Dynamics in a supercooled molecular liquid: theory and simulations

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.

Wave-Vector Dependence of the Dynamics in Supercooled Metallic Liquids

We present a detailed investigation of the wave-vector dependence of collective atomic motion in Au_{49}Cu_{26.9}Si_{16.3}Ag_{5.5}Pd_{2.3} and Pd_{42.5}Cu_{27}Ni_{9.5}P_{21} supercooled liquids close to the glass transition temperature. Using x-ray photon correlation spectroscopy in a previously uncovered spatial range of only a few interatomic distances, we show that the microscopic structural relaxation process mimics the structure and presents a marked slowing down at the main average interparticle distance. This behavior is accompanied by dramatic changes in the shape of the intermediate scattering functions, which suggest the presence of large dynamical heterogeneities at length scales corresponding to a few particle diameters. A ballisticlike mechanism of particle motion seems to govern the structural relaxation of the two systems in the highly viscous phase, likely associated with hopping of caged particles in agreement with theoretical studies.

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.

Structural and microscopic relaxations in a colloidal glass

The aging dynamics of a colloidal glass has been studied by multiangle dynamic light scattering, neutron spin echo, X-ray photon correlation spectroscopy and molecular dynamics simulations. The two relaxation processes, microscopic (fast) and structural (slow), have been investigated in an unprecedentedly wide range of time and length scales covering both ergodic and nonergodic regimes. The microscopic relaxation time remains diffusive at all length scales across the glass transition scaling with wavevector Q as Q(-2). The length-scale dependence of structural relaxation time changes from diffusive, characterized by a Q(-2)-dependence in the early stages of aging, to a Q(-1)-dependence in the full aging regime which marks a discontinuous hopping dynamics. Both regimes are associated with a stretched behaviour of the correlation functions. We expect these findings to provide a general description of both relaxations across the glass transition.

Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation

We analyze the slow glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory (MCT) of the glass transition. Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multicomponent calculation, but qualitative disagreement at small q when the system is treated as effectively monodisperse. The origin of the different small-q behavior is attributed to the interplay between interdiffusion processes and structural relaxation. Numerical solutions of the MCT equations are obtained taking properly binned partial static structure factors from the simulations as input. Accounting for a shift in the critical density, the collective density correlation functions are well described by the theory at all densities investigated in the simulations, with quantitative agreement best around the maxima of the static structure factor and worst around its minima. A parameter-free comparison of the tagged-particle dynamics however reveals large quantitative errors for small wave numbers that are connected to the well-known decoupling of self-diffusion from structural relaxation and to dynamical heterogeneities. While deviations from MCT behavior are clearly seen in the tagged-particle quantities for densities close to and on the liquid side of the MCT glass transition, no such deviations are seen in the collective dynamics.

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).

Structural and conformational dynamics of supercooled polymer melts: insights from first-principles theory and simulations

We report on quantitative comparisons between simulation results of a bead-spring model and mode-coupling theory calculations for the structural and conformational dynamics of a supercooled, unentangled polymer melt. We find semiquantitative agreement between simulation and theory, except for processes that occur on intermediate length scales between the compressibility plateau and the amorphous halo of the static structure factor. Our results suggest that the onset of slow relaxation in a glass-forming melt can be described in terms of monomer caging supplemented by chain connectivity. Furthermore, a unified atomistic description of glassy arrest and of conformational fluctuations that (asymptotically) follow the Rouse model emerges from our theory.

Computational probes of molecular motion in the Lewis-Wahnström model for ortho-terphenyl

We use molecular dynamics simulations to investigate translational and rotational diffusion in a rigid three-site model of the fragile glass former ortho-terphenyl, at 260 K< or =T< or =346 K and ambient pressure. An Einstein formulation of rotational motion is presented, which supplements the commonly used Debye model. The latter is shown to break down at supercooled temperatures as the mechanism of molecular reorientation changes from small random steps to large infrequent orientational jumps. We find that the model system exhibits non-Gaussian behavior in translational and rotational motion, which strengthens upon supercooling. Examination of particle mobility reveals spatially heterogeneous dynamics in translation and rotation, with a strong spatial correlation between translationally and rotationally mobile particles. Application of the Einstein formalism to the analysis of translation-rotation decoupling results in a trend opposite to that seen in conventional approaches based on the Debye formalism, namely, an enhancement in the effective rate of rotational motion relative to translation upon supercooling.

