DIPC 02/03 19

SCIENTIFICHIGHLIGHTS

Index

Understanding Biological Photoreceptors . . . . . . . . . . . . . . . . . . . . . . . . 20

Mixing One-dimensional Cold Atomic Gases . . . . . . . . . . . . . . . . . . . . . . . . 22

Role of Bulk and Surface Phonons In the Decay of Metal Surface States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Cherenkov Effect in Photonic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Interplay of Surface Plasmons and Image States . . . . . . . . . . . . . . . 28

Nonlinear Screening in Two-Dimensional Electron Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Non-gaussian Nature of the α-relaxation Of Glass-forming Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Chain Connectivity and Segmental Dynamics of Miscible Polymer Blends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Crossover from α-relaxation to Rouse Dynamics . . . . . . . . . . . . . . . . 36

Rings Dancing in the Disorder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

20 DIPC 02/03

by M.A.L. Marqués1, X. López2, D. Varsano1,3, A. Castro4,3 and A. Rubio1,3,5

We have implemented a new scheme to describe the photoresponse and

structural dynamics of bio-photoreceptors. The scheme can shed light into the initial

microscopic origin of vision, photosyntesis and bacteria luminiscence processes.

One of the most fundamental, intriguing andrelevant bio-physical process is the micro-scopic description of the photo-response ofbio-molecules. From the photosynthesis tothe human vision processes, DNA damageand bacteria bio-luminescence; those phe-nomena require an understanding of howlight is absorbed and how that energy istransfer from the photoreceptor sites to theactive biological centers. A famed organicmolecule is the azobenzene chromophore,(formed by joining two phenyl rings with theazo group) that undergoes a structuralchange (cis/trans-isomerization) under opti-cal irradiation, and it does so in a femtosec-ond time-scale. These light-induced ultrafast rotations around double bonds are at theheart of most photo-active bio-organic reac-

tions. In particular the first step of thehuman vision are related to cis/trans iso-

merization of the retinal chromophore ofrhodopsin (see figure). The induced struc-tural transformation upon light absorption isvery fast (few hundred femtoseconds;1fs=10-15s) and is associated to the presenceof ring structures in the molecule (as ben-zene or imidazoline groups).

The cited phenomena involve i) differentenergy (from covalent to van der Waalsbonding) and time scales (from fs for theelectron dynamics, to ps for the ionic motionand ms for structural reorganizations); ii)light-induced chemical reactions that areintrinsically non-adiabatic, and require tech-niques that go beyond the traditional Born-Oppenheimer separation of electronic andnuclear degrees of freedom. Therefore, thereis a clear need for a reliable theoretical frame-work to describe processes related to the

excited-state dynamics of biological com-plexes either in vacuo or in solution. In 2002we joined efforts with the theoretical quan-tum chemistry group to set up an ambitiousproject with the goal of developing a theoret-ical scheme able to predict the photo-induced dynamics in bio-molecular struc-tures. We present here the first results notic-ing that many other fascinating results arejust coming up. Our approach is based on adivide-and-conquer strategy where the activepart of the structure is fully described micro-scopically using quantum mechanicsschemes, whereas the environment (i.e., restof the protein, membrane and solvent) isdescribed using a classical molecularmechanics method (QM/MM approach). Thenovelty of our work is the simulation of thecombined electron-ion dynamics of the pho-toreceptor within the framework of time-dependent density functional theory(TDDFT). By solving a set of coupled time-dependent Schrödinger-like equations(including light sources as short laser puls-es), we identify the mechanisms active at thedifferent time-scales of the photo-process.

Understanding BiologicalPhotoreceptors

DIPC Highlight

Chromophore isomerisation is at theheart of biomolecular

photophysics.

1 Departamento de Física de Materiales, UPV/EHU, San Sebastián, 2 Departamento de Química, UPV/EHU, SanSebastián, 3 Donostia International Physics Center, San Sebastián, 4 Departamento de Física Teórica, Universidad deValladolid, Spain, 5 Centro Mixto CSIC-UPV/EHU, San Sebastián

DIPC 02/03 21

In this context, the Green FluorescentProtein (GFP) has become a unique tool inmolecular biology because of its fluorescentproperties and inertness when attached toother proteins. The optical absorption spec-trum of the wild type (wt)-GFP, measured at1.6 K, shows two main resonances at 2.63and 3.05 eV that are attributed to the twothermodynamically stable protonation statesof the chromophore (negative and neutralconfigurations, respectively). Excitation ateither frequency leads to fluorescent green-light emission, peaked at 2.44eV, which isthe main mechanism for energy release inwt-GFP. This internal photo-conversionprocess occurs very rapidly by excited-stateproton transfer for the neutral chromophore.The photo-physics of the GFP is governed bya complex equilibrium between the neutraland anionic configurations. Thus, GFP is theideal system to test our theoretical approach.First we determined the structure of the GFPand then computed the photo-absorptioncross section for visible light as it has to beproperly described before we could dream ofdescribing any dynamical process.

The GFP protein is folded in a b-sheet barrelconformation with the cromophore occupy-ing a central position inside the barrel (seefigure). The cromophore is formed by twoconsecutive rings, the phenol-type ring ofTyr66 and a five member heterocyle formedby the backbone of Tyr66, the carbonyl car-bon of Ser65 and the nitrogen of the back-bone of Gly67. The theoretical photo-absorption cross-section is compared to theexperiments in the figure (the dashed linecorresponds to the neutral chromophore, thedotted line to the anionic, whereas the greenand blue curves are the experimental resultsof S.B. Nielsen et al, PRL87, 228102 (2001)and of T.M.H. Creemers et al, PNAS 97,2974 (2001), respectively). The strength ofthe main p - p* transition is larger in theanionic than in the neutral GFP. It is, howev-er, possible to obtain a quantitative descrip-tion of the spectra of the wt-GFP by assum-ing a 4:1 ratio for the concentration of theneutral/anionic forms. This value is veryclose to the estimated experimental ratio of80% neutral and 20% anionic. Besides thegood description of experiments we noticedthat GFP is a rather anisotropic molecule inthe visible (see inset in the figure). Only lightpolarized along the pentagon-hexagonal ring

is absorbed with high yield. This propertycan be used to enhance the photo-dynamicalprocesses of GFP samples for opto-electronicdevices, e.g. depositing well oriented GFPmolecules on top of doped-semiconductorsubstrates we could get photovoltaic struc-tures with high efficiency.

We have shown that a combined QM/MM andTDDFT approach is able to reproduce theoptical response of the GFP. This is a majorstep toward the first-principles description ofexcited-state dynamic of important biologi-cal photo-receptors. Transient and time-resolved optical spectroscopy could be stud-ied. However, in spite of the good agree-ment, some questions remain open. Forexample, how does the excitation in the GFPtrigger the proton shuttle mechanism andwhat is the time-scale for this process? Toanswer these questions we have to gobeyond the present work including the excit-ed state dynamics of the environment (e.g.the proton-transfer involves structuralmodifications of the environment that haveto be properly described). Work along thisline is in progress. �

REFERENCEM.A.L. Marqués, X. López, D. Varsano, A. Castroand A. Rubio, Physical Review Letters 90,258101 (2003)

Our TDDFT approachconstitutes a majorstep towards the firstprinciples descriptionof the combined electron/ion dynamicsin bio-photoreceptors.

