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Determination of the macroscopic optical properties for composite materials

M Makowska-Janusik1 J-F Benard1 2

1Institute of Physics Jan Długosz University Al Armii Krajowej 13-15 42-200 Częstochowa Poland e-mail mmakowskaajdczestpl 2Laboratoire de Physique de lrsquoEtat Condenseacute- UMR CNRS 6087 F-72085 Le Mans Cedex 9 France e-mail Jifebngmailfr

Abstract The effect of polymeric matrix on the linear and nonlinear optical (NLO) property of disperse red (DR1) molecule embedded into poly(methyl methacrylate) (PMMA) is discussed The performed study is devoted to the simulations of the molecular polarizabilitities α and β(2ωωω) in vacuum and in polymer using local field approach The structure of the investigated system has been modeled by molecular dynamic simulations applying molecular mechanic CVFF force field method The obtained structural data are typical of amorphous structure Investigations of radial distribution function prove that location of chromophores in polymeric matrix is an intrinsic property of polymer The motion of polymer chain allows a rotation of dopants under influence of an external electric field The averaged modeled structural data were taken into account to compute the changes of chromophores optical properties affected by environment Quantum chemical time-dependent density functional theory (TDDFT) calculations of the first-order nonlinear optical properties were performed The local electric field computed using point dipole moment approach is significant however the obtained results show a small effect of PMMA on linear optical property of DR1 The effect of local electric field is more pronounced for the first hyperpolarizability PMMA matrix is appropriate for DR1 as host polymer because of high stability of beck relaxation but not good from electronic intra-molecular interaction which cancels NLO property of chromophore

1 Introduction Nonlinear optical (NLO) material can be regarded as being composed of a large number of polarizable molecules embedded in polymeric matrix The way to obtain a large and persistent second harmonic generation (SHG) effect is to dope an amorphous polymer with organic donor-acceptor molecules and to induce a polar orientation by an electric field at temperatures where the matrix is sufficiently mobile to allow fast alignment of the dopant molecules ie above its glass transition temperature Tg The most applicable polymeric matrixes are polymers with high thermal stability and optical transparency [1] Same guest molecules may be covalently bonded to the polymer chain and the other ones are only embedded into polymeric matrix Non-covalently bonded guest-host materials may be attractive if they are suitable to keep alignment of chromophores The experimental explanation of origin of the NLO response of composite materials is very difficult because optical susceptibilities are measured in condensed matter where the molecular properties are affected by the host matrix It is impossible to separate the physical properties of components Molecular simulations can help to explain the nature of the guest-host interaction and separate the different contribution of the material to the optical output signal Molecular modeling methods have been applied in an effort to understand the poling process on a microscopic level in these types of

XIII International Seminar on Physics and Chemistry of Solids IOP PublishingJournal of Physics Conference Series 79 (2007) 012030 doi1010881742-6596791012030

ccopy 2007 IOP Publishing Ltd 1

materials [2-4] A goal of many theoretical works is to find appropriate model describing optical properties of molecules incorporated in polymeric matrix and in consequence to find the most appropriate host material for particularly chosen chromophores In the presented work linear and nonlinear optical susceptibilities of guest-host polymer system are calculated using structures simulated by molecular dynamics methods Disperse red 1 (2-[4-(4-nitrophenylazo)-phenyl]- ethylamino-ethanol) push-pull chromophore (DR1) incorporated into poly(methyl methacrylate) (PMMA) matrix were chosen The DR1 together with its derivatives has long been investigated as an optical nonlinear dopant in polymers [5] solgel silica matrixes [6] and organic-inorganic hybrid materials [7] The electrical properties of the DR1 chromophores are computed with density functional theory (DFT) The second-order susceptibilities corresponding to second harmonic generation (SHG) are calculated using a local field approach The local field approximation modified to take partial poling order into consideration should be the most consistent with the experimental results The charge distribution leads to a new formulation of the discrete local-field model The optical response especially NLO output signal of chromophores embedded into polymeric matrix depends on their local environment 2 Theoretical approach In present work classical molecular dynamics was employed to model the behavior of the chromophores embedded into polymeric matrix under the application of an external electric field The fully atomistic simulations were performed to build the guest-host systems and then the quantum chemical calculations were used to study their linear and nonlinear optical properties Computations were execute on host-guest polymer system consisting of a poly(methyl methacrylate) (PMMA) matrix as host doped with disperse red 1 (2-[4-(4-nitrophenylazo)-phenyl]- ethylamino-ethanol) (DR1) molecules The chemical structures of used molecules are drawn in the Figure 1 The molecular dynamic simulations of host-guest system have been carried out in order to understand the mobility of polymer during process of alignment of chromophores and in order to predict the structure of system A goal of work is explanation of an influence of polymeric matrix on optical properties of embedded dopants

