
Gust, D. J. Phys. Chem. B, 2000, 104, 4307-4321.
32
14. Smirnov, S.N.; Liddell, P.A.; Vlassiouk, I.N.; Teslja, A.; Kuciauskas, D.; Braun, C. L.; Moore, A.L.; Moore, T.A. and Gust, D., J. Phys. Chem., in press
33
3 LONG-LIVED PHOTOINDUCED CHARGE TRANSFER STATE OF
SYNTHETICALLY AFFABLE PORPHYRIN – FULLERENE DYADS
3.1 Introduction
In this chapter we present photophysical investigations of porphyrin fullerene
dyads1-5 3 and 4 (Figure 3.1), which are attractive by their facile synthetic6-9 access
and high yields of charge separation. We show that quenching of porphyrin
fluorescence proceeds via direct electron transfer to fullerene as well as through
intermediate step of energy transfer onto fullerene. Separation between the two routes
is possible using the transient displacement current technique.
3.2 Experimental Section
Only three solvents: toluene, tetrahydrofuran (THF), and methylene chloride
(CH2Cl2), were used due to low solubilities of fullerene containing compounds in
other solvents. All solvents were of the HPLC grade (Aldrich) and were used without
further purification.
Absorption spectra were recorded using Perkin-Elmer Lambda 40 UV/Vis
spectrometer. The steady state fluorescence spectra were recorded using LS-100
spectrofluorimeter from PTI. Excitation wavelengths for P-C60 and ZnP-C60 were 500
and 530 nm respectively.
34
1 M=Zn
N
N
N
N
O O
OO
CH3 CH3
CH3
CH3
M
2 M=H2
4 M=H2
N+
N
N
N+
OO
O O
CH3CH3
CH3
CH3
M
3 M=Zn
COOEtCOOEt
5
Figure 3.1. Molecular structures for the molecules under study.
35
The measurements were performed using a Nd:YAG laser (“Orion SB-R”
from MPB) as an excitation source and a transient displacement current cell (a dipole
cell) with a 1 GHz digital oscilloscope TDS 684A (from Tektronix), scheme 1.
Details of the setup can be found elsewhere.10-13 The cell had two stainless steel
electrodes with 0.67 ± 0.05 mm gap (d) placed between two quartz windows through
which the excitation took place with the laser beam perpendicular to the electric field.
The energy of the laser beam was monitored before and after the cell and did not
exceed 100 µJ without a solute. All measurements were done at room temperature
using an external voltage of 600V. Toluene and THF solutions of ZnP–C60 dyad with
a typical concentration of 10-4 M were degassed and constantly refreshed during
measurements by means of solution circulation. No wavelength dependence of the
signal was observed for the three wavelengths used: 532 nm (second harmonic), 559
nm (CF4 shifted second harmonic) and 416 nm (H2 shifted third harmonic). The
former has a ca. 0.4 ns long pulse and the latter two are 20 ps in duration. All these
wavelengths excite primarily porphyrin: 416 nm – at the low energy shoulder of Soret
band, and the other two – in the Q-band. In many cases, few laser shorts were
sufficient to record a reliable signal but usually ca. 200 –500 shorts were recorded.
36
Scheme 3.1. PTDC setup. Upon photoexcitation, the ground state dipole moment µg changes to the µe. The dipole signal is measured as a voltage drop across R. The details of the setup can be found elsewhere.10a
3.3 Results
3.3.1 Spectroscopic Investigations
The new dyads described in this paper significantly differ from previously
reported designs of porphyrin – fullerene dyads with lactone spacers;14 ZnP–C60 (3)
and P–C60 (4) have greater separation distances between the porphyrin and fullerene
moieties and, thus, weaker interaction. Fig. 3.2 illustrates that the UV-Vis absorption
spectra of 3 and 4 in toluene agree well with the stoichiometric convolution of the
V0
C Rµg
Pg
hν
µe
Pe
∆P
v
37
spectra of C60 (5) and corresponding porphyrin, 1 or 2, respectively. A very minimal
spectral perturbation for porphyrin suggests that it is not tightly bound to fullerene. In
solvents of greater polarity, THF and CH2Cl2, distortions of porphyrin spectra are
recognizable, especially in methylene chloride, but still are much weaker than those
for the previously reported porphyrin-fullerene dyads.15 Another noticeable
peculiarity is the reversing the relative intensities of vibronic peaks in the Q-band for
ZnP in THF, which is also observed for the corresponding ZnP–C60 dyad. Such an
alteration in the Q-band intensities is usually associated with metal (Zn) coordination
of electron-reach solvent molecules.16
Despite the weak perturbations in the absorption spectra, porphyrin
fluorescence for both dyads is efficiently quenched in all solvents; more than a factor
of 60 in the fluorescence yield decline was observed (see Figure 3.3 and Table 3.1).
Opposite to the well investigated cases of porphyrin quenching by quinines,14 where
it proceeds exclusively via charge separation (CS) route, quenching by fullerene can
also be a result of energy transfer (Q) onto the fullerene. The latter route can
eventually also lead to the formation of the charge-separated state, P+-C60−, but with
some delay. Figure 3.4 illustrates these possibilities and labels the rate constants of
the reactions involved. A position of the CT state in either dyad depends on a solvent
and, for toluene, CT states lie higher then the triplet state of C60 (see Table 3.1).
38
Figure 3.2. Optical absorption spectra of the dyads in different solvents (solid lines) and their comparison with the convoluted sums of the absorption spectra of C60 (5) and a corresponding porphyrin (dashed lines). A - C: ZnP-C60 (3) and ZnP (1), D – F: P-C60 (4) and P (2). All spectra are normalized to approximately the same absorbance. Note that disagreement between the dyad spectra and the convoluted ones is observed only in highly polar methylene chloride (C and F), while in toluene (A and D) and THF (B and E) they are almost identical.
0.0
0.5
1.0
x12
A
Abs
orba
nce
0.0
0.5
1.0
x 20
B
Abs
orba
nce
400 500 6000.0
0.5
1.0
C
x 18
Abs
orba
nce
λ, nm
0.0
0.5
1.0x10
D
0.0
0.5
1.0
x10
E
400 500 6000.0
0.5
1.0
x10
F
λ, nm
39
Figure 3.3 Steady state fluorescence spectra for the dyads ZnP-C60 (3), A and C, and P-C60 (4), B and D, shown by solid lines and the corresponding porphyrins, ZnP (1) and P (2), shown by dashed lines in toluene (A and B) and THF (C and D). Fluorescence intensity is arbitrary but normalized to the same amount of absorbed photons at 530 nm, in case of 3 and 1, and 500 nm, in case of 4 and 2, respectively. Note that the fluorescence intensity for the dyads is always given on the right scale.
0
30
60
90
120
150
180
toluene
3
5
A
Fluo
resc
ence
0.0
0.3
0.6
0.9
1.2
1.5
1.8
550 600 650 700 7500
200
400
600
800
5
3
THF
C
Fluo
resc
ence
λ, nm
0.0
1.0
2.0
3.0
4.0
5.0
550 600 650 700 7500
500
1000
1500
6
4
THF
D
Fluo
resc
ence
λ, nm
0
5
10
15
0
70
140
210
280
350
Fluo
resc
ence
0
1
2
3
4
5
6
4
tolueneB
40
Table 3.1. The energies of the local singlet (ES), the local triplet (ET), and the charge separated (GCS) states for the dyads and fullerene.
ZnP-C60 (3) P-C60 (4) C60(COOEt)2 (5)
Solvent ESa ET
b GCSc ϕF
d ESa ET
b GCSc ϕF
e ESa ET
b Toluene 2.19 1.55 0.01f 1.99 1.75 0.017
THF 2.18 1.07 0.006 2.00 1.27 0.01
CH2Cl2 2.19 1.77
1.04 0.005 2.00 1.82
1.24 0.008 1.78 1.50g
a local first excited singlet energy of zero-zero transition in eV, b local triplet energy obtained from phosphorescence maxima except for fullerene, c calculated using equation (3.16) for RDA = 10 Å, d relative fluorescence yield, ϕF(3)/ϕF(1), e relative fluorescence yield, ϕF(4)/ϕF(2), f fullerene fluorescence is also observed for (5) in toluene; g ref. [17].
1ZnP*-C60
ZnP-1C60*
1(ZnP+-C60−)
3ZnP*-C60
ZnP-3C60*3(ZnP+-C60
−)
1P*-C60
1(P+-C60−)
3P*-C60
P-3C60*
3(P+-C60−)
E
kCRT
kCRT
kCRS
kCRS
P-1C60*
kQS
kQS
kISC
kISC
kCST
kCSS
kCST C60kCSSkCSS
C60kCSS
kISCC60
kISCC60
1ZnP-C601P-C60
kFkF
C60 kFC60kF
Figure 3.4. Approximate energy levels for different states of the dyads in toluene and the labels of the rate constants. Double arrows show the most essential transitions routes. In THF charge separated states are lower in energy than 3C60* for both dyads.
Fluorescence of ZnP–C60 in toluene, as shown in Fig. 3.3, consists of a
substantially quenched luminescence of porphyrin (two bands at 570 nm and 625 nm)
and a broad luminescence at 700 nm from the excited singlet state of fullerene, 1C60*.
41
No fluorescence of 1C60* was detected from ZnP–C60 in THF and methylene chloride
even though the fluorescence of C60 and 5 were clearly observed (see Fig. 3.5).
660 680 700 720 7400.0
0.1
0.2
0.3
0.4
0.5
0.6
Fluo
resc
ence
λ, nm
Figure 3.5. Steady state fluorescence spectra of C60(COOEt)2 in toluene (dashed line) and THF (solid line) with excitation at 330 nm.
Moreover, even when excited directly at the maximum absorption of C60 (330
nm), the dyad ZnP–C60 in THF does not show any detectable fluorescence of C60.
According to Figure 3.4, that can be realized either when quenching of the excited
1ZnP* happens via direct charge separation (kCSS), (i.e. no 1C60* is formed) or when
charge separation from 1C60* is very fast, with the rate constant kCSSC60> kISC
C60.
Alternatively, if electronic coupling of 1C60* and the charge transfer state, ZnP+–C60−,
is high due to their near degeneracy, neither of the two represents a state; they both
42
contribute to the mixed state with less than 100% charge transfer and no fluorescence
from 1C60*.
The free base form of the dyad, P–C60 (4), shows similarly efficient
fluorescence quenching of porphyrin in all solvents (Table 1), but the fullerene
luminescence is not detected even in toluene. Due to a partial overlap of the 1C60*
fluorescence with that of porphyrin, P, it is difficult to discard fluorescence of
fullerene completely.
3.3.2 Transient Displacement Current Measurements
The transient displacement current technique provides direct information
about dipole moments in the charge transfer state. It measures the photoinduced
voltage, v, across the load resistor, R, in a cell with a gap, d, between the electrodes of
area, S, under external voltage, V0. In the limit of fast dipole rotation (i.e. at quasi
equilibrium) the photoinduced voltage (photoresponse or dipole signal) is described
by equation (3.1):
dtdn
TkM
dRSV
dtd cs
B
csccsRC 3
20 ∆
Φ=+ϕντν (3.1)
where τRC is the RC time constant of the circuit and Φcs is the yield of the charge-
separated state.10 For small τRC, the dipole signal is proportional to the time derivative
of the dipole concentration, dncs/dt, while at large τRC, the signal is proportional to the
concentration, ncs, itself. In both cases, the signal, v, is proportional to the change of
43
the dipole moment squared, ∆Mcs2, caused by photoexcitation. Due to a small dipole
moment of the ground state, the latter is almost identical with the excited state dipole
moment squared, Mcs2. The coefficient ϕc combines the effects of solvent induced
change in the local field on the dipole and the solute’s molecular shape.12 In the
simplest case of a spherical molecular shape, the coefficient is given by equation
(3.2)10:
)2(3)2(
123
42
222
D
Dc
nn+
+
+=
εε
εεϕ (3.2)
For an arbitrarily shaped molecule, one can use the spherical approximation (3.2) and
treat Mcs as an effective dipole,10 which would include some solvent contribution. The
yield, Φcs, is then related to the squared ratio of the experimental effective dipole
moment and the theoretical one, as given in equation (3.3):
2
)((exp)
=Φ
theorMM
cs
cscs (3.3)
Charge separation in the majority of cases investigated here happens faster than the
time resolution of the transient displacement current technique. Thus, the only
recognizable variation of ncs happens due to charge recombination. When charge
separation is slow enough (as in one of the cases), the time variation of the
concentration, ncs, should have the appropriate growth term as well. Both terms are
combined in equation (3.4) :
CR
cs
CS
CScs ntn
dtdn
τττ
−−
=)/exp(
0 (3.4)
44
where n0 is the initial concentration of the locally excited species transforming into
the dipolar species during the charge separation time, τCS. The charge recombination
time in both cases is given by τCR.
Figure 3.6. Transient displacement current signals for ZnP-C60 (3) and P-C60 (4) in toluene (A and B) and THF (C and D) for 20 µJ absorbed energy at 396 nm and 600 V of external voltage. Solid lines show experimental signals and squares represent the best-fit curves calculated using parameters presented in the text and the Table 1. Dashed lines show laser pulse profile used in convolution. Note that the vertical scale is different for different signals.
Figure 3.6 shows the dipole signals of the two dyads in toluene and THF. The
amplitude and shape of the dipole signal depends on the yield of charge separated
state, Φcs, its dipole moment, Mcs, the time of charge separation, τcs, and the
0 5 10 15 20-0.5
0.0
0.5
1.0
1.5
2.0THF
D
Tim e (ns)
Pho
tore
spon
se (m
V)
0.0
0.5
1.0
1.5
toluene
B
Pho
tore
spon
se (m
V)
0 5 10 15 20
-0.2
0.0
0.2
0.4
0.6
0.8
THF
C
Time (ns)
Phot
ores
pons
e (m
V)
-2
0
2
4
6
8
10
tolueneA
Phot
ores
pons
e (m
V)
45
recombination time, τcr. The RC time, τRC, of the circuit can be calculated from the
geometrical parameters of the cell and the solvent dielectric constant.10 The rotation
time, τr, can be also estimated not to exceed 0.2 ns for the molecules under study in
these nonviscous solvents. Thus, in the fitting procedure we applied a simplified
model, where only three parameters were varied: τcs, τcr, and the effective dipole
moment, Mcs, which is an apparent dipole moment without correction for charge
separation assuming spherical approximation for the molecular cavity. The resulting
parameters from the best fits for the dipole signals are given in Table 3.2.
Table 3.2. Experimental fitting parameters for the dipole signals of dyads in different solvents.
ZnP-C60 (3) P-C60 (4) Solvent
Mcs, Da τcs, nsb τCR, nsc Mcs, Da τcs, nsb τCR, nsc
Toluene 35.2 0.9 ± 0.1 5.3 14.3 ≤ 0.2 6.2
THF >13.3d ≤ 0.2 4.5 31.7 ≤ 0.2 2.4e
CH2Cl2 f f f > 29.2 0.3 ± 0.1 1.5 ± 0.3
a the apparent dipole moment of the CS state in Debye with uncertainty on the order of ± 10%; b the apparent charge separation time; c the apparent charge recombination time equivalent to 1/kCRS; d noticeable electrochemical deterioration was observed, see text for details; e the intersystem crossing time of ca.15 ns is also observed; f dipole signal is overwhelmed by photodissociation
The dipole measurements show strong variation of the effective dipole
moment with solvent polarity. The greatest signal for ZnP-C60 dyad (3) is observed in
toluene with the corresponding effective dipole moment, Mcs = 35.2 D. The excited
46
state dipole moment of ZnP-C60 noticeably decreases in THF and appears even
smaller in methylene chloride. In the latter case it cannot be accurately evaluated due
to an overwhelming contribution from the “persistent” photocurrent of dissociated
ions. Moreover, there is an additional complication associated with electrochemical
instability of ZnP-C60 (3) in methylene chloride, which further complicates evaluation
of Mcs in that solvent. The dyad with free base porphyrin, P-C60 (4), has the opposite
trend for the excited dipole moment variation in these solvents: Mcs increases from
toluene to THF and further in methylene chloride.
Charge separation in all but one case proceeds faster than the time resolution
of the transient displacement current technique. Only in toluene can we
unambiguously recognize that the dipolar state is formed with some delay, ca. 0.9 ns.
It is important to note that it is also the only case, in which fullerene fluorescence
from the dyad is clearly observed (see Fig. 3.3). In all other cases, charge separation
is too fast to be resolved with our technique and, correspondingly, fluorescence from
C60 is not observed, either. The charge separation time for the P–C60 dyad (4) in
dichloromethane probably exceeds 0.2 ns as well (Table 2.2 lists it as 0.3 ns), but the
uncertainty in this case is also high due to three factors: comparability of this time
with the circuit RC time (ca. 1.8 ns due to high polarity of methylene chloride), the
recombination time is also short, τcr ~ 1.5 ns, and photodissociation, which produces
“persistent” photocurrent, complicates the analysis. Thus, there is some correlation
between fullerene fluorescence and slow formation of dipolar state, at least for the
case of ZnP–C60 dyad (3) in toluene.
47
Charge recombination times, τCR, in these dyads are in excess of a
nanosecond, as seen from Table 2.2, which should be viewed as relatively long for
such small systems, especially since the charge separation times are so short. Besides
that, they offer no surprises: as expected and usually observed in literature2,4,18, τCR
shorten with increasing solvent polarity. It is also important to note that solutions of
the dyads in polar solvents are not chemically stable in contrast to toluene solutions,
which are stable for days and are not noticeably affected by either laser irradiation or
by electrochemistry.
3.3.3 Chemical instability
In general, increasing solvent polarity causes accelerated decomposition of
both dyads in the dark, upon photolysis, and due to electrochemistry. Fullerene by
itself in either form, as free C60 or as its derivative 5, deteriorates noticeably in THF
and CH2Cl2 solutions within a few days. Moreover, in methylene chloride, the dyads
are also unstable and apparently break apart into the (cation radical of) porphyrin and
(anion radical of) fullerene. The mechanism of this chemical instability is not well
understood. The effect is mostly pronounced for ZnP-C60 (3), for which only the
“persistent” photocurrent from escaped (free) ions was observed. The dipole signal is
too weak and masked by the free ion current. The latter lasts for a few milliseconds
until ions recombine at the electrodes. An intermediate situation is observed for free
base P-C60 dyad (4). As Figure 3.7 illustrates, the transient displacement current for 4
48
in CH2Cl2 is the sum of the dipole signal (with the net zero integral, shown by
squares) and the remaining part that gradually levels off at a certain value as
“persistent” signal of free ions. Due to this instability of P-C60 dyad (4) in CH2Cl2,
only the low estimate dipole moment is possible, which suggests that it is fairly large
(see Table 2.2). Less polar THF does not have as pronounced affect on the
photodecomposition into ions, but some electrochemical decomposition of ZnP-C60
dyad (3) in THF was also observed,19 thus making the dipole moment for 3 in THF
given in Table 2.2 as the low estimate, as well.
0 10 20 30 40
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
Time (ns)
Pho
tore
spon
se (m
V)
Figure 3.7. Transient displacement current signal from P-C60 (4) in CH2Cl2 for 20 µJ absorbed energy at 396 nm and 600 V. Solid line shows the experimental signal and squares represent the best-fit curve calculated using parameters presented in Table 3.1. The dashed curve identifies the laser pulse while the dot-dashed line is the difference between the experimental signal and the dipole component from the fit. Note that the time scale is twice longer than that in Fig. 3.6.
49
3.4 Discussion
The time resolution of the dipole technique is insufficient to allow direct
evaluation of the kinetics for all routes of energy degradation in these dyads after
excitation. Most of the charge separation processes proceed faster than 0.3 ns, and
thus, leave only the yield of charge separation as an experimentally measurable
parameter. The yields can be obtained by comparing the experimental dipole moment
values with the theoretical ones, which can be calculated if molecular geometries are
known. Geometry information is needed not only for calculating the distance between
the donor/acceptor moieties, but also for evaluating molecular shape, because the
latter affects the apparent dipole moment.10-12
3.4.1 Ground state geometry
Due to a flexible bislactone linker, the center-to-center separation between the
fullerene and porphyrin moieties is not well defined. Accordingly, the shape of the
molecules is not apparent either. We performed molecular modeling using
Hyperchem package20 mostly at the semiempirical level, using AM1 approximations.
Each optimization was considered satisfactory upon reaching a 0.003 kcal/molÅ
gradient in the formation enthalpy. Due to a large molecular size, ab initio
calculations at a reasonable level of accuracy were impossible, and molecular
mechanics, such as MM+, provide unsatisfactory results with our molecules.
Parameterization of transition metal ions, even as placid as Zn, is poor. For example,
50
under MM+ approximation, Zn is “pulled” outside the porphyrin ring in ZnP (1) and
ZnP-C60 (3). Semiemprical AM1 calculations seem to be more reliable, the calculated
C60 diameter, 7.1 Å, is close to the experimental one.
The AM1 predicted geometry of the ground state for either ZnP-C60 (3) or P-
C60 (4) correlates with the lack of mutual absorption spectra perturbation of the
porphyrin and C60 components. The center-to-center separation between the C60 and
the porphyrin moieties, taken from the AM1 optimized structure, is identical for both
ZnP-C60 (3) and P-C60 (4) and has a very shallow minimum in between 10 Å and 12
Å, as shown in Figure 3.8. The uncertainty is quite high due to flexibility of the
linker. The dashed lines in Figure 3.8 illustrate that the thermal spread on the order of
kBT “permits” the center to-center separations from 9.3 Å to 12.3 Å. In the
corresponding geometries, the bislactone arms are extended so that the molecule
expands from the pseudo Cs symmetry, as illustrated by Figure 3.9.
MM+ provides better agreement with the structure obtained by AM1 when
solvent molecules are included into optimization. When dyad 4 is optimized with two
or three solvent molecules by MM+ (fullerene part of the dyad excluded), they tend to
squeeze inside the claw between porphyrin and fullerene, making the center-to-center
separation in the vicinity of 10 Å.
51
0
10
20
30
40
50
60
7 8 9 10 11 12
-2
0
2
4
6
8
X
dc
ba
µ,
D
kBT
∆Htotal ∆Hcoul
∆Hstress
∆H
, kca
l/mol
Center to center distance, RDA(A)
Figure 3.8. Calculations for ZnP-C60 (3) and P-C60 (4) dyads at different center-to-center separations. At the bottom - enthalpy of stress for the ground state, ∆Hstress (circles), estimated using AM1 approximation; coulombic attraction term in toluene, ∆Hcoulomb (solid line), from equation (3.5) ; and the “total” enthalpy, ∆Htotal (squares), from equation (3.6), which has a minimum at R0 = 8.6 Å. At the top – partitioning of the expected dipole moment for 100% charge transfer, Mcs (curve b), as a function of fullerene-porphyrin center-to-center separation into: a) that of the gas phase point charges part for that separation (µcs); c) the solvent polarization from equation (3.7) due to the dyad’s nonsphericity (Ms); and d) that from the polarization of ions in their mutual field using equation (3.9). See text for details. The cross identifies the dipole moment at the minimum enthalpy for toluene, 36.0 D.
52
OO
O
O
O
O
OO
A
B
Figure 3.9. Illustration of two isoenergetic (from calculation using AM1) geometries of the dyads: A - corresponds to 10.1 Å and B – to 12.1 Å of center-to-center separation.
3.4.2 Charge-separated state geometry
For evaluating geometry of the charge transfer state, one should take into account that
coulombic attraction between the positively charged cation radical of porphyrin and
the negatively charged anion radical of fullerene could enforce closing up of the
“molecular claw” and thus, make the center-to-center separation smaller. Usually,
geometries in the ground and excited states do not differ dramatically but for these
dyads, with a flexible linker, as we show below, geometry variation is noticeable. As
an approximation of the effect, we “mapped” the stress energy for the dyad in a gas
phase as a function of center-to-center distance in order to compare it with the
electrostatic energy. Starting with the AM1 optimized structure and applying MM+ to
the porphyrin moiety only, the porphyrin was first allowed to fold onto the fullerene.
After that, the AM1 optimization was initiated to the whole molecule and frequently
53
stopped along the way, where concurrent measurements of the formation enthalpy
and the center-to-center separation distances, RDA, were performed. As a result, the
data for Fig. 3.8 was collected. The excess stress energy, ∆Hstress (i.e. the extra
enthalpy of formation relative to that at the minimum, R0 = 10.1 Å), was compared to
the payoff advantage due to a greater coulombic attraction at a distance, RDA, scaled
by solvent dielectric constant, εs, as shown in equation (3.5):
−−=∆
00
2 114 RR
eHDAs
coulomb επε (3.5)
As Fig. 3.8 illustrates, in toluene with dielectric constant εs = 2.38 the stress
energy could be less than the electrostatic energy benefit for a range of center-to-
center distances shorter than 10.1 Å. The estimated “total” enthalpy, ∆Htotal is given
by equation (3.6) :
∆Htotal (RDA) = ∆Hstress + ∆Hcoulomb (3.6)
of the charge transfer state reaches a minimum at around 8.6 Å in toluene, as Fig. 3.8
illustrates. In more polar THF (εs = 7.58) and dichloromethane (εs = 8.93), coulombic
attraction becomes less significant and the minimum occurs near 9.7 Å (see Fig.