22 DIPC 02/03

by M.A. Cazalilla1 and A.F. Ho2,1

Just as mixing two fluids (e.g. water and oil) under certain conditions of

temperature and pressure can lead to a variety of phenomena, mixing

two types of cold atomic gases confined to one-dimension can lead to a number

of interesting quantum phenomena. This includes the usual demixing

(like the one observed at room temperature and pressure between oil and water),

collapse, or more interestingly the formation of “pairs” of atoms of different

species that are correlated over long distances.

Ever since the achievement of Bose-Einsteincondensation of a dilute gas of alkali(Rubidium) atoms in the summer of 1995,the field of cold atomic gases has madeastonishing experimental progress. The ulti-mate goal has become to learn how tomanipulate cold atomic gases to realize exot-ic phases of matter. The latter may findapplications in quantum information pro-cessing and storage. It is also expected thatthey can provide us with new and keyinsights into the physics of quantum many-body systems that may help us understandsome of the puzzling behaviour of the high-Tc copper-oxide superconductors and otherexotic materials.

One dimensional systems of cold atoms haveonly recently become available, and are veryinteresting because of the strong enhance-ment of correlations as the dimensionality ofthe system decreases. So far, most experi-ments are made with bosonic atoms (like87Rb) confined by very anisotropic potentials.However, not far in the future fermions (like6Li) will also be used. Bosons confined to onedimension (1D) are interesting per-se, asthere are not many realizations of these sys-tems in Nature (apart from spins in highlyanisotropic magnetic materials).

A single-component gas of cold bosons,when confined to 1D, will not undergo Bose-Einstein condensation since all possible fluc-tuations must propagate on a line and anykind of ordering (like Bose-Einstein conden-sation) will be strongly suppressed.However, in the finite-size systems of exper-imental interest, phase coherence can beapproximately maintained over many timesthe average atom-atom distance so that thesesystems resemble very much a Bose-EinsteinCondensate (BEC). This is why they are fre-quently called quasi-condensates. However,if the strength of the interactions isincreased, the (phase) fluctuations areenhanced and the system will not behave asa condensate anymore. This is the case as theextreme limit where no boson can pass eachother (i.e. the bosons become “hard core”) isapproached. A gas of hard-core bosons isknown in the jargon of the field as a Tonksgas, in honor of Lewi Tonks, who first dis-cussed the properties of a classical gas ofhard-core particles in 1936. Between theTonks gas limit and the quasi-condesate, thesystem exhibits a rather smooth crossover,and no new phenomena are expected.

On the other hand, when a two-component1D gas is considered (a binary mixture), the

Mixing One-dimensionalCold Atomic Gases

DIPC Highlight

The large tunability of cold atomic gases

allows to study interesting many body

phenomena.

1 Donostia International Physics Center, San Sebastián 2 School of Physics and Astronomy, University ofBirmingham, Edgbaston, U.K.

DIPC 02/03 23

resulting system exhibits a much richer andinteresting behaviour. First of all, just likewith ordinary (classical) fluids, the systemcan demix (like oil and water do at roomtemperature and pressure) if the two compo-nents repel sufficiently strongly, or it can col-lapse if they attract sufficiently strongly.However, the quantum nature of this matterleaves room for more surprises.

In 1974 two American theoretical physicistsstumbled upon a particular type of one-dimensional matter. When opposite-spinelectrons attract in a one-dimensional metalthey could form pairs. The analogy with theso-called Cooper pairs, discovered by LeonCooper in 1957, and which eventuallywould be instrumental for understanding themechanism of superconductivity in conven-tional superconductors (like lead or alu-minum), was unavoidable. However, asLuther and Emery cleverly pointed out, fluc-tuations would never allow the electron-pairs to condense (as Cooper pairs do insuperconductors), and therefore establish amacroscopic phase coherence throughoutthe system. That is why the system wouldexhibit a gap only to spin excitations andwould remain gapless for charge excitations.In contrast, in higher dimensional materialscondensation of Cooper pairs opens a gap toall excitations, both spin and charge, andonly in neutral systems (like in Helium 3)one can have a gapless collective modeknown as the Anderson-Bogoliubov mode.All in all, the model was the closest thing toa higher dimensional superconductor thatone can get in one dimension, and it goesunder the name of Luther-Emery liquid.

Remarkably, we found that the phenomenondiscovered by Luther and Emery can alsotake place in a binary mixture of two coldatomic gases. In our letter, we studied twotypes of these systems, depending on the sta-tistics of the components. Thus if the twocomponents are bosonic, we termed the mix-ture of B+B type, whereas it one of the com-

ponents is a boson and the other is a fermi-on, we termed it of B+F type. We found thatif the bosons of the same type repel eachother very strongly, i.e. if they are driven intothe Tonks gas regime, and provided thenumber of particles of each species and thevelocity are equal and different speciesattract, they could form the same type ofpairs that Luther and Emery found for a one-dimensional metal where electrons attracteach other.

In a mixture of a boson and a fermion, thishas interesting consequences, the pair (the“composite fermion”) will behave as a fermi-on and therefore carries a finite momentumwhich is of the order of the Fermi momen-tum. This is somewhat analogous to the con-densation of Cooper pairs at finite momen-tum that takes place in certain superconduc-tors under the influence of a strong magnet-ic field (the so-called Fulde-Ferrell-Larkin-Ovchinnikov state). However, the analogycannot be pushed too far, because in contrastto the latter systems, the composite fermionswould never condense even in higherdimensions due to their statistics. In 1Dhowever, for sufficiently strong attractionbetween the boson and the fermion, the gasof composite fermions would still acquiresome superfluid properties. �

REFERENCEM. A. Cazalilla and A. F. Ho, Physical ReviewLetters 91, 150403 (2003)

We have found an exotic phase where atoms of two differencespecies pair up in astrongly correlatedcold atomic gas confined to move in one dimension

Schematic phase diagram with the boson(s) in the Tonks limit. |ρ01- ρ02| is the density difference

24 DIPC 02/03

by A. Eiguren1, B. Hellsing2, F. Reinert3, G. Nicolay3, E. V. Chulkov1,4, V. M. Silkin4, S. Hüfner3 and P. M. Echenique1,4

Understanding the temporal evolution of quasiparticles (electron and holes) on metal

surfaces is of paramount importance to describe many important phenomena such as the

dynamics of charge and energy transfer, quantum interference, and localization. Typically,

the quantity used to characterize this temporal evolution is the lifetime, which refers to the

time the quasiparticle retains its identity. It is the interaction of the quasiparticle with the

metal (electrons, phonons...) what makes the lifetime finite. We present the first micro-

scopic analysis of the electron-phonon mechanism and find that its contribution, together

with the electron-electron mechanism, is crucial in order to understand the experimental

lifetime of the sp surface state on Cu (111) and Ag (111).