Figure 1 Schematic representation of the PMMA (a) and the structure of the investigated chromophore DR1(b)

21 Molecular dynamic simulations In this section are presented the details of the molecular dynamic (MD) simulations parameters used for all considered structures Molecular dynamics calculations were performed using the consistent valence force-field (CVFF) [89] This force field is devised for organic polymers and small molecules The MD simulations were performed using the GROMACS [10] program package with force field parameters as used in works [24] The potential energy was calculated using the terms

( )fieldnonbondooptorsionanglebond VVVVVVV +++++= (1)

CH 3O

O C

C H 3

H 2 C n

PMMA

NO2

NN

NCH3CH3

a) b)


2

where Vbond is the potential energy of bond stretching Vangle is the potential energy of the angle bending interactions Vtorsion is the potential energy of the torsional interactions Voop is the potential energy of the out of plane interactions and Vnonbond encompasses both non-bonded van der Waals and Coulomb interactions For both van der Waals and Coulomb interactions the cut-off distance was equal to half the length of one side of the simulated cubic unit cell Optionally for the poling stage of the calculation the potential energy of the external electric field Vfield was taken into account Three initial equivalent structures of PMMADR1 system were generated using Hyper-Chem program [11] Each created unit cell was cubic with an edge length appropriate to obtain density 090 gcm3 what corresponds to the liquid state of chosen polymeric system When the simulated cooling process was applied the size of unit cell decreases up to density 120 gcm3 what corresponds to the glassy state of investigated systems The unit cell of the investigated system consist one isotactic PMMA 90-mer with molecular weight 901258 amu and two molecules of DR1 The initial configurations of the investigated guest-host structure were optimized applying the conjugate gradient energy minimization method employing a convergence criterion of 10kcal mol-1Aring-1 The geometry-optimized structures were relaxed for 2 ns under NVT conditions (constant number of atoms constant volume and constant temperature of simulations) at 500 K to obtain equilibrated structures The relaxed structures were used for the proper MD simulations During MD simulations the external electric field was applied to align chromophores Then the system was cooled using simulated annealing up to final temperature 300 K when the density reached value equal to 120 gcm3 It was simulated in NPT ensemble (constant number of atoms constant pressure and constant temperature of simulations) under influence of external electric field Then the external electric field was removed and the system was simulated in NVT condition during 15 ns to check its stability The time step of simulation was 1 fs The neighbor list was updated each step The energies coordinates and velocities were recorded every one picosecond The partial charges employed on the molecules were calculated using ab initio method with the standard 6-31G basis set The geometries of the considered molecules were optimized in vacuum using the same basis set The charges applied for the monomer of PMMA are presented in work [2] 21 Quantum Chemical Computations Before the electronic properties calculation the structural optimization of the considered guest DR1 molecule in vacuum was performed Their geometry was optimized at restricted Hartree-Fock (RHF) level [12] with the standard 6-31G basis set in C1 symmetry The GAMESS program package [13] was used for these computations Then each molecule was rotated to align its static dipole moment along Z-axis The molecular polarizabilitities α and β of the investigated chromophores were calculated within an approach of time dependent density functional perturbation theory (TDDFPT) utilizing Amsterdam Density Functional (ADF) [14] program with ADF-RESPONSE module [15] The exchange-correlation (xc) functional potential was chosen in a form of Becke [16] for the exchange part and in the form of Perdew [17] for the correlation part The ADF uses Slater-type orbitals (STOs) and in present work have been chosen all-electron doubly polarized valence triple-ζ basis set (TZ2P) [18] 3 Results and discussion The investigated guest-host system was build using MD to investigate its structure stability and redistribution of chromophores in polymeric matrix The location of DR1 molecule in PMMA was studied by calculations of intermolecular radial distribution function (RDF) The center of mass (COM) of the nitro group and the dimethylamino group of chromophore were considered For the PMMA monomer the COMs of three following groups were used COO (carbonyl group) bCH3 (methyl group bonded to the backbone R-carbon atom) and sCH3 (said-chain methyl group bonded to COO) The RDF distance between different groups were calculated for each snapshot and for each of three equivalents investigated structures of PMMADR1


