Universal and nonuniversal features of glassy relaxation in propylene carbonate

The Interplay between the Theories of Mode Coupling and of Percolation Transition in Attractive Colloidal Systems

In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of the nature of such processes represents one of the most challenging unsolved problems in the field of material science. In this context, two important theories have contributed significantly to the interpretation of these phenomena: the Mode-Coupling theory (MCT) and the Percolation theory (PT). These theories are rooted on the two pillars of statistical physics, universality and scale laws, and their original formulations have been subsequently modified to account for the fundamental concepts of Energy Landscape (EL) and of the universality of the fragile to strong dynamical crossover (FSC). In this review, we discuss experimental and theoretical results, including Molecular Dynamics (MD) simulations, reported in the literature for colloidal and polymer systems displaying both glass and sol-gel transitions. Special focus is dedicated to the analysis of the interferences between these transitions and on the possible interplay between MCT and PT. By reviewing recent theoretical developments, we show that such interplay between sol-gel and glass transitions may be interpreted in terms of the extended F13 MCT model that describes these processes based on the presence of a glass-glass transition line terminating in an A3 cusp-like singularity (near which the logarithmic decay of the density correlator is observed). This transition line originates from the presence of two different amorphous structures, one generated by the inter-particle attraction and the other by the pure repulsion characteristic of hard spheres. We show here, combining literature results with some new results, that such a situation can be generated, and therefore experimentally studied, by considering colloidal-like particles interacting via a hard core plus an attractive square well potential. In the final part of this review, scaling laws associated both to MCT and PT are applied to describe, by means of these two theories, the specific viscoelastic properties of some systems.

Glassy dynamics of a binary Voronoi fluid: a mode-coupling analysis

The binary Voronoi mixture is a fluid model whose interactions are derived from the Voronoi-Laguerre tessellation of the configurations of the system. The resulting interactions are local and many-body. Here we perform molecular-dynamics (MD) simulations of an equimolar mixture that is weakly polydisperse and additive. For the first time we study the structural relaxation of this mixture in the supercooled-liquid regime. From the simulations we determine the time- and temperature-dependent coherent and incoherent scattering functions for a large range of wave vectors, as well as the mean-square displacements of both particle species. We perform a detailed analysis of the dynamics by comparing the MD results with the first-principles-based idealized mode-coupling theory (MCT). To this end, we employ two approaches: fits to the asymptotic predictions of the theory, and fit-parameter-free binary MCT calculations based on static-structure-factor input from the simulations. We find that many-body interactions of the Voronoi mixture do not lead to strong qualitative differences relative to similar analyses carried out for simple liquids with pair-wise interactions. For instance, the fits give an exponent parameter λ ≈ 0.746 comparable to typical values found for simple liquids, the wavevector dependence of the Kohlrausch relaxation time is in good qualitative agreement with literature results for polydisperse hard spheres, and the MCT calculations based on static input overestimate the critical temperature, albeit only by a factor of about 1.2. This overestimation appears to be weak relative to other well-studied supercooled-liquid models such as the binary Kob-Andersen Lennard-Jones mixture. Overall, the agreement between MCT and simulation suggests that it is possible to predict several microscopic dynamic properties with qualitative, and in some cases near-quantitative, accuracy based solely on static two-point structural correlations, even though the system itself is inherently governed by many-body interactions.

Dynamical properties of densely packed confined hard-sphere fluids

Numerical solutions of the mode-coupling theory (MCT) equations for a hard-sphere fluid confined between two parallel hard walls are elaborated. The governing equations feature multiple parallel relaxation channels which significantly complicate their numerical integration. We investigate the intermediate scattering functions and the susceptibility spectra close to structural arrest and compare to an asymptotic analysis of the MCT equations. We corroborate that the data converge in the β-scaling regime to two asymptotic power laws, viz. the critical decay and the von Schweidler law. The numerical results reveal a nonmonotonic dependence of the power-law exponents on the slab width and a nontrivial kink in the low-frequency susceptibility spectra. We also find qualitative agreement of these theoretical results to event-driven molecular dynamics simulations of polydisperse hard-sphere systems. In particular, the nontrivial dependence of the dynamical properties on the slab width is well reproduced.

Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields

The generalized Langevin equation (GLE) can be derived from a particle-bath Hamiltonian, in both classical and quantum dynamics, and provides a route to the (both Markovian and non-Markovian) fluctuation-dissipation theorem (FDT). All previous studies have focused either on particle-bath systems with time-independent external forces only, or on the simplified case where only the tagged particle is subject to the external time-dependent oscillatory field. Here we extend the GLE and the corresponding FDT for the more general case where both the tagged particle and the bath oscillators respond to an external oscillatory field. This is the example of a charged or polarizable particle immersed in a bath of other particles that are also charged or polarizable, under an external ac electric field. For this Hamiltonian, we find that the ensemble average of the stochastic force is not zero, but proportional to the ac field. The associated FDT reads as 〈F_{P}(t)F_{P}(t^{'})〉=mk_{B}Tν(t-t^{'})+(γe)^{2}E(t)E(t^{'}), where F_{p} is the random force, ν(t-t^{'}) is the friction memory function, and γ is a numerical prefactor.

Characteristic length scales of the secondary relaxations in glass-forming glycerol

We investigate the secondary relaxations and their link to the main structural relaxation in glass-forming liquids using glycerol as a model system. We analyze the incoherent neutron scattering signal dependence on the scattering momentum transfer, Q , in order to obtain the characteristic length scale for different secondary relaxations. Such a capability of neutron scattering makes it somewhat unique and highly complementary to the traditional techniques of glass physics, such as light scattering and broadband dielectric spectroscopy, which provide information on the time scale, but not the length scales, of relaxation processes. The choice of suitable neutron scattering techniques depends on the time scale of the relaxation of interest. We use neutron backscattering to identify the characteristic length scale of 0.7 Å for the faster secondary relaxation described in the framework of the mode-coupling theory (MCT). Neutron spin-echo is employed to probe the slower secondary relaxation of the excess wing type at a low temperature ( ∼ 1.13T g . The characteristic length scale for this excess wing dynamics is approximately 4.7 Å. Besides the Q -dependence, the direct coupling of neutron scattering signal to density fluctuation makes this technique indispensable for measuring the length scale of the microscopic relaxation dynamics.

Optical Kerr effect of liquid and supercooled water: the experimental and data analysis perspective

The time-resolved optical Kerr effect spectroscopy (OKE) is a powerful experimental tool enabling accurate investigations of the dynamic phenomena in molecular liquids. We introduced innovative experimental and fitting procedures, that enable a safe deconvolution of sample response function from the instrumental function. This is a critical issue in order to measure the dynamics of liquid water. We report OKE data on water measuring intermolecular vibrations and the structural relaxation processes in an extended temperature range, inclusive of the supercooled states. The unpreceded data quality makes possible a solid comparison with few theoretical models: the multi-mode Brownian oscillator model, the Kubo's discrete random jump model, and the schematic mode-coupling model. All these models produce reasonable good fits of the OKE data of stable liquid water, i.e., over the freezing point. The features of water dynamics in the OKE data becomes unambiguous only at lower temperatures, i.e., for water in the metastable supercooled phase. We found that the schematic mode-coupling model provides the more rigorous and complete model for water dynamics, even if its intrinsic hydrodynamic approach does not give a direct access to the molecular information.

Simulated glass-forming polymer melts: dynamic scattering functions, chain length effects, and mode-coupling theory analysis