The sp surface state in the L-gap of the(111)-surface of noble metals forms a two-dimensional (2D) electron gas and the elec-tron-electron (e-e) contribution to the holelifetime has been rationalized in terms of adominant contribution from intrabandtransitions within the 2D surface stateband, screened by the underlying 3D bulkelectron system, and in terms of interbandtransitions (bulk states → surface state)(Science, 288, 1399 (2000)). However, anappropriate calculation of the electron-phonon (e-p) contribution to the lifetimebroadening of surface states has not beendone yet. Many properties of metals, suchas resistivity, specific heat, and supercon-ductivity, reflect the importance of the e-pinteraction. The strength of this e-p cou-pling is usually measured in terms of aparameter λ that depends on the energyand momentum involved in the processunder consideration. We have presented atheoretical analysis of the e-p contribution

to the lifetime broadening of surface elec-tron states, taking into account all electronand phonon states involved in the e-p scat-tering process. The theoretical analysis isbased on a calculation of the full Eliashbergspectral function, which enables us toresolve, in detail, the contributions fromdifferent phonon modes, as well as, thegeneral temperature dependence. Includingthe e-e interaction, our theoretical resultsare compared with new energy and temper-ature dependent high-resolution photoe-mission data.

In Fig.1 the calculated temperature depen-dent e-p contribution (solid lines) to thelifetime broadening Γ together with e-e con-tribution Γee (dotted lines) is compared withthe measured temperature dependence of Γ(circles) for Cu (111) and Ag (111). Theinsert shows the measured energy distribu-tion curves for Cu (111) for selected tem-peratures.

Role of Bulk and SurfacePhonons in the Decay ofMetal Surface States

DIPC Highlight

Electron-phonon interaction gives

important contribution to electron (hole)

dynamics on metal surfaces and

controls temperaturedependence of this

dynamics.

1 Departamento de Física de Materiales and Centro Mixto CSIC-UPV/EHU, San Sebastián 2 Department of Physics,Chalmers University of Technology and Göteborg University, Sweden 3 Fachrichtung Experimentalphysik, Universitätdes Saarlandes, Saarbrücken, Germany 4 Donostia International Physics Center, San Sebastián

DIPC 02/03 25

In Fig.2 the calculated Γep (red lines) as wellas Γee+ Γep (black lines) are shown for Cu(111) and Ag (111) together with the exper-imental results (diamonds) as a function ofenergy at T=30K. As follows from Fig. 2, thecontribution from only the Rayleigh mode(blue lines) gives about 40% of Γep beyondthe maximum phonon frequencies, indicat-ing that bulk phonons give most of the con-tributions in this range. But for bindingenergies below the maximum of theRayleigh mode energy, this mode alone rep-resent on average about the 85% of Γep.

Detailed comparison of the theoreticalresults with photoemission data (this workand Phys. Rev. B 63, 115415 (2001)) aswell as with scanning tunnelling spec-troscopy results (Science, 288, 1399(2000)) shows an excellent agreementbetween the theory and experiments thatopens new perspectives in investigations ofdynamical processes on clean metal sur-faces as well as on surfaces with adatomsand adlayers at different temperatures. �

REFERENCEA. Eiguren, B. Hellsing, F. Reinert, G. Nicolay, E.V. Chulkov, V. M. Silkin, S. Hüfner and P. M.Echenique, Physical Review Letters 88, 066805(2002)

Surface phonon modes are crucially important for the description of electron dynamicson surfaces.

Fig.1. Temperature dependence of the lifetime of the sp surface state

Fig. 2. Lifetime broadening of the electron state depending on its binding energy

26 DIPC 02/03

by F. J. García de Abajo1, A.G. Pattantyus-Abraham2, N. Zabala1,3, A. Rivacoba1,4, M.O. Wolf 2, and P. M. Echenique1,4

Like the wake produced by a boat moving faster than surface waves in a quiet

lake, fast electrons moving faster than light in a dielectric produce the so-called

Cherenkov radiation, which leads ultimately to stopping of the projectiles.

This effect has been observed for electrons traversing photonic crystals, where light

is subject to a periodically modulated dielectric constant and allowed to propagate

within so-called photon bands, similar to electronic bands in solids. The electrons lose

energy to produce photons with probability proportional to the local density of the

photonic states at the position of the electron beam. This permits us to map photonic

bands by observing the energy and angle distribution of the transmitted electrons.

Light can be slowed in matter so thatcharges traveling faster that it may losepart of their energy to produced a cone ofCherenkov light emission, similar to thewake of a boat moving faster than surfacewaves in water. The same phenomenoncan take place if the charges move inside aphotonic crystal, where light is subject topropagation only along certain directionsfor given frequencies, and the resultinglight emission must reflect the complexi-ties of the photonic band structure inthese materials.

Our group, working in collaboration withDr. Andras Pattantyus and Dr. MichaelWolf of the University of British Columbia(Canada), have managed to prove thiseffect by observing energy losses in fastelectrons transmitted through poresdrilled in 1-micron thick alumina films.The transmitted electrons exhibited amarked tendency to lose energy in the 7-8.5 eV region, depending on the velocityof the electrons and in good agreementwith calculations of light emission proba-

Cherenkov Effect inPhotonic Crystals

DIPC Highlight

Cherenkov light canreflect how photons

propagate in photonic crystals.

Fig. 1. Cherenkov losses in a photonic crystal

1 Centro Mixto CSIC-UPV/EHU and Donostia International Physics Center, San Sebastián 2 Department of Chemistry,University of British Columbia, Vancouver, Canada 3 Departamento de Electricidad y Electrónica, UPV/EHU Bilbao,Spain 4 Departamento de Física de Materiales, UPV/EHU, San Sebastián

DIPC 02/03 27

bility, which is more pronounced at thoseenergies. The electrons were made to passthrough the holes without actually touch-ing the material, and the fact that aluminais transparent across distances of severalmicrons at those photon energies led theresearchers to conclude that the observedenergy losses must arise from Cherenkovlight emission. More precisely, Fig. 1shows a transmission electron microscopeimage of a porous alumina film (a), aschematic view of one of the holes show-ing the electron trajectory (b), and the dis-tribution of electrons as a function of theenergy that they have lost (c), theory(symbols) compared with experiment(curve), with clear evidence of theCherenkov effect (7 eV peak).

Unlike Cherenkov emission in a homoge-neous medium, the restriction imposed bya 2D patterning of holes in the aluminafilms limited this emission to within theabovementioned energies. Further analysisof the bending in the trajectory of the elec-trons can provide a basis for direct map-ping of photonic bands by fast electrons,theory suggets (see Physical Review Letters

Photonic bands are mapped by energy and angle distributions of fast electrons transmitted through photonic crystals.

Fig. 2. Mapping photonic bands with fast electrons

91, 143902, 2003), as shown in Fig. 2, thatdepicts a schematic diagram of a two-dimensional crystal made of cylindricalholes, along with its first Brillouin zone(a), the band structure of this crystal andits variation with light momentum parallelto the cylinders q (b), and a cut of thebands along the ω=qv plane (c). Electronsmoving with velocity v along the cylinderscan only sense photonic states that satisfythis condition. The underlying densityplot in (c) shows the probability that theelectrons lose a certain amount of energyw with their trajectory is deflected by agiven momentum within the first Brillouinzone. �

REFERENCEF. J. García de Abajo, A. G. Pattantyus-Abraham,N. Zabala, A. Rivacoba, M. O. Wolf, and P. M.Echenique, Physical Review Letters 91, 143902(2003)

28 DIPC 02/03

by A. García-Lekue1, J.M. Pitarke1,2, E.V. Chulkov2,3, A. Liebsch4 and P.M. Echenique2,3

Our investigations on the combined effect of single-particle and collective surface

excitations in the decay of image-potential states on Ag surfaces provide new insight to

elucidate the origin of the long-standing discrepancy between experimental measure-

ments and previous theoretical predictions for the lifetime of these states. Although sur-

face-plasmon excitation had been expected to reduce the image-state lifetime, we have

demonstrated that the subtle combination of the spatial variation of s-d polarization in Ag

and the characteristic non-locality of many-electron interactions near the surface yields

surprisingly long image-state lifetimes, in agreement with experiment.