3

Figure 2 Partial radial distribution function between the center of mass of sCH3 group of PMMA and dimethylamino group of DR1 at 500 K (black line) and 300 K (blue line) The obtained RDFs are typical for amorphous structures We have found that the RDFs of poled structures in the liquid state are similar to those of the unpoled ones The external electric field does not affect partial intermolecular RDF The smallest distance between PMMA matrix and chromophores is present between COMs of sCH3 group of polymer and COMs dimethylamino group of DR1 (Figure 2) and is equal to 04 nm

The same value is noticed for the distance between COMs of nitro group of DR1 and methyl side groups of polymer The RDF data presented for the PMMA polymeric matrix and different kind of organic chromophores [41920] as well as inorganic ones [20] give similar results Investigated chromophores embedded into PMMA matrix are always located at 04 nm form polymer The distance between different dopants and polymer does not depend on a kind of chromophores It is the polymeric intrinsic property Distance between polymer and chromophore does not change during phase transition of the system For the liquid and solid state of the investigated guest-host system the free volume around dopand stay the same The faster rotation of chromophores is achieved by the higher motion of the side groups of polymer The mobility of polymeric group allows the rotation of chromophores The mobility of the polymer can be characterized based on the torsional autocorrelation function (TACF) which is defined in work [21] In the Figure 3 the torsional autocorrelation function of side-chain mobility of the PMMA polymer doped by DR1 is presented One can clearly see that the mobility of side-chain groups of polymer in liquid state is mach higher than its mobility in solid state system as it was expected Compare to the results presented in work [4] the mobility of polymer depends from the dopant The mobility of side-chain polymeric groups of PMMADR1 liquid state system is higher then for PMMADMANS structure It has significant influence on the dopant alignment results The external field-induced reorientation of the DR1 molecules was investigated by computing cos θ(t) where θ(t) is the time-dependent angle between the static dipole moment of the chromophore and the external electric field The degree of alignment depends on the electric field strength (see Figure 4) The appropriate alignment of DR1 molecules in PMMA polymeric matrix may be obtained using external electric field with intensity 5 kVmicrom The used intensity is much less then the one applied for PMMADMANS system [4] This is due to the much higher mobility of polymeric side-chain groups in PMMADR1 system than for PMMADMANS It proves the theory that the mobility of polymer allowed a rotation of dopants embedded into matrix It is crucial parameter of alignment efficiency The external electric field with intensity equal to 5 kVmicrom was used to align chromophores at 500K and then to solidified system using simulated annealing method described particularly in [422] To investigate an influence of polymeric matrix on linear and nonlinear optical property of DR1 molecule two stages of quantum chemical calculations were performed First the electronic property of isolated molecule was computed and second using the structure obtained by MD simulations the environmental effect was taken into account The best will be to calculate the optical parameters for the λ=2πχω=106 microm It is known that DFT theory decreases HOMO-LUMO energy gap splitting

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(∆EHOMO-LUMO) and we where obliged to take the excitation length of light appropriate for the computed energy gap (∆EHOMO-LUMOlt2ω) which was equal to 166 eV In this case excitation wave length was taken equal to 746 nm In Table 1 the results of the computed optical polarizability and hyperpolarizability of the isolated DR1 molecule are presented Applying local field theory linear and nonlinear macroscopic susceptibilities are related to molecular properties by local field factors which describe the effect of environment one the electronic properties of dopants To take into account the finite size and shape of the molecules a model developed in Ref [23] was applied In the present work the local electric field was calculated in the center of mass of DR1 molecule applying point dipole theory

Figure 3 Torsional autocorrelation function of side-chain mobility of the PMMA polymer doped by DR1 in liquid (solid line) and solid (dashed) state

Figure 4 Average value of the dipole moment vector of DR1 along the field direction (z-axis) for electric field poled and unpoled structures

Table 1 Optical polarizability and hyperpolarizability of DR1 computed by DFT for the isolated molecule and applying the local field approach

Optical property Isolated molecule [au] Molecule in PMMA [au] α (0)av α(ω)av α(2ω)av

32347 34159 44944

31584 33166 41723

β(0)z 15721 13332 β(2ω)z 44692 33829

The local electric field calculated using the method described above is equal to Fx Fy Fz = 104 -004 -049 GVm The absolute field value is rather small compared with values computed for crystal such as urea in dipolar approximation (7 GVm) [24] but is higher than for PMMADMANS system and can be compared with PMMADPDADNB [25] Very important is that obtained local electric field in direction of dipole moment of the chromophore (Fz) has opposite turn In this case used polymeric matrix decreases the value of polarizabilities The local field effect on linear optical property of DR1 is in the range of 2-7 and it may be omitted during quantum chemical calculations (see Table 1) because it is within the bounds of the error The pronounced change is seen for the NLO property of dopant applying local field effect (about 15 for the static β(0)z and 24 for β(2ω)z) Only the z-