3.10). The overall distributions of ∆Htotal (RDA) appear to have narrower minima than
that in the ground state of the dyads, but the spread of possible center-to-center
separations is still high. Greater folding in toluene makes the center-to-center
separation slightly smaller than that in THF. Choosing ½ kBT excess energy above the
minima as a criteria for evaluating a thermally accessible spread, one estimates the
54
center-to-center separation for charge separated states to be R0 = 8.6 ± 0.5Å in toluene
and R0 = 9.7 ± 1.0 Å in THF.
7 8 9 10 11 12
-2
0
2
4
6
80
10
20
30
40
50
60
∆Hstress∆Htotal
kBT
∆Hcoul
∆H, k
cal/m
ol
Center to center distance, RDA(A)
X
dc
b
a
µ, D
Figure 3.10. Calculations for ZnP-C60 and P-C60 dyads at different center-to-center separations in THF . The same as in Fig. 3.8 calculations for the dyads in THF. The “total” enthalpy now has the minimum at R0 = 9.7 Å but the corresponding dipole moment is close to that in toluene, 36.2 D.
55
3.4.3 Dipole moments
The preceding structural analysis is necessary for determination of the
theoretical dipole moment for 100% charge separation in the “equilibrium geometry”
described above.
The positive and negative charges are placed onto the porphyrin and fullerene
moieties to mimic the charge distribution of the charge separated state. The resulting
dipole moment, µcs, is still not the dipole moment we need to compare with the
experimental one. First of all, since the dyads have nonspherical shapes, solvent
polarized by the solute also has a nonzero contribution, Ms, to the dipole moment.12
Solvent contribution, for each, case can be calculated using equation (3.7) by
integrating the electric polarization of the solvent caused by charges, qi, placed at
specific positions ri in the dyad12:
( )∫ ∑
>
−−
−=
sVV ii
i
i
s
ss dVrr
rr
qM
341
πεε
(3.7)
The solvent contribution for these elongated dyads is negative. Therefore, it
decreases the effective dipole moment and is quite significant, as Figures 3.8 and 3.10
demonstrate for toluene and THF, respectively (by circles). Obviously, the solvent
induced dipole moment, Ms, is greater for more polar THF. The first moment of
charge distribution in the dyad, given by equation (3.8), describes the dipole moment
of the dyad itself :
56
DAii
ics Rerqrrr
== ∑µ (3.8)
where distance RDA represents the separation between the “centers of mass” of the
negative and positive charges placed at fullerene and porphyrin, respectively.
Another contribution arises from the mutual polarization of the porphyrin and
fullerene moieties.13 The polarizability contribution given in equation (3.9) is also
negative but has the opposite trend with dielectric constant:
( )3||60 sincosˆDAs
DAPPC
R
ReE
εθαθαααµα
rrr
⊥++−==∆ (3.9)
Here θ is the angle between RDA and the porphyrin plane; αC60 = 80 Å3 is the
polarizability of fullerene anion radical, which is isotropic, while the polarizability of
porphyrin cation radical is higher in its plane, αP|| = 89 Å3, than that perpendicular to
the plane, αP⊥ = 11 Å3. The polarizabilities were calculated for the AM1 optimized
structures of the corresponding ions also using the AM1 approximation (the electric
field in calculations was taken as if produced by a unit charge at 10 Å away from the
ion’s center). Similar values were obtained when ZINDO/S approximation was used
for the polarizability calculations.
The total value of the dipole moment for a dyad with 100% charge separation
is thus given by the contributions of all these effects. Since the contributions are
small, a linear approximation of equation (3.10) can be used:
Mcs = µcs + Ms + ∆µα (3.10)
57
Corresponding graphs for Mcs are given in Fig. 3.8 for toluene and in Figure
3.10 for THF. If we assign the theoretical dipole moments for CS states as those for
the minima of ∆Htotal, theoretical dipole moments in toluene (as indicated by a cross
in Figure 3.8) should be Mcs = 36.0 ± 1.7 D and the dipole moment for THF (a cross
in Figure 3.10) is Mcs = 36.2 ± 3.4/2.0D. Using these dipole moments, the yields of
charge separation can be estimated according to equation (3.3).21 In toluene, it
measures to the yield of 0.97 ± 0.08 for ZnP-C60 and 0.17 ± 0.02 for P-C60. In THF,
the yield for P-C60 increases to 0.78 ± 0.09/0.13, while that for ZnP-C60 can only be
estimated as exceeding > 0.15. Analogously, the lower limit for the charge transfer
yield for P-C60 in methylene chloride solvent is given as > 0.75.
3.4.4 Electron transfer rates
Finally, we need to explain the yields by evaluating all possible routes for
charge separation. We can only estimate the rates of charge separation and will use
Marcus nonadiabatic theory22,23 for that, according to which the rate constant of
charge separation, kcs, can be calculated from equation (3.11):
FCFVk DAcs 22h
π= (3.11)
where VDA is the exchange integral between the donor and acceptor, and the Franck-
Condon thermally weighted factor is given by equation (3.12):
58
∆−=
TkG
TkFCF
B
cs
B
#exp
41
πλ (3.12)
which has the activation free energy barrier, ∆G#cs, provided by equation (3.13):
( )
λλ
4
2# +∆
=∆ cscs
GG (3.13)
and is dependent on both, the free energy of the reaction, ∆Gcs, and the so-called
reorganization energy, λ. Equation (3.14) illustrates that the latter includes two terms:
λ = λout + λint, (3.14)
the internal reorganization energy, λint, and the solvent reorganization energy, λout.
The solvent contribution is usually estimated using semicontinuum approximation for
a solvent characterized by the low frequency dielectric constant, εs, and its high
frequency part, εop = no2, given by the refractive index, no. As it is usually assumed,
the donor and acceptor are described as spheres with radii rD and rA. The solvent
reorganization is then given by equation (3.15):
−
−+=
sopDAADout
Rrre
εεπελ 111
21
21
4 0
2
(3.15)
where RDA is the distance between the ion’s centers. The internal reorganization
energy, λint, depends on the nature of species involved. We estimated λint using
semiempirical calculations (AM1)20 as a difference between the enthalpies of the
fullerene and porphyrin ions in their optimized geometries and in the geometries
corresponding to neutral molecules.24 Reorganization of bislactone linker was
neglected. Calculated this way, reorganization energy for fullerene is the smallest,
59
0.05 eV, while λint for porphyrins are larger, 0.16 eV and 0.26 eV for ZnP(1) and
P(2), respectively. The total reorganization energies are given in Table 3.3, where
ionic sizes were taken to be rD = 4.5 Å for porphyrin, and rA = 5.0 Å for fullerene.
Table 3.3. Reorganization energy for the charge transfer reactions from porphyrin to fullerene in different solvents. The center-to-center separation is taken RDA = 10 Å.
ZnP-C60 P-C60 λint, eVa 0.22 0.31
Toluene 0.26 0.36 THF 0.83 0.92 λ, eVb CH2Cl2 0.84 0.94
a − internal reorganization energy estimated using AM1; 0.05 eV of that value is due to the fullerene reorganization and the remaining is due to porphyrin; no contribution from the dyad folding is included; b – the total reorganization energy, λ = λout + λint, where λout is calculated from equation (3.15)
The energies of charge separated states were analogously calculated using
equation (3.16) (Weller’s formula):
DAsADsADCS R
err
eEEGεπεεπε 0
2
0
2
411
93.811
8−
+
−+−= (3.16)
where oxidation potentials for porphyrin and Zn-porphyrin in methylene chloride
were taken from literature: ED = 0.83eV and 0.63eV, respectively,25 and the reduction
potential of fullerene in the same solvent, EA = -0.55eV.14 The difference in Gibbs
free energy between the charge-separated state and a locally excited state, given by
equation (3.17):
∆GCS = GCS - ES (3.17)
defines a driving force of the charge transfer reaction from that excited state. Energies
of the local excited states were measured as averaged between zero-zero transition
60
energies from fluorescence and absorption spectra of dyads and porphyrins (Table
3.1). Triplet excited state energies were measured from phosphorescence maxima.
Inspection of Table 3.1 reveals that in toluene both dyads have their CS states higher
in energy than fullerene’s triplet state. Accuracy of ECS in Table 3.1 is probably no
better than ± 0.3 eV due to a combination of uncertainty for measuring ED and EA,
oversimplification of approximating ECS by equation(3.16), and breadth in RDA
values. Despite that, we are pretty confident in correctness of placing the CS state for
ZnP-C60 (3) in toluene above the triplet state of fullerene (5). The confidence is based
on the radical induced intersystem crossing effects observed in this system.11 Spin
multiplicity of CS state can be either of singlet or triplet. The latter can only be
produced via intersystem crossing from the singlet CS state because the triplet state of
porphyrin, and associated with it triplet CS state, is quenched by fullerene. This
intersystem crossing process is slow by itself but can be accelerated by radical species
such as oxygen11 (see chapter 5). If the CS state energy is higher than that of the
triplet state of fullerene, then charge recombination from the triplet CS state can
proceed much faster to the 3C60 rather than to the ground state. As a result, the
lifetime of the CS state shortens with increasing concentration of oxygen, as was
experimentally observed for both dyads in toluene.11 Only when the CS state’s energy
is lower than that of the locally excited triplets, then intersystem crossing inhibits
charge recombination by promoting singlet CS state into the long-lived triplet CS
state.11 CS states in both dyads in toluene are higher in energy than that of ET (of
61
3C60), and oxygen enhances recombination, while in polar THF (with lowered CS
states energies) oxygen inhibits charge recombination instead.11
Since the electronic coupling elements, VDA, are unknown and it is difficult to
separate coupling “through space” and “through bond” for these dyads, we will
neglect a possible variation of VDA between the two dyads and in different solvents.
Instead, we will presume that Franck-Condon (FC) factors calculated using equation
(3.12) provide a sufficient base for evaluating relative rates of charge separation in
these dyads. Listed in Table 3.4, these coefficients represent relatively well the trends
that we observed for the CS yields from different states in the dyads. First of all, the
smallest FC factor (i.e. the smallest charge separation rate) is from the porphyrin
singlet excited state of 1ZnP-C60 (3) in toluene. Correspondingly, fluorescence from
1C60 was observed only in this case and the dipole signal showed a delay in CS state
formation, ca. 0.9ns. The FC factor for charge separation from 1C60
Table 3.4. Franck –Condon factors for charge separation rates from different excited states (in eV-1) in three solvents calculated using equation(3.12). Separation distance is presumed RDA = 10Å and the reorganization energies are taken from Table 3.3.
Solvent 1ZnP-C60a ZnP-1C60
b 1P-C60a P-1C60
b
Toluene 1.4 ×10-2 3.5 2.1 0.18
THF 0.86 1.7 1.2 0.30
CH2Cl2 0.68 1.7 1.3 0.36 a CS state is formed from 1ZnP-C60 or 1P-C60, identified as kCSS in Scheme 1; b CS state is formed from ZnP-1C60 or P-1C60, identified as kC60
CSS in Scheme 1.
62
is relatively high, in agreement with high overall yield of charge separation. Thus it is
likely that the CS state of ZnP-C60 (3) in toluene is primarily formed via an
intermediate locally excited state of fullerene, and the alternative route of direct
charge transfer from porphyrin to fullerene is of a lesser importance. In THF and
methylene chloride, on the other hand, the predicted rates of direct charge separation
from excited porphyrin are high. In agreement with that, neither fullerene
fluorescence nor a measurable delay in charge separation was observed in these cases.
Unfortunately, in both these polar solvents, the dyad shows low electrochemical
stability, especially in CH2Cl2, making it difficult to confirm the predicted high yield
of charge separation in these solvents.
The free base dyad, P-C60 (4), is more electrochemically stable in polar
solvents, and the predicted high yields of charge separation in THF and CH2Cl2 are
consistent with observed large dipole moments for 4 in these solvents. Less obvious is
the situation for dyad 4 in toluene: a small apparent yield of charge separation is
difficult to match with the observed total quenching of porphyrin fluorescence and the
lack of fullerene fluorescence, especially since the rate of charge separation is
predicted to be high. The apparent contradiction can be resolved by proposing that the
CS state and the local excited state of 1C60* are interchanging with each due to their
close energies (see Table 3.1). Since a contribution to the dyad absorption from
fullerene in the visible range is small, such a coupling would be difficult to detect in
the absorption. As a result, the above evaluation of the dipole moment value, which
presumes 100% charge transfer, is no longer applicable. Instead, a “mixed wave
63
function” describing the contributions from both, the charge separated “state”, ψcs,
and the locally excited one of 1C60*, ψC60, has to be constructed using equation (3.17):
6021 Ccs cc ψψ +=Ψ (3.17)
Depending on the relative energies of the two “states” and the electronic
coupling element, VDA, the relative contributions, c1 and c2, and the corresponding
dipole moment, µ, of the resulting mixed state, as given in equation (3.18):
csc µµ 21= (3.18)
will vary. For a strong enough coupling, the dipole moment, µ, approaches half the
value of µcs, which seems to be close to the experimentally observed value (see Table
3.2).
3.5 Conclusions
We have demonstrated that the two porphyrin-fullerene dyads, ZnP-C60 (3)
and P-C60 (4), show promising qualities for mimicking the photosynthetic system.
High yields of photoinduced charge separation in low polarity solvents lasting for a
few nanoseconds were observed by the transient displacement current technique. It
was shown that charge separation in these dyads proceeds via a combination of direct
electron transfer and transfer through an intermediate energy transfer state. The
effects of molecular flexibility, electronic and nuclear polarizability, and solvent
polarity were shown to have a significant role in explaining the observed dipole
64
moments. Facile synthesis used for these dyads could be applied towards construction
of further extended compounds with high yields of photoinduced charge separation.
3.6 References
1. a) The Photosynthetic Reaction Center (Eds.: J. Deisenhofer, J. R. Norris), Academic Press, San Diego, 1993; b) Huber R, Angew. Chem. 1989, 101, 849; Angew. Chem. Int. Ed. Engl. 1989, 28, 848; c) Deisenhofer J, Michel H, Angew. Chem. 1989, 101, 872; and Angew. Chem. Int. Ed. Engl. 1989, 28, 829.
2. a) Gust D, Moore TA in Topics in Current Chemistry, vol. 159, Photoinduced Electron Transfer III (Ed.: J. Mattay), Springer, Berlin, 1991; b) Wasielewski MR, Chem. Rev. 1992, 92, 435; c) Gust D, Moore TA, Moore AL, Acc. Chem. Res. 1993, 26, 198; d) Kurreck H, Huber M, Angew. Chem. 1995, 107, 929; Angew. Chem. Int. Ed. Engl. 1995, 34, 849; e) Tauber AY, Kostiainen RK, Hynninen PH, Tetrahedron 1994, 50, 4723; f) Borovkov VV, Gribkov AA, Kozyrev AN, Brandis AS, Ishida A, Sakata Y, Bull. Chem. Soc. Jpn. 1992, 65, 1533; g) Maruyama K, Yamada H, Osuka A, Chem. Lett. 1989, 5, 833; h) Tauber AY, Helaja J, Kilpeläinen I, Hynninen PH, Acta Chem. Scand. 1997, 51, 88.
3. Hirsch A, The Chemistry of the Fullerenes, Thieme, Stuttgart, 1994.
4. a) Imahori H, Sakata Y, Adv. Mater. 1997, 9, 537; b) Gust D, Moore TA, Moore AL, Res. Chem. Intermed. 1997, 23, 621; c) Martín N, Sánchez L, Illescas B, Pérez I, Chem. Rev. 1998, 98, 2527; d) Diederich F, Kessinger R, Acc. Chem. Res. 1999, 32, 537; e) Imahori H, Sakata Y, Eur. J. Org. Chem. 1999, 2445-2457; f) Linssen TG, Dürr K, Hanack M, Hirsch A, J. Chem. Soc., Chem. Commun. 1995, 103; g) Drovetskaya T, Reed CA, Boyd P, Tetrahedron Lett. 1995, 36, 7971; h) Kuciauskas D, Lin S, Seely GR, Moore AL, Moore TA, Gust D, Drovetskaya T, Reed CA, Boyd PDW, J. Phys. Chem. 1996, 100, 15926; i) Dietel E, Hirsch A, Eichhorn E, Rieker A, Hackbarth S, Röder B, J. Chem. Soc., Chem. Commun. 1998, 1981; j) Tomé AC, Enes RF, Tomé JPC, Rocha J, Neves MGPMS, Cavaleiro JAS, Elguero J, Tetrahedron 1998, 54, 11141; k) Cheng P, Wilson SR, Schuster DI, J. Chem. Soc., Chem. Commun. 1999, 89; l) Bourgeois JP, Diederich F, Echegoyen L, Nierengarten JF, Helv. Chim. Acta 1998, 81, 1835; m) Helaja J, Tauber AY, Abel Y, Tkachenko NV, Lemmetyinen H, Kilpeläinen I, Hynninen
65
PH, J. Chem. Soc., Perkin Trans. 1 1999, 2402; n) Tkachenko NV, Rantala L, Tauber AY, Helaja J, Hynninen PH, Lemmetyinen H, J. Am. Chem. Soc. 1999, 121, 9378; o) Zheng G, Dougherty TJ, Pandey RK, J. Chem. Soc., Chem. Commun. 1999, 2469; p) Kräutler B, Sheehan CS, Rieder A, Helv. Chim. Acta 2000, 83, 583; q) Kräutler B, Rieder A, J. Am. Chem. Soc. 2000, 122, 9050; r) Montforts F-P, Kutzki O, Angew. Chem. 2000, 112, 612; s) Kutzki O, Walter A, Montforts F-P, Helv. Chim. Acta 2000, 83, 2231.
5. a) Marcus RA, Angew. Chem. 1993, 105, 1161; Angew. Chem. Int. Ed. Engl. 1993, 32, 1111; b) Sakata Y, Imahori H, Tsue H, Higashida S, Akiyama T, Yoshizawa E, Aoki M, Yamada K, Hagiwara K, Taniguchi S, Okada T, Pure Appl. Chem. 1997, 69, 1951; c) Imahori H, Hagiwara K, Akiyama T, Aoki M, Taniguchi S, Okada T, Shirakawa M, Sakata Y, Chem. Phys. Lett. 1996, 263, 545.
6. a) Schumm O, Hoppe-Seyler´s Z. Physiol. Chem. 1928, 178, 1; b) Dinello RK, Chang CK in The Porphyrins, vol. I A (Ed.: D. Dolphin), Academic Press, New York, 1978, pp. 294–296.
7. Zehnder B, PhD thesis (Research group A. Eschenmoser), ETH Zürich (CH), 1982.
8. Wedel M, Montforts F-P, Tetrahedron Lett. 1999, 40, 7071.
9. Bingel C, Chem. Ber. 1993, 126, 1957.
10. (a) Smirnov SN, Braun CL, Rev. Sci. Instr., 1998, 69, 2875-2887, (b) Smirnov SN, Braun CL, Greenfield SR, Svec WA, Wasielewski MR J. Phys. Chem. 1996, 100, 12329-12336; (c) Smirnov SN, Liddell PA, Vlassiouk IV, Teslja A, Kuciauskas D, Braun CL, Moore AL, Moore TA, Gust D, J. Phys. Chem. A, 2003, 107, 7567-7573.
11. a) Smirnov S, Vlassiouk I, Kutzki O, Wedel M, Montforts F-P, J. Am. Chem. Soc., 2002, 124, 4212-4213; b) Vlassiouk I, Smirnov S, Kutzki O, Wedel M, Montforts F-P, J. Phys. Chem., 2002, 106, 8657-8666.
12. Vlassiouk I, Smirnov S J. Phys. Chem. A, 2003, 107, 7561-7566.
66
13. Mylon SE, Smirnov SN, Braun CL J. Phys. Chem. 1998, 102, 6558-6564.
14. Armaroli N, Marconi G, Echegoyen L, Bourgeois J-P, Diederich F Chem. Eur. J., 2000, 6, 1629-1645.
15. a) Asahi T, Ohkohchi M, Mataga N, J. Phys. Chem. 1993, 97, 13132-13137; b) Heitele H, Pollinger F, Haberle T, Michelbeyerle ME, Staab HA J. Phys. Chem. 1994, 98, 7402-7410; c) Johnson DG, Niemczyk MP, Minsek DW, Wiederrecht GP, Svec WA, Gaines GL, Wasielewski MR J. Am. Chem. Soc. 1993, 115, 5692-5701; d) Wynne K, Lecours SM, Galli C, Therien MJ, Hochstrasse RM J. Am. Chem. Soc. 1995, 117, 3749-3753.
16. Imahori H, Hagiwara K, Aoki M, Akiyama T, Taniguchi S, Okada T, Shirakawa M, Sakata Y, J. Am. Chem. Soc., 1996, 118, 11771-11782.
17. Guldi D, Asmus K-D, J. Phys. Chem. A 1997, 101, 1472-1481.
18. Komamine S, Fujitsuka M, Ito O, Moriwaki K, Miyata T, Ohno T J. Phys. Chem. A 2000, 104, 11497-11504.
19. ZnP-C60 dyad (3) changes absorption in THF after passing through the cell even without irradiation but the dipole measurements take shorter time and we carry experiments only using fresh solutions without recirculation. Nevertheless, one can estimate that a noticeable portion of the solution decomposes inside the cell, on a single pass. A pronounced isosbestic point at 418 nm indicates that the dyad apparently decomposes into a single absorbing in this region specie, most likely a derivative of fullerene, because porphyrin absorption drops dramatically. It seems that Zn-porphyrin oxidizes and deposits at the cathode (a thin film formation is evident), while fullerene derivative remains in the solution. Amazingly, no electrochemistry is observed with either ZnP or fullerene by themselves or for the free-base P-C60 dyad (4). Such a distinct partitioning is probably due to THF molecule coordination by Zn in the porphyrin,15 but it has not been confirmed. Since laser excitation during dipole experiments is centered at porphyrin absorption (396 nm or 416 nm), far from absorption of the electrochemical products, and only fresh solutions were investigated, the electrochemistry effects were of low significance. Nonetheless, since absorption by other species, besides
67
the dyad ZnP-C60 (3), can contribute, the corresponding dipole moment for 3 in THF should be treated as the lower estimate.
20. Hyperchem Release 6.0 Pro.; Hyprcube Inc.: Gainesville, FL.
21. The effective dipole moment is the square root of the squared dipole moment increase, µ = (µexc
2 − µg2)1/2. In most cases, including this one, the effect of the
ground state dipole moment makes an insignificant difference between µexc and µ. The ground state dipole moments, mg, for the dyads are not known but can be estimated using semiemprical AM1 model for both, ZnPor-C60 and Por-C60, to be almost identical, µg = 4.3 D. The experimental dipole moment, µexc = (µ2 + µg
2)1/2, alters only slightly from the effective one and in toluene becomes µexc = 35.5 D (vs. µ = 35.2 D) for ZnPor-C60 and µexc = 14.9 D (rather than µ = 14.3 D) for Por-C60, respectively.
22. a) Marcus RA J. Chem. Phys. 1965, 43, 679; b) Marcus RA Annu. Rev. Phys. Chem. 1964, 15, 155
23. (a) Brunschwig BS, Ehrenson E, Sutin N J. Am. Chem. Soc. 1984, 106, 6858 (b) Sutin N. In Electron Transfer in Inorganic, Organic, and Biological Systems; Bolton JR, Mataga N, Mclendon G, Eds. Advances in Chemistry Series 228; American Chemical Society: Washington, DC, 1991; p 25.
24. . As it is clear from the table, the internal reorganization energy differs between the calculated as a difference in the enthalpy of an ion in minimized geometry of the ion, ∆Hionic conf(ion), and corresponding neutral species, ∆Hneutral conf(ion): δ∆H(ion) = ∆Hionic conf(ion) - ∆Hneutral conf(ion), and that for the neutral species: δ∆H(ion) = ∆Hneutral conf(neutral) - ∆Hionic conf(neutral). This discrepancy reflects the limitation of a simple Marcus approximation. We choose λint = δ∆H(ion) as the smallest between the two.