Comparing landscape calculations with calorimetric data on ortho-terphenyl, and the question of the configurational fraction of the excess entropy

Mossa et al. [Phys. Rev. E 65, 041205 (2002)] have calculated the total and configurational entropies of supercooled ortho-terphenyl liquid using the potential-energy landscape formalism and a simplified model of the intermolecular potential. I show here that the agreement of their calculated configurational entropy with the experimental data depends on what is assumed about the configurational fraction of the excess entropy and its temperature dependence. In particular, if the configurational fraction is taken as 0.70 and independent of temperature the agreement is excellent; if a marked temperature dependence of that fraction inferred from calorimetric data is assumed the agreement is only fair at best. This marked temperature dependence of the configurational fraction also implies some implausible behavior of contributions to the excess entropy at the Kauzmann temperature, but no obvious reason for disregarding it presents itself.

Evidence for the weak steric hindrance scenario in the supercooled-state reorientational dynamics

We use molecular-dynamics computer simulations to study the translational and reorientational dynamics of a glass-forming liquid of dumbbells. For sufficiently elongated molecules the standard strong steric hindrance scenario for the rotational dynamics is found. However, for small elongations we find a different scenario--the weak steric hindrance scenario--caused by a new type of glass transition in which the orientational dynamics of the molecule's axis undergoes a dynamical transition with a continuous increase of the nonergodicity parameter. These results are in agreement with the theoretical predictions by the mode-coupling theory for the glass transition.

Static properties of a simulated supercooled polymer melt: structure factors, monomer distributions relative to the center of mass, and triple correlation functions

We analyze structural and conformational properties in a simulated bead-spring model of a nonentangled, supercooled polymer melt. We explore the statics of the model via various structure factors, involving not only the monomers, but also the center of mass (CM). We find that the conformation of the chains and the CM-CM structure factor, which is well described by a recently proposed approximation [Europhys. Lett. 58, 53 (2002)]], remain essentially unchanged on cooling toward the critical glass transition temperature T(c) of mode-coupling theory. Spatial correlations between monomers on different chains, however, depend on temperature, albeit smoothly. This implies that the glassy behavior of our model cannot result from static intrachain or CM-CM correlations. It must be related to interchain correlations at the monomer level. Additionally, we study the dependence of interchain correlation functions on the position of the monomer along the chain backbone. We find that this site dependence can be well accounted for by a theory based on the polymer reference interaction site model. We also analyze triple correlations by means of the three-monomer structure factors for the melt and for the chains. These structure factors are compared with the convolution approximation that factorizes them into a product of two-monomer structure factors. For the chains this factorization works very well, indicating that chain connectivity does not introduce special triple correlations in our model. For the melt deviations are more pronounced, particularly at wave vectors close to the maximum of the static structure factor.

Structural relaxation in supercooled orthoterphenyl

We report molecular-dynamics simulation results performed for a model of molecular liquid orthoterphenyl in supercooled states, which we then compare with both experimental data and mode-coupling-theory (MCT) predictions, aiming at a better understanding of structural relaxation in orthoterphenyl. We pay special attention to the wave number dependence of the collective dynamics. It is shown that the simulation results for the model share many features with experimental data for real system, and that MCT captures the simulation results at the semiquantitative level except for intermediate wave numbers connected to the overall size of the molecule. Theoretical results at the intermediate wave number region are found to be improved by taking into account the spatial correlation of the molecule's geometrical center. This supports the idea that unusual dynamical properties at the intermediate wave numbers, reported previously in simulation studies for the model and discernible in coherent neutron-scattering experimental data, are basically due to the coupling of the rotational motion to the geometrical-center dynamics. However, there still remain qualitative as well as quantitative discrepancies between theoretical prediction and corresponding simulation results at the intermediate wave numbers, which call for further theoretical investigation.