We present molecular-dynamics simulations for a fully flexible model of polymer melts with different chain length N ranging from short oligomers (N = 4) to values near the entanglement length (N = 64). For these systems we explore the structural relaxation of the supercooled melt near the critical temperature T c of mode-coupling theory (MCT). Coherent and incoherent scattering functions are analyzed in terms of the idealized MCT. For temperatures T > T c we provide evidence for the space-time factorization property of the β relaxation and for the time-temperature superposition principle (TTSP) of the α relaxation, and we also discuss deviations from these predictions for T ≈ T c. For T larger than the smallest temperature where the TTSP holds we perform a quantitative analysis of the dynamics with the asymptotic MCT predictions for the late β regime. Within MCT a key quantity, in addition to T c, is the exponent parameter λ. For the fully flexible polymer models studied we find that λ is independent of N and has a value (λ = 0.735 ) typical of simple glass-forming liquids. On the other hand, the critical temperature increases with chain length toward an asymptotic value T c (∞) . This increase can be described by T c (∞) - T c(N) ∼ 1/N and may be interpreted in terms of the N dependence of the monomer density ρ, if we assume that the MCT glass transition is ruled by a soft-sphere-like constant coupling parameter Γ c = ρ c T c (-1/4), where ρ c is the monomer density at T c. In addition, we also estimate T c from a Hansen-Verlet-like criterion and MCT calculations based on structural input from the simulation. For our polymer model both the Hansen-Verlet criterion and the MCT calculations suggest T c to decrease with increasing chain length, in contrast to the direct analysis of the simulation data.

Excess wing in glass-forming glycerol and LiCl-glycerol mixtures detected by neutron scattering

The relaxational dynamics in glass-forming glycerol and glycerol mixed with LiCl is investigated using different neutron scattering techniques. The performed neutron spin echo experiments, which extend up to relatively long relaxation time scales of the order of 10 ns, should allow for the detection of contributions from the so-called excess wing. This phenomenon, whose microscopic origin is controversially discussed, arises in a variety of glass formers and, until now, was almost exclusively investigated by dielectric spectroscopy and light scattering. Here we show that the relaxational process causing the excess wing can also be detected by neutron scattering, which directly couples to density fluctuations.

Depolarized light scattering spectra of molecular liquids: Described in terms of mode coupling theory

Depolarized light scattering spectra of eight molecular liquids as obtained from applying tandem-Fabry-Pérot interferometry and double monochromator are analyzed in the frame work of the mode coupling theory (MCT). The susceptibility spectra are fitted to the numerical solution of the schematic F12 model of MCT and the validity of the asymptotic laws is discussed. The model is able to quantitatively describe the spectra up to the boiling point, where the main (structural) relaxation and the contribution of the microscopic (vibrational) dynamics essentially merge, and down to the moderately super-cooled liquid where glassy dynamics establishes. The changes of the spectra with temperature are mapped to only two control parameters, which show a smooth variation with temperature. Strong correlation between experimental stretching parameters and extrapolated values from the model is found. The numerical solutions are extrapolated down to Tc, where the asymptotic scaling laws can be applied. Although the spectra apparently follow scaling relations, the application of the asymptotic laws usually overestimates Tc by up to 12 K. In all the cases, the experimental spectra are outside the applicability regime of the asymptotic laws. This is explained by more or less strong vibrational contributions. Within a phenomenological approach which extends the spectral analysis down to Tg and which allows for separating fast and slow dynamics, the strength of the fast dynamics 1 - frel is revealed. It shows the cusp-like anomaly predicted by MCT; yet, the corresponding critical temperature is significantly higher than that derived from the F12 model. In addition, we demonstrate that close to Tg, the susceptibility minimum is controlled by the interplay of the excess wing and the fast dynamics contribution.

Evidence of two distinct local structures of water from ambient to supercooled conditions

The liquid and supercooled states of water show a series of anomalies whose nature is debated. A key role is attributed to the formation of structural aggregates induced by critical phenomena occurring deep in the supercooled region; the nature of the water anomalies and of the hidden critical processes remains elusive. Here we report a time-resolved optical Kerr effect investigation of the vibrational dynamics and relaxation processes in supercooled bulk water. The experiment measures the water intermolecular vibrations and the structural relaxation process in an extended temperature range, and with unprecedented data quality. A mode-coupling analysis of the experimental data enables to characterize the intermolecular vibrational modes and their interplay with the structural relaxation process. The results bring evidence of the coexistence of two local configurations, which are interpreted as high-density and low-density water forms, with an increasing weight of the latter at low temperatures.

