Light scattering by longitudinal acoustic modes in molecular supercooled liquids I: phenomenological approach

We derive expressions for the intensity of the Brillouin polarized spectrum of a molecular liquid formed of axially symmetric molecules. These expressions take into account both the molecular dielectric anisotropy and the modulation of the local polarisability by density fluctuations. They also incorporate all the retardation effects which occur in such liquids. We show that the spectrum splits into a q-independent rotational contribution and q-dependent term, which reflects the propagation of longitudinal acoustic modes. In the latter, the two light scattering mechanisms enter on an equal footing and generate three scattering channels. We study the influence of the two new channels and show that they may substantially modify the Brillouin line-shape when the relaxation time of the supercooled liquid and the period of the acoustic excitation are of the same order of magnitude. Received 14 August 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: franosch@hmi.de     

On the theory of light scattering in molecular liquids

The theory of light scattering for a system of linear molecules with anisotropic polarizabilities is considered. As a starting point for our theory, we express the result of a scattering experiment in VV and VH symmetry as dynamic correlation functions of tensorial densities ρ _lm(q) with l = 0 and l = 2. l, m denote indices of spherical harmonics. To account for all observed hydrodynamic singularities, a generalization of the theory of Schilling and Scheidsteger [1] for these correlation functions is presented, which is capable to describe the light scattering experiments from the liquid regime to the glassy state. As a microscopic theory it fulfills all sum rules contrary to previous phenomenological theories. We emphasize the importance of the helicity index m for the microscopic theory by showing, that only the existence of m = 1 components lead to the well known Rytov dip in liquids and to the appearance of transversal sound waves in VH symmetry in the deeply supercooled liquid and the glass. Exact expressions for the phenomenological frequency dependent rotation translation coupling coefficients of previous theories are derived. Received 3 July 2000 and Received in final form 7 November 2000     

Light scattering by transverse waves in supercooled liquids and application to metatoluidine

We discuss the hydrodynamic equations which describe the shear dynamics of a liquid composed of anisotropic molecules, both in its normal and its supercooled phases. We use these equations to analyze 90 depolarized light scattering experiments performed in the supercooled phase of a glass forming liquid, metatoluidine, and show that the information extracted from this analysis is consistent with independent shear viscosity measurements performed on that liquid in the same temperature range. Received 28 April 1998     

Elastic anomalies and orientational glass transition in Na(CN) Cl mixed crystals. A Brillouin spectroscopic study

High performance Brillouin spectroscopy (BS) has been used to study the elastic properties (static and dynamic) of the orientational glassy state of Na(CN)_xCl_1-x samples ). The temperature behaviour of the elastic properties reveals a more complex scenario for the orientational glass transition than generally believed. The shear elastic constant shows the well-known c ₄₄ ( T ) anomaly, indicated by a minimum, found in other cyanide mixed crystals. The results obtained for the hypersonic attenuation are in clear contradiction with the dynamic character of the c ₄₄ ( T )-minimum. The temperature behaviour of the longitudinal elastic constant c₁₁ of very dilute Na(CN)_xCl_1-x samples shows two striking features: i) Similar to the anomalous temperature behaviour of c ₄₄ ( T ), lowering the temperature c ₁₁ ( T ) first decreases, goes through a minimum and then rises again. The minimum takes place at a temperature above the temperature, , where c ₄₄ ( T ) reaches its minimum value. ii) A kink-like anomaly of c ₁₁ ( T ) is observed at lower temperatures. This second anomaly is similar to the classical one observed in canonical glasses at their glass transition temperature . Received 8 April 1999 and Received in final form 3 June 1999     

Pressure and temperature variation of the depolarized light scattering spectra of the fragile glass-former liquid salol

The pressure and temperature dependences of the depolarized light scattering spectra of salol have been measured at isobaric condition P = 1 bar for T between 328 and 393 K, and at isothermal condition T = 343 K for P between 1 and 625 bar, i.e. outside the metastable liquid region. The experimental results for both the α- and β-relaxations can be well described by the Mode Coupling Theory. The independence of the power-law parameters a, and consequently b and γ, from the thermodynamic variables T and P is demonstrated.The critical temperature T _c at 1 bar and the critical pressure P _c at T = 343 K have been determined from the normal liquid state. Received 2 May 2000     