Solvent δ∆H(ion), eV δ∆H(neutral), eV
P 0.27 0.50
ZnP 0.16 0.25
C60 0.05 0.05
C60 (7) 0.06 0.06
68
25. The porphyrin handbook edited by Kadish K. M., Kevin M. Smith, Roger Guilard, Vol 9.
69
4 CHARACTERIZATION OF THE GIANT TRANSIENT DIPOLE GENERATED
BY PHOTOINDUCED ELECTRON TRANSFER IN A CAROTENE-
PORPHYRIN-FULLERENE MOLECULAR TRIAD
4.1 Introduction
One approach to mimicry of photosynthetic energy conversion has been the
construction of large “supermolecules” consisting of covalently linked chromophores,
electron donors and electron acceptors. Such molecules can demonstrate the
intramolecular transfer of singlet and triplet excitation energy and photoinduced
electron transfer to generate long-lived, energetic charge-separated states. Many of
these artificial reaction centers feature porphyrins as the primary light-absorbing
species and as models for the chlorophylls of natural reaction centers.1-6 These
molecules not only serve as mimics of natural solar energy conversion, but also as
potential components of molecular-scale optoelectronic devices.7-20 The charge-
separated states produced upon excitation are typically the raison d’être for such
artificial reaction centers. Although transient absorption techniques may be used to
identify these states and follow their formation and decay with time, these techniques
do not yield information about the charge distribution character of the states. The
dipole moment of a transient charge-separated state is one of its most basic and
important properties, but methods for measuring this quantity are limited.
The transient microwave conductivity technique has been applied to a number
of systems producing transient dipoles,21-27 and has permitted the determination of
70
important information that was previously unavailable by other methods. However,
that technique has intrinsic limitations in time resolution and a requirement for very
low solvent polarity. In addition, an estimate for the rotational time of the transient
dipolar species is required in order to determine the dipole moment. More recently, it
has been shown that the transient dc photocurrent technique not only yields
information on the dipole moments of transient charge-separated species, but also is
compatible with a wide range of solvent polarities, depends only weakly on molecular
rotational times, and has subnanosecond time resolution.28,29
One type of artificial photosynthetic reaction centers prepared to date consists
of a porphyrin (P) bearing a carotenoid polyene (C) and an electron acceptor.1,3,7,30-36
An example is molecular triad 1, in which the acceptor is a fullerene (C60) moiety.37
Transient absorption and emission experiments have shown that in 2-
methyltetrahydrofuran (MTHF) solution, excitation of the porphyrin moiety of C-P-
C60 yields, C-1P-C60, which decays with a rate constant of 3.3 × 1011 s-1 to give a C-
P•+-C60•− charge-separated state with a quantum yield of unity. Light absorbed by the
fullerene also leads to formation of C-P•+-C60•− with a yield of essentially 1.
Competing with charge recombination to yield the ground state (kCR1 = 2.1 × 109 s-1),
electron transfer from the carotenoid (kCT2 = 1.5 × 1010 s-1) to yield a final C•+-P-C60•−
charge-separated state is facile. In MTHF this species is formed with a quantum yield
of 0.88, based upon light absorbed by the porphyrin chromophore.
Although it is clear from the photochemistry discussed above that the C•+-P-
C60•− state in 1 must have a very large dipole moment, its exact magnitude is
71
unknown. Even though it is certain that the positive charge resides on the carotenoid
moiety, its highly delocalized and polarizable π-electron system makes prediction of
the dipole moment in 1 and other carotenoid-containing artificial reaction centers
difficult. For this reason, we have used the transient dc photocurrent technique to
investigate transient dipoles formed after excitation of 1 in 2-methyltetrahydrofuran
and tetrahydrofuran.
4.2 Results
4.2.1 Transient absorption measurements
Transient absorption measurements were done by Dr. Gust group at Arizona
State University.
As mentioned above, the rate constants and quantum yields for the various
photophysical and electron transfer steps for 1 in MTHF at ambient temperatures
have been previously reported.37 The quantum yield of the final C•+-P-C60•− state in
tetrahydrofuran (THF) at ambient temperatures has now been determined as well.
Solutions (~1 × 10-5 M) of 1 in THF and MTHF were made up with identical
absorbance, and excited with ~5 ns laser pulses at 575 nm, 590 nm and 620 nm,
where essentially all of the light is absorbed by the porphyrin moiety. The transient
absorbance of the carotenoid radical cation in C•+-P-C60•− was monitored near its
maximum at 950 nm, and the maximum amplitudes were determined for the two
72
solvents. Based on the quantum yield Φcs (MTHF) = 0.88 for 1 in MTHF mentioned
above, a yield of Φcs (THF) = 0.59 for C•+-P-C60•− in THF was determined.
4.2.2 Molecular modeling
Interpretation of dipole moment data in terms of molecular structure requires
knowledge of molecular structure and conformations. Molecular modeling using the
MM+ molecular mechanics approach (HyperChem38) yielded the lowest-energy
ground state conformation of 1 shown in Figure 4.1. This linear extended
conformation for the molecule is consistent with previous calculations and NMR
determinations of molecular structure for related carotenoporphyrins.38-41
4.2.3 Transient DC photocurrent measurements
Details of the experimental setup can be found elsewhere.29 Theory can be
found in chapter 2 and ref. [42,43]. The sample of triad 1 in solution is excited
between two parallel stainless steel electrodes separated by a distance d (1.2 mm and
0.7 mm were used) and confined by two quartz windows. When the sample is excited
with a 20 ps laser pulse, photoinduced charge separation generates C•+-P-C60•− as
described above. The formation time for that charge-separated state (59 ps in MTHF)
is much shorter than the time response of the apparatus (ca. 0.5 ns), allowing us to
treat its formation as instantaneous. The final charge-separated state has a different,
73
much larger dipole moment than the ground state. The applied voltage V0 (500 V)
causes the newly formed giant dipoles to
Figure 4.1. Structure and the lowest-energy conformation for triad 1 as calculated using MM+ molecular mechanics methods. The double bonds in the carotenoid conjugated backbone and the amide partial double bond are all trans. There are several other conformations of essentially equal energy and with similar interatomic distances that can be generated by 180° rotations about the 6’-7’ bond, or single bonds in the amide linkage.
reorient with a rotation time, τr, causing a change in the angular distribution of dipole
moments with respect to the applied electric field. This results in a displacement
current measured across a load resistor R and digitized on the TDS 684A oscilloscope
as a function of time t.
N CO N
CH3N N
N NH
HH
74
4.2.4 Photoinduced voltage curves
Figure 4.2 shows the photoinduced voltage measured at ambient temperature
in the displacement current mode for a THF solution of 1. Excitation was with a 396
nm (Figure 4.2A) or 559 nm (Figure 4.2B) laser pulse. In both cases, the
photoresponse has been normalized to an absorbed energy of 9.3 µJ. Each response
consists of a positive region, and a negative region of much smaller amplitude. The
shape of the positive region is primarily a function of the rotation time, τr, and the
initial dipole orientation defined by the polarization at excitation. To simplify, we
excited at the magic angle, but found almost no difference with other polarizations.
That seems to be reasonable for this case, where transitions with two orthogonal
polarizations in the porphyrin both result in the same charge separated state and their
combination produces close to uniform initial distribution of dipoles. The negative
portion of the photoresponse reflects the lifetime of the charge-separated state, τCR.
Since τCR is considerably longer than the laser pulse and molecular rotation portion of
the signal, the amplitude of this negative portion is too small to permit one to obtain a
precise value for the lifetime of C•+-P-C60•−.
Figure 4.3 shows the results of for 1 in 2-methyltetrahydrofuran taken under
conditions similar to those used in Figure 4.3. Excitation was at 396 nm. The results
in Figure 4.3A were obtained in the displacement current mode, and are very similar
to those obtained in tetrahydrofuran. The signal amplitude in the negative region is
75
again too small to allow determination of a reliable charge recombination time. The
data in Figure 4.3B were measured in the charge displacement mode. In this mode,
the rotational time τr is manifested in the rise time of the photoresponse, and the
decay of the positive signal is a function of the lifetime of the charge-separated state,
τCR.
4.2.5 Analysis of the data
The results in Figures 4.2 and 4.3 were fitted using methods previously described.29
The results in tetrahydrofuran measured at either wavelength yield best fit rotational
times τr of 7.5 ± 0.5 ns (the fits are shown in the figures). The corresponding data in
Figure 4.3 give an indistinguishable value, 7.5 ± 0.5 ns. The similarity of these two
times is expected, given the similar viscosities of the two solvents, but the time
constants are somewhat high and require a detailed discussion, which we present
later. The measurement in the charge displacement mode (Figure 4.3B) allows
determination of the lifetime of C•+-P-C60•− with an accuracy of ~10%: τCR = 300 ns.
This lifetime also yields reasonable fits to the decays of the small negative
components of the displacement current curves in Figures 4.2 and 4.3A.
76
Figure 4.2. Photoresponse of C-P-C60 triad in THF as measured in the displacement current mode. Solid lines are the photoresponse of C-P-C60 triad 1 in tetrahydrofuran as measured in the displacement current mode in the cell with a 1.2 mm gap. Excitation was at 396 (A) or 559 (B) nm, and the responses have been normalized to the same amount of absorbed energy, 9.3 µJ. The squares represent the best fit to the experimental data, and yield the parameter values reported in the text. The dotted lines show the shape of the laser excitation pulse.
0 20 40 60 80
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
B
λexc = 559 nm, THF
Time (ns)
Pho
tore
spon
se (V
)
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
A
λexc = 396 nm, THF
Pho
tore
spon
se (V
)
77
Figure 4.3. Photoresponse of C-P-C60 triad in 2-MTHF as measured in the displacement current mode and the charge displacement mode. Photoresponse of C-P-C60 triad in 2-MTHF as measured in the displacement current mode and the charge displacement mode. Solid lines are the photoresponse of C-P-C60 triad 1 in 2-methyltetrahydrofuran as measured in the cell with a 1.2 mm gap in the displacement current mode (A) and the charge displacement mode (B). Excitation was at 396 nm, and the responses have been normalized to the same amount of absorbed energy as in Figure 4.2, 9.3 µJ. The squares represent the best fit to the experimental data, and yield the parameter values reported in the text. The dotted lines show the shape of the laser excitation pulse.
0 20 40 60 80
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
A
λext =396nm, MTHF
Time (ns)
Pho
tore
spon
se (V
)
0 100 200 300 400 500
0.000
0.001
0.002
0.003
0.004
0.005
0.006
Time (ns)
Pho
tore
spon
se (V
)
B
λext =396nm, MTHF
78
The amplitudes of the photoresponse curves in Figures 4.2 and 4.3 are related
to the magnitude of the dipole moment of C•+-P-C60•−. Without taking into account
the less than unity quantum yield of charge separation (i.e. assuming Φcs = 1) and
taking Aa ~ 044 the fitting of the dipole signal in THF yielded µcs values of 109 D with
excitation at 396 nm and 80 D, with 559 nm excitation. In MTHF with excitation at
396 nm, fitting the data from either the displacement current or charge displacement
experiments under the abovementioned assumptions yielded µcs = 137 ± 5 D. The
dielectric constants of tetrahydrofuran, ε(THF) = 7.52 and 2-methyl-tetrahydrofuran,
ε(MTHF) = 6.97 as well as their respective refractive indexes, nD(THF) = 1.405 and
nD (MTHF) = 1.406, were taken from the literature.45
The apparent µcs values must be first corrected for the quantum yield Φcs. As
mentioned above, the optically measured quantum yield of C•+-P-C60•− in THF is Φcs
(THF) = 0.59. This yield is based on light absorbed only by the porphyrin or fullerene
moieties. Light energy absorbed by the carotenoid is not transferred effectively (<
10%) to the porphyrin in this molecule, and is essentially ineffective in charge
separation. The absorption spectrum of 1 is reasonably approximated by a linear
combination of the spectra of porphyrin, carotenoid, and fullerene model
compounds.37 On this basis, at 396 nm, 91% of the absorption is due to the porphyrin
and fullerene moieties. Thus, Φ396 (THF) = 0.91 × 0.59 = 0.54. With excitation at 559
nm, only 51% of the absorbed light is harvested by the porphyrin and fullerene
moieties, and Φ559 (THF) = 0.51 × 0.59 = 0.30. In MTHF, the yield of charge
79
separation in 1, at 0.88, is considerably higher than it is in tetrahydrofuran, and Φ396
(MTHF) = 0.91 × 0.88 = 0.80. When normalized by the yield, Φcs, the dipole
moments in all three cases become identical within our accuracy, µcs = 153 ± 6 D.
Note that if the spherical approximation for molecular shape were used in eq. (7) (Aa
= 1/3), the dipole moment would be considerably smaller, 110 D.
4.3 Discussion
4.3.1 Magnitude of the dipole moment
To the best of our knowledge, the dipole moment determined for C•+-P-C60•−
surpasses previous champions24-26, 28 and is the largest ever experimentally
determined for a single molecule. Division of the 153 D value by 4.8 D/Å yields a
separation of 31.9 ± 1.2 Å between the centers of positive and negative charge. For
comparison, the calculated conformation shown in Figure 4.1 suggests a separation
distance of 34 Å between the center of negative charge placed at the center of
fullerene and the center of positive charge in the center of carotenoid. The agreement
is remarkable.
There are a few caveats to the above analysis. These include the possibilities
of: (i) oversimplification of molecular shape46 (ii) coulombic attraction between the
polarizable chromophores, (iii) overestimation of the quantum yield of charge
80
separation, and (iv) a conformational change in the charge separated state. Below we
will discuss each possibility.
4.3.1.1 Molecular shape.
The approximation of Aa = 0 made above oversimplifies the effect of
molecular shape. At the same time, for an extended molecule like the triad 1,
approximation as an ellipsoid is also too far from reality. An alternative evaluation42
is based on separating the contribution to the total dipole moment, Mcs, made by the
solute, µcs, and the solvent polarized by the solute, Ms (see Chapter 2).
We apply this approach for calculating Ms and mimic the distribution of
charges in the charge separated state of triad 1 by placing a single negative unit
charge in the center of the fullerene and distributing the positive charge evenly along
the carotene backbone. The resulting value of the dipole moment Ms with that charge
distribution is very weakly sensitive to the van der Waals radii of the atoms, which
are used to represent the molecular shape. Moreover, other distributions of positive
charge with the same dipole moment, either with four quarters of a unit charge on C9`,
C13`, C9, and C13 carbons or even just a single unit charge in between C15 and C15’
carbons, as labeled on Figure 4.1, provide the same result within 1% accuracy. Using
van der Waals radii from the literature, 47 we calculated Ms = -46 ± 1 D, which brings
the total dipole moment of the charge transfer state to µcs = Mcs - Ms = 110 + 46 = 156
± 6 D. That number is in better agreement with the expected value of 163 D = 34 Å ×
81
4.8 D/Å calculated for the lowest energy conformation of the ground state molecular
structure shown in Figure 4.1.
4.3.1.2 Effect of mutual polarizability
Given the partial double bond character of the amide bond linking the
carotenoid and porphyrin moieties, the conjugated π-electron system of the
carotenoid extends all the way to the point where the meso-aryl ring joins the
porphyrin macrocycle. The orbital overlap is interrupted at this point because the
steric influence of the flanking methyl groups forces the aryl ring nearly
perpendicular to the macrocycle (Figure 4.1). It is therefore possible to write
resonance structures for the carotenoid radical cation in which the positive charge
resides close to the porphyrin macrocycle. Semi-empirical AM1 calculations for β-
carotene show that upon oxidation to the radical cation, charge is significantly
delocalized over the 14 carbon atoms in the center of the π-electron system.48 Thus, in
the charge-separated state, coulombic attraction by the negative charge on the
fullerene would tend to move the center of positive charge on the carotenoid closer to
the porphyrin, decreasing the dipole moment. If the polarizability of the carotenoid
radical cation (and fullerene radical anion) were large enough, this effect would
contribute to reducing the observed dipole moment. Semi-empirical AM1 calculations
on the radical cation of the carotenoid canthaxanthin show disappearance or
significant lowering of the bond length alternation for the conjugated system, relative
82
to the neutral carotenoid, and this would lead to an increase in electric
polarizability.48,49
Krawczyk has reported50,51 experimental values for the transition moments of
the first two optical absorptions of the radical cation of the carotenoid astaxanthin:
M01 = 7.5 D (E10 = 7810 cm-1) and M02 = 16.D (E20 = 12000 cm-1). The ground-state
polarizability α(carotene+) of the cation radical can be estimated from these values
using perturbation theory:
α = 2(M012/E10 + M02
2/E20 + …) ≈ 285 Å3 (4.1)
There are no experimental data on polarizability of fullerene anion radical.
Semiempirical (AM1) calculations that we performed using HyperChem38 suggest
that it is close to that of a neutral molecule, α(C60−) = 80 Å3. Incidentally, analogous
calculations for carotene+ imply its anisotropic polarizability to be different from that
of the neutral molecule, along the primary axis it is α||(carotene+) ~ 490 Å3, while
α||(carotene) ~ 190 Å3. The correction to the dipole moment due to the electric
polarizability may be estimated51 from eq. (4.2):
( )( ) 260 ~)(||reEcaroteneC
εαααµ +− +=∆ (4.2)
where r is the separation of the centers of positive and negative charge. Applying this
equation to the triad 1 and using the total polarizability α = 570 Å3 yields a correction
of ∆µ < 0.4 D. The polarizability of the radical cation of the carotenoid moiety of 1 is
likely somewhat higher than the above estimate, given further extension of the π-
83
electron system in the dyad, but it still seems unlikely that the effect will contribute
significantly.
4.3.1.3 Quantum yield
Eq. (3.1) indicates that overestimating the quantum yield of formation of C•+-
P-C60•− will result in an underestimation of the dipole moment. Thus, this is in
principle a possible cause for the slightly small measured dipole moment in 1. The
factors affecting the quantum yield measurement for 1 have been discussed.37 The
estimate is based on rate constants for the various electron transfers and decay
pathways for the relevant excited states in 1 and model compounds. Barring the
occurrence of unexpected new decay pathways or unexpected changes in rate
constants for the excited and intermediate charge-separated states in 1 relative to the
model compounds, it is unlikely that the quantum yield estimates would be in error
enough to account entirely for the differences between the observed and expected
dipole moment. However, the occurrence of such unknown effects cannot be
completely excluded as a possibility.
4.3.1.4 Molecular conformation
If the molecular conformation of C•+-P-C60•− is different from that in Figure
4.1, and brings the centers of charge closer together, the measured dipole moment
84
would be smaller than expected. There are number of possibilities for such
conformations, including rotation about the carbon-nitrogen amide bond of 1 to
generation a cis conformation, or generation of cis configurations or s-cis
conformations in the carotenoid backbone. It is unlikely that any of these isomers are
present to any appreciable extent in the ground state of the triad. X-Ray and NMR
data and MM+ calculations show the all-trans conformation in the amide and
carotenoid backbone as the most stable.38-40 However, it is conceivable that rotation
about some bonds in the carotenoid chain may occur after formation of the radical
cation to yield conformations with a smaller dipole moment. Semi-empirical (AM1)
calculations on β-carotene and similar carotenoids show that one-electron oxidation
leads to significant bond length equalization between the single and double bonds in
the entire conjugated carotenoid backbone between the β-ionyl rings.48 This would be
expected to facilitate rotation about bonds that are formally double in the ground-state
structure. Indeed, Kispert and coworkers48 have reported that electrochemical or ferric
chloride oxidation of all-trans canthaxanthin and β-carotene leads to significant trans
to cis isomerization, with cis isomers occurring in about 40% of the products. The
mechanism was proposed to be facile isomerization in the radical cation, followed by
comproportionation reactions that regenerate neutral carotenoids. Calculations (AM1)
of the transition state energies for rotation about formally double bonds indicated
much lower barriers for the radical cations than for the neutral species. The authors
suggest that similar isomerizations could occur in carotenoid-containing molecules
such as 1 that have long-lived charge-separated states.48 If such carotenoid
85
isomerization of the radical cation occurs in 1, it could contribute to lowering the
measured dipole moment.
4.3.2 Rotation times
Based on simple hydrodynamic theory, the rotational diffusion time for a
sphere of volume V in a medium of viscosity η is given by the Einstein law52,53 as:
Tk
VD B
spherητ ==
61 (4.3)
For a sphere with the van der Waals volume equal to that of the triad 1, V = 1890 Å3,
and for the solvent viscosity of THF, η(25°C) = 0.46 cP,45 at room temperature (T =
298 K) one obtains the τspher value of 0.22 ns, which is over an order of magnitude
smaller than the measured τr. As was discussed above, triad 1 is far from being a
spherical molecule. Unfortunately, there is no a simple limiting approximation for
rotation time for molecules with extended arbitrary shapes. The only approximation
other than spherical is that of an ellipsoid of revolution, in which, according to
Perrin,54,55 there are two diffusion coefficients, D|| and D⊥, for rotation about the
longitudinal and equatorial semiaxes:
( )( ) DSD 2|| 1213
γγ
−−
= (4.4)
( )[ ]( ) DSD 4
2
1223
γγγγ
−−−
=⊥ (4.5)
86
Here the aspect ratio γ = b/a has meaning as the ratio of the longitudinal and
equatorial semiaxes. The value D is calculated from eq. (4.3) for a sphere of the same
volume. In the case of a prolate ellipsoid of revolution (γ < 1), S is given by:
( )[ ]γγγ
γ ln11ln1
2
2−−+
−=S (4.6)
Approximating triad 1 as a prolate spheroid is still not a perfect representation of its
shape – the definition of semiaxes is ambiguous. Nevertheless, if we use the van der
Waals volume, V, and take the molecule’s length to be the longitudinal axis, 2a~ 55.2
Å, we can estimate that γ ~ 0.139.44 Equations (4.5, 4.9) can be approximated in the
limit of very small γ as: 55
) − (0.2
≈=⊥
⊥ γγτ
τln36
12
spher
D, (4.7)
where τspher is given by eq. (4.3). For γ ~ 0.139 eq. (4.7) gives the estimated rotational
time about the equatorial semiaxis, τ⊥ = 1.8 ns. This is closer to the measured value of
7.5 ns, but the applicability of eqs. (4.4-4.7) for an extended molecule like triad 1 is
very questionable. The calculated τ⊥ is very sensitive to many factors such as the
aspect ratio γ and the charge distribution. For example, the value of τ⊥ will be
increased up to the experimental value of τr ~7.5 ns if one assumes a much smaller
aspect ratio, γ ~ 0.057, while maintaining the same molecular volume. That aspect
ratio corresponds to an “average” diameter of triad 1, 2b ~ 3.2 Å. Also, the
hydrodynamic approximation underestimates the total friction for charge transfer
states. Triad 1 in its charge transfer state produces strong electric field over a large
87
surrounding volume. The high amplitude of this field as well as its large gradient can
noticeably alter solvent properties and the triad’s interaction with the solute. As has
been discussed in the literature, rotational relaxation of dipolar and ionic species in
polar solvents can be slower than the hydrodynamic model suggests due to the so-
called dielectric friction and solvent attachment effects.56-59
4.3.3 Lifetime of the charge-separated state
Between the two modes of dipole signal measurements, the most reliable
determination of the decay characteristics of the giant dipole comes from the charge
displacement mode (Figure 4.3B), where the signal was found to decay exponentially
with a time constant τCR ~300 ns. Given the signal-to-noise ratio of the data in Figure
4.3B, this is consistent with the lifetime of 340 ns determined by transient absorption
measurements in this solvent.37
4.4 Conclusions
The transient dc photocurrent measurements have verified the formation and
decay of a giant dipole coincident with the light-induced formation and decay of the
C•+-P-C60•− charge-separated state in triad 1. The record magnitude of the dipole
moment, ~ 160 D, is close to the value estimated from the distance between the center
of the negatively charged fullerene and a positive charge near the center of the
88
carotenoid moiety for the molecule in an extended conformation, ~ 33-34 Å. Given
several conceivable sources of discrepancy in the treatment, this agreement is
remarkable.
4.5 References
1. Gust, D.; Moore, T. A. In The Porphyrin Handbook, 8; Kadish, K. M., Smith, K. M., Guilard, R., Eds.; Academic Press: New York, 2000; pp 153-190.
2. Wasielewski, M. R. Chem. Rev. 1992, 92, 435-461.
3. Gust, D.; Moore, T. A.; Moore, A. L. Acc. Chem. Res. 1993, 26, 198-205.
4. Kurreck, H.; Huber, M. Angew. Chem. Int. Ed. Engl. 1995, 34, 849-866.
5. Maruyama, K.; Osuka, A.; Mataga, N. Pure Appl. Chem. 1994, 66, 867-872.
6. Sakata, Y.; Imahori, H.; Tsue, H.; Higashida, S.; Akiyama, T.; Yoshizawa, E.; Aoki, M.; Yamada, K.; Hagiwara, K.; Taniguchi, S.; Okada, T. Pure & Appl. Chem. 1997, 69, 1951-1956.
7. Gust, D.; Moore, T. A.; Moore, A. L. Acc. Chem. Res. 2001, 34, 40-48.
8. Gust, D.; Moore, T. A.; Moore, A. L. IEEE Eng. Med. Biol. 1994, 13, 58-66.
89
9. Ashton, P. R.; Johnston, M. R.; Stoddart, J. F.; Tolley, M. S.; Wheeler, J. W. J. Chem. Soc., Chem. Commun. 1992, 1128-1131.