Ions in glass-forming glycerol: close correlation of primary and fast β relaxation

We provide broadband dielectric loss spectra of glass-forming glycerol with varying additions of LiCl. The measurements covering frequencies up to 10 THz extend well into the region of the fast β process, commonly ascribed to caged molecular dynamics. Aside from the known variation of the structural α relaxation time and a modification of the excess wing with ion content, we also find a clear influence on the shallow loss minimum arising from the fast β relaxation. Within the framework of mode-coupling theory, the detected significant broadening of this minimum is in reasonable accord with the found variation of the α-relaxation dynamics. A correlation between α-relaxation rate and minimum position holds for all ion concentrations and temperatures, even below the critical temperature defined by mode-coupling theory.

Glassy relaxation and excess wing in mode-coupling theory: the dynamic susceptibility of propylene carbonate above and below T(c)

We explore the possibility of describing experimental susceptibility spectra of the glass former propylene carbonate with a two-component schematic model of mode-coupling theory (MCT) from above the melting point down to temperatures far below the critical temperature of MCT. By introducing a phenomenological time-dependent hopping rate, the spectra are reproduced in the full frequency and temperature range available. Literature data of dielectric susceptibilities and depolarized Brillouin light-scattering spectra are combined with our measurements of photon correlation spectroscopy to cover up to 18 decades in frequency of spectra for two different dynamical variables. A consistent description of all data sets is obtained by adjusting only a few physically motivated parameters. In particular the excess wing or slow β-relaxation commonly observed in the susceptibility spectra can consistently be modeled as originating from a coupling of the individual experimental probe correlator to the collective density fluctuations.

MD simulation of concentrated polymer solutions: structural relaxation near the glass transition

We examine by molecular dynamics simulations the relaxation of polymer-solvent mixtures close to the glass transition. The simulations employ a coarse-grained model in which polymers are represented by bead-spring chains and solvent particles by monomers. The interaction parameters between polymer and solvent are adjusted such that mixing is favored. We find that the mixtures have one glass transition temperature T(g) or critical temperature T(c) of mode-coupling theory (MCT). Both T(g) and T(c) (> T(g)) decrease with increasing solvent concentration φ(S). The decrease is linear for the concentrations studied (up to φ(S) = 25%). Above T(c) we explore the structure and relaxation of the polymer-solvent mixtures on cooling. We find that, if the polymer solution is compared to the pure polymer melt at the same T, local spatial correlations on the length scale of the first peak of the static structure factor S(q) are reduced. This difference between melt and solution is largely removed when comparing the S(q) of both systems at similar distance to the respective T(c). Near T(c) we investigate dynamic correlation functions, such as the incoherent intermediate scattering function φ(q)(s)(t), mean-square displacements of the monomers and solvent particles, two non-Gaussian parameters, and the probability distribution P(ln r; t) of the logarithm of single-particle displacements. In accordance with MCT we find, for instance, that φ(q)(s)(t) obeys the time-temperature superposition principle and has α relaxation times τ(q)(s) which are compatible with a power law increase close (but not too close) to T(c). In divergence to MCT, however, the increase of τ(q)(s) depends on the wavelength q, small q values having weaker increase than large ones. This decoupling of local and large-length scale relaxation could be related to the emergence of dynamic heterogeneity at low T. In the time window of the α relaxation an analysis of P(ln r; t) reveals a double-peak structure close to T(c). The first peak corresponds to "slow" particles (monomer or solvent) which have not moved much farther than 10% of their diameter in time t, whereas the second occurs at distances of the order of the particle diameter. These "fast" particles have succeeded in leaving their nearest-neighbor cage in time t. The simulation thus demonstrates that large fluctuations in particle mobility accompany the final structural relaxation of the cold polymer solution in the vicinity of the extrapolated T(c).