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component was chosen for the analysis because the dipole moment of the molecule was aligned in the z-axes direction and the laser beam was polarized along z-direction 4 Conclusions In this work the optical and NLO properties of the DR1 molecules incorporated into PMMA polymeric matrix were studied The distance between dopants and the polymer depends on the kind of polymer The considered host-guest system permits the conclusion that the location of the chromophore in PMMA matrix is an intrinsic property of a polymer and is not affected by the dopants The optical properties of the system were calculated in the approach of the local field theory The local field effect is much more pronounced for the SHG susceptibility than for the linear optical properties The PMMA matrix cancel the NLO property of DR1 The alignment stability of PMMADR1 is very important Acknowledgement The presented work was realized with financial support of Polish Ministry of Science and Higher Education in the frame of project N202 068 311876 References [1] Man H T and Yoon H N Adv Mater 4 159-168 [2] Kim W K and Hayden L M Fully atomistic modeling of an electric field poled guest-host

nonlinear optical polymer J Chem Phys 111 5212-5222 [3] Robinson B H and Dalton L R Monte carlo statistical mechanical simulations of the

competition of intermolecular electrostatic and poling-field interactions in defining macroscopic electro-optic activity for organic chromophorepolymer materials J Phys Chem A 104 4785-4795

[4] Makowska-Janusik M Reis H Papadopoulos M G Economou I G and Zacharopoulos N Molecular dynamics simulations of electric field poled nonlinear optical chromophores incorporated in a polymer matrix J Phys Chem B 108 588-596

[5] Bohm N Matemy A Kiefer W Steins H Muller M M and Schottner G 1996 Macromolecules 29 2599

[6] Marino I G Bersani D Lottici P P 2000 Opt Mater 15 175 Marino I G Bersani D and Lottici P P 2001 Opt Mater 15 279

[7] Hou Z J Liu L Y Xu L Xu Z L Wang W C and Li F M 1999 Chem Mater 11 3177 [8] Hagler A T Huler E and Lifson S Energy functions for peptides and proteins I Derivation

of a consistent force field including the hydrogen bond for amide crystals J Am Chem Soc 96 5319-5327

[9] Kitson D H and Hagler A T Theoretical studies of the structure and molecular dynamics of a peptide crystal Biochem 27 5246-5257

[10] Berendsen H J C Spoel D J and Drunen R Gromacs A message-passing parallel molecular dynamics implementation Comp Phys Comm 91 43-56 Lindahl E Hess B and Spoel D J Gromacs 30 A package for molecular simulation and trajectory analysis J Mol Model 7(8) 306-317 Spoel D J Buuren A R Apol E Tieleman P J Sijbers A L T M Hess B Feenstra K A Lindahl E Drunen R and Berendsen H J C Gromacs-user manual Department of Biophysical Chemistry University of Groningen Groningen Germany 2002

[11] HyperChemreg Computational Chemistry Publication HC50-00-03-00 October 1996 Hypercube Inc

[12] Almlof J Faegri Jr K and Korsell K K 1982 J Comp Chem 3 385 [13] Schmidt M W Baldridge K K Boatz J A Elbert S T Gordon M S Jensen J H Koseki S

Matsunaga N Nguyen K A Su S J Windus T L Dupuis M and Montgomery J A 1993 J Comput Chem 14 1347

[14] Velde G and EJ Baerends 1998 J Comput Phys 99 84 Gisbergen S J A Snijders J G and Baerends E J 1999 J Comp Phys 118 119 Baerends E J Berces A Bo C Boerribter P M Cavallo L Deng L Dickson R M Ellis D E Fan L Fisher T H Fonseca Guerra C Gisbergen S J A Groeneveld J A Gritsenko O V Harris F E Hoek P Jacobsen H Kessel G Kootstra F Lenthe Om V P Relasesinga Philipsen P H T Post D Pye C C Ravenek W Ros P Schipper P R T Schreckenbach G Snijders J G Sola M Swerhone D Velde G Vernooijs P Versluis L Visser O Wezenbeek E Wiesenekker G Wolff S K Woo T K and Ziegler T ADF Program System Release 200401