Fundamental concepts in condensed matterphysics are those of surface plasmons andimage states. Surface plasmons, which arequanta of collective oscillations of electronsat metal surfaces, crop up in a number ofscenarios from electron energy loss to thecolourful appearance of suspensions of smallmetallic particles, surface-plasmon reso-nance technology, and a wide range of pho-tonic applications. Image states are quan-tized electronic states that are observed out-side certain metal surfaces due to the attrac-tive image potential that occurs between theelectron and the solid. Image states dynam-ics provides insight into the investigation ofthe coupling of excited surface electronicstates with the underlying substrate. Thiscoupling of these states with the underlyingsubstrate is known to govern the cross sec-tions and branching ratios of practically allelectronically induced adsorbate reactions atmetal surfaces.

In most metals, there is no interplay betweensurface plasmons and image states, which isdue to the fact that the surface-plasmonenergy is typically too large for image statesto couple with them. In silver, however, thepresence of occupied narrow bands of d elec-trons considerably reduces the surface-plas-mon energy, and the relaxation of imagestates via the creation of surface collectiveexcitations becomes feasible in this material.

The broadening (and therefore finite life-time) of the first (n=1) image state at the Γpoint on the Ag(100) surface mainly origi-nates in processes in which the image-stateelectron with an energy of 3.9 eV above theFermi level decays into an empty state withenergy still above the Fermi energy. Theseprocesses can be realized by transferringenergy and momentum to an excitation ofthe medium, thereby creating either an elec-tron-hole pair or a collective surface excita-tion of energy smaller than 3.9 eV. The ener-gy of surface plasmons in Ag is 3.7 eV.

The inelastic broadening of excited states insolids can be obtained from the projection(over the excited state wavefunction) of theimaginary part of the so-called electron self-energy of many-body theory, which accountsfor the many-body interactions in the solid.Following this formalism, we have investi-gated the decay of the Ag (100) n=1 imagestate by treating Auger-like single-particleand collective surface excitations on the samefooting. A consistent treatment of these decaychannels is particularly important because ofthe near-degeneracy of the image state ener-gy with the Ag (100) surface plasmon.

The surprising and novel result of our workis that, although the imaginary part of theimage-state self-energy is enhanced due tothe presence of the plasmon decay channel,interferences resulting from the non-locality

Interplay of SurfacePlasmons and Image States

DIPC Highlight

The coupling of excitedstates with the solid

governs the cross sections and branching

ratios of practically allelectronically induced

adsorbate reactions atmetal surfaces.

1 Departamento de Física de Materia Condensada, UPV/EHU, Bilbao, Spain 2 Centro Mixto CSIC-UPV/EHU and Donostia International Physics Center, San Sebastián 3 Departamento de Física de Materiales, UPV/EHU,San Sebastián 4 Institut für Festkörperforschung, Forschungszentrum Jülich, Germany

of the self-energy lead to a smaller overallimage-state broadening, in agreement withexperiment. This elucidates the origin of thelong-standing discrepancy between experi-mental measurements and previous theoreti-cal predictions for the lifetime of these states.

First-principles descriptions of electrondynamics in the bulk of noble metals showthat deviations from electron dynamics in agas of sp electrons mainly originate in theparticipation of d electrons in the screeningof electron-electron interactions. Hence, inorder to avoid the use of too-expensive abinitio techniques at the noble metal surfaceAg (100), the approach we have undertakenis based on (i) the use of a physically moti-vated one-dimensional potential which accu-rately accounts for the dynamics of spvalence electrons, and (ii) the replacement ofoccupied d bands in Ag by a polarizablemedium giving rise to additional screening.We emphasize that our approach provides acoherent treatment of single-particle and col-lective surface excitations.

The n=1 image-state wave function on Ag(100) (dotted line in the figure, where z isthe coordinate normal to the surface) has amaximum at a few angstroms outside thecrystal edge (z=0), which we choose to belocated half a lattice spacing beyond the lastatomic layer. The solid line in the figureshows the imaginary part of the n=1 image-state self-energy (this nonlocal quantity Im[-Σ]couples the coordinates z and z') versus z fora fixed value of z' outside the solid (red cir-cle). We note that the main peak of Im[-Σ]

does not occur at z=z', as would be the casein the interior of the solid; instead, it lagsbehind and remains localized near the sur-face where the image-state wave function isnegative. Consequently, there is a majorinterference contribution to the projection ofIm[-Σ] over the image-state wave function,which is negative and yields a large reduc-tion of the image-state broadening.

The role that the screening of d electronsplays lowering the surface-plasmon energy,and therefore opening a new coupling ofimage states with the solid, is particularlypronounced on the vacuum side of the sur-face, where negative interference dominates.Hence, the combined effect of decay via sur-face plasmons and nonlocality of the self-energy is a considerably reduced lifetimebroadening. While in the absence of d elec-trons the broadening of the n=1 image stateon Ag (100) would be 18 meV, our theory(with d electrons and surface-plasmon decayincluded) yields a broadening of 12 meV(i.e., a lifetime of 55x10-15s) in excellentagreement with recently reported time-resolved two-photon photoemission (TR-2PPE) measurements. �

REFERENCEA. García-Lekue, J. M. Pitarke, E. V. Chulkov, A.Liebsch, and P. M. Echenique, Physical ReviewLetters 89, 096401 (2003)

Despite the enhancementof the image-state self-energy in Ag due tothe decay via surface plasmons, the highly nonlocal character of the self-energy in the surface region ultimatelyleads to a surprisinglysmall lifetime broadening,in agreement with experiment.

Energetic diagram of the decay of the first Ag (100) image state

Wave function and imaginary part of the n=1 image state self-energy

DIPC 02/03 29

30 DIPC 02/03

by E. Zaremba1,2, I. Nagy3,2, and P.M. Echenique4

A charged impurity or projectile inmersed in a metal induces the rearrangement

of the electrons around it, providing the total screening of the charge. Typically,

the impurity represents such a strong perturbation that a nonlinear screening theory is

needed to account for the modifications of the local electronic structure. The possible

realization of quasi-two-dimensional systems in a variety of contexts (semiconductor

heterostructures, electrons on the surface of liquid helium, layered materials...),

has led us to study the screening of a point charge in a two-dimensional electron gas

using a density functional method. In marked contrast to the three-dimensional case,

we find that the screened potential for a proton supports a bound state even in the

high-density limit.