On the nature of the high-frequency relaxation in a molecular glass former: a joint study of glycerol by field cycling NMR, dielectric spectroscopy, and light scattering

Fast field cycling (1)H NMR relaxometry is applied to determine the dispersion of spin-lattice relaxation time T(1)(omega) of the glass former glycerol in broad temperature (75-360 K) and frequency (10 kHz-30 MHz) ranges. The relaxation data are analyzed in terms of a susceptibility chi(")(omega) proportional, variantomegaT(1)(omega), related to the second rank (l=2) molecular orientational correlation function. Broadband dielectric spectroscopic results suggest the validity of frequency temperature superposition above the glass transition temperature T(g). This allows to combine NMR data of different temperatures into a single master curve chi(")(omegatau(alpha)) that extends over 15 decades in reduced frequency omegatau(alpha), where tau(alpha) is the structural alpha-relaxation time. This master curve is compared with the corresponding ones from dielectric spectroscopy (l=1) and depolarized light scattering (l=2). At omegatau(alpha)<1, NMR susceptibility is significantly different from both the dielectric and light scattering results. At omegatau(alpha)>1, there rather appears a difference between the susceptibilities of rank l=1 and l=2. Specifically, at omegatau(alpha)>>1, where the susceptibility is dominated by the so-called excess wing, the NMR and light scattering spectra (both l=2) rather coincide with each other and are about three times more intense than the dielectric (l=1) spectrum. This is explained by assuming that the high frequency dynamics correspond to only small-angle excursions. Below T(g), dielectric and NMR susceptibility compare well and exhibit an exponential temperature dependence.

Broadband dielectric spectroscopy on benzophenone: alpha relaxation, beta relaxation, and mode coupling theory

We have performed a detailed dielectric investigation of the relaxational dynamics of glass-forming benzophenone. Our measurements cover a broad frequency range of 0.1 Hz to 120 GHz and temperatures from far below the glass temperature well up into the region of the small-viscosity liquid. With respect to the alpha relaxation this material can be characterized as a typical molecular glass former with rather high fragility. A good agreement of the alpha relaxation behavior with the predictions of the mode coupling theory of the glass transition is stated. In addition, at temperatures below and in the vicinity of T(g) we detect a well-pronounced beta relaxation of Johari-Goldstein type, which with increasing temperature develops into an excess wing. We compare our results to literature data from optical Kerr effect and depolarized light scattering experiments, where an excess-wing-like feature was observed in the 1-100 GHz region. We address the question if the Cole-Cole peak, which was invoked to describe the optical Kerr effect data within the framework of the mode coupling theory, has any relation to the canonical beta relaxation detected by dielectric spectroscopy.

Crossover behavior and multistep relaxation in a schematic model of the cut-off glass transition

We study a schematic mode-coupling model in which the ideal glass transition is cut off by a decay of the quadratic coupling constant in the memory function. (Such a decay, on a time scale tau I , has been suggested as the likely consequence of activated processes.) If this decay is complete, so that only a linear coupling remains at late times, then the alpha relaxation shows a temporal crossover from a relaxation typical of the unmodified schematic model to a final strongly slower-than-exponential relaxation. This crossover, which differs somewhat in form from previous schematic models of the cutoff glass transition, resembles light-scattering experiments on colloidal systems, and can exhibit a "slower-than- alpha " relaxation feature hinted at there. We also consider what happens when a similar but incomplete decay occurs, so that a significant level of quadratic coupling remains for t>>tau I . In this case the correlator acquires a third, weaker relaxation mode at intermediate times. This empirically resembles the beta process seen in many molecular glass formers. It disappears when the initial as well as the final quadratic coupling lies on the liquid side of the glass transition, but remains present even when the final coupling is only just inside the liquid (so that the alpha relaxation time is finite, but too long to measure). Our results are suggestive of how, in a cutoff glass, the underlying "ideal" glass transition predicted by mode-coupling theory can remain detectable through qualitative features in dynamics.

Irreducible memory function and slow dynamics in disordered systems

We show how the irreducible memory function can be obtained in a rather straightforward way, and that it can be expressed in terms of two contributions representing two parallel decay channels. This representation should be useful for treating systems with a slow time dependence and where eventually some internal degrees of freedom enters in the relaxation process, and cuts off an underlying ideal ergodic to nonergodic transition. We also show how the irreducible memory function under certain mild conditions defines a regenerative stochastic process, or a two level stochastic system. This leads to a picture with dynamical heterogeneities, where the statistical properties asymptotically are ruled by limit processes. This can explain the universal behavior observed in many glass-forming systems.