10. Bissell, R. A.; de Silva, A. P.; Gunaratne, H. N.; Lynch, P. M.; Maguire, G. E.; Sandanayake, K. S. Chem. Rev. 1992, 187-195.
11. Debreczeny, M. P.; Svec, W. A.; Wasielewski, M. R. Science 1996, 274, 584-587.
12. Gunter, M. J.; Johnston, M. R. J. Chem. Soc., Chem. Commun. 1992, 1163-1165.
13. Harriman, A.; Ziessel, R. Chem. Commun. 1996, 1707-1716.
14. Mirkin, C. A.; Ratner, M. A. Annu. Rev. Phys. Chem. 1992, 43, 719-754.
15. O'Neil, M. P.; Niemczyk, M. P.; Svec, W. A.; Gosztola, D. J.; Gaines, G. L. I.; Wasielewski, M. R. Science 1992, 257, 63-65.
16. Shiratori, H.; Ohno, T.; Nozaki, K.; Yamazaki, I.; Nishimura, Y.; Osuka, A. Chem. Commun. 1998, 1539-1540.
17. Wagner, R. W.; Lindsey, J. S.; Seth, J.; Palaniappan, V.; Bocian, D. F. J. Am. Chem. Soc. 1996, 118, 3996-3997.
18. Chambron, J.-C.; Harriman, A.; Heitz, V.; Sauvage, J.-P. J. Am. Chem. Soc. 1993, 115, 7419-7425.
19. Chambron, J.-C.; Harriman, A.; Heitz, V.; Sauvage, J.-P. J. Am. Chem. Soc. 1993, 115, 6109-6114.
90
20. Linke, M.; Chambron, J.-C.; Heitz, V.; Sauvage, J.-P. J. Am. Chem. Soc. 1997, 119, 11329-11330.
21. Warman, J. M.; de Haas, M. P. In Time Resolved Conductivity Techniques DC to Microwave, "Pulse Radiolysis" Tabata, Y., Ed.; CRC: Boca Raton, 1990; p 101.
22. Fessenden, R. W.; Hitachi, A. J. Phys. Chem. 1987, 91, 3456
23. de Haas, M. P.; Warman, J. M. Chem. Phys. 1982, 73, 35
24. Paddon-Row, M. N.; Oliver, A. M.; Warman, J. M.; Smit, K. J.; de Haas, M. P.; Oevering, H.; Verhoeven, J. W. J. Phys. Chem. 1988, 92, 6958-6962.
25. Warman, J. M.; de Haas, M. P.; Oevering, H.; Verhoeven, J. W.; Paddon-Row, M. N.; Oliver, A. M.; Hush, N. S. Chem. Phys. Lett. 1986, 128, 95-99.
26. Warman, J. M.; de Haas, M. P.; Paddon-Row, M. N.; Cotsaris, E.; Hush, N. S.; Oevering, H.; Verhoeven, J. W. Nature (London) 1986, 320, 615-616.
27. Visser, R. J.; Weisborn, P. S.; van Kan, P. J.; Huizer, B. H.; Varma, C. A. G. O.; Warman, J. M.; de Haas, M. P. J. Chem. Soc., Faraday Trans. 2 1985, 81, 689-1985.
28. Smirnov, S. N.; Braun, C. L.; Greenfield, S. R.; Svec, W. A.; Wasielewski, M. R. J. Phys. Chem. 1996, 100, 12329-12336.
29. Smirnov, S. N.; Braun, C. L. Rev. Sci. Instrum. 1998, 69, 2875-2887.
91
30. Gust, D.; Mathis, P.; Moore, A. L.; Liddell, P. A.; Nemeth, G. A.; Lehman, W. R.; Moore, T. A.; Bensasson, R. V.; Land, E. J.; Chachaty, C. Photochem. Photobiol. 1983, 37S, 46.
31. Moore, T. A.; Gust, D.; Mathis, P.; Mialocq, J.-C.; Chachaty, C.; Bensasson, R. V.; Land, E. J.; Doizi, D.; Liddell, P. A.; Lehman, W. R.; Nemeth, G. A.; Moore, A. L. Nature (London) 1984, 307, 630-632.
32. Gust, D.; Moore, T. A. Adv. Photochem. 1991, 16, 1-65.
33. Ohkouchi, M.; Takahashi, A.; Mataga, N.; Okada, T.; Osuka, A.; Yamada, H.; Maruyama, K. J. Am. Chem. Soc. 1993, 115, 12137-12143.
34. Osuka, A.; Yamada, H.; Maruyama, K.; Mataga, N.; Asahi, T.; Yamazaki, I.; Nishimura, Y. Chem. Phys. Lett. 1991, 181, 419-426.
35. Osuka, A.; Yamada, H.; Maruyama, K.; Mataga, N.; Asahi, T.; Ohkouchi, M.; Okada, T.; Yamazaki, I.; Nishimura, Y. J. Am. Chem. Soc 1993, 115, 9439-9452.
36. Osuka, A.; Yamada, H.; Shinoda, T.; Nozaki, K.; Ohno, O. Chem. Phys. Lett. 1995, 238, 37-41.
37. Kuciauskas, D.; Liddell, P. A.; Lin, S.; Stone, S.; Moore, A. L.; Moore, T. A.; Gust, D. J. Phys. Chem. B 2000, 104, 4307-4321.
38. HyperChem Release 6.0 Pro.; Hyprcube Inc.: Gainesville, FL.
39. Chachaty, C.; Gust, D.; Moore, T. A.; Nemeth, G. A.; Liddell, P. A.; Moore, A. L. Org. Magn. Reson. 1984, 22, 39-46.
40. Gust, D.; Moore, T. A.; Liddell, P. A.; Nemeth, G. A.; Makings, L. R.; Moore, A. L.; Barrett, D.; Pessiki, P. J.; Bensasson, R. V.; Rougée, M.; Chachaty, C.;
92
de Schryver, F. C.; Van der Auweraer, M.; Holzwarth, A. R.; Connolly, J. S. J. Am. Chem. Soc. 1987, 109, 846-856.
41. Gust, D.; Moore, T. A.; Moore, A. L.; Devadoss, C.; Liddell, P. A.; Hermant, R. M.; Nieman, R. A.; Demanche, L. J.; DeGraziano, J. M.; Gouni, I. J. Am. Chem. Soc. 1992, 114, 3590-3603.
42. Onsager, L., J. Am. Chem. Soc. 1936, 58, 1486
43. Vlassiouk, I.; Smirnov S., J. Phys. Chem. in press
44. We can take molecule’s length to be the longitudinal axis 2a and then calculate the equatorial axis 2b from the molecule’s volume, V = 4πab2/3. Taking the molecule’s total length to be the distance between the most remote atoms in the all trans conformation, 2a ~ 55.2 Å, and the van der Waals volume from the modeling (V = 1890 Å3), one calculates b = 3.84 Å, γ ~ 0.139 and Aa ~ 0.046.
45. Handbook of Organic Solvents; David R. Lide; CRC press: 1995
46. Kirkwood, J., J. Chem. Phys., 1939, 7, 911
47. Bondi, A., J. Phys. Chem., 1964, 68, 441
48. Broszeit, G.; Diepenbrock, F.; Gräf, O.; Hecht, D.; Heinze, J.; Martin, H.-D.; Mayer, B.; Schaper, K.; Smie, A.; Strehblow, H.-H. Liebigs Ann. Chem. 1997, 2205-2213.
49. Gao, G.; Wei, C. C.; Jeevarajan, A. S.; Kispert, L. D. J. Phys. Chem. 1996, 100, 5362-5366.
93
50. Krawczyk, S. Chem. Phys. 1998, 230, 297-304.
51. Krawczyk, S. Chem. Phys. Lett. 1998, 294, 351-356.
52. Mylon, S. E.; Smirnov, S. N.; Braun, C. L. J. Phys. Chem. 1998, 102, 6558-6564.
53. Einstein, A. Ann. Physik 1906, 19, 371-371.
54. Fleming, G. R.; Morris, J. M.; Robinson, G. W. Chem. Phys. 1976, 17, 91-100.
55. Perrin, F. J. Phys. Radium 1934, 5, 497-511.
56. Perrin, F. J. Phys. Radium 1936, 7, 1-11.
57. Spears, K.G.; Steinmettz, K.M. J. Phys. Chem. 1985, 89, 3623-3629
58. Horng, M.-L.; Gardecki, J.A.; Maroncelli, M. J. Phys. Chem. A 1997, 101, 1030-1047
59. Kumar, P.V; Maroncelli, M. J. Chem. Phys. 2000, 112, 5370-5381
94
5 RADICAL INDUCED IMPEDING OF CHARGE RECOMBINATION
5.1 Introduction
Mimicking photosynthesis has been a long-standing goal of research in the
field of photoinduced electron transfer. Optimization of that process requires that the
light induced charge separation effectively competes with undesired relaxation via
energy transfer and back electron transfer. Numerous studies have demonstrated the
importance of the redox properties of the donor and acceptor moieties, the separation
distance in the donor-acceptor pair, and the reorganization energy of species
involved.1-6 Increasing the distance between separated charges usually impedes their
recombination and often improves the yield of charge separation. Nevertheless, mere
distancing the donor and acceptor moieties participating in photoinduced charge
separation is often not sufficient.
Novel approaches to slowing recombination of the charge transfer states
include the use of electrolytes,7 and magnetic fields.8 The latter takes advantage of
intersystem crossing within the ion radical pair driven by magnetic nuclei on the ion
radicals. Since the triplet pair recombination to the ground state is a spin forbidden
process, the lifetime of such ion pair state is substantially longer.9 The intersystem
crossing time is usually on the order of 10-7 s due to small magnetic fields from the
nuclei and thus might happen within the lifetime of the singlet ion pair state but with
not very high yield.
95
High magnetic fields from stable radicals can more rapidly induced the
intersystem crossing and thus improve the yield and lifetime of charge separation. We
will show that stable radicals, such as oxygen and TEMPO, can be employed either as
catalysts or inhibitors10 of the back electron transfer reaction from a fullerene radical
anion to a porphyrin-like cation in the photoinduced charge separated state of four
dyads. This is the first example in which O2, the most important biological oxidant,
acts as an inhibitor rather than an active participant (oxidant)11 or a catalyst12 of back
electron transfer. The effect of radicals was investigated using four types of
porphyrin-C60 linked molecules shown in Figure 5.1. The important role of
intersystem crossing induced by paramagnetic species will be demonstrated and the
mechanism of its utilization will be suggested.
N N
N NM
O O
O O
N
N
N
NM
MChl-C60; M=Zn, 2H MPor-C60; M=Zn, 2H
Figure 5.1. Molecular structures for the four molecules under study.
96
The mechanisms of interaction of the electronically excited states of organic
molecules with molecular oxygen have been a classic problem in photochemistry and
a field of intensive research for decades.13,14 Unique involvement of molecular
oxygen in electron transfer phenomena arises from the combination of different roles
it plays: it is a fairly good electron acceptor and thus can oxidize excited state of
some molecules9 but besides that, as a paramagnetic species in the ground state (3Σg−),
it can also induce intersystem crossing between the singlet and triplet states of
molecules.13 Such a combination results in different mechanisms for quenching of
singlet and triplet excited states. Equations (5.1-5.7) below demonstrate a traditional
description of bimolecular processes for the excited singlet (5.1-5.4) and triplet (5.5-
5.7) state relaxation caused by molecular oxygen.
1M* + 3O2 3(1M* ...3O2)
k1
k2
k4
k3
k-d
kd[O2] 3M* + 1O2* (1∆g, 1Σg
+) (5.1) 3M* + 3O2 (5.2)
1M + 1O2* (1∆g, 1Σg
+) (5.3)
1M + 3O2 (5.4)
Molecule in its excited singlet state, 1M*, can relax upon collision with the
ground state molecular oxygen 3O2 either to the (excited) triplet state, 3M*, or directly
to the ground state, 1M. Intersystem crossing (reaction 5.2) is thought to be the most
efficient route for the deactivation of 1M*.13 Indeed, the reaction (5.1) in many cases
does not proceed due to a small S-T energy gap and the other energy transfer reaction
(5.4), is usually inefficient because of a small Franck-Condon factor. Reaction (5.3) is
97
believed to be slow because the corresponding process is spin-forbidden. The
reaction (5.2), is believed to proceed via transient charge transfer state, M+…O2−,
where oxygen serves as an electron accepting species.13 The energy of such a
transient CT state often is higher than the triplet state energy making the
corresponding rate constant often less than diffusion controlled.
Excited triplet molecule, 3M*, reacts with oxygen via more options (reactions
5.5-5.7):
5(3M* ... 3O2) 3M* + 3O2 (5.5)
3(3M* ...3O2) 3(1M ...3O2)
1M + 3O2 (5.6)
1(3M* ...3O2) 1(1M ...1O2*) 1M + 1O2* (1∆g,
1Σg+) (5.7)
5/9kd[O2]
k-d
3M* + 3O2 ken
3/9k[O2]
1/9kd[O2]
kic
k-d
k-d
k-d
k-d
Due to the spin statistics, the total spin state for the collided pair of the triplet
molecule, 3M*, and the ground state oxygen can be either zero, one or two. Assuming
that the reactions proceed without change of the total spin in the pair, as shown in
reactions (5.5-5.7), simple spin-statistical assessments of these processes can be
made. For example, only 3/9th of the collisions with oxygen happen in a triplet spin
state and thus can lead to the triplet state relaxation via reaction (5.6). The remaining
5/9th of the diffusional encounters (5.5) happen in a quintet spin state and thus are
spin forbidden towards any relaxation involving change of the spin states of the
molecule and oxygen. One-ninth of the collisions happen in a singlet state (7) and can
result in what is formally called the energy transfer process, yielding the ground state
98
singlet of the molecule, 1M, and an excited singlet state of oxygen. Depending on the
triplet state energy, there are two possible singlet states of oxygen, 1Σg+ (1.62 eV) and
1∆g (0.98 eV), that can be produced in the quenching. The collisions encountered in
the total triplet state (reaction 5.6) have an option to produce the ground state
molecule via intersystem crossing in a spin allowed fashion. The last two reactions
are also believed to proceed via transient charge transfer state.13
Transient charge transfer state, M+…O2− is required for decoupling electron
spins in M. Thus intersystem crossing efficiency drops when energy of M+…O2−
noticeably exceeds that of M*. We suggest that in cases where excited state of a dyad
A-D already has charge transfer character, A−-D+, i.e. electron spins already are
decoupled, the role of paramagnetic species can be reduced to pure magnetic
dephasing of the spin states in A−-D+. In the latter case there is no need for charge
transfer onto paramagnetic species.
5.2 Experimental Section
Synthesis of the dyads used in this study was described elsewhere.15-19
Solvents, toluene and THF (both HPLC grade), and TEMPO (2,2,6,6-tetramethyl-1-
piperidinyloxyl) were purchased from Aldrich and used without further purification.
Light induced dipole moment changes were measured using standard time-
resolved transient displacement current setup.20 Solution of a dyad with a typical
concentration 10-4 M was circulated through a dipole cell. The cell has two parallel
99
flat stainless steel electrodes and quartz windows for laser excitation. In this geometry
the incident light is perpendicular to the electric field but light polarization can be
varied from parallel to perpendicular with respect to the electric field. All
experiments were done at room temperature and external voltage 600V applied across
0.70 ± 0.05 mm gap between the electrodes. Third harmonic of a Nd:YAG laser
(“Orion SB-R” from MPB) shifted on CH4 (to make 396 nm) was used for excitation.
The laser pulse duration was ca. 20 ps and the incident energy was kept below 100
µJ. Charge displacement (dipole) signal was measured across the 1MΩ input
resistance of a P6243 active probe (Tektronix) and digitized by a 1 GHz digital
oscilloscope, TDS 684A (Tektronix). In the experiments with polar solvent (THF),
because of a high dark current, the 1 MΩ probe could not be used and the signal was
measured across 50 Ω, i.e. in the displacement current mode.20
Oxygen concentration was varied by changing its partial pressures above the
solution (up to 3.7 atm) and the amount was calculated using Henry coefficient 120
atm/mole.21 Zero oxygen concentration was achieved by bubbling solutions with pure
nitrogen for 5 min. TEMPO concentration in the solution was monitored by optical
absorbance. Absorption spectra were recorded using Perkin-Elmer Lambda 40
UV/Vis spectrometer.
Locally excited triplet state energies of chlorins and phorphyrins were
estimated from the phosphorescence spectra of their toluene solutions frozen to 77 K.
For that purpose, glassified droplets of a solution in a quartz dewar filled with liquid
nitrogen were excited by laser (at 396 nm) and luminescence spectra were measured
100
using SD2000 CCD spectrometer from Ocean Optics. Fluorescence was eliminated
from the detection by setting ca. 1 ms delay on the CCD shutter. The singlet state
energies were measured analogously in room temperature solutions and the results are
published elsewhere.19
Phosphorescence of singlet oxygen was measured under irradiation with the
same laser using InGaAs photodiode (G8370, Hamamatsu, with 1.5 V of reverse bias)
terminated by a high load resistance. The oxygen luminescence at 1270 nm was
filtered by a Si filter made from a Si wafer. Such an inexpensive filter efficiently
filters out luminescence shorter than 950 nm and transmits ca. 8% in the range of
oxygen phosphorescence. Small amount of residual fluorescence (and
phosphorescence) of porphyrins/chlorins and C60 was nevertheless detected. The
oxygen luminescence portion was obtained by subtracting luminescence without
oxygen from that one with oxygen. The resulting time resolution (enforced by a large
load resistor) did not allow accurate measure of the oxygen formation time but
characteristic decay time, τ = 29 µs, of oxygen phosphorescence is clearly recognized
and agrees well with published values.22
101
5.3 Results and Discussion
5.3.1 Dipole measurements with O2
In our studies we have characterized the two series of dyads between the
fullerene C60 and either porphyrin15 or chlorin16,17 linked molecules (ZnP-C60, P-C60,
ZnChl-C60, and Chl-C60, see Figure 5.1) using the transient displacement current
technique.18,19
Table 5.1 summarizes the photoinduced dipole measurements data in toluene
and shows that the dipole moments after excitation are similar among the dyads
except for Por-C60, in which the yield of charge separation in toluene is noticeably
less than unity.
Table 5.1. Dipole moments, µ, and the energies of the local triplet (ET) and the charge transfer states (ECT) for the four dyads along with the singlet charge recombination rates in toluene (kCRS).
ZnChl-C60 Chl-C60 ZnPor-C60 Por-C60 C60(COOEt)2
µ, Da 39 41 37 15b 0 ET, eVc 1.47 1.77 1.78 1.82 1.50d ECT, eVe 1.32 1.52 1.52 1.72 -
kCRS, 109s-1 0.71 0.25 0.19 0.16 -
a apparent dipole moment in Debye, also reflects the yield of the CT state; see also ref. 23, b smaller due to the much less than unity yield of the CT state in toluene, c local triplet energies of appropriate porphyrin derivatives obtained from the maxima of phosphorescence spectra except for the last one, where the triplet energy is that of C60, d ref. 24, e calculated using Eq. 9, see also ref. 25
102
The latter yield increases in more polar solvents and the dipole moment
becomes close to that of other dyads.19 All in all, the four dyads represent four
energetically different realizations of charge separated states with approximately
equal separations distance between donor (porhyrin or chlorin) and acceptor (C60)
moieties.25
Fig. 5.2 demonstrates what is usually expected of oxygen in photoinduced
electron transfer: the lifetime of the charge separated state in ZnPor-C60 created upon
laser excitation, shortens with oxygen concentration. The same effect is observed for
two other dyads, Por-C60 and Chl-C60. The rate constants of quenching are almost
identical for all three dyads (see Table 5.2), which lets us conclude that they are equal
to the diffusion control rate constant in toluene, kd = 2.2 ×1010 M-1s-1. The situation is
quite different for ZnChl-C60. Fig. 5.3 displays that addition of oxygen in this
solution produced a longer-lived component instead. Upon further oxygen
concentration increase, the enhancement of long-lived component intensity is
accompanied by shortening of its lifetime.
103
Table 5.2. Rate constants of “oxygen quenching” for the four dyads and fullerene in toluene.
ZnChl-C60 Chl-C60 ZnPor-C60 Por-C60 C60(COOEt)2
kS,a 1010M-1s-1 b 2.2 2.3 2.1 kisc,c 1010M-1s-1 1.15 b b b k-isc,d 1010M-1s-1 0.4 b b b
ϕ(1O2)e < 0.05 0.9 0.9 1.0 a charge recombination rate from the 1CT, b not observed, c intersystem
crossing rate constant from 1CT to 3CT, d intersystem crossing rate constant from
3CT to 1CT, e relative quantum yield of singlet oxygen . See text for details.
All these phenomena are consistent with oxygen induced intersystem
crossing depicted in Figure 5.4 and by reactions (5.8, 5.10):
1(D+--A−) + 3O2 3[1(D+--A−) .. 3O2]
3[3(D+--A−) ... 3O2] (D--3A) + 3O2
1(D--A) 3(D+--A−) + 3O2
kd[O2]
k-d
kCRT
k-d(5.8)
kCRS
Being a paramagnetic species in the ground state, oxygen can induce
intersystem crossing without participation in actual electron transfer, opposite to
what is thought of the oxygen effect in neutral molecules. The process can take
advantage of already separated charges in the CT state and thus weakly coupled
spins.
104
0 5 10 150
2
4
6
8
10
0.00 0.01 0.02 0.030
2
4
6
8
10
PO2
= 0 atm 0.2 1.0 2.4 3.7
A
Time, ns
Phot
ores
pons
e (m
V)
B
ZnPor-C60 Por-C60 Chl-C60
[O2], M
k S[O2]
x 10
-8s
Figure 5.2. A. Transient displacement charge signals for ZnPor – C60 dyad in toluene with varying oxygen concentrations from 0 M to 20.3 mM, achieved by different oxygen pressure above the solution. All signals are normalized to the same amount of absorbed energy, 50 µJ, from excitation at 396nm and 600V of external voltage applied across the 0.60 mm electrode gap. B. Rates of back electron transfer induced by oxygen, kS[O2], for the three dyads: - ZnPor – C60, - Por – C60, and - Chl – C60 in toluene obtained from fitting the signals in A. Solid line is a guide to an eye. Rate constants obtained from linear fits to each set individually,23 are given in Table 5.2.
105
0.00 0.01 0.02 0.03
0
1
2
3
4
0 5 10 15 20 2501234567
B
[O2], M
k Q x
10-8
s
PO2
= 2.4 atm 1.0 0.2 0
A
time, ns
Pho
tore
spon
se (m
V)
Figure 5.3 A. Transient displacement charge signals for ZnChl – C60 dyad in toluene at different oxygen concentrations: - 0 M, achieved by bubbling with N2, g - 1.67 mM, achieved by bubbling with air, n- 8.35 mM, achieved by bubbling with pure oxygen, and - 20.3 mM, achieved by pressurising the cell to 2.43 atm of pure oxygen. All signals are normalized to the same amount of absorbed energy, 50 µJ, from excitation at 396nm and 600V of external voltage applied across the 0.60 mm electrode gap.B. Quenching rates obtained from fitting the signals in A using two models: 1) g - forward intersystem crossing and - reverse intersystem crossing; relaxation only from singlet pair recombination with kCRS = (1.43 ns)-1; 2) the same (g) forward intersystem crossing and n - triplet quenching. The lines show linear fits with the rate constants: g - kisc = 1.15 ×1010 M-1s-1, - k-isc = 6.1 ×1010 M-1s-1, n - kT = 3.9 ×109 M-1s-1, as shown in Table 5.1 and Fig. 5.5.
106
1ZnChl*-C60
ZnChl-1C60*
1(ZnChl+-C60−)
3ZnChl*-C60
ZnChl-3C60*3(ZnChl+-C60−)
X
1Chl*-C60
1(Chl+-C60−)
3Chl*-C60
Chl-3C60*3(Chl+-C60
−)
X
X
E
O2
O2kCRTkCRT
kCRSkCRS
Chl-1C60*
Figure 5.4. Schematic energy diagram for the two chlorin-C60 dyads.
Very inhomogeneous field of encountered paramagnetic oxygen can flip
the nearest spin with greater probability than the farthest (for example, horizontal
parenthesis show oxygen as interacting stronger with A− in the reaction (5.8))
and thus induce the S-T transitions in the dyad. The process will proceed without
changing the total spin and its projection in the pair of dyad + oxygen. With this
reasonable restriction, there are only two possible configurations that can be
produced upon collision of the dyad and oxygen, both with equal probability.