Brillouin scattering study of transverse elastic waves in the α, incommensurate and β phases of AlPO4

Transverse and pseudo-transverse elastic waves have been studied in several scattering geometries in order to investigate the temperature dependences of C E ₆₆ and C E ₁₄ over the range 300-1100 K, including the transitions near 860 K. These results complete those on C E ₄₄ we have obtained in a previous work. All these constants display discontinuities at the lock-in transition. In the phase, the results are analysed in term of lowest order couplings between strains (e) and the order parameter (Q). The main features are described by the lowest order biquadratic e2Q2 coupling, in particular for C E ₄₄ in a large temperature range. However, it appears that a contribution of the next coupling term arises for C E ₆₆ below K and that the first two lowest order terms have to be taken into account even just below the lock-in transition in the case of C E ₁₄ . The temperature dependence of Q has been deduced and it can be well described in the framework of Landau's theory. Received: 2 October 1997 / Received in final form: 3 December 1997 / Accepted: 29 January 1998     

Application of the Sherman-Morisson formula to scattering problems by multi-component systems

The scattering matrix for multi-component systems is recalculated using the extended form of the Sherman-Morisson formula. The matrix elements are given explicitly in closed form. The Gibbs-Duhem relation separates the density and composition contributions. Received 5 April 2002     

Mode-coupling crossover in viscous toluene revealed by neutron and light scattering

The dynamics of supercooled toluene, studied in a GHz-THz range by incoherent neutron and depolarized light scattering, is found to be in full accord with mode coupling predictions. Around the susceptibility minimum, neutron spectra are wavenumber independent and proportional to light scattering data; the fast -relaxation scaling law applies; amplitude and frequency diverge with power laws that extrapolate towards a crossover temperature K. Received: 20 June 1997 / Accepted: 3 November 1997     

Hypersonic wave anomalies in Cs3H(SeO4)2 at the transitions above room temperature

The elastic properties of Cs3H ( SeO4 ) ₂ are investigated by Brillouin spectroscopy in the temperature range 20-220 covering the two transitions III II and II I occurring at and , respectively. Phase I is known to be a protonic conductive one. Discontinuities of elastic constants are generally observed at both transitions, implying first orderness. In phases II and I, a slight broadening of the Brillouin lines is detected. The results are discussed in comparison with compounds of the families XHSeO4 (X = NH4, Rb and Cs) and CsH2BO4 (B = As and P) which also undergo a transition to a superionic phase. In the conductive phase, it appears that the lattice anharmonicity is weaker in Cs3H ( SeO4 ) ₂ than in these other compounds. Received 16 October 1998     

Electric field light scattering by flexible linear polyelectrolytes in aqueous solution

Electric field light scattering results on aqueous solutions of linear, flexible NaPSS at minimal ionic strength are reported. Samples of molecular weights between 356 kg/mol and 2870 kg/mol were investigated. With increasing field strength the intensity as a function of wavenumber develops a pronounced oscillating behaviour. Besides the well-known first peak a second maximum is observed at the position at which a weak maximum for some samples already occurs at zero field. The overall intensity strongly depends on the frequency of the electric field. The electro-optical effect shows a maximum at 300 kHz. Increasing the particle concentration gives a large increase of the peak maximum, normalized to concentration. If plotted versus scattering angle the relative intensity increase is maximum for samples of medium molecular weight. The results strongly indicate a stretching and alignment of the chains, thus leading to or enlarging the short range order of the chains. Received 9 April 1999 and Received in final form 18 August 1999     

Dynamical precursor of nematic order in a dense fluid of hard ellipsoids of revolution

We investigate hard ellipsoids of revolution in a parameter regime where no long range nematic order is present but already finite-size domains are formed which show orientational order. Domain formation leads to a substantial slowing down of a collective rotational mode which separates well from the usual microscopic frequency regime. A dynamic coupling of this particular mode into all other modes provides a general mechanism which explains an excess peak in spectra of molecular fluids. Using molecular dynamics simulation on up to 4096 particles and on solving the molecular mode coupling equation we investigate dynamic properties of the peak and prove its orientational origin. Received 19 September 2001 and Received in final form 19 March 2002     