Cole-Cole law for critical dynamics in glass-forming liquids

Within the mode-coupling theory (MCT) for glassy dynamics, the asymptotic low-frequency expansions for the dynamical susceptibilities at critical points are compared to the expansions for the dynamic moduli; this shows that the convergence properties of the two expansions can be quite different. In some parameter regions, the leading-order expansion formula for the modulus describes the solutions of the MCT equations of motion outside the transient regime successfully; at the same time, the leading- and next-to-leading-order expansion formulas for the susceptibility fail. In these cases, one can derive a Cole-Cole law for the susceptibilities; and this law accounts for the dynamics for frequencies below the band of microscopic excitations and above the high-frequency part of the alpha peak. It is shown that this scenario explains the optical-Kerr-effect data measured for salol and benzophenone (BZP). For BZP it is inferred that the depolarized light-scattering spectra exhibit a wing for the alpha peak within the Gigahertz band. This wing results from the crossover of the von Schweidler law part of the alpha peak to the high-frequency part of the Cole-Cole peak; and this crossover can be described quantitatively by the leading-order formulas of MCT for the modulus.

Boson peak in supercooled liquids: Time domain observations and mode coupling theory

Optical heterodyne-detected optical Kerr effect (OHD-OKE) experiments are presented for the supercooled liquid acetylsalicylic acid (aspirin - ASP). The ASP data and previously published OHD-OKE data on supercooled dibutylphthalate (DBP) display highly damped oscillations with a periods of approximately 2 ps as the temperature is reduced to and below the mode coupling theory (MCT) temperature T(C). The oscillations become more pronounced below T(C). The oscillations can be interpreted as the time domain signature of the boson peak. Recently a schematic MCT model, the Sjogren model, was used to describe the OHD-OKE data for a number of supercooled liquids by Gotze and Sperl [W. Gotze and M. Sperl, Phys. Rev. E 92, 105701 (2004)] , but the short-time and low-temperature behaviors were not addressed. Franosch et al. [T. Franosch, W. Gotze, M. R. Mayr, and A. P. Singh, Phys. Rev. E 55, 3183 (1997)] found that the Sjogren model could describe the boson peak observed by depolarized light-scattering (DLS) experiments on glycerol. The OHD-OKE experiment measures a susceptibility that is a time domain equivalent of the spectrum measured in DLS. Here we present a detailed analysis of the ASP and DBP data over a broad range of times and temperatures using the Sjogren model. The MCT schematic model is able to describe the data very well at all temperatures and relevant time scales. The trajectory of MCT parameters that fit the high-temperature data (no short-time oscillations) when continued below T(C) results in calculations that reproduce the oscillations seen in the data. The results indicate that increasing translational-rotational coupling is responsible for the appearance of the boson peak as the temperature approaches and drops below T(C).

Tagged-particle dynamics in a hard-sphere system: mode-coupling theory analysis

The predictions of the mode-coupling theory of the glass transition (MCT) for the tagged-particle density-correlation functions and the mean-squared displacement curves are compared quantitatively and in detail to results from Newtonian- and Brownian-dynamics simulations of a polydisperse quasi-hard-sphere system close to the glass transition. After correcting for a 17% error in the dynamical length scale and for a smaller error in the transition density, good agreement is found over a wide range of wave numbers and up to five orders of magnitude in time. Deviations are found at the highest densities studied, and for small wave vectors and the mean-squared displacement. Possible error sources not related to MCT are discussed in detail, thereby identifying more clearly the issues arising from the MCT approximation itself. The range of applicability of MCT for the different types of short-time dynamics is established through asymptotic analyses of the relaxation curves, examining the wave-number and density-dependent characteristic parameters. Approximations made in the description of the equilibrium static structure are shown to have a remarkable effect on the predicted numerical value for the glass-transition density. Effects of small polydispersity are also investigated, and shown to be negligible.