Frequency dependence and equilibration of the specific heat of glass-forming liquids

We have performed molecular dynamics simulations on a glass-forming liquid consisting of a three-dimensional binary mixture of soft spheres. We show that a peak in the specific heat versus temperature can occur because a glassy system that shows no signs of aging progresses so slowly through the energy landscape that the minimum sampling time needed to obtain accurate thermodynamic averages exceeds the observation time. We develop a systematic technique to determine the equilibrium value of the specific heat and the minimum sampling time. Below the temperature of the specific heat peak, the minimum sampling time is orders of magnitude longer than the alpha relaxation time. We find that an equilibrium system that is not undergoing structural relaxation or aging has a frequency dependent specific heat that rises as the frequency decreases. The rise occurs at frequencies corresponding to periods that are long enough for the system to sample statistically independent energies. When the period is comparable to the minimum sampling time, the frequency dependent specific heat reaches a plateau. As a result, the specific heat has a frequency dependence at frequencies orders of magnitude lower than is implied by the inverse alpha relaxation time.

Liquid stability in a model for ortho-terphenyl

We report an extensive study of the phase diagram of a simple model for ortho-terphenyl, focusing on the limits of stability of the liquid state. Reported data extend previous studies of the same model to both lower and higher densities and to higher temperatures. We estimate the location of the homogeneous liquid-gas nucleation line and of the spinodal locus. Within the potential energy landscape formalism, we calculate the distributions of depth, number, and shape of the potential energy minima and show that the statistical properties of the landscape are consistent with a Gaussian distribution of minima over a wide range of volumes. We report the volume dependence of the parameters entering in the Gaussian distribution (amplitude, average energy, variance). We finally evaluate the locus where the configurational entropy vanishes, the so-called Kauzmann line, and discuss the relative location of the spinodal and Kauzmann loci.

Free energy and configurational entropy of liquid silica: fragile-to-strong crossover and polyamorphism

Recent molecular dynamics (MD) simulations of liquid silica, using the "BKS" model [Phys. Rev. Lett. 64, 1955 (1990)]], have demonstrated that the liquid undergoes a dynamical crossover from super-Arrhenius, or "fragile" behavior, to Arrhenius, or "strong" behavior, as temperature T is decreased. From extensive MD simulations, we show that this fragile-to-strong crossover (FSC) can be connected to changes in the properties of the potential energy landscape, or surface (PES), of the liquid. To achieve this, we use thermodynamic integration to evaluate the absolute free energy of the liquid over a wide range of density and T. We use this free energy data, along with the concept of "inherent structures" of the PES, to evaluate the absolute configurational entropy S(c) of the liquid. We find that the temperature dependence of the diffusion coefficient and of S(c) are consistent with the prediction of Adam and Gibbs, including in the region where we observe the FSC to occur. We find that the FSC is related to a change in the properties of the PES explored by the liquid, specifically an inflection in the T dependence of the average inherent structure energy. In addition, we find that the high T behavior of S(c) suggests that the liquid entropy might approach zero at finite T, behavior associated with the so-called Kauzmann paradox. However, we find that the change in the PES that underlies the FSC is associated with a change in the T dependence of S(c) that elucidates how the Kauzmann paradox is avoided in this system. Finally, we also explore the relation of the observed PES changes to the recently discussed possibility that BKS silica exhibits a liquid-liquid phase transition, a behavior that has been proposed to underlie the observed polyamorphism of amorphous solid silica.

Confirmation of anomalous dynamical arrest in attractive colloids: a molecular dynamics study

Previous theoretical simulation and experimental studies have indicated that particles with a short-ranged attraction exhibit a range of dynamical arrest phenomena. These include very pronounced reentrance in the dynamical arrest curve, a logarithmic singularity in the density correlation functions, and the existence of "attractive" and "repulsive" glasses. Here we carry out extensive molecular dynamics calculations on dense systems interacting via a square-well potential. This is one of the simplest systems with the required properties, and may be regarded as canonical for interpreting the phase diagram, and now also the dynamical arrest. We confirm the theoretical predictions for reentrance, logarithmic singularity, and give a direct evidence of the existence, independent of theory, of two distinct glasses. We now regard the previous predictions of these phenomena as having been established.