Heterogeneous dynamics at the glass transition in van der Waals liquids: Determination of the characteristic scale

Recent experiments have demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous. The characteristic size of these heterogeneities has been measured to be a few nanometers at T _g. We extend here a recent model for describing the heterogeneous nature of the dynamics which allows both to derive this length scale and the right orders of magnitude of the heterogeneities of the dynamics close to the glass transition. Our model allows then to interpret quantitatively small probes diffusion experiments. Received 29 March 2002 and Received in final form 11 November 2002 RID="a" ID="a"e-mail: long@lps.u-psud.fr     

Light scattering with swollen hexagonal phases

We investigate, using quasi-elastic light scattering, some features of the long-wavelength, low-frequency modes of the hexagonal phase often encountered in the study of lyotropic (surfactant-solvent) systems. The hexagonal phase is swollen by an oil-based ferrofluid, allowing magnetically aligned samples to be prepared. We show experimentally the anisotropy of the two lowest-frequency modes. We develop a model which predicts that these slow modes are associated to particle diffusion and tube motion. With the help of microscopic as well as phenomenological analyses, we suggest that the latter presumably corresponds to a peristaltic mode. Confinement effects on the one-dimensional, Brownian diffusion of the colloids along the tube axis together with the coupling between the two modes are studied experimentally, varying the tube diameter to particle size ratio. Received 7 July 1999     

Scaling of broadband dielectric data of glass-forming liquids and plastic crystals

The Nagel scaling and the modified scaling procedure proposed recently by Dendzik et al. have been applied to broadband dielectric data on two glass-forming liquids (glycerol and propylene carbonate) and three plastic crystals (ortho-carborane, meta-carborane, and 1-cyano-adamantane). Our data extend the upper limit of the abscissa range to considerably higher values than in previously published analyses. At the highest frequencies investigated, deviations from a single master curve show up which are most pronounced in the Dendzik scaling plot. The loss curves of the plastic crystals do not scale in the Nagel plot, but they fall onto a separate master curve in the Dendzik plot. In addition, we address the question of a possible divergence of the static susceptibility near the Vogel-Fulcher temperature. For this purpose, the low-temperature evolution of the high-frequency wing of the dielectric loss peaks is investigated in detail. No convincing proof for such a divergence can be deduced from the present broadband data. Received 14 June 1999 and Received in final form 4 October 1999     

Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T _g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T _g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T _g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation. Received 21 March 2000 and Received in final form 4 December 2000     

Collapse of sodium polyacrylate chains in calcium salt solutions

The sodium salt of polyacrylic acid (NaPA) precipitates in the presence of Ca²⁺-ions. This phase behaviour can be represented by a phase diagram where the critical NaPA concentration is plotted versus the critical Ca²⁺ concentration resulting in a straight line as a phase boundary. The location of this phase boundary is influenced by the presence of an inert monovalent salt like NaCl. The present contribution focuses on the coil dimensions of NaPA chains in dilute aqueous solution corresponding to the one phase region of such a phase diagram. A variety of parameters with which the size and shape of the polyelectrolyte chains can be modulated are revealed. Approaching the phase boundary by decreasing the NaPA concentration at a constant Ca²⁺ content leads to a collapse of the NaPA chains. Combined static and dynamic light scattering suggests a compact spherical shape as the final state of this transition, both in 0.1 M NaCl and in 0.01 M NaCl. In the lower NaCl concentration, indication is presented for the existence of a cigar or pearl necklace like intermediate. Most strikingly, the collapsed chains can be reexpanded by increasing the concentration of inert NaCl at constant content of NaPA and Ca²⁺. Clearly, excessive Na⁺-ions displace the Ca²⁺-ions from the NaPA chains. Received 18 July 2000 and Received in final form 24 August 2000     

Fast intramolecular dynamics of triphenyl phosphite investigated by <Emphasis Type="Bold">2</Emphasis>H NMR

The first analysis of rapid intramolecular motions of triphenyl phosphite by ²H NMR is presented. The fragile slowing down of the primary relaxation is followed by a solid-echo method. The occurrence of a fast reorientation of the phenyl side groups is demonstrated in the supercooled liquid state, identified as a two-fold flip on the basis of simple lineshape simulations. Coexistence of both static and motionally averaged components in “two phase” spectra indicate a broad distribution of correlation times for this relaxation. This dynamical behavior is shown to persist in the glacial phase. Received 28 May 2002 / Received in final form 1st October 2002 Published online 31 December 2002     