Today condensed matter physics is by far thelargest field of physics. It is concerned withthe study of solids. A subtle task consideringthe huge number of particles one has to dealwith (a mollar quantity of a solid contains asmany as 1023 atoms). Different theories havebeen developed in finding approximations tohandle this problem. Among them, moderndensity-functional theory (DFT) makes twokinds of contribution to the science of mul-tiparticle quantum systems. The first is in thearea of fundamental understanding, since DFTfocuses on quantities in the real coordinatespace, principally on the electron densityn(r). This quantity, similarly to the exchange-correlation hole density, is physical andtransparent. Their understanding provides acomplementary insight into the nature ofmultiparticle systems. The second contribu-tion is practical. The theory leads to self-con-sistent field equations, similar to the Hartreeequations, in which the effects due to theinterparticle Coulomb interaction and the

Pauli exclusion principle are included byaddition of the exchange-correlation potential.

The capability of this practical mappingbetween the real, interacting many-electronsystem and an idealized system of noninter-acting electrons moving in an effective sin-gle-particle potential, still remained as a non-trivial question for reduced dimensions. Thepossible realization of two-dimensional (2D)electron systems in a variety of context (semi-conductor heterostructures, image or band-gap surface states at metal surfaces, and lay-ered materials) confirms the relevance of thisquestion. In all these cases, the interaction ofexternal charges with the two-dimensionalelectron gas (2DEG) is a problem of bothfundamental and practical interest. Experi-mentally, the powerful scanning tunnelingmicroscopy offers a direct means of deter-mining the modulated electron densitythrough the observation of induced Friedeloscillations. Furthermore, transport of elec-

Nonlinear Screening inTwo-Dimensional ElectronGases

DIPC Highlight

In the high density limit,the screening density in a two-dimensional

electron gas is simply pro-portional to the

perturbing potential.

1 Department of Physics, Queen’s University, Kingston, Ontario, Canada 2 Donostia International PhysicsCenter, San Sebastián 3 Department of Theoretical Physics, Technical University of Budapest, Hungary 4 Departamento de Física de Materiales and Centro Mixto CSIC-UPV/EHU, San Sebastián

DIPC 02/03 31

trons is often limited in real matter by impu-rity scattering and, thus, a detailed knowledgeof the scattering potential is also needed. All these reasons motivated us to investigatewithin the context of DFT, the nonlinearscreening of a point charge, Z, located in theplane of a 2DEG.

As is the case in 3D, the screening potentialof a negatively charged impurity (an antipro-ton, for instance) repels electrons almostcompletely from the charge, leaving exposedthe positive background of the metal, whichneutralizes the impurity. This repulsion,however, is not enough to create an attractivepotential sufficiently strong to bind an elec-tron, as was suggested in a linear treatmentof the screening.

The results for a positive impurity are quitedifferent. In marked contrast to the situationin 3D, we find that the screened potential fora proton supports a bound state even in thehigh-density limit. This result would invali-date the applicability of perturbation theoryin this limit. We prove, however, that theresults of linear theory are in fact correcteven though bound states exist. These resultsfind application in a variety of problems,such as charged impurity scattering and thestopping power of charged projectiles, wealso calculated. �

REFERENCE“Nonlinear Screening in Two-Dimensional ElectronGases”, E. Zaremba, I. Nagy, and P.M. Echenique,Physical Review Letters 90, 046801 (2003)

In a two-dimensional electron gas, a proton canbind two electrons even in the high density limit.

Fig. 1. Nonlinear (solid) and linear (chain) screened potentials for an antiproton

Fig. 2. Bound state eigenvalue for a proton as a function ofthe 2D electron gas density

Figure 1: Fs(Q,t) measured on PI at 340 K. Solid lines:fits with Eq. (1). Inset: master curve giving the

Q-dependence of τwβ built with results from six different

polymers (see legend), applying polymer-dependentnormalising factors (tp). Solid line: Gaussian behaviour.

32 DIPC 02/03

by J. Colmenero1,2,3, A. Arbe2, F. Alvarez1,2, M. Monkenbusch4, D. Richter4, B. Farago5 and B. Frick5

Molecular dynamics (MD) simulations on glass forming systems of very dif-

ferent nature (Selenium, ortotherphenyl, water,…) have shown a series of “uni-

versal features” for the non-Gaussian parameter α2(t) corresponding to the self-

motion of the atoms in the α-relaxation regime. A combination of MD-simula-

tions and neutron scattering on polyisoprene has allowed us to establish that

the above mentioned “universal features“ of α2(t) can also be found in glass-

forming polymers, and are nicely captured by a simple anomalous jump diffu-

sion model with a distribution of jump lengths.

One of the most intriguing problems in con-densed matter physics is the glass transitionphenomenon, caused by the freezing of thestructural (α) relaxation in a glass-formingsystem. Therefore, the understanding of themolecular motions during this relaxation isof utmost importance to shed some light onthe glass formation process. Neutron scatter-ing (NS) and Molecular Dynamics (MD) sim-ulations are essential for this goal. Duringlast years, extensive NS investigations of theincoherent scattering function Fs(Q,t) haveestablished a universal behaviour for the self-atomic motions in the α-relaxation regime ofglass forming systems including polymers.As Figure 1 evidences, Fs(Q,t) shows astretched exponential functional form char-acterized by the exponent β:

Fs(Q,t) ∝ exp[-(t/τw)β] (1)with a characteristic time τw that clearlydepends on Q, τw(Q). This observation impliesthe diffusive nature of the atomic motions inthis regime. Further-more, in the Q-regimeapprox. 0.2 ≤ Q ≤ 1.5 Å-1 the Q-dependenceof τw in polymers can be described as τw(Q)∝ Q-2/β (inset of Fig. 1), implying a Gaussianform of Fs(Q,t) with negligible values for thenon-Gaussian parameter α2(t).

This is in apparent contradiction to resultsfrom MD-simulations on glass forming systemsother than polymers. There, α2(t) shows amaximum that increases with decreasingtemperature and shifts according to the ther-mal behaviour of the structural relaxationtime. Thus the question arises: Do glassforming polymers behave in a different way?To answer this question we decided to take atwofold approach: we performed fully atom-

Non-gaussian Nature ofthe α-relaxation ofGlass-forming Systems*

DIPC Highlight

How do atoms move during the

structural relaxation?Key to understand

the glass transition!