Structural probe of a glass-forming liquid: generalized compressibility

We introduce a structural quantity to probe the glass transition. This quantity is a linear generalized compressibility which depends solely on the positions of the particles. We have performed a molecular dynamics simulation on a glass-forming liquid consisting of a two-component mixture of soft spheres in three dimensions. As the temperature is lowered (or as the density is increased), the generalized compressibility drops sharply at the glass transition, with the drop becoming more and more abrupt as the measurement time increases. At our longest measurement times, the drop occurs approximately at the mode coupling temperature T(C). The drop in the linear generalized compressibility occurs at the same temperature as the peak in the specific heat. By examining the inherent structure energy as a function of temperature, we find that our results are consistent with the kinetic view of the glass transition in which the system falls out of equilibrium. We find no size dependence and no evidence for a second order phase transition, though this does not exclude the possibility of a phase transition below the observed glass transition temperature. We discuss the relation between the linear generalized compressibility and the ordinary isothermal compressibility, as well as the static structure factor.

Equilibration times in numerical simulation of structural glasses: comparing parallel tempering and conventional molecular dynamics

Generation of equilibrium configurations is the major obstacle for numerical investigation of the slow dynamics in supercooled liquid states. The parallel tempering (PT) technique, originally proposed for the numerical equilibration of discrete spin-glass model configurations, has recently been applied in the study of supercooled structural glasses. We present an investigation of the ability of parallel tempering to properly sample the liquid configuration space at different temperatures, by mapping the PT dynamics into the dynamics of the closest local potential energy minima (inherent structures). Comparing the PT equilibration process with the standard molecular dynamics equilibration process we find that the PT does not increase the speed of equilibration of the (slow) configurational degrees of freedom.

Dynamics and configurational entropy in the Lewis-Wahnström model for supercooled orthoterphenyl

We study thermodynamic and dynamic properties of a rigid model of the fragile glass-forming liquid orthoterphenyl. This model, introduced by Lewis and Wahnström in 1993, collapses each phenyl ring to a single interaction site; the intermolecular site-site interactions are described by the Lennard-Jones potential whose parameters have been selected to reproduce some bulk properties of the orthoterphenyl molecule. A system of N=343 molecules is considered in a wide range of densities and temperatures, reaching simulation times up to 1 micros. Such long trajectories allow us to equilibrate the system at temperatures below the mode coupling temperature T(c) at which the diffusion constant reaches values of order 10(-10) cm(2)/s and thereby to sample in a significant way the potential energy landscape in the entire temperature range. Working within the inherent structures thermodynamic formalism, we present results for the temperature and density dependence of the number, depth and shape of the basins of the potential energy surface. We evaluate the total entropy of the system by thermodynamic integration from the ideal-noninteracting-gas state and the vibrational entropy approximating the basin free energy with the free energy of 6N-3 harmonic oscillators. We evaluate the configurational part of the entropy as a difference between these two contributions. We study the connection between thermodynamical and dynamical properties of the system. We confirm that the temperature dependence of the configurational entropy and of the diffusion constant, as well as the inverse of the characteristic structural relaxation time, are strongly connected in supercooled states; we demonstrate that this connection is well represented by the Adam-Gibbs relation, stating a linear relation between logD and the quantity 1/TS(c). This relation is found to hold both above and below the critical temperature T(c)-as previously found in the case of silica-supporting the hypothesis that a connection exists between the number of basins and the connectivity properties of the potential energy surface.

Molecular dynamics simulation of the fragile glass former orthoterphenyl: a flexible molecule model. II. Collective dynamics

We present a molecular dynamics study of the collective dynamics of a model for the fragile glass former orthoterphenyl. In this model, introduced by Mossa, Di Leonardo, Ruocco, and Sampoli [Phys. Rev. E 62, 612 (2000)], the intramolecular interaction among the three rigid phenyl rings is described by a set of force constants whose value has been fixed in order to obtain a realistic isolated molecule spectrum. The interaction between different molecules is described by a Lennard Jones site-site potential. We study the behavior of the coherent scattering functions F(t)(q,t), considering the density fluctuations of both molecular and phenyl-ring centers of mass; moreover we directly simulate the neutron scattering spectra taking into account both the contributions due to carbon and hydrogens atoms. We compare our results with the main predictions of the mode-coupling theory and with the available coherent neutron scattering experimental data.