Static and dynamic properties of supercooled thin polymer films

The dynamic and static properties of a supercooled (non-entangled) polymer melt are investigated via molecular-dynamics (MD) simulations. The system is confined between two completely smooth and purely repulsive walls. The wall-to-wall separation (film thickness), D, is varied from about 3 to about 14 times the bulk radius of gyration. Despite the geometric confinement, the supercooled films exhibit many qualitative features which were also observed in the bulk and could be analyzed in terms of mode-coupling theory (MCT). Examples are the two-step relaxation of the incoherent intermediate scattering function, the time-temperature superposition property of the late time α-process and the space-time factorization of the scattering function on the intermediate time scale of the MCT β-process. An analysis of the temperature dependence of the α-relaxation time suggests that the critical temperature, T _c, of MCT decreases with D. If the confinement is not too strong ( D≥10monomer diameter), the static structure factor of the film coincides with that of the bulk when compared for the same distance, T - T _c(D), to the critical temperature. This suggests that T - T _c(D) is an important temperature scale of our model both in the bulk and in the films. Received 12 September 2001     

Shrinking of anionic polyacrylate coils induced by Ca2+, Sr2+ and Ba2+: A combined light scattering and ASAXS study

Anionic polyacrylate chains (NaPA) form precipitates if alkaline earth cations are added in stoichiometric amounts. Accordingly, precipitation thresholds were established for three different alkaline earth cations Ca²⁺, Sr²⁺ and Ba²⁺. Close to the precipitation threshold, the NaPA chains significantly decrease in size. This shrinking process was followed by means of combined static and dynamic light scattering. Intermediates were generated by varying the ratio [MCl₂]/[NaPA] with M denoting the respective alkaline earth cation. All experiments were performed at an inert salt level of 0.01M NaCl. Similar coil-to-sphere transitions could be observed with all three alkaline earth cations Ca²⁺, Sr²⁺ and Ba²⁺. Based on these findings, supplementary conventional and anomalous small-angle X-ray scattering experiments using selected intermediates close to the precipitation threshold of SrPA were performed. The distribution of Sr counterions around the polyacrylate chains in aqueous solution provided the desired scattering contrast. Energy-dependent scattering experiments enabled successful separation of the pure-resonant terms, which solely stem from the counterions. The Sr²⁺ scattering roughly reflects the monomer distribution of the polyacrylate chains. Different ratios of the concentrations of [ SrCl₂]/[NaPA] revealed dramatic changes in the scattering curves. The scattering curve at the lowest ratio indicated an almost coil-like behaviour, while at the higher ratios the scattering curves supported the model of highly contracted polymer chains. Most of X-ray scattering experiments on intermediate states revealed compact structural elements which were significantly smaller than the respective overall size of the NaPA particles.     

Mobility in thin polymer films ranging from local segmental motion, Rouse modes to whole chain motion: A coupling model consideration

Large increases of mobility of local segmental relaxation observed in polymer films as the film thickness is decreased, as evidenced by decreases of the glass temperature, are not found for relaxation mechanisms that have longer length scales including the Rouse relaxation modes and the diffusion of entire polymer chains. We show that the coupling model predictions, when extended to consider polymer thin films, are consistent with a large increase of the mobility of the local segmental motions and the lack of such a change for the Rouse modes and the diffusion of entire polymer chains. There are two effects that can reduce the coupling parameter of the local segmental relaxation in thin films. One is the chain orientation that is induced parallel to the surface when the film thickness h becomes smaller than the end-to-end distance of the chains and the other is a finite-size effect when h is no longer large compared to the cooperative length scale. Extremely thin ( ≈ 1.5 nm) films obtained by intercalating a polymer into layered silicates have thickness significantly less than the cooperative length scale near the bulk polymer glass transition temperature. As a result, the coupling parameter of the local segmental relaxation in such thin films is reduced almost to zero. With this plausible assumption, we show the coupling model can explain quantitatively the large decrease of the local segmental relaxation time found experimentally. Received 1 August 2001 and Received in final form 1 December 2001