1 Departamento de Física de Materiales UPV/EHU, San Sebastián 2 Unidad de Física de Materiales CSIC-UPV/EHU,San Sebastián 3 Donostia International Physics Center, San Sebastián 4 Institut für Festkörperforschung,Forschungszentrum Jülich, Germany 5 Institut Laue-Langevin, Grenoble, France

DIPC 02/03 33

istic MD-simulations and NS measurementson the same polymer, polyisoprene (PI) [1].Figure 2 shows the obtained Q-dependenceof τw. An impressive agreement is foundbetween both kinds of results, validating theMD-simulations. The data univocally con-firm the Gaussian-like behaviour in the Q-range approx. Q ≤ 1 Å-1, while clear signa-tures of deviations become evident at higherQ-values.Having established confidence on the real-ism of our MD-simulations, we can takeadvantage of them and compute magnitudesthat are not easily experimentally accessible,like α2(t) and the mean squared displace-ment <r2(t)> of the main chain protons. Theyare shown in Fig. 3(a), while Fig. 3(b) dis-plays the calculated Fs(Q,t) for several Q-val-ues. As reported for the other glass-formingsystems, a main maximum is indeed foundfor α2(t) at t*≈ 4ps, just in the early stages ofthe decaging process identified with the α-relaxation. The shadowed area in Fig. 3shows the region where α2(t) takes signifi-cant values. For low Q-values this area onlycovers the initial part of the slow decay (α-regime) of Fs(Q,t). However, as Q increases,the marked time range starts to cover almostcompletely the slow decay. This naturallyexplains the finding of the deviations fromGaussian behaviour of Fs(Q,t) at high Q-values.What could be the origin of such deviations?The way the characteristic time departs fromthe Gaussian expectation (Fig. 2) stronglyreminds us on the very well known manifes-

We find polymer behavior similar to other glass formingsystems

Non-Gaussian behaviorseems to reflect thediscrete nature of themotions underlying thestructural relaxation

Figure 2: Master curve constructed combining NSand MD-simulations results for PI. T-dependent shiftfactors aT have been applied. Dashed line: Gaussian

prediction; solid line: description in terms of theanomalous jump diffusion model with the distribution

of jump lengths shown in the inset.

Figure 3: MD-simulations results for PI: (a) Timeevolution of <r2(t)> (�) and α2(t) (•). Solid line:

anomalous jump diffusion model prediction for α2(t).(b) Fs(Q,t). Solid lines: fits with Eq. (1) (t ≥ 5 ps).

The shadowed area covers the time range of the full-width at half-maximum of the main peak of α2.

tations of the discrete nature of diffusion insimple jump diffusion models. Basing on thissimilarity, we have proposed a model thatconsiders a distribution of elementary jumplengths underlying the anomalous diffusionundergone by the atoms in the α-process [1].Such an extremely simple approach allows avery accurate description of the Q-depen-dence of τw (Fig. 2). The associated distribu-tion of jump lengths ƒ(λ) (inset of Fig. 2)shows a maximum at about 0.4 Å. Thismodel also semiquantitatively reproduces thebehaviour of α2(t) [see Fig. 3(a)], within itsrange of validity (above 1 ps approximately)[1]. It is finally noteworthy that the main“universal features” reported in the literaturefor α2(t) are also naturally deduced in thisapproach [1]. This suggests that the essenceof the universal deviations from Gaussianbehaviour in the self-motions of atoms dur-ing the structural relaxation regime lies in thedistribution of discrete steplengths underly-ing the anomalous diffusion. �

*An extended version of this paper has also beenrecently published in the MODELLING section ofthe Scientific Highlights of the 2003 ANNUALREPORT of the Institut Laue-Langevin (ILL),Grenoble (France)

REFERENCE

[1] A. Arbe, J. Colmenero, F. Alvarez, M.Monkenbusch, D. Richter, B. Farago and B. Frick,Physical Review Letters 89 (2002) 245701; Phys.Rev. E 67 (2003) 51802

Figure 1: Schematic representation of the length scale dependence of the effective concentration.

34 DIPC 02/03

by E. Leroy3, A. Alegría1,2 and J. Colmenero1,2,3

We have experimentally demonstrated the ability of the effective

concentration concept to quantitatively predict the component dynamics

in three model miscible polymer blends.

Polymer materials, usually referred to asplastics, are found everywhere in the normallife. A route used to obtain new polymermaterials is by combining already existingpolymers, which allows tuning the desiredproperties of the resulting material. Amongthe broad range of multicomponent polymermaterials, a family of both, fundamental andtechnological interest is that of the binarymiscible polymer blends. These systems arehomogeneous mixtures of macromolecularchains of two types. However, they presentwhat is referred to as dynamical heterogene-ity, i.e., the motions of the segments of thetwo polymer components occur with signifi-cantly different time scales. A way to under-stand the dynamic heterogeneity of misciblepolymer blends is to consider the chain con-

nectivity effects. In a miscible polymer blendA/B, the chain connectivity imposes that thelocal environment of a segment for instanceof polymer A is (on average) necessarily rich-er in this component as compared to thebulk mean composition . Thus, the moreflexible component of the blend will movefaster than the more rigid one despite thesystem is miscible. To account quantitativelyfor this effect, the concept of effective localconcentration has been introduced. The effec-tive local concentration sensed by a polymercomponent, can formally be expressed as:

eff= S+(1- S) eq.1being S the so called “self-concentration” ofthe polymer segment considered. Obviously,the value of eff depends on the consideredlength scale, approaching unity for veryshort length scales and the average concen-tration, , for large length scales (see figure1). Recently, it has been proposed that therelevant length scale for the polymer seg-mental dynamics (the molecular motionsresponsible of the glass transition phenome-non) is the Kuhn length (lK), defined as thelength along the chain contour that makesthe orientation of a given chain bond to beindependent of the orientation of the chainbond at the origin. On the basis of thisassumption S can be calculated as the con-centration of monomers of a given chaincomponent within a volume V~lK

3 centeredin a segment of the same chain.

The existence of two different segmentaldynamics in a miscible blend would implythe presence of two distinctive glass transi-tion processes — and therefore they should

Chain Connectivity andSegmental Dynamics ofMiscible Polymer Blends

DIPC Highlight

Polymer blending is a convenient way for obtaining new

materials with tailor made properties.

1 Departamento de Física de Materiales UPV/EHU, San Sebastián 2 Unidad de Física de Materiales CSIC-UPV/EHU,San Sebastián 3 Donostia International Physics Center, San Sebastián

DIPC 02/03 35

depict two glass transition temperatures, Tg-each associated to one of the two polymercomponents. The way that has been pro-posed to calculate these effective glass transi-tion temperatures Tgeff( ) for each compo-nent in the blend is to use the concentrationdependence of the macroscopic (average)glass transition temperature Tg( ), as mea-sured in a standard differential scanningcalorimetric (DSC) experiment, according tothe following relationship:

Tgeff( )=Tg( eff) eq.2Dielectric measurements on miscible poly-mer blends can be used to investigate selec-tively a single component if the other doesnot contribute to the dielectric relaxationprocess. Taking advantage of this capability,in this work[1] we have tested in a quantita-tive way the accuracy of the effective con-centration approach above described toaccount for the dynamical heterogeneity ofmiscible polymer blends.Three model miscible blends have beenstudied by combining DSC and ThermallyStimulated Depolarization Current (TSDC).This second technique can be considered asa dielectric sensitive equivalent of DSC and itallows determining the glass transition tem-perature sensed by the dielectrically activesegments present in the polymer blend. Thethree blend systems studied take profit ofthis selectivity. In poly(vinyl methylether)/polystyrene (PVME/PS), only the lowerTg component (PVME) is dielectrically active.In polystyrene/poly-o-chlorostyrene (PS/PoClS),PoClS is the dielectrically active and thehighest Tg component. Finally, in PVME/PoClSboth components are dielectrically active butwith a very high Tg difference, which shouldallow to resolve the corresponding dielectriccontributions. DSC measurements showed asingle heat capacity step for all blends, con-firming their miscibility. Some typical TSDCmeasurements are illustrated in figures 2. Itis apparent that whereas for pure PVME bothtechniques provide essentially the samevalue of Tg, for the PVME/PS blends the TSDCpeak maximum occurs at a temperature sig-nificantly different (lower) than the calori-metric Tg, (middle point of the heat capacitystep). The glass transition temperaturesobtained for the PVME/PoClS blends usingboth DSC and TSDC data are plotted onfigure 3. To have a quantitative test of the“effective concentration” approach, for each

blend system, we first fitted the concentra-tion dependence of the bulk glass transitiontemperature measured by DSC. In a secondstep, we calculated the corresponding valuesof Tgeff of the dielectrically active componentaccording to eq 2. A remarkably good quan-titative agreement between the experimentalvalues and the calculated Tgeff curves can beobserved for all measured blends (see Fig. 3).This result demonstrates the ability of theeffective concentration approach to accountquantitatively for the dynamical heterogene-ity of miscible polymer blends. Furthermore,this good agreement pointed out to lk as therelevant length scale for the glass transitionphenomenon in polymers, i.e. a fewnanometers, which is much shorter than thatcommonly assumed. �

REFERENCE

[1] E. Leroy, A. Alegría, and J. ColmeneroMacromolecules 35, 5587 (2002)

Figure 3: Concentration dependence of the macroscopicand effective glass transition temperatures on

PVME/PoClS blends. The lines for the effective glass transition temperatures of the two components

(solid lines) were obtained from that of the macroscopicTg( ) (dotted line) using eq. 2.

Figure 2: Determination of the glass transition temperatures. DSC: macroscopic Tg and TSDC: Tgeff

of the dielectrically active component.

Two different segmentaldynamics would implytwo distinctive glasstransition temperatures.

Dielectric techniquesallow us to investigateselectively the dynamicsof a single component in blend systems.

The effective concentration concept captures quantitatively the dynamical heterogeneity of miscible polymer blends.

Neutron Spin Echogives the answer: It is!

Figure 1. Schain(Q,t). Solid lines: prediction of the Rouse model.

36 DIPC 02/03

by A. Arbe1, J. Colmenero1,2,3, D. Richter4, M. Monkenbusch4, L. Willner4, B. Farago5

We report on a large experimental effort exploring the dynamics of poly(vinyl

ethylene) on length scales covering Rouse dynamics and below. The results establish for

the first time the simultaneous existence of a generic sublinear diffusion regime which

underlies the α-process in addition to the Rouse process. Both regimes are separated by

a well defined dynamic cross over. From that the size of the Gaussian blobs making up

the Rouse model is determined directly. The glassy dynamics is identified as subdiffusive

motions occurring within these Gaussian blobs.

Polymers show at the same time the generalproperties of glass forming systems — withthe α-relaxation as the most relevant dynam-ical process —and features arising from theirchain-like nature— the chain motions aredescribed by the Rouse model, that treats thedynamics of a Gaussian chain (beads andsprings) in a heat bath.For a large number of polymers, neutronscattering studies performed at time scalesclose to the structural relaxation time ts andin the Q-range 0.2 Å-1 ≤ Q approx. have

shown that the protons perform sublineardiffusion with a mean-square displacement(msd) <r2(t)> ~ tβ (β: stretching exponent,0.4 ≤ β ≤ 0.6) [1]. This behavior is similarto that predicted by the Rouse model (<r2(t)>~ t0.5). On the other hand, molecular dynam-ics (MD) simulations [2] and Mode CouplingTheory (MCT) calculations [3] on coarse-grained polymer models (bead and springmodels) show the existence of a subdiffusiveregime (<r2(t)> ~ tx, x ≈ 0.5-0.6) after theplateau reflecting the “cage effect”. Thisregime was related to the Rouse dynamics ofpolymer chains. Furthermore, also quasielas-tic neutron scattering experiments on glassforming polymers taken at high Q wereinterpreted in terms of Rouse motion [4].However, in real polymers the preconditionof Gaussian beads can only be fulfilled onlarger scales. The question thus arises: is itpossible to experimentally clarify the inde-pendent existence of a generic dynamicregime of sublinear diffusion associated withthe α-process aside the Rouse process?We have performed Neutron Spin Echo(NSE) measurements on the single chaindynamic structure factor Schain(Q,t), relatedto the collective segment motion within onechain, and the self correlation functionSself(Q,t), originated from the proton selfmotion, for poly(vinyl ethylene) (PVE). The

Crossover from α-relaxation to RouseDynamics

DIPC Highlight

Is it possible to experimentally clarify

the independent existence of a generic

dynamic regime of sublinear diffusion

associated with the αα-process aside the

Rouse process?

1 Departamento de Física de Materiales UPV/EHU, San Sebastián 2 Unidad de Física de Materiales CSIC-UPV/EHU,San Sebastián 3 Donostia International Physics Center, San Sebastián 4 Institut für Festkörperforschung,Forschungszentrum Jülich, Germany 5 Institut Laue-Langevin, Grenoble, France

DIPC 02/03 37

instruments used were IN15 (ILL) and theNSE spectrometer at the FRJ-2 (Jülich). For afirst time we have been able to distinguishclearly two separated dynamic regimes ofsublinear diffusion [5].Figure 1 compares the experimental Schain(Q,t)with the Rouse prediction. For small Q thedata follow well the theory. Thus, in this Q-range the particles within the chain per-form sublinear diffusion: <r2(t)> ~ t0.5.However, at the highest Q’s investigated (Q >QR = 0.11 Å-1) severe deviations are evident(see the figure). Turning to Sself(Q,t) (Figure 2(a)), we canproof the existence of a second Gaussiansubdiffusive regime at short length scales bythe construction of a Q-independent msd[Figure 2(b)] for Q ≥ 0.20 Å-1. This follows<r2(t)> ∝ t0.5 (solid line). Thus, for t < tR =τw

Rouse(QR) ≈ 100 ns the data reveal a subdif-fusive regime which is obviously distinctfrom the Rouse process. This regime isindeed that relevant for the α-relaxation:both, τs as well as the time a proton moves asfar as the average intermolecular distance d,lie in this region (see the figure) [5]. For t ≥tR, the mean squared displacements followsthe Rouse prediction <r2(t)>Rouse.The cross over between the Rouse- and thesubdiffusive α-regime becomes most clear ifwe focus on the Q-dependent characteristicrelaxation times (Figure 3). The two regimesare separated by a step at Qc ≈ 0.13 Å-1. Across over length scale lc ≈ π/Qc = 24 Å maybe obtained, that would be identified withthe size of a Gaussian blob underlying theRouse model. For PVE this corresponds toabout ten monomers or twenty bonds. Theα-process evolves then from the motion of

the atoms within the polymer which are sub-ject to specific intra- and inter-molecularforces. The coarse grained MD-simulationsand MCT calculations based on bead andspring models [2,3] do not reveal this α-regime, since it appears to relate to the inter-nal dynamics within the Gaussian blobs. �

REFERENCES

[1] Colmenero, J; Alegría, A; Arbe, A; Frick, B.Physical Review Letters 1992, 69, 478.[2] Binder, K; Baschnagel, J; Paul, W. Prog.Polym. Sci. 2003, 28, 115.[3] Chong, S.H; Fuchs, M. Physical ReviewLetters 2002, 88, 185702.[4] Allen, G; Higgins, J.S; Macounachie A;Ghosh, R.E. Chem. Soc. Faraday Trans. II 1982,78, 2117.[5] Richter, D; Monkenbusch, M; Willner, L;Arbe, A; Colmenero, J; Farago, B. EurophysicsLetters 2004, 66, 239.