Nearly logarithmic decay of correlations in glass-forming liquids

Nearly logarithmic decay of correlations, which was observed for several supercooled liquids in optical-Kerr-effect experiments [Phys. Rev. Lett. 84, 2437 (2000)]; Phys. Rev. Lett. 90, 197401 (2003)]], is explained within the mode-coupling theory for ideal glass transitions as a manifestation of the beta-peak phenomenon. A schematic model, which describes the dynamics by only two correlators, one referring to density fluctuations and the other to the reorientational fluctuations of the molecules, yields for strong rotation-translation coupling response functions in agreement with those measured for benzophenone and Salol for the time interval extending from 2 ps to about 20 and 200 ns, respectively.

Real space origin of temperature crossovers in supercooled liquids

We show that the various crossovers between dynamical regimes observed in experiments and simulations of supercooled liquids can be explained in simple terms from the existence and statistical properties of dynamical heterogeneities. We confirm that dynamic heterogeneity is responsible for the slowing down of glass formers at temperatures well above the dynamic singularity Tc predicted by mode-coupling theory. Our results imply that activated processes govern the long-time dynamics even in the temperature regime where they are neglected by mode-coupling theory. We show that alternative interpretations based on topographic properties of the potential energy landscape are inefficient ways of describing simple physical features which are naturally accounted for within our approach. We show in particular that the reported links between mode coupling and landscape singularities do not exist.

Viscoelastic dynamics of polymer thin films and surfaces

The strain relaxation behavior in a viscoelastic material, such as a polymer melt, may be strongly affected by the proximity of a free surface or mobile interface. In this paper, the viscoelastic surface modes of the material are discussed with respect to their possible influence on the freezing temperature and dewetting morphology of thin polymer films. In particular, the mode spectrum is connected with mode coupling theory assuming memory effects in the melt. Based on the idea that the polymer freezes due to these memory effects, surface melting is predicted. As a consequence, the substantial shift of the glass transition temperature of thin polymer films with respect to the bulk is naturally explanied. The experimental findings of several independent groups can be accounted for quantitatively, with the elastic modulus at the glass transition temperature as the only fitting parameter. Finally, a simple model is put forward which accounts for the occurrence of certain generic dewetting morphologies in thin liquid polymer films. It demonstrates that by taking into account the viscoelastic properties of the film, a morphological phase diagram may be derived which describes the observed structures of dewetting fronts. It is demonstrated that dewetting morphologies may also serve to determine nanoscale rheological properties of liquids.

Relaxation processes in an epoxy resin studied by time-resolved optical Kerr effect

The dynamics of the epoxy resin phenyl glycidyl ether, a fragile glass-forming liquid, is investigated in the liquid and supercooled phases by time-resolved optical Kerr effect experiment with an heterodyne detection technique. We tested the mode-coupling theory and found that the predicted dynamic scenario allows to reproduce properly the measured signal, for t>1 ps, in the whole temperature interval investigated. Furthermore, the values of T(c) and lambda, obtained from the analysis of three different and independent dynamic regimes (alpha regime, von Schweidler, beta regime), are in remarkable agreement. Moreover, relaxation times obtained from optical Kerr effect and dielectric spectroscopy measurements are compared. The two time scales differ only for a constant factor in the whole temperature interval investigated.

Brillouin-scattering study of propylene carbonate: an evaluation of phenomenological and mode coupling analyses

Brillouin-scattering spectra of the molecular glass-forming material propylene carbonate (PC) in the temperature range 140 K to 350 K were analyzed using both the phenomenological Cole-Davidson memory function and a hybrid memory function consisting of the Cole-Davidson function plus a power-law term representing the critical decay part of the fast beta relaxation. The spectra were also analyzed using the extended two-correlator schematic mode-coupling theory (MCT) model recently employed by Götze and Voigtmann to analyze depolarized light backscattering, dielectric, and neutron-scattering spectra of PC [Phys. Rev. E 61, 4133 (2000)]. We assess the ability of the phenomenological and MCT fits, each with three free fitting parameters, to simultaneously describe the spectra and give reasonable values for the alpha-relaxation time tau(alpha).