They are shown in reaction (5.8) at equilibrium and involve singlet, 1(D+--A−),
and triplet, 3(D+--A−), CT states of the dyad. If the energy of the CT state lies
above that of the locally excited triplet states of porphyrin and C60, then charge
recombination from the triplet state of a dyad, 3(D+--A−), to the locally excited
107
triplet state, with the rate constant kCRT, will result in a complete depletion of the
CT state. According to the Weller’s equation:
DAADADCT rrr
EEE38.2
4.1411112.721
−
+
−+−=
εε (5.9)
and using the redox potentials of porhyrins (+0.83V for Por and +0.63V for Zn-
Por vs. SCE),26 chlorins(+0.63V for Chl and +0.43V for Zn-Chl vs. SCE)27 and
fullerene (−0.55V for fullerene vs. SCE)28 all in methylene chloride (ε2=8.93),
the energies of the dyads25 were estimated in toluene (ε1 = 2.38), see Table 5.1.
As one can see, only ZnChl-C60 has its CT energy below that of triplet C60, other
three dyads have their energies higher. The rate constant of the oxygen induced
charge recombination reaction in these three dyads will be equal the rate constant
of diffusional collisions, given that recombination from 3(D+--A−) into the 3C60
(kCRT) is faster than the dyad-oxygen dissociation rate, kCRT >> -kd.29 If, on the
other hand, all locally excited triplet states are higher in energy than the CT state,
like in ZnChl-C60, then collisions with oxygen will produce no result in half the
cases; the other half will experience intersystem crossing and end up in the triplet
CT state. The spin projection of the triplet CT state of the dyad is not definite in
this process but the projection of the pair of the two triplet states, 3(D+--A−) and
3O2, should be the same as that of the initial spin of 3O2. Thus, the rate of oxygen
induced intersystem crossing from 1(D+--A−) into 3(D+--A−) should be equal half
the diffusion controlled rate, which is in remarkable agreement with the
108
experimental constants of Table 5.1 (see also Figure 5.3), kisc = 1.15×1010 M-1s-1
= 1/2 kd.
To further confirm this interpretation we conducted experiments with the
same dyads in more polar THF solutions. Enhanced solvation of the CT state of a
dyad in THF causes it to move lower in energy than that of 3C60 even for Por-C60;
using Equation (5.9) we estimate it to be 1.25 eV. As a result, charge recombination
into 3C60 becomes insignificantly slow for Por-C60 in THF and collisions with oxygen
produce long-lived triplet CT states, 3(D+--A−), instead of quenching.
The triplet CT of the dyad, even though created via collisions with oxygen, is
also vulnerable to oxygen quenching. As Fig.5.3 illustrates, the lifetime of this state
gradually shortens while its intensity increases. If treated as a simple quenching, i.e.
deactivation to the ground state, the rate constant of such a process would be 3.9 ×109
M-1s-1. Figure 5.5 represents such a fitting on the example of the dipole signal curve
with 1 atm of partial pressure of oxygen. The same Figure 5.5 offers also an
alternative mechanism of such quenching, which is parallel to the mechanism of
intersystem crossing in singlet CT and involves reverse intersystem crossing. Since
distant charges in the CT state of dyads have relatively small exchange interaction,
their energies are almost degenerate and the reverse intersystem crossing (5.10):
3(D+--A−) + 3O2 3[3(D+--A−) .. 3O2]
3[1(D+--A−) ... 3O2] 1(D--A) + 3O2
1(D+--A−) + 3O2
1/3kd[O2]
k-d
kCRS
k-d
(5.10)
109
can be induced by oxygen in opposite direction, analogous to reaction (5.8). The
difference is that only one third of randomly encountered complexes, [3(D+--
A−)…3O2] happen in an appropriate for that triplet spin state. Again, opposite to the
case of oxygen induced quenching of locally excited triplet molecules (reactions 5.5-
-5.7), where triplet state pairs are believed to be coupled with the ground state of the
quenched molecule via transient electron transfer onto oxygen, M+…O2−, in the
intramolecular CT state there is no need for such transient formation of superoxide
ion, O2−. As in the case of oxygen interaction with singlet CT, the intersystem
crossing process can proceed without changing the total spin and the spin projection
for the 3[3(D+--A−)…3O2] complex. Reaction (5.10) suggests that the inverse
intersystem crossing rate, k-isc, for the triplets should vary between 1/3 and 1/6 of the
diffusion controlled rate constant depending on the relation between the rate constants
of charge recombination, kCRS, and that for dissociation of the complex, k-d. Since the
recombination into the ground state is not very fast, kCRS ≤ 109s-1, as compared to the
dissociation rate constant, k-d ~ 109s-1 (see Eq. (5.18) below), one might expect that
the effective rate constant for reverse intersystem crossing, k-isc, should exceed 1/6 kd.
When only reaction (5.10) in combination with (5.8) is used for describing the dipole
signal time evolution, a reasonably good fit can be obtained for rates corresponding to
k-isc = 6 ×109 M-1s-1, i.e. approximately kd/3.7.
110
0 10 20 30 40
1
10
Time, ns
Pho
tore
spon
se (m
V)
Figure 5.5. Transient displacement charge signal for ZnChl – C60 dyad in toluene with 8.35 mM of oxygen (the same as curve n in Fig, 5.3A) shown by points and the three fitting curves: the dotted line – using the scheme with the intersystem crossing time, τisc = 8.3 ns, and the “triplet state lifetime”, τT = 25 ns; the dash-dotted line – τisc = 8.3 ns, and the reverse intersystem crossing time, τ-isc = 25 ns; the solid line – τisc = 8.3 ns, τ-isc = 20 ns. In all cases the lifetime of the singlet state is τS = 1.43 ns; the system response time is 0.6 ns.
111
5.3.2 Singlet oxygen measurements
From spin statistics, 1/9th of the collision events between triplet CT state and
oxygen happen in the overall singlet state and thus may result in generation of singlet
oxygen as described by reaction (5.11):
1[3(D+--A−) .. 3O2] 1[(D+--A)..O2
−] 1(D--A) + 1O2* (5.11)1/9kd[O2]
k-d
3(D+--A−) + 3O2
The lowest excited singlet state of oxygen, 1∆g, has energy (0.98 eV) which is lower
than that of the CT state. Thus it is very tempting to claim the relevance of singlet
oxygen formation in reaction (5.11) for direct quenching of triplet CT states. The
yield of singlet oxygen in (5.11) should be relatively small and is described by the
equation (5.12) (see also Appendix A):
( )
+++
+=
169][
][
2
22
1
α
ϕ
CRSICisc
ICisc
kkOk
kOkO , (5.12)
where kd is the diffusion rate constant, kIC – intramolecular (not induced by oxygen)
intersystem crossing rate constant, and kCRS – the charge recombination rate constant
to the ground state. We assumed here the limiting spin statistical values for the rate
constant in equation (5.10), k-isc = 1/6kd and the overall rate constant in (5.11) as k∆ =
α/9kd, where α – is efficiency of charge transfer from C60− to oxygen (see Appendix
A for details). Fig. 5.6 illustrates the predicted concentration dependence of ϕ(1O2)
from equation (5.12) and the experimental data for singlet oxygen yield. Due to a
high error, we cannot unambiguously prove that reaction (5.11) has indeed the overall
112
constant k∆ = 1/9kd but the formation of singlet oxygen, nevertheless, is likely to
occur. Presuming that the reaction (5.11) is indeed diffusion limited, i.e. k∆ = 1/9kd,
the kinetic data can be fitted with a nice matching to spin statistical values for: kisc =
1/2kd, k-isc = 1/6kd, and k∆ = 1/9kd (see Figure 5.3). The solid line in Figure 5.5
demonstrates a good quality of the fitting.
In the other three dyads singlet oxygen can also be formed but via a different
route – through quenching of 3C60. Since the singlet oxygen formation yield from
quenching of 3C60 is close to unity,30 one can conclude that ϕ(1Ο2) = ϕ(3C60), which
leads to following concentration dependence of the yield:
( )ICCRSd
ICd
kkOkkOk
O++
+=
][][
2
22
1ϕ , (5.13)
Figure 5.6 illustrates that the experimental data fit well with equation (5.13) and
kIC ~ 2×107 s-1 is in a good agreement with what the rate of electron spin flipping on
magnetic nuclei is supposed to be for porhyrin--fullerene CT state with a negligible
spin-spin coupling.31,32
The agreement of the experimental data with (5.13) once again confirms that
3C60 is formed in reactions between Chl-C60, Por-C60 and ZnPor-C60 dyads and
oxygen, while in the case of ZnChl-C60 the triplet state of ion pair, 3(ZnChl+-C60−), is
formed instead. The latter also is affected by oxygen in two ways: it is shuffled back
to 1(ZnChl+-C60−) and probably forms singlet oxygen as well.
113
Figure 5.6. Top: Kinetic of singlet oxygen luminescence at 1270 nm for solution of C60 in toluene and 1 atm of O2. Solid line - experimental, - fit with the rise time equal the RC time and the decay time of 29 µs. Bottom: Concentration dependence of the oxygen luminescence yield normalized to that of C60 solution; n - ZnChl – C60 in toluene and the solid line representing fit using equation (12) with kIC = 2×107 s-1, kd = 2.3×1010 M-1s-1, kCRS = 7.0×108 s-1, and two values of α : α = 1 (dash-dot line) and α = 0.3 (dash line) ; g P–C60 in toluene and the solid line representing fit using equation (13) with kd = 2.3×1010 M-1s-1, kIC = 2×107 s-1
0 50 100 150 200
0 .00
0 .05
0 .10
0 .15
T im e (µs )
1 O2*
lum
ines
cenc
e
0 .000 0.005 0.010 0.015 0.020 0.025 0.0300.0
0.2
0.4
0.6
0.8
ϕ(1 O
2*)
[O 2], M
114
5.3.3 Dipole measurements with TEMPO and heavy atoms
Since oxygen involvement in the intersystem crossing process is only due to its
nonzero spin, other paramagnetic species should perform the same task equally well.
Indeed, a stable radical TEMPO produces the same discrimination in reacting with
the dyads, i.e. Chl-C60, Por-C60 and ZnPor-C60 dyads suffer shortening of their
photoinduced CT lifetimes with almost identical rate constant in toluene, kS =
1.0×1010M-1s-1, while the fourth dyad, ZnChl-C60, experiences intersystem crossing to
the long-lived triplet CT state with half as big the rate constant, kisc = 5.0×109M-1s-1.
Unlike oxygen, TEMPO’s spin is 1/2, but it makes the interaction with a singlet
CT no different from that with oxygen, as is illustrated by equation (5.14):
1(D+--A−) + 2T 2[1(D+--A−) .. 2T] 2[3(D+--A−) ... 2T] (D--3A) + 2T
3(D+--A−) +2T
kd[T]
k-d
kCRT
k-d(5.14)
We label TEMPO here and later as T. Spin statistics in reactions between the
triplet CT and TEMPO, even though it have fewer options (see equation 5.15),
theoretically make almost no difference in the outcome of reverse intersystem
crossing as well, the rate constant of reverse intersystem crossing (in a doublet pair)
should still be k-isc = 1/6kd, as with oxygen. The quartet pair presumably dissociates
without reacting since TEMPO does not have any states with higher multiplicity than
a doublet in the energy range of less than 1.5 eV:
115
3(D+--A−) + 2T 2[3(D+--A−) .. 2T] 2[1(D+--A−) .. 2T] 1(D--A) + 2T
1/3kd[T]
k-d
kCRS
k-d (5.15)2/3kd[T]
k-d
4[3(D+--A−) .. 2T] 1(D+--A−) + 2T
Thus reverse intersystem crossing takes place only when TEMPO and the CT state
form complex in a doublet state. Experimentally (see Fig. 5.7) we found that the rate
of reverse intersystem crossing was concentration dependent and not only exceeded
the value corresponding to 1/6 kd (rate constant at low concentration) but even
surpassed 1/3 kd and became almost equal to that of the forward intersystem crossing
rate at higher concentrations.
Even though dyads collide with radicals (TEMPO) infrequently, at high
concentration collisions with two and more radicals become more and more common.
Such multiple collisions help the remaining 2/3 of initially “idle” encounters to
become involved in the intersystem crossing process as well. Noninstantaneous
dissociation of encounter complexes between the dyad and a radical at high radical
concentration provides a possibility of encountering with other radicals and thus
complicating the reaction into a higher order by TEMPO. In the next chapter we
mimic such multiple collisions by introducing a “dissociation rate constant”, k-d, of
single radical from a complex. This rate constant is presumably spin-independent and
we also assume for simplicity that for triple complexes (TEMPO..DYAD..TEMPO),
because of the two radicals involved, the dissociation is twice as fast, i.e. with 2k-d.
116
Figure 5.7. Reverse intersystem crossing rate for ZnChl-C60 dyad in toluene induced by O2 (top) and TEMPO (bottom). Experimental data are shown by g and calculations using model “High Radical Concentrations” – by lines. The limiting cases for k-isc = kd/6 and k-isc = kd/2 are shown by dotted lines. The dashed and solid lines represent effective reverse intersystem crossing rates for different dissociation rate constants, k-d, of the complex between the CT state and paramagnetic species. Case of oxygen: dashed lines from the top to the bottom – k-d = 109 s-1, k-d = 2.0×109 s-1, solid line - k-d = 1.4×109 s-1; case of TEMPO: k-d = 5 ×108 s-1, k-d = 7 ×108 s-1 for dashed lines and k-d = 7×108 s-1 for solid line, respectively.
0.00 0.01 0.02 0.030
1
2
3
k-isc= kq/6
k-isc= kq/2
[O2], M
k -isc[O
2] x 1
0-8 s
0.00 0.02 0.04 0.06 0.08 0.100
1
2
3
4
k-isc= kq/6
k-isc= kq/2
[TEMPO], M
k -isc[T
EM
PO] x
10-8
s
117
Note that multiple collisions have almost no effect on the rate constant of forward
intersystem crossing (which remains 1/2kd) but the reverse process has the order of
reaction by concentration of TEMPO greater than one and the resulting effective rate
constant can be greater than 1/6kd. By varying the rate of dissociation, k-d, we found
that the experimental data are best fit with k-d (TEMPO) = (7 ± 2) ×108 s-1 (see Figure
5.7A). The same analysis with oxygen (see Figure 5.7B) implies that k-d is greater by
a factor of two, k-d(O2) = (1.4 ± 0.4) ×109 s-1, which is in a good agreement with the
ratio between the diffusion constants for the two radicals (compare kS in Table 5.2
and Table 5.3).
5.3.4 Intersystem crossing rates at high radical concentrations
In this chapter we consider peculiarities of intersystem crossing induced by high
concentration of radicals when recombination is only allowed in singlet state, i.e. all
locally excited triplet states are high in energy than that of CT state. Our goal is to
understand the departure of intersystem crossing in equations (5.8, 5.10, 5.11, 5.14
and 5.15) from simple spin statistical one for “single” collisions, where kisc = 1/2kd
and k-isc = 1/6kd, to collisions with more than a single radical. It is expected that such
collisions should increase the intersystem reactions orders with respect to
concentration of radicals. The resulting system of (linear differential) equations can
be numerically solved, and the solution fitted using model with two states,
118
interchanging with rate constants kisc and k-isc, respectively. Two cases are addressed:
radicals with spin ½ (such as TEMPO), and radicals with spin 1 (such as oxygen).
First, take the case of spin 1/2. Limiting to no more than double collisions, the
following kinetic scheme can be derived:
1CT
2(1CT..T) 2(3CT..T) 3CT
1(T..1CT..T) 1(T..3CT..T)
4(3CT..T)3(T..1CT..T) 3(T..3CT..T)
Ground state
kCRS
kCRS
k-d
kCRS
2k-d3/4kdTk-d
k-d
kFLIP
kFLIP
kFLIP
kFLIP
kFLIP
kFLIP
kCRS
2k-d
k-d
k-d
2k-d
3/4kdT
1/4kdT1/4kdT1/3kdT
2/3kdT
3/8kdTkdT
Figure 5.8. Kinetic scheme for multiple collisions with TEMPO
where 1CT and 3CT refer to the singlet and triplet charge transfer states, respectively,
T – represents a paramagnetic species, doublet TEMPO in this case, and kCRS – is the
rate constant of charge recombination from the singlet state, 1CT, to the ground state
of the dyad. Note that all complexes possessing 1CT (i.e. 1CT, 2(1CT..T), 1(T..1CT..T)
and 3(T..1CT..T)) deactivate to the ground state with the same rate constant kCRS. The
triplet 3CT and all complexes possessing it, on the other hand, do not recombine
themselves and can do that only after conversion into the 1CT. Assuming that
complexes between the CT states and radicals last some time defined by a spin
independent dissociation rate constant, k-d, these complexes can encounter with
119
another radical. Such multiple collisions complicate the scheme dramatically, as it is
obvious from Figure 5.8, and we shall walk through the scheme starting from the
initially formed 1CT on the left. Collisions of the 1CT with a T proceed with the
diffusion controlled pseudo first order rate constant, kdT, (only rate constant kd is
shown for simplicity) and results with 100% probability in a formation of the doublet
complex, 2(1CT..T). The complex can dissociate into the 1CT and T with the
dissociation constant, k-d, or recombine into the ground state with kCRS. Intersystem
crossing in the 2(1CT..T) complex can progress into the 2(3CT..T), while the total spin
and projection are conserved. We formally label that intersystem crossing within the
complex by the constant kFLIP. The latter is faster than the dissociation constant (kFLIP
>> k-d) and also describes the reverse intersystem crossing from 2(3CT..T). By
labeling the intersystem crossing within 2(1CT..T) 2(3CT..T) with the same rate in
both directions we identify that the two states are in equilibrium and the probabilities
to be found in either state are equal. Each of these complexes, have a chance to
collide with another radical T before dissociation (and recombination, for 1CT). The
singlet containing complex, 2(1CT..T), upon collision with another doublet T, has
three times greater probability to form a triplet complex, 3(T..1CT..T), than the singlet
one, 1(T..1CT..T). Either of the two permits intersystem crossing between 1CT and
3CT without changing the total spin and projection of the complex. These three-
molecule complexes can also dissociate back to the 2(1CT..T) but, since there are two
independent possibilities for each one to lose a T, the corresponding rate constants of
dissociation for either 1(T..1CT..T) or 3(T..1CT..T) are twice as high, 2k-d. The other
120
doublet complex, 2(3CT..T), originally formed via intersystem crossing from
2(1CT..T) can dissociate into a stand alone 3CT or collide with another T and form in
¾ cases a 3(T..3CT..T), or the 1(T..3CT..T), in remaining ¼ cases. The most important
route at low T concentration involves dissociation of 2(3CT..T) into a 3CT, collision of
which with T reforms 2(3CT..T) only in 1/3 cases. The other 2/3 of collisions
withdraw into a formation of idle 4(3CT..T). These 2/3 of “inefficient” at low
concentration collisions can become fruitful again if multiple collisions with
additional T are considered. Even though 5/8 of such collisions stall in an idle
5(T..3CT..T) state, 3/8th of them form a productive 3(T..3CT..T) state, for which
intersystem crossing can be either directly realized into a 3(T..1CT..T) or dissociate
into a familiar 2(3CT..T). Either way enhances the probability for reverse intersystem
crossing (from 3CT to 1CT) and thus it makes the overall rate constant k-isc greater
than 1/3 kd at high concentration of radicals.
It has to be noted that the overall forward intersystem crossing rate constant,
kisc, remains almost unchanged and equal 1/2kd, while the reverse one can be
dramatically increased from the value 1/6kd (at low concentrations and/or high k-d) to
almost 1/2kd at the other extreme. The results of modeling do not depend on the value
of kFLIP for as long as it is larger than k-d; the value of k-d, on the other hand, has a
dramatic effect on concentration dependence of the reverse intersystem crossing rate.
Fig.5 demonstrates how changing the k-d from 1010s-1 to 108s-1 affects the rate from
one extreme behavior to another; while the best fit to the experimental dependence
corresponds to k-d = 7×108s-1.
121
The following Figure 5.9 describes the same effect of multiple collisions with
oxygen:
3(1CT...3O2)
1(3O2...1CT...3O2)
3(3O2...1CT...3O2)
5(3O2...1CT...3O2)
1(3O2...3CT...3O2)
3(3O2...3CT...3O2)
5(3O2...3CT...3O2)
1(3CT...3O2)
3(3CT...3O2)
5(3CT...3O2)
3CT1CT
k-d 2k-d
kFLIP
kFLIP
kFLIP
kFLIP
kFLIP
kFLIP
kFLIP
kFLIP2k
-d
2k-d
2k-d
k-d
k-d
2/3k-d
2/3k-d
2/3k-d
k-d
k-d
k-d
5 9k d
O2
59 k
d O2
1 9k d
O2
5 9k d
O2
1 9k d
O2
1 9k d
O21
5 kd O
2
kdO21 3
k dO
2
13 kdO2
1 3k d
O2
13 kdO2
kdO2
Figure 5.9. Kinetic scheme for multiple collisions with oxygen.
Due to a greater spin multiplicity, the scheme is more complicated than the
previous Scheme (Figure 5.8). As shown, it is already somewhat simplified. We
omitted the arrows for all complexes with 1CT representing their recombination to the
ground state, which happens to all of them with the same rate constant, kCRS. Also for
the sake of shortening, we excluded the unfruitful complex 7(3O2..3CT..3O2), for
which no intersystem crossing takes place. The same Figure 5.7 illustrates results of
Figure 5.8 evaluation and displays that the best fit to experimental data is observed
with k-d = 1.4 ×108s-1, again twice the analogous value for k-d with TEMPO.
122
5.3.5. Effects of heavy atoms and magnetic field
Intersystem crossing in aromatic molecules can be often induced by the so
called heavy atom effect, in particular by a noble gas Xe.13 We observed no effect of
Xe on the dipole signal in any of the dyads up to a partial pressure of 2 atm.
The intersystem crossing processes that we discussed here, both forward and
reverse, can be successfully explained as happening with conservation of the total
spin and its projection in the “complexes” between the CT state of a dyad and radicals
(either oxygen or TEMPO). Thus external magnetic field would not affect the relative
energies of the states involved in the intersystem conversion and the rates should be
field independent. Indeed, magnetic fields of up to 0.15 T made no difference on the
dipole signals.
5.3.6. Discussion
The mechanism of intersystem crossing that we propose here does not require
charge transfer from the dyad to a radical. Instead, the radical’s role is to break a
coherency of spin precession in the radical pair representing the CT states of a dyad.
There two crucial questions in need of discussing in order to complete the picture.
They are: 1) what is the detailed mechanism of intersystem crossing, whether it is fast
enough to make the reactions to be diffusion (and spin statistics) limited; and 2) is
there a real complexation between the dyads and radicals or encounters are very
123
transient? Concerning the latter, some authors12 consider importance of specific
interaction with oxygen as a ligand.
Let us start by comparing the above measured rate constants with the diffusion
controlled one. Diffusion constants, D, for each molecule in toluene (viscosity, η =
0.552 mPa·s) can be estimated using Stokes Equation:
3 2636 V
TkrTkD BB
πηηπ== (5.16)
where kB is the Boltzman constant and T is absolute temperature. The molecular
volumes, V, were calculated using their optimized structures: V(O2) = 29.5 cm3/mol
(rO2 = 2.27Å), V(dyad) = 445 cm3/mol (rD =5.62 Å), V(TEMPO) = 171.3cm3/mol (rT
= 4.09 Å); the effective radius of each molecule, r = (3V/4π)1/3, is given in
parentheses. Presuming that thus calculated diffusion coefficients, Ddyad = 6.9×10−6
cm2/s, DTEMPO = 9.5×10−6 cm2/s, and DO2 = 1.7×10−5 cm2/s, are fairly accurate,31 we
can estimate the “reaction radius” from the equation:
R = kd /4πΝΑ(Ddyad + Dradical) (5.17)
where the quenching rate constant kS can be used instead of kd. Using data from Table
5.3, in case of TEMPO Equation (5.17) yields RTD = 7.4 Å, which is close to the sum
of the effective radii, rD + rT = 9.7 Å, while for oxygen (based on Table 5.2), the
quenching radius, ROD = 12.1 Å, noticeably exceeds the sum of the Van der Waals
radii, rD + rO2 = 7.7 Å, of the dyad and oxygen.
124
Table 5.3. Rate constants of “TEMPO quenching” for the four dyads in toluene.
ZnChl-C60 ZnPor-C60 kS, 109M-1s-1 a 9.1 kisc, 109M-1s-1 4.4 a k-isc, 109M-1s-1 3.0b a
a not observed, b at the initial slope. See text for details.