A cross over length scale lc ≈ 24 Å (≈ tenmonomers) defines the size of a Gaussianblob underlying theRouse motion. The αα-process relates to the internal dynamicswithin the blobs.

Figure 3. τwQ4 from Sself(Q,t) (full squares) and deduced from Schain(Q,t).

Figure 2. (a) Sself(Q,t). Solid lines: KWW fits (Aexp[-(t/τw)β]) with β=0.5. (b) Protons msd obtained from the curves in (a) for Q > QR.

Figure 1. PSF monomer. The chain continues in the blue ends.

38 DIPC 02/03

by S. Arrese-Igor1, A. Arbe2, J. Colmenero1,2,3, A. Alegría1,2 and B. Frick4

By means of quasielastic neutron scattering we have studied the phenylene rings’

dynamics in the engineering thermoplastic polysulfone in the glassy state. The wide

dynamic range covered has allowed us to identify the simultaneous occurrence of fast

oscillations and π-flips. A model combining these two motions nicely describes the results

in the whole dynamic range investigated. The structural disorder characteristic of the

amorphous state leads to broad distributions of characteristic times.

Have you ever realized the importance ofplastics in your daily life? Look around. Youcan find them in your computer, printer, furniture, car,...everywhere. This is becausethey are durable, light, cheap, and their goodmechanical and thermal properties makethem suitable for a huge number of applica-tions. Engineering thermoplastics like poly-carbonate or polysulfone have for these rea-sons a salient important technological signif-icance. Their interesting ultimate mechanicalproperties are probably related to the abilityof these polymers to accommodate a stresswith highly activated molecular motions, inthese cases likely involving π-flips of theirphenylene rings. That is why considerableefforts have been made to identify the mole-cular origin of the so called secondary relax-ations in polymers. Though the existence ofthese processes and their main general fea-tures are established for many decades, theirmicroscopic origin remains elusive. This isdue to the fact that they have traditionallybeen studied by relaxation techniques likeMechanic (MS) and Dielectric (DS) Spec-troscopy that do not provide microscopicinformation and space resolution. On theother hand, the few existing NeutronScattering (NS) studies on the molecularmotions behind the secondary relaxations inpolymers have been performed close orabove the glass transition temperature Tg,where the main α-relaxation is also active.

Here we have exploited NS capabilities fordeciphering the microscopic motions under-gone by polysulfone phenylene rings deep inthe glassy state with a twofold aim: con-tribute to the fundamental question aboutthe origin of secondary relaxations in poly-mers and provide useful information for fur-ther design of plastics with tailor mademechanical properties.

The measurements were performed at theInstitute Laue-Langevin (ILL) on polysulfone(Tg = 460 K) with deuterated methyl groups(Figure 1), covering the micro- (≈ 0.1 ps to20 ps) and mesoscopic (≈ 100 ps to 1 ns)timescales. The spatial resolution of NS tech-niques has been exploited to identify thenature of the dynamical processes detected.The geometry of the motions involving

Rings Dancing in The Disorder*

DIPC Highlight

Understanding the molecular motions

underlying secondaryrelaxations in polymers

can help to design materials with tailor

made properties.

1 Departamento de Física de Materiales UPV/EHU, San Sebastián 2 Unidad de Física de Materiales CSIC-UPV/EHU,San Sebastián 3 Donostia International Physics Center, San Sebastián 4 Institut Laue-Langevin, Grenoble, France

DIPC 02/03 39

phenylene rings can be envisaged throughthe Q-dependence of the scattered intensi-ties. As commented above, a movement thatis suspected to occur is a π-flip of the pheny-lene ring. Then the motion of the aromatichydrogens would correspond to a jump overtwo equivalent positions separated by 4.3 Å,leading to a maximum in the quasielasticintensity at about 1 Å-1. Is this expectationrealized in our experiments? Look at Figure2. For the highest temperatures investigated,the motion observed in the mesoscopic win-dow indeed corresponds to such a flip.However, on the other extreme, the lowesttemperatures showing relaxational featureson the microscopic window display a com-pletely different Q-modulation, that wouldreflect a much more restricted motion inspace (amplitudes of ≈ 1.5 Å). This dynami-cal process might be interpreted as pheny-lene ring small angle oscillations around themain chain axis, and clearly dominates in themicroscopic window. However, with increas-ing temperature contributions of the π-flipsalso appear there (see the clear “bump” at450 K). In a similar way, at mesoscopic scalesthe high Q-intensity resolved at T ≤ 300 Kindicates the contribution of the small ampli-tude motions. Thus, both processes con-tribute to both windows. A global descrip-tion considering the two motions is neces-sary to reproduce the experimental results inthe full dynamic range investigated.

A model considering statistically indepen-dent π-flips and small angle oscillations forphenylene ring motion [1] allows a nicedescription of the experimental observa-tions. Reflecting the effect of disorder in

these relaxation mechanisms, broad distribu-tions of activations energies have to beinvoked (Figure 3). They are originated bythe packing heterogeneity characteristic forthe amorphous nature of polymers. Themean activation energy value obtained forthe flips, ≈ 0.43 eV, agrees well with thatfound by spectroscopic techniques in similarsystems for the secondary γ-relaxation—responsible for the good mechanical proper-ties. On the other hand, the oscillationsshow an amplitude that increases with tem-perature and a mean activation energy, about0.2 eV, close to that determined for methylgroup rotations by NMR and the δ-relaxationby MS. In the proposed scenario, the appar-ent activation energy for flips would repre-sent a real potential barrier over which thephenylene ring jumps. In contrast, oscilla-tions would take place – probably correlatedwith other fast motions with small associatedspatial scales like methyl group rotations —as a result of rapid fluctuations of the singleparticle potential seen by the phenylene ring,and produced by the surrounding atoms. Inthis case, the apparent activation energy foroscillations would only reflect the character-istic time of such fluctuations.�

*An extended version of this paper has also beenrecently published in the SOFT MATTER sectionof the Scientific Highlights of the 2003 ANNUALREPORT of the Institut Laue-Langevin (ILL),Grenoble (France)

REFERENCES

[1] S. Arrese-Igor, A. Arbe, A. Alegría, J. Colmenero and B. Frick, J. Chem. Phys. 120,423 (2004)

Disorder leads to broad distributionsof barriers

Neutron scatteringallows to identify two kinds of motion for phenylene rings

The microscopicmotions here unveiledseem to be responsiblefor the secondaryrelaxations observedby spectroscopic techniques

Figure 2: Q-dependence of the magnitudes reflecting the geometry of themotion in the mesoscopic (a) and microscopic (b) timescales. Lines indicate the

expectation for jumps of the aromatic protons between two equivalent posi-tions separated a distance d= 4.3 Å (dashed lines) and d= 1.5 Å (solid lines).

Figure 3: Activation energy distributions forthe flip and oscillatory motion.