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[15] Gisbergen S J A Snijders J G and Berends E J 1999 Comput Phys 118 119 [16] Becke A D 1988 Phys Rev A 38 3098 [17] Perdew J P Density functional approximation for the correlation energy of the

inhomogeneous electron gas 1986 Phys Rev B 33 8822 [18] J Dunning 1971 J Chem Phys 55 716 KG Dyall 2002 Journal Theor Chem Acc 108

335 erratum 2003 Theor Chem Acc 109 284 [19] Makowska-Janusik M Kassiba A Failleau G and Boucleacute J Interface effects on the NLO

properties of guest-host materials 2006 Materials Science 24 891-900 [20] Makowska-Janusik M Influence of the Polymeric Matrix on the NLO Molecular Response in

Guest-Host Materials 2007 Nonlinear Optics Quantum Optics 37 75-85 [21] van der Spoel D and Berendsen H J C 1997 Biophys J 72 2032 [22] Makowska-Janusik M Reis H Papadopoulos M G and Economou I G Peculiarities of electric

field alignment of nonlinear optical chromophores incorporated into thin film polymer matrix 2005 Theor Chem Acc 114 153-158

[23] Luty T 1976 Chem Phys Lett 44 335 Reis H Papadopoulos M G Calaminici P Jug K and Koster A M 2000 Chem Phys 261 359 Bounds P J and Munn R W 1981 Chem Phys 59 47

[24] Reis H Papadopoulos M G and Munn R W (1998) J Chem Phys 109 6828 [25] Reis H Makowska-Janusik M and Papadopoulos M G Nonlinear optical susceptibilities of

poled guest-host systems a computational approach 2004 J Phys Chem B 108 8931-8940


7

Determination of the macroscopic optical properties for composite materials

M Makowska-Janusik1 J-F Benard1 2

1Institute of Physics Jan Długosz University Al Armii Krajowej 13-15 42-200 Częstochowa Poland e-mail mmakowskaajdczestpl 2Laboratoire de Physique de lrsquoEtat Condenseacute- UMR CNRS 6087 F-72085 Le Mans Cedex 9 France e-mail Jifebngmailfr

Abstract The effect of polymeric matrix on the linear and nonlinear optical (NLO) property of disperse red (DR1) molecule embedded into poly(methyl methacrylate) (PMMA) is discussed The performed study is devoted to the simulations of the molecular polarizabilitities α and β(2ωωω) in vacuum and in polymer using local field approach The structure of the investigated system has been modeled by molecular dynamic simulations applying molecular mechanic CVFF force field method The obtained structural data are typical of amorphous structure Investigations of radial distribution function prove that location of chromophores in polymeric matrix is an intrinsic property of polymer The motion of polymer chain allows a rotation of dopants under influence of an external electric field The averaged modeled structural data were taken into account to compute the changes of chromophores optical properties affected by environment Quantum chemical time-dependent density functional theory (TDDFT) calculations of the first-order nonlinear optical properties were performed The local electric field computed using point dipole moment approach is significant however the obtained results show a small effect of PMMA on linear optical property of DR1 The effect of local electric field is more pronounced for the first hyperpolarizability PMMA matrix is appropriate for DR1 as host polymer because of high stability of beck relaxation but not good from electronic intra-molecular interaction which cancels NLO property of chromophore

1 Introduction Nonlinear optical (NLO) material can be regarded as being composed of a large number of polarizable molecules embedded in polymeric matrix The way to obtain a large and persistent second harmonic generation (SHG) effect is to dope an amorphous polymer with organic donor-acceptor molecules and to induce a polar orientation by an electric field at temperatures where the matrix is sufficiently mobile to allow fast alignment of the dopant molecules ie above its glass transition temperature Tg The most applicable polymeric matrixes are polymers with high thermal stability and optical transparency [1] Same guest molecules may be covalently bonded to the polymer chain and the other ones are only embedded into polymeric matrix Non-covalently bonded guest-host materials may be attractive if they are suitable to keep alignment of chromophores The experimental explanation of origin of the NLO response of composite materials is very difficult because optical susceptibilities are measured in condensed matter where the molecular properties are affected by the host matrix It is impossible to separate the physical properties of components Molecular simulations can help to explain the nature of the guest-host interaction and separate the different contribution of the material to the optical output signal Molecular modeling methods have been applied in an effort to understand the poling process on a microscopic level in these types of


ccopy 2007 IOP Publishing Ltd 1





CH 3O

O C

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NO2

NN

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a) b)


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determination of the macroscopic optical properties for - iopscience

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