Thus, these estimates confirm our assignment of kS as being equal to kd, i.e. the
corresponding reactions being diffusion limited. We noted above that the dissociation
rate constant, k-d, changes by almost the same factor, ca. 2, between oxygen and
TEMPO as do the corresponding kd for the two “quenchers.” Such a correlation,
especially since the latter shows agreement with the diffusion limited mechanism,
suggests that “dissociation” is also “diffusion controlled,” i.e. that encounters
between the dyad and a quencher molecules are transient. The rate constant of
diffusion controlled separation of a pair of noninteracting molecules from the distance
R can be estimated from the equation:
k-d = (Ddyad + Dradical)/R2 (5.18)
using the sum of their diffusion coefficients. Plugging in for R the sum of the Van der
Waals radii, as above, gives the estimates k-d = 1.7×109 s-1 for TEMPO, and k-d = 4.0
×109s-1 for oxygen, respectively. Due to a crudeness of estimate in equation (5.18)
and diffusion coefficient (5.17), these numbers can be viewed as agreeing quite well
with the corresponding experimental ones, k-d (TEMPO) = 0.7×109 s-1 and k-d (O2) =
1.4×109s-1. Besides, the latter values are the low limit approximation since they were
125
obtained by ignoring dyad collisions with more than two radicals, thus overestimating
the residence time of radical near the dyad. Thus, we can undoubtedly conclude that
encounters of dyads with radicals does not form bound complexes with them but
rather is fully controlled by diffusion. Equations (5.17) and (5.18) can be combined
into a ratio:
kd/k-d = 4πR3, (5.19)
where diffusion coefficient is eliminated together with associated inaccuracy of its
estimate. This ratio is proportional to the reaction volume and, as already mentioned,
is the same for the two radicals. The upper limit for “reaction radius” obtained this
way is close to 18 Å for both cases, and may suggest that procedure based on
combination of equations (5.16) and (5.17) overestimates diffusion coefficient. Not
trying to overemphasize these estimates, we concentrate on the main conclusion,
which is that all observed reactions are diffusion (and spin statistics) limited.
In order for such a description to hold, the rate constants of spin flipping in a
dyad “contacting” with a radical, kflip, should be greater than what we labeled as the
dissociation rate constant, k-d. Radical ion pair of the dyad experiences a nonuniform
magnetic field from a neighboring radical. If one of the spins is in a closer proximity
to the radical, their interaction will cause the spin scrambling, i.e. S-T0 relaxation, in
the spin state of the dyad. The interaction between spins involves spin exchange and
spin dipole-dipole interactions. The former is also responsible for possible charge
transfer onto the radical, the latter is weaker at short distances but declines more
gradually at longer distances:
126
Edip ~ µB2/r3 (5.20)
where µB – is Bohr magneton, and r - is the separation distance between two spins.
The Lande factor, the spin values and the angular part provide together a factor on the
order of one (actually, slightly greater than one). Since spin flipping is induced by the
difference of radical spin interaction with the two spins of dyad, the separation
distance, r, in (5.20) has to be smaller than the center-to-center distance between the
dyad and the radical, R, used in equations (5.17-5.19). For the sake of approximation
we take r ~ 5 Å. The corresponding rate of spin flipping then can be estimated as:
h
dipflip
Ek ~ (5.21)
and equals kflip ~ 5×109 s-1, which is indeed greater than k-d. Thus, even without
contribution from exchange interaction, the rate of spin flipping induced by
neighboring radical is sufficient for S-T0 interconversion in the dyad before radical
dissociation.
5.4 Conclusions
Thus we have shown that oxygen and other radicals can play an unusual role in
photoinduced electron transfer processes, namely they can impede charge
recombination. As paramagnet species, they can induce intersystem crossing into the
triplet CT state, which, depending on relative energies of the CT state with respect to
locally excited triplet state(s), may result in formation of a long lived triplet CT state.
The resulting triplet CT state is also affected by radicals and can induce reverse
127
intersystem crossing, usually with a small rate, due to spin statistics. Such a
mechanism most likely plays a role in naturally occurring photoinduced electron
transfer reactions where oxygen or other paramagnetic species are involved. It can
also be applied in manipulating outcomes in artificial photoinduced electron transfer
processes.
5.5 References
1. Gust, D.; Moore, T. A. In The Porphyrin Handbook; Kadish, K. M., Smith, K. M., Guilard, R., Eds.; Academic: San Diego, CA, 2000; Vol. 8, pp 153-190.
2. Langen, R.; Chang, I.-J.; Germanas, J. P.; Richards, J. H.; Winkler, J. R.; Gray, H. B. Science 1995, 268, 1733.
3. Wasielewski, M. R. In Photoinduced Electron Transfer; Fox, M. A., Chanon, M., Eds.; Elsevier: Amsterdam, 1988; Part A, p 161.
4. Jordan, K. D.; Paddon-Row, M. N. Chem. Rev. 1992, 92, 395.
5. Fukuzumi, S.; Itoh, S. In Advances in Photochemistry; Neckers, D. C., Volman, D. H., von Bünau, G., Eds.; Wiley: New York, 1998; 25, pp 107-172.
6. Warman, J. M.; De Haas, M. P.; Verhoeven, J. W.; Paddon-Row, M. N. In Advances in Chem. Phys. (Electron Transfer: From Isolated Molecules to Biomolecules, Pt. 1), 1999, Vol. 106, pp 571-601.
7. Piotrowiak, P. in Photochemistry and Radiation Chemistry: Complementary Methods for the Study of Electron Transfer; Advances in Chemistry Series, No. 254; J.F. Wishart and D.G. Nocera ed., 1998, ACS, Washington D.C. pp 219-230.
128
8. Kuciauskas D., Liddell P., Moore A, Moore T., Gust D., J. Am. Chem. Soc., 1998, 120, 10880-10886.
9. Grzeskowiak, K.N., Smirnov, S.N., Braun, C.L., J. Phys. Chem., 1994, 98, 5661-5664.
10. Smirnov, S., Vlassiouk, I., Kutzki, O., Wedel, M., Montforts, F.-P., J. Am. Chem. Soc., 2002, 124, 4212-4213.
11. Singlet Oxygen; Frimer, A. A., Ed.; CRC: Boca Raton, FL, 1985; Vols. I-IV.
12. Fukuzumi S., Imahori H., Yamada H., El-Khouly M., Fujitsuka M., Ito O., Guldi D., J. Am. Chem. Soc., 2001, 123, 2571-2575.
13. Wilkinson, F.; McGarvey, D. J.; Olea, A. F. J. Am. Chem. Soc. 1993, 115, 12144-12151.
14. Birks, J. B. Photophysics of Aromatic Molecules; Wiley-Interscience: New York, 1970.
15. Wedel, M.; Montforts, F.-P., Tetrahedron Lett. 1999, 40, 7071-7074.
16. Kutzki, O.; Montforts, F.-P., Angew. Chem. Int. Ed. Engl. 2000, 39, 599-601.
17. Kutzki, O.; Walter, A.; Montforts, F.-P., Helv. Chim. Acta, 2000, 83, 2231-2245.
18. Kutzki, O.; Wedel, M.; Montforts, F.-P.; Smirnov, S.; Cosnier, S.; Walter, A., Proc. Electrochem. Soc. 2000, 8, 172-181.
19. Montforts, F.-P.; Vlassiouk, I.; Smirnov, S.; Wedel, M., Kutzki, O., Chem.-Eur. J., in press
129
20. Smirnov, S.; Braun, C. Rev. Sci. Instr., 1998, 69, 2875-2887.
21. Grewer, C.; Brauer H.-D., J. Phys. Chem., 1994, 98, 4230-4235.
22. Okamoto, M.; Tanaka, F. J. Phys. Chem., 1993, 97, 177-180.
23. The effective dipole moment is the square root of the squared dipole moment increase, µ = (µexc
2 − µg
2)1/2. In most cases, including this one, the effect of the ground state dipole moment makes an insignificant difference between µexc and µ. The ground state dipole moments, µg, for the dyads are not known but can be estimated using semiemprical AM1 model. As shown in the Table below, the effect on calculated µexc is within the accuracy of our dipole moment measurements. More dramatic effect is from the unknown yields of the CT states, which apparently are less than 100%, since the expected dipole moment for two charges separated by 10 Å is 48D.
ZnChl-C60 Chl-C60 ZnPor-C60 Por-C60 µ, D 39 41 37 15
AM1 calculated µg, D 6.8 8.0 4.4 4.3 µexc = (µ2
+ µg2)1/2, D 39.6 41.8 37.3 15.6
24. Guldi, D. M.; Asmus, K.-D., J. Phys. Chem. A, 1997, 101, 1472-1481.
25. rD and rA were taken 5 and 4.4 Å, respectively. The center-to-center separation distance was calculated from the structures optimized by semiempirical AM1 using Hyperchem 6.0 package. The distances were 9.9 Å for Por-C60 dyads and 10.1 Å for Chl-C60 dyads.
26. The porphyrin handbook edited by Kadish K. M., Kevin M. Smith, Roger Guilard, Vol. 9.
27. Mossler, J. “Synthesis, Spectroscopic Characterization and Electron Transfer Properties of Covalently Linked Chlorin- and Bacteriochlorin-Quinones as Model Compounds for Photosynthesis”, Ph.D. Thesis, FU Berlin, 1999 – p.154 .
130
28. Armaroli, N.; Marconi, G.; Echegoyen, L.; Bourgeois, J.-P. and Diederich, F., Chem. Eur. J., 2000, 6, 629-1645
29. Based on simple Markus-like estimates, the rate constant kCRT is similar to that for charge separation in Por-C60 and ZnChl-C60, i.e. is greater than 1010 s-1. In ZnPor-C60, kCRT is much greater than the charge separation rate constant, which is relatively slow, 109 s-1.
30. Prat, F.; Stackow, R.; Bernstein, R.; Qian, W.; Rubin, Y.; Foote, C, J. Phys. Chem. A, 1999, 103, 7230-7235.
31. Tadjikov, B. and Smirnov, S., Phys. Chem. Chem. Phys., 2001, 3, 204 – 212.
32. Schulten, K. and Wolynes, P. G. J. Chem. Phys., 1978, 68, 3292.
131
6 OPTICAL AND ELECTRICAL SENSING OF THE DNA HYBRIDIZATION INSIDE ALUMINA NANOPORES DNA INSIDE OF ALUMINA NANOPORES
6.1 “Direct” Detection and Separation of DNA Using Nanoporous Alumina Filters
6.1.1 Introduction
Utilization of bioaffinity interactions is an indispensable tool of modern
biochemical research. Bioaffinity interactions such as DNA-DNA and antigen-
antibody are employed for identification of the presence of a particular DNA
sequence in a sample, for detection and identification of microbial and viral species,
for verification of efficacy and function in medical diagnostics. Specificity of these
interactions can be also employed for purification.
Detecting ss-DNA fragments by utilizing their hybridization with
complementary sequences immobilized on a surface is at the heart of the DNA chip
technology. Various methods have been employed for identification of the
hybridization event: fluorescence,1 surface enhanced Raman,2 SPR,3 interferometric,4
and others.5 Currently, the method of choice is fluorescence detection due to its high
sensitivity but it requires modification of the DNA. There is an apparent need for
more direct methods of DNA/RNA detection that are inexpensive and reliable and
would not require tagging of DNA with fluorescent dyes. Detection by optical
absorption (either UV or IR) is usually not considered due to their low sensitivity.
However, with an increased surface area density, the advantage of direct detection by
absorption should become more attractive.
132
In this “proof of concept” report we demonstrate that modified
nanoporous alumina filters can be used for DNA detection and separation. Here
we utilize UV and IR absorption for direct detection of unmodified DNA but
other detection techniques can be also applied.
6.1.2 Results and discussion
Figure 6.1 shows the DNA immobilization procedure inside the nanopores.
Immobilization consists of three steps: Silanization, activation by glutaraldehyde and
final aminated ssDNA attachment.6
Figure 6.2 illustrates that, using this approach, high optical densities (OD ~ 1)
can be reliably obtained with ss-DNA 21-mers on AAO filters. Higher loadings, OD
> 1.6, are easily achievable but are inconvenient for UV absorbance measurements
with an ordinary spectrometer.7 Similar results were obtained with smaller pore
diameters (20 nm) AAO. The absorbance of OD = 1.0 from Figure 6.2 corresponds to
the DNA surface density of ca. 2.6×1012 cm-2.
133
Figure 6.1 Immobilization scheme.
Al2O3
OH
Al2O3
Al2O3
N HH
SiO O
O
CH3CH3 N
SiO OO CH3CH3
OH
O O
HH
(CH3O)3Si
NH2
NH2
Al2O3
N
SiO OO CH3CH3
N
DNA
DNA
134
220 240 260 280 300 3200.0
0.5
1.0
1.5
0.8
1.0
1.2
1.4
1.6
Initial
after complementaryss-DNA added
9M urea added
Abs
orba
nce
@ 2
60 n
mB
A
A
bsor
banc
e
Wavelength (nm)
Figure 6.2. UV absorption spectra of a 200 nm AAO filter (60 µm thick) with: A ss-DNA 21-mer immobilized inside the pores and B after hybridization with a complementary 21-mer. The insert illustrates the reversibility and reproducibility of hybridization and denaturation (with 9 M urea).
135
3500 3000 2500 2000 15000.00
0.05
0.10
0.15B
A
A
bsor
banc
e
Wavenumber, cm-1
Figure 6.3. A IR absorption of a 200 nm filter with immobilized 21-mer and after its hybridization with a complementary 41-mer, B.
Upon hybridization with the complementary 21-mer, the UV absorbance
increases to 1.45, which accounts to ca. 70% hybridization efficiency. The
hybridization efficiency decreases to 50% when no glutaraldehyde neutralization was
performed. Similar hybridization efficiency was obtained with a complementary 41-
mer. The high hybridization efficiency is corroborated by infrared (IR) spectra shown
in Figure 6.3, where two-fold absorption increase in the regions of in-plane double
bond8 vibrations near 1700 cm-1 and in the hydrogen region 3300 cm-1 are observed.
Due to background variations we could not assess the conformation (B or A) of the
136
hybridized DNA. No increase of either UV or IR absorption was observed with a
noncomplementary ss-DNA (21-mer or 41-mer) on the same filter. The bound
complementary ss-DNA can be eluted by either using denaturing solutions, as shown
in Figure 6.2, or by heating the filter in water; the procedure can be repeated
numerous times without noticeable loss of the surface immobilized ss-DNA.
Fluctuations in the absorption are due to slight variation of the filter placement in the
cuvette. It can be minimized in a flow cell configuration.
Figure 6.4 provides additional confirmation that the increase in UV absorption
is due to DNA hybridization. The melting temperature observed for the immobilized
hybrid, Tm= 62oC, is very close to that measured in solution. The small amplitude of
the apparent hypochromism on the filter is due to dilution into a larger volume.
40 50 60 70 800.96
0.97
0.98
0.99
1.00
Nor
mal
ized
Abs
orba
nce
Temperature oC
Figure 6.4. Normalized temperature variation of the UV absorption at 260 nm for the immobilized hybrid between the 21-mer and the 41-mer of curve B in Figure 6.2 in 0.1 M NaCl.
137
The AAO filter with covalently immobilized DNA can be also used as an
affinity separation tool for specific target ss-DNA. A solution is simply passed
through the filter and the bound target ss-DNA is then eluted in the purified form by
denaturing the hybrid at an elevated temperature or by using a denaturing solutions
(the principle is shown on Figure 6.5). We demonstrate this on a filter with 200 nm
pores, on which 3.0 nmoles of ss-DNA was immobilized (OD = 0.75 for the 21-mer
used). When excess (6 nmoles) of the complementary ss-DNA (also a 21-mer) in 0.1
M NaCl was slowly passed through that filter at room temperature (25oC), 1.6 nmoles
of the target ss-DNA was captured. This corresponds to almost the same filter
capacity as estimated above using 41-mer. The captured DNA was eluted with >90%
efficiency by 9 M urea solution, as observed by UV absorption spectra changes of the
filter and the solutions.
Figure 6.5. Schematic representation of the DNA purification using developed technique. AAO filter modified with ssDNA is placed in the syringe. Solution containing mixture of the ssDNAs pushed through the filter. ssDNAs which are complementary to the immobilized one, binds to the filter, while others pass through freely.
138
When a mixture of 6 nmol of noncomplementary 21-mer ss-DNA and 0.3
nmol of the complementary 21-mer labeled with the Cy5 dye at 5’ was passed
through the same filter, 85% of the complementary ss-DNA was captured, while the
noncomplementary ss-DNA did not bind, as shown in Figure 6.6.
300 400 500 600 7000.0
0.5
1.0
1.5
x 30
B
AC
AB
C
Abs
orba
nce
Wavelength (nm)
0.00
0.01
0.02
0.03
0.04
Figure 6.6. Absorption spectra of 1 mL solution originally with 185 nM of Cy5-tagged ss-DNA (21-mer) before (A) and after a single pass through the AAO affinity filter (C). B spectrum of the filter with hybridized Cy5 tagged complementary ss-DNA.
Details on the immobilization, hybridization procedures, calculation examples
and experimental techniques can be found in Appendix B.
139
6.2 Sensing DNA hybridization via ionic conductance through nanoporous electrode
Malfunction of ion channels in biological cells leads to alteration of a trans-
membrane potential and can cause cell death. Understanding of such important
fundamental biological phenomena, as well as, possibility to control ion flow attracts
a great interest to the study of ionic transport through nanopores. Recently, the idea of
controlling the mass transport of specific species through nanopores by means of UV
light9, pH of solution10, charge11,12 and size13 of an ion was explored. Biosensors and
separation membranes that are based on selective nanopores have evolved into a very
promising field.14-16 Technological advances in the last decade have made it possible
to manufacture nanopores with dimensions comparable to the sizes of biological
polymers such as short DNA and peptides. Some groups take advantage of such an
approach and use single nanopores to resolve sequences of individual DNA
molecules linked to a degree of partial pore blockage by the DNA.17 To our best
knowledge, control of the ion current through nanopore arrays by hybridization of
DNA with its complementary immobilized inside the nanopores has not been
demonstrated.
Here we explore this alternative approach and investigate variation of ionic
conductivity in nanopores caused by DNA immobilization at the pore walls and its
subsequent hybridization with a complementary DNA strand (Figure 6.7). We believe
that this method could be also employed with other biological objects, which possess
strong enough bioaffinity interactions.
140
Figure 6.7. Proposed sensor: variation of ionic conductivity in nanopores caused by DNA immobilization at the pore walls and its subsequent hybridization with a complementary DNA strand
In the previous section 6.1, we have shown that alumina nanoporous
membranes with 200 nm pore diameter can be used for DNA separation and optical
detection by hybridizing with single stranded DNA (ss-DNA) covalently immobilized
inside the pores.16 Here we present investigation of electrical manifestation of the
hybridization event, namely altering the ionic current through alumina nanoporous
membranes by immobilized ss-DNA upon its hybridization with target DNA.
Electrical detection is more desirable due to possibilities of miniaturization,
integration into existing detection schemes, and realization of parallel arrays.
141
6.2.1 Results and discussion
A flat platinum working electrode was placed in close contact with the tested
side of a membrane, while a screen counter electrode was in contact with the opposite
side (see Figure 6.8).
Counter Electrode
Working Electrode
Counter Electrode
Working Electrode
B
A
1
2
3
4
65 7
Figure 6.8. Experimental electrochemical cell. Two options for filter (4) orientation (A - working electrode (1) at the 20 nm side of the membrane; B - at the 200 nm side) in the homemade electrochemical cell with stainless steel screen counter electrode (2) and reference minielectrode (5), immersed in solution (7). Working electrode is made of Pt and the cell body (3 and 6) – from Plexiglas.
Such geometry minimizes contribution from the solution outside the
membrane, which is mostly distinguishable at high frequencies. Cyclic voltammetry
in Fig.6.9A clearly shows that both reductive and oxidative currents decrease after
DNA hybridization occurs inside the nanopores and when the 20 nm side is oriented
towards the working electrode. The scan rate of 100mV/s was sufficiently high so that
142
the thickness of the diffusion layer was shorter than the membrane thickness. As
expected, no noticeable current change was observed at the 200 nm side of the same
filter (Fig. 6.9B) since the length of ds-DNA is much smaller then the pore diameter.
0 .6 0 .4 0 .2 0 .0-4
-2
0
2
4
0 .4 0 .2 0 .0
A
V
B
I, 10
-4A
V
Figure 6.9. CV in the region for Fe(CN)63-/4- oxidation/reduction: (A) at the 20 nm
side of a modified membrane and (B) 200nm side. Solid black lines –21-mer ss-DNA immobilized inside pores, red dash-dot - the DNA is hybridized with a complementary 21-mer strand, blue dash – after denaturing with 9M urea. Voltage vs Ag/AgCl; 100 mV/s; 10 mM Fe(CN)6
3-/10 mM Fe(CN)64- in 0.1 M KCl.
The higher current amplitude on the 200 nm side is primarily due to a higher
ion mobility through larger pores but a possible difference in effective areas of
contact with the working electrode can have a small contribution as well.12 The CV
amplitude does not change on either sides when a noncomplementary target DNA
was used, which agrees with lack of its hybridization, also confirmed by optical
measurements.16 The current amplitude on the 20 nm side recovers to its original
143
value upon DNA denaturing with 9 M urea, while no effect was observed again for
the 200 nm side. Because of a small Debye length, λD = 0.307/c1/2, in 0.1 M KCl (~ 1
nm),19 no specificity to the ion charge is anticipated. Indeed, similar results were
obtained with positively charged Ru(NH3)62+/3+ redox pair.20 Change in conductivity
can also be observed in direct current, as shown in Fig. 6.10, where variation of
charge due to reduction of Fe(CN)63- traveling through the filter (at the 20 nm side) is
given as a function of time.
The accumulation of charge appears proportional to the square root of time,
from where the net diffusion coefficient, D, can be estimated from known
concentration of Fe(CN)63- and the electrode area, A, using Equ.(6.1):19
Q(t)=2AF[Fe(CN)63-](Dt/π)1/2 (6.1)
where F is the Faraday constant.
The net value of D, measured at long times in Fig. 6.10, drops from ~ 1.1×10-6
cm2/s in the case of immobilized ss-DNA to ~ 6.2×10-7cm2/s upon DNA
hybridization. This estimate agrees with measurements of ion flux through the filter20
and previously reported observations on unmodified filters.12 The diffusion
coefficient of Fe(CN)63- is nonuniform through the filter thickness but, on the time
scale exceeding the diffusion time through the wide part of the membrane, tD, the
anisotropy in its orientation diminishes.
144
0 2 4 6 8 10 12 140.0
0.5
1.0
1.5
2.0
2.5
1 10 1001.0
1.5
2.0 A
B
C
harg
e. m
C
Time1/2, s1/2
I(200
nm)/I
(20n
m)
Time (s)
Figure 6.10. Chronocoulometric plot for charge passed through the modified nanoporous membrane modified with 21-mer ss-DNA immobilized inside pores filter before (A) and after (B) hybridization with complementary 21-mer. Working electrode is at the 20 nm side in both cases. Other conditions are similar to those in Fig. 6.9: 10 mM Fe(CN)63-/10 mM Fe(CN)64- in 0.1 M KCl; 0 V vs. Ag/AgCl. The insert illustrates the ratio between the currents through unmodified membrane oriented by the 200 nm side, I (200nm), and the 20 nm side, I(20nm), towards the working electrode.
As the insert in Fig.6.10 shows, the anisotropy declines within ca. 6 seconds,
in agreement with the estimated diffusion time through 200 nm portion of the
membrane:19
tD = L2/4D (6.2)
145
During the time tD of electrolysis, nearly half of ferricyanide ions from inside
the membrane are reduced at the working electrode. Similarly in CV measurements,
the anisotropy is large at fast scan rates and declines with its lowering.
Information on ion flow is conveniently illustrated through the frequency dependence
of cell impedance, Z, measured at the half-wave voltage for the redox pair (0.22 V vs.
Ag/AgCl). Fig. 6.11 shows this in the form of a Nyquist plot for -ImZ vs. ReZ in the
frequency range from 105 to 10-2 Hz. Again, the impedance appears higher when the
filter is oriented with the 20 nm side towards the working electrode and increases
when ss-DNA inside the pores is hybridized with a complementary oligomer of target
DNA.
Figure 6.11. Nyquist plot for impedance at 0.22 V (vs. Ag/AgCl) for the same filter and conditions as in Fig.6.9. (A) 20 nm side of a membrane, (B) 200 nm side. Solid black lines – 21-mer ss-DNA is immobilized inside pores, red dash-dot - immobilized DNA is hybridized with a complementary strand, blue dash – after denaturing with 9 M urea.
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
1.2
*
A
Z', kΩ
-Z",
kΩ
0.0 0.2 0.4 0.6 0.8 1.0
B
Z', kΩ
146
The 200 nm side is practically unaffected by DNA hybridization. Since the
modulation voltage in impedance measurements is small, the anisotropy effect
between the 20 nm and 200 nm sides persists over a broad range of frequencies.