Anomaly of the nonergodicity parameter and crossover to white noise in the fast relaxation spectrum of a simple glass former

We present quasielastic light scattering and dielectric spectra of the glass former alpha-picoline. At high temperatures the evolution of the susceptibility minimum is well described by the mode coupling theory (MCT). Below the critical temperature T(c) the simple scaling laws of MCT fail due to the appearance of the excess wing of the alpha process, which shows a universal evolution as a function of log(10)tau(alpha). Taking this into account, however, we observe the predicted cusplike anomaly of the nonergodicity parameter as well as a crossover to "white noise."

Microscopic dynamics of molecular liquids and glasses: role of orientations and translation-rotation coupling

We investigate the dynamics of a fluid of dipolar hard spheres in its liquid and glassy phases, with emphasis on the microscopic time or frequency regime. This system shows rather different glass transition scenarios related to its rich equilibrium behavior, which ranges from a simple hard sphere fluid to long range ferroelectric orientational order. In the liquid phase close to the ideal glass transition line and in the glassy regime a medium range orientational order occurs leading to a softening of an orientational mode. To investigate the role of this mode we use the molecular mode-coupling equations to calculate the spectra straight phi"lm(q,omega) and chi"lm(q,omega). In the center of mass spectra straight phi"00(q,omega) and chi"00(q,omega) we found, besides a high frequency peak at omega(hf), a peak at omega(op), about one decade below omega(hf) x omega(op) has almost no q dependence and exhibits an "isotope" effect omega(op) proportional to I(-1/2), with I the moment of inertia. We give evidence that the existence of this peak is related to the occurrence of medium range orientational order. It is shown that some of these features also exist for schematic mode coupling models.

Calcium rubidium nitrate: mode-coupling beta scaling without factorization

The fast dynamics of viscous calcium rubidium nitrate is investigated by depolarized light scattering, neutron scattering, and dielectric loss. Fast beta relaxation evolves as in calcium potassium nitrate. The dynamic susceptibilities can be described by the asymptotic scaling law of mode-coupling theory with a shape parameter lambda=0.79; the temperature dependence of the amplitudes extrapolates to T(c) approximately equal 378 K. However, the frequencies of the minima of the three different spectroscopies never coincide, in conflict with the factorization prediction, indicating that the true asymptotic regime is unreachable.

Multiple-scattering effects on smooth neutron-scattering spectra

Elastic and inelastic incoherent neutron-scattering experiments are simulated for simple models: a rigid solid (as used for normalization), a glass (with a smooth distribution of harmonic vibrations), and a viscous liquid (described by schematic mode-coupling equations). In cases where the input scattering law factorizes into a wave-number-dependent amplitude and a frequency-dependent spectral distribution, the latter is only weakly affected by multiple scattering, whereas the former is severely distorted.

Reorientational relaxation of a linear probe molecule in a simple glassy liquid

Within the mode-coupling theory (MCT) for the evolution of structural relaxation in glass-forming liquids, correlation functions and susceptibility spectra are calculated characterizing the rotational dynamics of a top-down symmetric dumbbell molecule, consisting of two fused hard spheres immersed in a hard-sphere system. It is found that for sufficiently large dumbbell elongations, the dynamics of the probe molecule follows the same universal glass-transition scenario as known from the MCT results of simple liquids. The alpha-relaxation process of the angular-index j=1 response is stronger, slower, and less stretched than the one for j=2, in qualitative agreement with results found by dielectric-loss and depolarized-light-scattering spectroscopy for some supercooled liquids. For sufficiently small elongations, the reorientational relaxation occurs via large-angle flips, and the standard scenario for the glass-transition dynamics is modified for odd-j responses due to precursor phenomena of a nearby type-A MCT transition. In this case, a major part of the relaxation outside the transient regime is described qualitatively by the beta-relaxation scaling laws, while the alpha-relaxation scaling law is strongly disturbed.