The described effect of conductance change in nanopores has a complex
nature with contributions from: a) volume exclusion due to additional DNA upon
hybridization, b) the ionic mobility change inside the pores entangled with charged
DNA strings, and c) distribution of pore diameters. This complexity reveals in the
initial decrease of impedance after immobilization of ss-DNA inside the nanopores,
as compared to an unmodified filter. In contrast, the impedance always increases
(amplitude of CV decreases) upon hybridization of already immobilized DNA with
the complementary oligomer. The changes are observed exclusively on the 20 nm
side. Similarly, the ratio between the CV amplitudes on 20 nm and 200 nm sides first
increases from the initial value of 0.74 for unmodified filter to ca. 0.87 upon
immobilization of ss-DNA but then drops to ca. 0.62 after DNA hybridization.20 The
impedance increase is dependent on the surface coverage of immobilized ss-DNA and
the degree of its hybridization with target DNA, as illustrated by Table 6.1 and Fig.
6.12. The impedance increases nonlinearly with surface concentration of ss-DNA
upon “complete” hybridization (approximately 93% as judged by optical absorption)
with the complimentary 21-mer. Quantitative analysis of this dependence should be
taken with great caution because the concentration measured by optical absorption is
accurate only for the 200 nm portion of the filter, which covers most of its 60 µm
147
thickness and DNA; concentration at 20 nm side can differ for either ss-DNA or ds-
DNA cases.
The described geometry is not convenient for real time monitoring of the
hybridization effect and analysis of the concentration dependence of the signal.
However, it allows for unambiguous discrimination of the pore blocking effect from
various phenomena that alter rates of redox reactions at the flat electrode.18 Based on
the data presented, the effect of hindered ion mobility inside modified nanopores, size
of which is comparable to DNA length, is clearly confirmed. Fig.6.11 suggests that
the mobility drop can be quite dramatic.
Table 6.1. Effect of the immobilized DNA surface density inside AAO on its impedance change at 0.01 Hz at 20nm side upon DNA hybridization.
∆|Z| at 0.01 Hz
NΩ, cm-2 Complementarya Noncomplementaryb
1 ×1012 75% <3%
8 ×1011 33% n/a
6 ×1011 23% n/a
a complementary 21-mer as in Ref. 10, shows 93% hybridization efficiency inside pores as measured by optical absorption; b noncomplementary 21-mer as in Ref.8, shows less than 3% hybridization efficiency inside pores as measured by optical absorption
148
Figure 6.12. Impedance increase at 0.01 Hz upon complete DNA hybridization as a function of surface density of initial ss-DNA. The solid line serves as a guide for eye.
The inflection point in the Nyquist plot at the 20 nm side is observed in the
vicinity 0.1 Hz (on the Warburg portion of the plot of Fig.6.11, as well as, in the Bode
plot20). This should correspond to the diffusion coefficient on the order of 10-7 cm2/s,
if one assigns the inflection point frequency to the inverse time of ion traveling
through 1 µm of modified pore. This diffusion coefficient is almost two orders of
magnitude smaller than that in the bulk solution but the value is consistent with the
estimates based on optical measuring of ion flux through the membrane.20 Although
some dependence on the ion charge might be expected if lower ionic strengths were
0.0 0.2 0.4 0.6 0.8 1.00
20
40
60
80∆|
Z|, %
Density, 1012/cm2
149
used, for 0.1 M KCl this effect disappears20 in agreement with previous
observations.12
6.3 Conclusions
We have shown that alumina nanoporous filters can be successfully employed
for immobilization of DNA using aminosilanes and glutaraldehyde linker. The high
surface density of DNA (~ 4×1012 cm-2) and high efficiency of hybridization (ca. 70%)
in combination with high surface area, make this system very attractive for further
development of various DNA/RNA detection methods. The moderate transparency of
AAO in the UV and IR regions allow direct detection of DNA hybridization by
optical absorption without any modification of the target ss-DNA. The standard
approach with fluorescent dye-tagged ss-DNA target can also take advantage of the
AAO filter through high density of immobilized ss-DNA and stability to
thermocycling, combined with excellent transparency in the visible range.
The unique advantage of using AAO filter is in a convenient combination of
detection and separation/purification possibilities for unmodified target ss-DNA (and
RNA). Close to quantitative efficiency of binding the complementary DNA (>80%)
from a solution by a single pass through the modified filter and a low interference
from noncomplementary ss-DNA make this a promising method for various
applications.
150
We also show that the same membranes can be used for electrical detection of
complementary target DNA sequences without need for their modification. Electrical
detection should offer a greater versatility in miniaturization, integration into
inexpensive detection schemes and realization of parallel arrays, i.e. DNA chip.
Better understanding should be achieved with uniform distribution of nanopore
diameter and length. The suggested approach is far from being optimized but
theoretical sensitivity limit can be conservatively estimated using our experimental
data by taking electrodes of 5 µm × 5 µm area and 0.5 µm thick oxide pores of 20 nm
diameter. In that case, less than 10-17 moles of complementary target DNA is required
to hybridize surface immobilized ss-DNA with the same density, 1012 cm-2, as in the
described cell and achieve more than 70% impedance increase, as shown here for
similar densities. We are progressing towards experimental realization of this
estimate and hope to achieve even better sensitivity.
6.4 References
1. Fodor, S.P.; Rava, R.P.; Huang, X.C.; Pease, A.C.; Holmes, C.P.; Adams, C.L. Nature 1993, 464, 555
2. Cao, Y.C.; Jin, R.C.; Mirkin, C.A. Science 2002, 297, 1536
3. Brockman, J.M.; Nelson, B.P.; Corn, R.M. Annu. Rev. Phys. Chem. 2000, 51, 1
4. Pan, S.; Rothberg, L.J. Nanoletters, 2003, 3, 811
151
5. Bailey, R.C.; Nam,J.-M.; Mirkin, C.A.; Hupp, J.T. J. Am.Chem.Soc. 2003, 125, 13541
6. Hermanson, G.T. Bioconjugate Techniques, Academic Press, 1996
7. The apparent optical density of a clean filter with 200 nm pores in water at 260 nm is ca. 2. That is the primary reason for working with less than maximum loading
8. Liquier, J.; Taillandier, E. Ch.6 in Infrared Spectroscopy of Biomolecules, H.Mantsch and D.Chapman Ed
9. Liu, N.; Dunphy, D.R.; Atanassov, P.; Bunge, S. D.; Chen, Z.; Lopez, G.P.; Boyle, T.J.; Brinker, C. J. Nano Lett. 2004, 4, 551-554.
10. (a) Casasús, R.; Marcos, M.D.; Martínez-Máñez, R.; Ros-Lis, J.V.; Soto, J.; Villaescusa, L.A.; Amorós, P.; Beltrán, D.; Guillem, C. and Latorre, J. J.Am.Chem.Soc. 2004, 126, 8612-8613. (b) Siwy, Z.; Heins, E.; Harrell, C.C.; Kohli, P. and Martin, C.R. J.Am.Chem.Soc. 2004, 126, 10850-10851.
11. Nishizawa, M.; Menon, V.P.; Martin, C.R. Science 1995, 268, 700.
12. Bluhm, E.A.; Bauer, E.; Chamberlain, R.M.; Abney, K.D.; Young, J.S.; Jarvinen, G.D., Langmuir, 1999, 15, 8668.
13. Jirage, K.B.; Hulteen, J.C.; Martin, C.R. Science 1997, 278, 655.
14. (a) Kohli, P.; Wirtz, M.; Martin, C.R. Electroanalysis 2004, 16, 9-18. (b) Kohli, P.; Harrell, C.C.; Cao, Z.; Gasparac, R.; Tan, W.; Martin, C.R. Science 2004, 305, 984-986.
152
15. Gyurcsányi, R.E.; Vigassya, T.; Pretsch, E. Chem. Comm. 2003, 20, 2560-2561.
16. Vlassiouk, I.; Krasnoslobodtsev, A.; Smirnov, S.; Germann, M. Langmuir 2004, 20, 9913-9915.
17. (a) Chen, P.; Mitsui, T.; Farmer, D.; Golovchenko, J.; Gordon, R.; Branton, D. Nano Lett. 2004, 4, 1333-1337. (b) Deamer, D.W.; Brandon, D. Acc. Chem. Res. 2002, 35, 817-825. (c) Chang, H.; Kosari, F.; Andreadakis, G.; Alam, M.A.; Vasmatzis, G.; Bashir, R. Nano Lett. 2004, 4, 1551-1556.
18. Katz, E.; Willner, I. Electroanalysis 2003, 15, 913-947.
19. Bard, A.; Faulkner, L. Electrochemical Methods. Fundamentals and Applications. (John Wiley & Sons, 2001).
20. Appendix C contains: a) information on sequences used, b) procedure for electrochemical measurements, c) ssDNA surface density and d) hybridization efficiency calculations, e) SEM images of the filters, f) measurements of ion flux through membrane, g) electrochemical measurements with Ru(NH3)6
2+/3+redox pair, and h) variation of the ratio between CV at 20nm and 200nm sides as a function of filter modification.
APPENDICES
APPENDIX A DERIVATION OF EQUATIONS (5.12) AND (5.13)
155
Singlet oxygen can be formed in processes with conservation of the total spin
and its projection, i.e. only when the ground state 3O2 collides with a triplet state. The
latter can be either a locally excited triplet (such as 3C60) or a triplet state of 3CT. It’s
been shown that collision with triplet 3C60 leads to formation of singlet oxygen, 1O2
with unit probability,1 which is not surprising because of a long lifetime of 3C60. We
will follow the same assumption and will assign ϕ(1Ο2*) = ϕ(3C60), when the latter is
formed. That leads to the following concentration dependence of the ϕ(1Ο2*) yield:
( )ICCRSd
ICd
kkOkkOk
O++
+=
][][
2
22
1ϕ , (A.1),
equal the ratio of the rate of 3C60 production (within the dyad itself, with the rate
constant kIC , and via collisions with oxygen, with the pseudo first order rate constant
kd[O2]) to the total rate of CT deactivation. Thus the additional route of singlet 1CT
recombination with the kCRS rate constant is added in the denominator.
In cases such as ZnChl-C60 in toluene, where 3C60 state has higher energy than
that of the 3CT, formation of 3C60 is energetically blocked and the only option for
1O2* creation is via the triplet state of 3CT. Not all collisions of 3CT with oxygen
produce 1O2*. The only spin allowed process in the total singlet state of the
encounter (that happen in the 1/9th of the collisions) lead to that, according to the
equation:
1[3(D+--A−) .. 3O2] 1[(D+--A)..O2
−] 1(D--A) + 1O2* (A.2) 1/9kdO2
k-d
kCRO23(D+--A−) + 3O2kCSO2
156
Here we explicitly label the rate constant of charge separation within the
complex as kCSO2. It competes with complex dissociation that proceeds with the rate
constant k-d. Charge recombination is presumed to be exclusively into 1O2* with the
rate constant kCRO2. Neglecting recombination into the original complex simplifies the
treatment at the expense of a minimal overestimate of the overall yield.
Collisions in the total triplet state (reaction 5.11) and in the quintet state do not
lead to 1O2* formation because of the spin. The easiest approach to find the yield is
through considering equilibrium situation. Assuming that generation of the singlet
1CT state proceeds with the rate G, the rates of change of the concentrations [1CT]
and [3CT] are zero:
0]][[]][[][][
0]][[91]][[]][[][
23
2111
1
23
23
211
3
=++−−−=
=−−+=
−
−
GOCTkOCTkCTkCTkdtCTd
OCTkOCTkOCTkCTkdtCTd
isciscICCRS
disciscIC
(A.3),
where again kCRS – is the inverse lifetime of the singlet 1CT state, kIC – is the
interconversion rate constant in the CT complex without intervention of oxygen. The
forward intersystem crossing rate constant in the CT complex induced by oxygen, kisc
= kd/2, is three times than that for the reverse process (from 3CT to 1CT), k-isc = kd/6.
Solving equations (A.3) in combination with (A.2) results in the following
dependence of the singlet oxygen yield on oxygen concentration:
( )
+++
+=
− 19
][
][
2
22
1
d
iscCRSICisc
ICisc
kk
kkOk
kOkO
α
ϕ (A.4)
157
where efficiency of charge transfer to C60, α, is less than unity due to the competition
with complex dissociation:
dCSO
CSO
kkk
−+=
2
2α (A.5)
The resulting yield is given by:
( )
+++
+=
169][
][
2
22
1
α
ϕ
CRSICisc
ICisc
kkOk
kOkO (A.6)
References 1. Terazima, M.; Hirota, N.; Shinohara, H.; Saito, Y. J. Phys. Chem., 1991, 95, 6490-6495.
APPENDIX B
SUPPORTING INFORMATION FOR 6.1 SECTION “DIRECT” DETECTION
AND SEPARATION OF DNA USING NANOPOROUS ALUMINA
FILTERS
159
All procedures and measurements were done at 25oC unless mentioned otherwise.
Immobilization procedure:
1. A fresh AAO filter (13 mm in diameter 60 µm thick with 200 nm pores of 1×109
cm-2 density, Anodisc 13, Fisher) is first boiled in nanopure water for 1 hour and
then dried in argon. Results presented here are for the filters that also had a
transition layer of 20 nm diameter pores and 1µm thick.
2. After that the filter is immersed into a 5 % acetone solution of APS (3-amino-
propyltrimethoxysilane, Aldrich) for 1 h. Because of a low acidity of alumina and
hindered diffusion in nanopores, this silanization step had to be longer than what
was used for silanization of flat quartz and glass surfaces
3. After thorough washing in acetone and baking at 120oC for 30 min, the filter is left
overnight in 25% aqueous solution of glutaraldehyde (Aldrich)
4. Following thorough washing with nanopure water and drying with argon, ca.30 µL
of aqueous solution of 5’-aminated DNA (1 mM) is placed onto the filter and kept
at high humidity overnight
5. Finally, the filter is thoroughly washed by passing 1 M NaCl solution through it.
Neutralization of glutaraldehyde:
We found that neutralization of glutaraldehyde by propylamine improves
hybridization efficiency. Similar to step 4 above, it was performed overnight from 10-
5 M aqueous solution of propylamine.
160
Hybridization procedure: 1. Hybridization is done by a complementary ss-DNA from 1 M NaCl solution at
either room temperature or initially heating for an hour at 85oC and slow cooling to
room temperature
2. To minimize unhybridized reading, the filter is thoroughly washed by passing 1 M
NaCl solution through it until no measurable absorbance at 260 nm for the eluting
solution is observed. Usually no more than 2 mL is required.
3. The reverse process, dehybridization (denaturation) is performed at temperatures
above 70oC for 1 h in water and slow cooling or, alternatively, at room temperature
by passing 9 M urea.
UV-Vis Measurements:
UV-Vis spectra were measured on Perkin-Elmer Lambda 40 spectrometer and
Carey 100 Bio UV-Vis spectrophotometer. The latter was used for temperature
variation measurements. In either case, the filter was placed inside a quartz cuvette
with 1 cm path length against its front wall and the cuvette was filled with 1 M NaCl.
To alleviate the effect of scattering by the filter (which is quite high in the UV
region), a similar cuvette with a filter free of bound DNA was placed in the
comparison arm of the spectrometer. The apparent optical density of a clean filter
with 200 nm pores in water at 260 nm is ca. 2. For that reason, we had to work with
less than maximum loading. In sensor application, the modified with ss-DNA filter
can be used as a base signal and thus alleviate the complication. The filter scattering
161
can probably be decreased by changing the pore diameter and the pore density of the
filters.
FT-IR Measurements:
Perkin Elmer Spectrum One FT-IR spectrometer was used for recording IR
absorption spectra of the argon-dried filters (they were dried by a gentle argon stream
onto filters initially soaked in 0.1 M NaCl) that were placed in a holder. The
background signal was measured with a similar unmodified filter. No measurements
were possible below 1250 cm-1 due to high background signal in that region.
DNA sequences: Surface bound 21-mer: 5’NH2–GCT TAG GAT CAT CGA GGT CCA,
ε1(260nm)=2.25×105 M-1cm-1
Complement 41-mer: 5’-CCG CTG AAT TGC ACC CGT CGT GGA CCT CGA
TGA TCC TAA GC , ε2 (260 nm) = 4.2 ×105 M-1cm-1
Complement 21-mer: 5’-TGG ACC TCG ATG ATC CTA AGC, ε3(260 nm) =
2.25×105 M-1cm-1
Noncomplement 21-mer:5’-GGC CTT AAT CGG ATA GAG TGA, ε4(260 nm) =
2.38×105 M-1cm-1
Complement_dye 21-mer: Cy5-5’-TGG ACC TCG ATG ATC CTA AGC, ε5(260
nm) = 2.25×105 M-1cm-1 ; ε6(647 nm) = 1.94×105 M-1cm-1
162
Calculations:
Effective Surface Area: The pores with the d = 200nm diameter and l = 60 µm
long, provide the effective area greater by a factor α = 4πdl/πd2 = 940 as compared to
the flat surface of that diameter.
Surface Density of immobilized DNA: For optical density of OD = 1.0 and ss-
DNA with ε1 = 2.25×105 M-1cm-1, the capacity, C, of a filter for DNA can be
calculated as C = OD/(1000*ε1) = 4.4 ×10-9 mole/cm2 of the filter cross-section area.
It corresponds to C/α = 4.7×10-12 moles per cm2 of DNA per surface area of the oxide
or 35 nm2 per DNA molecule. For OD = 1.6 such calculations come out as C =
5.8×10-9 mole per cm2 or ca. 29 nm2 per DNA.
Hybridization Efficiency with the 21-mer by UV of the filter with neutralized
glutaraldehyde: For calculating the hybridization efficiency, β, from the UV
absorption with the complementary 21-mer, one has to take into account DNA
hypochromism, which was measured to be 1-η ∼ 18% for the hybrid (see Fig.A
below). Thus, from the OD change in Fig.1 from 1.0 to 1.46, one gets β~0.7:
1.46/1.0 = [β(ε1+ ε2)η + (1- β)ε1] /ε1 = > 1.46 = [2βη + (1- β)] or β ~ 0.7
163
60 70 80 90
0.40
0.42
0.44
0.46
0.48
0.50100µL of Comp 21 (A=0.5) +100µL of ControlA21 (A=0.5)1.0 M NaCl
Abs
orba
nce
@ 2
60 n
m
T, oC
30 40 50 60 70 801.4
1.5
1.6
1.7
1.8
1.9
400 µL Comp21 (A=1.72) +400 µL Control21A (A=1.72)0.1M NaCl
Abs
orba
nce
T,C
Comp21+ControlA21
Figure B1. Stoichiometric solution of the 21-mer with its complementary 21-mer shows ca. 20% hypochromism at 260 nm in 1 M NaCl with Tm = 79oC and ca.18% in 0.1 M NaCl with Tm = 67oC.
164
Hybridization Efficiency with the 41-mer of the filter without glutaraldehyde
neutralization: Similarly, for calculating the hybridization efficiency with the
complementary 41-mer on the filter without neutralized glutaraldehyde (see Fig. B2),
the hypochromism was measured to be 1-η ∼ 12% for the hybrid (see Fig.B3). Thus,
from the OD change in Fig.1 from 0.85 to 1.5, one gets β ~ 0.5: 1.5/0.85 = [β(ε1+
ε2)η + (1- β)ε1] /ε1 = > 1.76 = [2βη + (1- β)] or β ~ 0.5
250 300 350
0.0
0.5
1.0
1.5 B
C
A
Abs
orba
nce
Wavelength (nm)
Figure B2. UV absorption spectra of a 200 nm AAO filter (60 mm thick) with: A – ss-DNA 21-mer immobilized inside the pores; B - same as A after hybridization by a complementary 41-mer; C – same as B after denaturing in 70oC water for 1 hour and then cooling.
165
50 55 60 65 70 75 80
0.88
0.92
0.96
1.00
100µL of Comp41 (A=1.7) +100µL of ControlA21 (A=0.8)[NaCl]=0.2M
Nor
mal
ized
Abs
orba
nce
T, oC
Figure B3. Stoichiometric solution of the 21-mer and the 41-mer (1.8 µM of each) shows ca.12% hypochromism at 260 nm in 0.2 M NaCl with Tm = 67oC
Hybridization Efficiency with the 41-mer by IR absorption of the filter: The
IR absorption peaks vary in position and intensity for different bases1 and change
upon hybridization.1 Nevertheless, both the surface bound ss-DNA 21-mer and the
target ss-DNA 41-mer, have fairly even representations of all bases (with slightly
greater amount of cytosine in the 41-mer), the 3300 cm -1 and 1700 cm-1 absorption
bands increase without recognizable change in the shape. Both bands increase
approximately identically by a factor of 2. Neglecting the spectral variations due to
166
hybridization, one would estimate β from: 2 = [β(21+ 41) + (1- β)21] /21 = > or β ~
0.5
Hybridization Efficiency with the 21-mer by UV of solution: Initial solution
of Comp21 with OD = 1.33 (6 nmoles in 1 mL) was passed through the filter in two
0.5 mL aliquots with a clearly greater efficiency of binding for the first aliquot (see
Fig.B4). The total change of absorbance ∆OD = 0.36 corresponds to 1.6 nmoles of
the target ss-DNA 21-mer hybridized on the filter.
200 220 240 260 280 3000.0
0.4
0.8
1.2
Abso
rban
ce
λ, nm
Initial 1.0 mL solution of Comp21 First 0.5 mL after passing through filter Second 0.5 ml after passing through filter Average of the previous two solutions
Figure B4. UV absorption of the target ss-DNA 21-mer solution before and passing through the modified filter.
167
Optical Absorption Sensitivity Estimate:
The sensitivity of absorption depends on the extinction coefficient (size) of
the target ss-DNA. The detection limit can be estimated from the expression for
optical density:
OD = (N/S)*ε/6×1020
where N – is the number of molecules adsorbed (hybridized on) to the surface cross
section S. A conservative estimate for the detectable threshold in absorbance is OD ~
0.03. In a flow system with rigid filter alignment, the detectable change in absorption
can be easily made better. Presuming that the target is a 50-mer, i.e., the extinction
coefficient ε ~5.5 ×105 M-1cm-1, and the detection area spot of S = 10-3 cm2, the
minimum number of detectable target ss-DNA can be estimated as N ~ 0.03 × 10-3 ×
6×1020/5.5 ×105~ 3×1010 or in 50 fmol range. Sensitivity to longer ss-DNA would be
even higher because of a greater extinction coefficient.
References
1. Liquier, J.; Taillandier, E. Ch.6 in Infrared Spectroscopy of Biomolecules, H.Mantsch and D.Chapman Ed.
APPENDIX C SUPPORTING INFORMATION FOR 6.2 SECTION SENSING DNA
HYBRIDIZATION VIA IONIC CONDUCTANCE THROUGH NANOPOROUS ELECTRODES
169
All procedures and measurements were done at 25oC unless mentioned otherwise.
DNA sequences:
Surface bound 21-mer (A): 5’NH2–GCT TAG GAT CAT CGA GGT CCA,
ε1(260nm)=2.25×105 M-1cm-1
Complement 21-mer: 5’-TGG ACC TCG ATG ATC CTA AGC, ε3(260 nm) =
2.25×105 M-1cm-1
Surface bound 21-mer without a complement sequence (B): 5’NH2-GGC CTT AAT
CGG ATA GAG TGA, ε4(260 nm) = 2.38×105 M-1cm-1
Electrochemical Measurements:
All electrochemical measurements were performed using 604B
electrochemical analyzer (CH Instruments), flat platinum working electrode and a
reference Ag/AgCl minielectrode and stainless steel screen counter electrode. Before
each experiment working electrode was polished with 0.05µ gamma alumina powder
using polishing kit (CH Instruments). Stainless mesh (Fisher) was employed as a
counter electrode. Electrochemical measurements were done using 10mM solutions
of analyte (Fe(CN)6-3/-4 or Ru(NH3)6
2+/3+) in 0.1 M KCl. CV rate was 100mV/s. The
Bode impedance spectra were obtained at the equilibrium voltage 0.22V vs. Ag/AgCl
by applying 5mV ac voltage.
170
Surface Density of immobilized DNA.
Surface Density of immobilized DNA was calculated from the optical density
at 260 nm and known extinction coefficient. A 940 fold increase in surface area of the
porous filter was included n calculations. For example, OD = 0.36 of ss-DNA with ε1
= 2.25×105 M-1cm-1, the capacity, C, of a filter for DNA can be calculated as C =
OD/(1000*ε1) = 1.6 ×10-9 mole/cm2 of the filter cross-section area. It corresponds to
C/α = 1.7×10-12 moles per cm2 of DNA per surface area of the oxide or 100 nm2 per
DNA molecule.
250 3000.0
0.2
0.4
OD=0.358OD=0.289OD=0.218
Abs
orba
nce
λ, nm
Figure C1. UV Absorbance spectra of immobilized ssDNA at nanoporous 20nm membrane. DNA densities are shown in Table 6.1
171
Hybridization efficiency.
For calculating the hybridization efficiency, β, from the UV absorption with the
complementary 21-mer, one has to take into account the DNA hypochromism, which
was measured to be 1-η ∼ 18% for the hybrid. Thus, from the OD change in Fig. C2
from 0.35 to 0.59, one gets β from:
0.59/0.36 = [β(ε1+ ε3)η + (1- β)ε1] /ε1 = > β ~ 0.93
220 240 260 280 300 320
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Abs
orba
nce
λ, nm
Figure C2. UV absorbance change upon hybridization of immobilized ssDNA by complementary 21-mer.
172
Bode plot for impedance vs frequency.
10-2 10 -1 100 101 102 103 104 105
102
103
20 nm side: dsD N A ssD N A
200 nm side: dsD N A ssD N A
Log|
Z|
Log(f)
Figure C3. Low frequency portion of the Bode plot for two orientations of the filter. Note the arrow indicating the frequency of indentation in the Nyquist plot of Fig.6.11
173
E. Structure of the filter.
174
Figure C4. SEM image of the 200 nm side (A) and 20 nm side (B) of the “20nm” Whatman filter.3
Figure C5. SEM image of gold nanowires prepared by electroreduction of gold from solution into nanoporous alumina filter from the 20 nm side. The transition layer (*) from 20 nm to the nominal diameter 200 nm is clearly visible at the bottom.3 Similar description of the membrane can be also found in the literature.1
Diffusion of Fe(CN)6-3/-4 through 200 and 20 nm pores. Ionic flux measurements.
The difference in diffusion coefficients between 200nm and 20 nm pores is
illustrated by optical measurements of the kinetics of Fe(CN)6-3/-4 diffusion through
alumina membranes. Two different membranes were used: “200 nm” has the nominal
diameter of 200 nm throughout its 60 µm thickness, and the “20 nm” one that has the
structure described above – with 20 nm nominal diameter through only 1 µm out of
the total 60 µm thickness and 200 nm throughout the rest of the filter thickness. A
membrane was placed in the middle of a U-shaped cell separating two equal volumes
10 µm
*
175
of 5 mL each. One half of the cell was filled with 10 mM Fe(CN)6-3/-4 in 0.1M KCl,
while the other half was filled only with 0.1M KCl. Open surface of the membrane
was equal S = 0.32 cm2 in all measurements. The diffusion kinetics was monitored by
measuring absorbance of Fe(CN)6-3/-4 in the second half of the cell. Each kinetics (see
Fig. C6) was fitted by the first order exponential growth. The initial flux and overall
kinetics are different when unmodified 200nm and 20nm filters are used; the rise
times are τrise= 645 min and 826 min, respectively. The ratio is consistent with
electrical measurements (Figures C8), where the ratio between the impedances or CV
signals is also close to 0.75.
The diffusion coefficient inside 200nm and 20nm pores can be estimated from
the flux2 :
J = DαS∇C = DαSC/L, orSL
tV
CCD
α∆∆
= , (C1)
where V = 5mL is the volume of each half of the U-tube, ∆C is the initial
concentration change during time, ∆t, and L = 60µm – is the membrane thickness, S =
0.32 cm2– its area and α ≤ 1 is the fraction of open pores. For the 200 nm membrane,
the diffusion coefficient of Fe(CN)6 is estimated: D200 ~1.1×10-6/α cm2/s, smaller than
that in the bulk, D ~ 4 ×10-6 cm2/s. For the 20 nm membrane, the cross-section is not
uniform and the formula for the flux modifies:
1
20
2002001
2020011
−−
−+=
+
−=
DD
Ll
LCSD
Dl
DlLCSJ
βαα
βα (C2)
176
Since there is ~ 30% decline in the flux through 20 nm membrane, as
compared with 200 nm membrane, the mobility through the small diameter portion
must be smaller: D20/ D200 ~ 0.06 (α/β). Some decrease can be due to a lower fraction
of open pores in 20 nm membrane, β. The ratio, α/β, is likely on the order of unity,
hence, the diffusion coefficient in 20 nm pores, D20, must be more than one order of
magnitude smaller than that in 200 nm pores, D200
0 3 7 10 13 17 20 230.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
B
A
Abs
orba
nce
at 4
51nm
Time, hours
Figure C6. Diffusion of Fe(CN)6-3/-4 through 200 nm membrane. Black circles, red
line – experimental data and the exponential fit for diffusion of Fe(CN)6-3/-4 through
200 nm membrane. Black squares, blue line – experimental data and the fit for diffusion of Fe(CN)6
-3/-4 through 20nm membrane. The rise times are τrise = 645 min and 826 min, respectively.
177
CV in modified filter with Ru(NH3)6
2+/3+ Redox Probe.
To illustrate insignificance of the ion charge, experiments with a positively
charged redox pair, Ru(NH3)62+/3+, were also conducted and presented in Fig. C7.
0 .2 0 .1 0 .0 -0 .1 -0 .2 -0 .3 -0 .4
-2 .0
-1 .5
-1 .0
-0 .5
0 .0
0 .5
1 .0
1 .5
2 .0
0 .2 0 .1 0 .0 -0 .1 -0 .2 -0 .3 -0 .4
BA
I, 10
-4 A
V
H y b r id iz e d D e n a tu re d
H y b r id iz e d D e n a tu re d
V
Figure C7. CV in the region for Ru(NH3)6
2+ /3+ oxidation/reduction: (A) at the 20 nm side of a modified membrane and (B) 200nm side. Solid blue lines –21-mer ss-DNA immobilized inside pores, red - the DNA is hybridized with a complementary 21-mer strand. Voltage vs Ag/AgCl; 100mV/s; 10 mM Ru(NH3)6
2+ in 0.1 M KCl. Surface density of ss-DNA is 1*1012 cm-2.
178
Variation of CV anisotropy with modification.
Ratio between the CV amplitudes on 20 nm and 200 nm sides is another way
of representing the effect of varying mobility inside small pores.
0.6
0.8
1.0
1.2
1.4
20nm/200nm with dsDNA
20nm/200nm with immobilized ssDNA
20nm/200nm of unmodifed membrane
No membrane 200nm unmodifed membrane
Rel
ativ
e am
plitu
de o
f CV
at 1
00m
V/s
Figure C8. Anisotropy factor in CV (ratio of the amplitudes on 20nm side to that at 200 nm, measured at 100 mV/s) as a function of surface modification. Circle - unmodified filter; a green up triangle – ss-DNA immobilized (density ca. 8 ×1011 cm-
2); a blue down triangle – after hybridization. For comparison, ratio of the CV amplitudes without membrane to that on the 200 nm side of unmodified membrane is shown by a black square. References.
1. Hernandez, A.; Calvo, J.I.; Pradanos, P.; Palacio, L.; Rodriguez, M.L.; de Saja, J.A., J. Membr. Sci. 1997, 137, 89.
2. a) Bluhm, E.A.; Bauer, E.; Chamberlain, R.M.; Abney, K.D.; Young, J.S.; Jarvinen, G.D., Langmuir, 1999, 15, 8668.; b)E.A. Bluhm, N.C. Schroeder, E.
179
Bauer, J.N. Fife, R.M. Chamberlin, K.D. Abney, J.S. Young, G.D. Jarvinen, Langmuir, 2000, 16, 7056.
3. Nanowires growth and SEM photographs were done by P. Takmakov.
APPENDIX D ELECTRIC POLARIZATION CALCULATION OF DILUTE POLAR
SOLUTIONS. FOR ARBITRARY SHAPED MOLECULES
181
Program below first reads the molecule geometry from file saved in
“Brookhaven PDB” format. Positive charges in the molecule must be marked as
francium atoms, while negative charges must be represented as boron atoms. Number
of positive and negative charges is unlimited, however program normalizes them to
the unity, thus one can create a desired distribution of charges.
Program gives a variety of data; the main features are dipole moment in the
gas phase, the solvent polarization (Em) in debyes, and total maximum dipole
moment in a particular solvent. Details of the theory can be found in chapter 2.
program IVAN implicit none
REAL :: NumberOfCarbons, NumberOfNitrogens, NumberOfHydrogens, NumberOfOxygens, NumberOfMinu, NumberofPlu, NumberOfPoints
CHARACTER(LEN=20) :: data_file ! Getting the filename
PRINT *,"Filename with extension" READ *,data_file
! Get Number of Points PRINT *,"Number of Points?" READ *,NumberOfPoints
CALL HYPER (data_file, NumberOfCarbons, NumberOfNitrogens,NumberOfHydrogens, NumberOfOxygens, NumberOfMinu, NumberofPlu, NumberOfPoints)
end program IVAN
!!!!!!!!!!!! CALCULATION OF ATOMS NUMBER !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE HYPER (data_file, NumberOfCarbons, NumberOfNitrogens, NumberOfHydrogens, NumberOfOxygens, NumberOfMinu, NumberofPlu, NumberOfPoints) implicit none
182
! Variable declaration REAL :: Col5,Col6,Col7 INTEGER :: ios CHARACTER(LEN=20), INTENT(IN) :: data_file
REAL,INTENT(OUT) :: NumberOfCarbons, NumberOfNitrogens, NumberOfHydrogens, NumberOfOxygens, NumberOfMinu, NumberofPlu
REAL,INTENT(IN) :: NumberOfPOints CHARACTER(LEN=20) :: Col1,Col2,Col4 CHARACTER(LEN=1) :: Col3 LOGICAL :: found
! Zeroing all atoms NumberOfCarbons=0 NumberOfHydrogens=0 NumberOfNitrogens=0 NumberOfOxygens=0 NumberOfPlu=0 NumberOfMinu=0
! Openning the file
OPEN (UNIT=7,FILE=data_file, STATUS="OLD",IOSTAT=ios) IF (ios/=0) THEN
PRINT '("Error number23 ",I3," during opening of ", A)',ios,data_file STOP
END IF
! REWIND TR TO THE BEGINNING OF THE FILE REWIND (UNIT=7,IOSTAT=ios) IF (ios/=0) THEN
PRINT '("Error number1 ",I3," during opening of ", A)',ios,data_file STOP
END IF ! READ FILE DO
READ (UNIT=7, FMT=*, IOSTAT=ios) Col1,Col2,Col3,Col4,Col5,Col6,Col7
! TEST ON END OF THE FILE
IF (ios<0) THEN EXIT
! TEST ON ANOTHER TYPE OF ERROR
183
END IF SELECT CASE (Col1) CASE ("CONECT") Col3="END OF FILE" CASE ("END") Col3="END OF FILE" CASE ("HETATM") SELECT CASE (Col3) CASE ("C")
NumberOfCarbons=NumberOfCarbons+1 CASE ("N") NumberOfNitrogens=NumberOfNitrogens+1 CASE ("H") NumberOfHydrogens=NumberOfHydrogens+1 CASE ("O")
NumberOfoxygens=NumberOfOxygens+1 CASE ("F") NumberOfPlu=NumberOfPlu+1 CASE ("B") NumberOfMinu=NumberOfMinu+1 END SELECT END SELECT
END DO PRINT *,"Carbons",NumberOfCarbons PRINT *,"Nitrogens",NumberOfNitrogens PRINT *,"Hydrogens",NumberOfHydrogens PRINT *,"Oxygens",NumberOfOxygens PRINT *,"Minus centers",NumberOfMinu PRINT *,"Plus centers",NumberOfPlu
CALL COORD (data_file, NumberOfCarbons, NumberOfNitrogens, NumberOfHydrogens,NumberOfOxygens,NumberOfMinu, NumberofPlu,NumberOfPoints)
END SUBROUTINE HYPER
!!!!!!!!!!!!!!!!! TAKING COORDINATES FROM FILE!!!!!!!!!!!!!!!!!!!!!! SUBROUTINE COORD (data_file,NumberOfCarbons,NumberOfNitrogens,NumberOfHydrogens,NumberOfOxygens,NumberOfMinu, NumberofPlu,NumberOfPoints) implicit none
! Variable declaration REAL,INTENT(IN) :: NumberOfPOints INTEGER :: BadPoint,Fin,RadiusSphere,test,u
184
REAL,DIMENSION(1:(NumberOfPoints+1)**3,1:3) :: Field,FieldCoord,FieldAlongDipole REAL :: Col5,Col6,Col7,werty,RadiusC,RadiusN,RadiusH,RadiusO,RadiusB,Xmin,Ymin,Zmin,Xplus,Yplus,Zplus,Dirx,Diry,Dirz,Xcentr,Ycentr,Zcentr,Increasing,x,y,z,CellSize,Distance,XFil,YFil,ZFil,RadiusFr,Sphere,GasDipole,Epsilon,a,b,Percent,Em,Phi,TotalDipole,BeforeIntegral,consta
INTEGER :: ios,q,Point CHARACTER(LEN=20), INTENT(IN) :: data_file
REAL,INTENT(IN) :: NumberOfCarbons, NumberOfNitrogens, NumberOfHydrogens, NumberOfOxygens,NumberOfMinu, NumberofPlu
CHARACTER(LEN=20) :: Col1,Col2,Col4 CHARACTER(LEN=1) :: Col3 LOGICAL :: found
! Coordinates Array REAL,DIMENSION(1:NumberOfCarbons,1:3) :: Carbon REAL,DIMENSION(1:NumberOfNitrogens,1:3) :: Nitrogen REAL,DIMENSION(1:NumberOfHydrogens,1:3) :: Hydrogen REAL,DIMENSION(1:NumberOfOxygens,1:3) :: Oxygen REAL,DIMENSION(1:NumberOfMinu,1:3) :: Minu REAL,DIMENSION(1:NumberofPlu,1:3) :: Plu INTEGER :: i,j,l,m,s,w
! VAN DER VAALS VOLUMES RadiusC=0.9 RadiusN=0.9 RadiusH=0.6 RadiusO=0.9 RadiusB=0.0 RadiusFr=0.0
! =1 all variables which are used for counting i=1 j=1 l=1 m=1 s=1 w=1 test=0
! Open File OPEN (UNIT=7,FILE=data_file, STATUS="OLD",IOSTAT=ios) IF (ios/=0) THEN
185
PRINT '("Error number23 ",I3," during opening of ", A)',ios,data_file
STOP END IF
! REWIND TR TO THE BEGINNING OF THE FILE REWIND (UNIT=7,IOSTAT=ios)
IF (ios/=0) THEN PRINT '("Error number1 ",I3," during opening of ", & A)',ios,data_file STOP END IF
! READ FILE DO
READ (UNIT=7, FMT=*, IOSTAT=ios) Col1,Col2,Col3,Col4,Col5,Col6,Col7
SELECT CASE (Col1) CASE ("CONECT") Col3="END OF FILE" CASE ("END") Col3="END OF FILE" CASE ("HETATM")
! COORDINATES TO ARRAY SELECT CASE (Col3) CASE ("C") Carbon(i,1)=Col5 Carbon(i,2)=Col6 Carbon(i,3)=Col7 i=i+1 CASE ("N") Nitrogen(j,1)=Col5 Nitrogen(j,2)=Col6 Nitrogen(j,3)=Col7 j=j+1 CASE ("H") Hydrogen(l,1)=Col5 Hydrogen(l,2)=Col6 Hydrogen(l,3)=Col7 l=l+1 CASE ("O") Oxygen(m,1)=Col5 Oxygen(m,2)=Col6 Oxygen(m,3)=Col7
186
m=m+1 CASE ("F") Plu(s,1)=Col5 Plu(s,2)=Col6 Plu(s,3)=Col7 s=s+1 CASE ("B") Minu(w,1)=Col5 Minu(w,2)=Col6 Minu(w,3)=Col7 w=w+1 END SELECT END SELECT END DO
!!!!!!!!!!!!!!SOME PRELIMINARY CALCULATION!!!!!!!!!!!!! Xmin=0 Ymin=0 Zmin=0 Xplus=0 Yplus=0 Zplus=0 Fin=1 consta=(1.601e-19)/(4*3.14*8.854e-12) ! PRINT *,consta
!!!!!!!!!!!!!!CALCULATION OF AVERAGE COORD OF + AND -!!!!!!! DO q=1,NumberOfMinu,1 Xmin=Xmin+Minu(q,1)/NumberOfMinu Ymin=Ymin+Minu(q,2)/NumberOfMinu Zmin=Zmin+Minu(q,3)/NumberOfMinu END DO DO q=1,NumberOfPlu,1 Xplus=Xplus+Plu(q,1)/NumberOfPlu Yplus=Yplus+Plu(q,2)/NumberOfPlu Zplus=Zplus+Plu(q,3)/NumberOfPlu END DO PRINT *,"Center mass (negative charge) ",Xmin,Ymin,Zmin PRINT *,"Center mass (positive charge) ",Xplus,Yplus,Zplus
!!!!!!!!!!!!!!COSINE CALCULATION!!!!!!!!!!!!!!!!!!!!!
Dirx=(-Xmin + Xplus)/Sqrt((-Xmin + Xplus)**2 + (-Ymin + Yplus)**2 + (-Zmin + Zplus)**2) Diry=(-Ymin + Yplus)/Sqrt((-Xmin + Xplus)**2 + (-Ymin + Yplus)**2 + (-Zmin + Zplus)**2)
187
Dirz=(-Zmin + Zplus)/Sqrt((-Xmin + Xplus)**2 + (-Ymin + Yplus)**2 + (-Zmin + Zplus)**2)
PRINT *,"Cosines with axies X,Y,Z ",Dirx,Diry,Dirz
!!!!!!!!!!!!!!CENTER OF DIPOLE CALCULATION!!!!!!!!!!!!!!!!
Xcentr=(Xmin+Xplus)/2 Ycentr=(Ymin+Yplus)/2 Zcentr=(Zmin+Zplus)/2 PRINT *,"Center of 'dipole' is located at",Xcentr,Ycentr,Zcentr
!!!!!!!!!!!!!Radius of the effective sphere,CellSize and increasing are calculated here!!!
RadiusSphere=Sqrt((Xcentr - Xplus)**2 + (Ycentr - Yplus)**2 + (Zcentr - Zplus)**2)+1 PRINT *,"INPUT RADIUS OF THE MOLECULE, CALCULATED ONE ~?",RadiusSphere
READ *,RadiusSphere a=RadiusSphere CellSize=RadiusSphere sphere=0 Increasing=2*CellSize/(NumberOfPoints-1) PRINT *,"'Effective' radius of the sphere'",RadiusSphere PRINT *,"Cell Size",CellSize PRINT *,"Increasing",Increasing
!!!!!!!!! MAIN CYCLES START HERE!!!!!!!!!! Point=0 x=Xcentr-CellSize DO WHILE (x<XCentr+CellSize+Increasing) y=Ycentr-CellSize DO WHILE (y<YCentr+CellSize+Increasing) z=ZCentr-CellSize DO WHILE (z<ZCentr+CellSize+Increasing) test=0
!!!!!!!!!!!!TEST ON VAN-DER-VAALS VOLUME !!!!!!!!!!!!!!! !!!!!!!!!!CARBON ATOMS !!!!!!!!!!!!!
DO q=1,NumberOfCarbons,1 Distance=Sqrt((x-Carbon(q,1))**2+(y-Carbon(q,2))**2+(z-Carbon(q,3))**2)
IF (Distance<RadiusC) THEN test=test+1
188
END IF END DO
!!!!!!!!!!NITROGEN ATOMS!!!!!!!!!!! DO q=1,NumberOfNitrogens,1
Distance=Sqrt((x-Nitrogen(q,1))**2+(y-Nitrogen(q,2))**2+(z-Nitrogen(q,3))**2)
IF (Distance<RadiusN) THEN test=test+1 END IF END DO
!!!!!!!!!HYDROGEN ATOMS!!!!!!!!!!! DO q=1,NumberOfHydrogens,1
Distance=Sqrt((x-Hydrogen(q,1))**2+(y-Hydrogen(q,2))**2+(z-Hydrogen(q,3))**2)
IF (Distance<RadiusH) THEN test=test+1 END IF END DO
!!!!!!!!!!OXYGEN ATOMS!!!!!!!!!!! DO q=1,NumberOfOxygens,1
Distance=Sqrt((x-Oxygen(q,1))**2+(y-Oxygen(q,2))**2+(z-Oxygen(q,3))**2)
IF (Distance<RadiusO) THEN test=test+1 END IF END DO
!!!!!!!!!!! "B" atom for fullerene center!!!!!!!!!!!! DO q=1,NumberOfMinu,1
Distance=Sqrt((x-Minu(q,1))**2+(y-Minu(q,2))**2+(z-Minu(q,3))**2)
IF (Distance<RadiusB) THEN test=test+1 END IF END DO
!!!!!!!!!!!!!Fr for positive centers!!!!!!!!!!!! DO q=1,NumberOfPlu,1
189
Distance=Sqrt((x-Plu(q,1))**2+(y-Plu(q,2))**2+(z-Plu(q,3))**2)
IF (Distance<RadiusFr) THEN test=test+1 END IF END DO
!!!!!!!!!! TEST IF POINT X,Y,Z IS OUTSIDE OF THE OUTER SPHERE !!!!!!!!!!!
Distance=Sqrt((x-Xcentr)**2+(y-Ycentr)**2+(z-Zcentr)**2)
IF (Distance>RadiusSphere) THEN test=test+1 u=u+1 END IF
!!!!!!!!!!!!!!!Inside Sphere!!!!!!!!!!1
Distance=Sqrt((x-Xcentr)**2+(y-Ycentr)**2+(z-Zcentr)**2)
IF (Distance<Sphere) THEN test=test+1 u=u+1 END IF XFil=0 YFil=0 ZFil=0 werty=0
!!!!!!!!!!!!FIELD CALCULATION!!!!!!!!!!!
!!!!!!!!!!! MINUS FILED CALCULATION!!!!!!!!! ! PRINT *,x,y,z IF (test==0) THEN DO q=1,NumberOfMinu,1 XFil=XFil-
((1/NumberOfMinu)*(x-Minu(q,1))/(((x-Minu(q,1))**2+(y-Minu(q,2))**2+(z-Minu(q,3))**2))**1.5)
YFil=YFil-((1/NumberOfMinu)*(y-Minu(q,2))/(((x-Minu(q,1))**2+(y-Minu(q,2))**2+(z-Minu(q,3))**2))**1.5)
ZFil=ZFil-((1/NumberOfMinu)*(z-Minu(q,3))/(((x-Minu(q,1))**2+(y-Minu(q,2))**2+(z-Minu(q,3))**2))**1.5)
END DO
190
!!!!!!!!!!!!PLUS FIELD CALCULATION!!!!!!!!!!
DO q=1,NumberOfPlu,1
XFil=XFil+((1/NumberOfPlu)*(x-Plu(q,1))/(((x-Plu(q,1))**2+(y-Plu(q,2))**2+(z-Plu(q,3))**2))**1.5)
YFil=YFil+((1/NumberOfPlu)*(y-Plu(q,2))/(((x-Plu(q,1))**2+(y-Plu(q,2))**2+(z-Plu(q,3))**2))**1.5)
ZFil=ZFil+((1/NumberOfPlu)*(z-Plu(q,3))/(((x-Plu(q,1))**2+(y-Plu(q,2))**2+(z-Plu(q,3))**2))**1.5)
END DO ELSE
BadPoint=BadPoint+1 END IF ! PRINT *,XFil,YFil,ZFil,x,y,z FieldAlongDipole(Fin,1)=(XFil*Dirx)+(YFil*Diry)+(ZFil*Dirz) Fin=Fin+1 Point=Point+1 z=z+Increasing END DO y=y+Increasing END DO
!!!!!!!!!!!! PERCENT PRINTING!!!!!!!!!!!! IF (100*(x-(Xcentr-CellSize))/(2*CellSize)-Percent>10)
THEN Percent=100*(x-(Xcentr-CellSize))/(2*CellSize) PRINT *,'Done%',Percent END IF x=x+Increasing END DO DO q=1,Fin-1,1 werty=werty+FieldAlongDipole(q,1) END DO GasDipole=Sqrt((Xmin-Xplus)**2+(Ymin-Yplus)**2+(Zmin-
Zplus)**2)*4.803 werty=werty*(Increasing)**3 PRINT *,"DIELECTRIC CONSTANT?" READ *,Epsilon
191
PRINT *,"TOTAL POINTS CALCULATED",Point,"; TOTAL NUMBER OF 'BAD' POINTS",BadPoint
PRINT *,"E Projection", werty,"e*A" BeforeIntegral=(4.8*(Epsilon-1)/(4*3.14159*Epsilon)) PRINT *,"Beforeintegral=",Beforeintegral Em=werty*BeforeIntegral PRINT *,"Em=",Em,"D" Phi=(1/a**3)*(2*(Epsilon-1))/(2*Epsilon+1) PRINT *,"Phi=",Phi," A^-3" TotalDipole=(GasDipole+Em)/(1-
(Phi*(Beforeintegral/4.8)*4*3.14159*(a**3)/3)) PRINT *,"Total=",TotalDipole,"D" PRINT *, "Inner Sphere",sphere,"Outer sphere",RadiusSphere PRINT *, "GAS DIPOLE MOMENT",GasDipole,"D" END SUBROUTINE COORD