Distribution of Diffusion Constants and Stokes-Einstein Violation in supercooled liquids

It is widely believed that the breakdown of the Stokes-Einstein (SE) relation between the translational diffusivity and the shear viscosity in supercooled liquids is due to the development of dynamic heterogeneity i.e. the presence of both slow and fast moving particles in the system. In this study we \emph{directly} calculate the distribution of the diffusivity for a model system for different temperatures in the supercooled regime. We find that with decreasing temperature, the distribution evolves from Gaussian to bimodal indicating that on the time scale of the typical relaxation time, mobile (fluid like) and less mobile (solid like) particles in the system can be \emph{unambiguously} identified. We also show that less mobile particles obey the Stokes-Einstein relation even in the supercooled regime and it is the mobile particles which show strong violation of the Stokes-Einstein relation in agreement with the previous studies on different model glass forming systems. Motivated by some of the recent studies where an ideal glass transition is proposed by randomly pinning some fraction of particles, we then studied the SE breakdown as a function of random pinning concentration in our model system. We showed that degree of SE breakdown increases quite dramatically with increasing pinning concentration, thereby providing a new way to unravel the puzzles of SE violation in supercooled liquids in greater details.Comment: will appear in JCP 201

Density-temperature scaling of the fragility in a model glass-former

Dynamical quantities such as the diffusion coefficient and relaxation times for some glass-formers may depend on density and temperature through a specific combination, rather than independently, allowing the representation of data over ranges of density and temperature as a function of a single scaling variable. Such a scaling, referred to as density - temperature (DT) scaling, is exact for liquids with inverse power law (IPL) interactions but has also been found to be approximately valid in many non-IPL liquids. We have analyzed the consequences of DT scaling on the density dependence of the fragility in a model glass-former. We find the density dependence of kinetic fragility to be weak, and show that it can be understood in terms of DT scaling and deviations of DT scaling at low densities. We also show that the Adam-Gibbs relation exhibits DT scaling and the scaling exponent computed from the density dependence of the activation free energy in the Adam-Gibbs relation, is consistent with the exponent values obtained by other means

Breakdown of the Stokes-Einstein relation in two, three and four dimensions

The breakdown of the Stokes-Einstein (SE) relation between diffusivity and viscosity at low temperatures is considered to be one of the hallmarks of glassy dynamics in liquids. Theoretical analyses relate this breakdown with the presence of heterogeneous dynamics, and by extension, with the fragility of glass formers. We perform an investigation of the breakdown of the SE relation in 2, 3 and 4 dimensions, in order to understand these interrelations. Results from simulations of model glass formers show that the degree of the breakdown of the SE relation decreases with increasing spatial dimensionality. The breakdown itself can be rationalized via the difference between the activation free energies for diffusivity and viscosity (or relaxation times) in the Adam-Gibbs relation in three and four dimensions. The behavior in two dimensions also can be understood in terms of a generalized Adam-Gibbs relation that is observed in previous work. We calculate various measures of heterogeneity of dynamics and find that the degree of the SE breakdown and measures of heterogeneity of dynamics are generally well correlated but with some exceptions. The two dimensional systems we study show deviations from the pattern of behavior of the three and four dimensional systems both at high and low temperatures. The fragility of the studied liquids is found to increase with spatial dimensionality, contrary to the expectation based on the association of fragility with heterogeneous dynamics

The Adam-Gibbs relation for glass-forming liquids in 2, 3 and 4 dimensions

The Adam-Gibbs relation between relaxation times and the configurational entropy has been tested extensively for glass formers using experimental data and computer simulation results. Although the form of the relation contains no dependence on the spatial dimensionality in the original formulation, subsequent derivations of the Adam-Gibbs relation allow for such a possibility. We test the Adam-Gibbs relation in 2, 3, and 4 spatial dimensions using computer simulations of model glass formers. We find that the relation is valid in 3 and 4 dimensions. But in 2 dimensions, the relation does not hold, and interestingly, no single alternate relation describes the results for the different model systems we study.Comment: Submitted to Phys. Rev. Let

Dependence of the fragility of a glass former on the softness of interparticle interactions

We study the influence of the softness of the interparticle interactions on the fragility of a glass former, by considering three model binary mixture glass formers. The interaction potential between particles is a modified Lennard-Jones type potential, with the repulsive part of the potential varying with an inverse power $q$ of the interparticle distance, and the attractive part varying with an inverse power $p$. We consider the combinations (12,11) (model I), (12,6) (model II) and (8,5) (model III) for (q,p) such that the interaction potential becomes softer from model I to III. We evaluate the kinetic fragilities from the temperature variation of diffusion coefficients and relaxation times, and a thermodynamic fragility from the temperature variation of the configuration entropy. We find that the kinetic fragility increases with increasing softness of the potential, consistent with previous results for these model systems, but at variance with the thermodynamic fragility, which decreases with increasing softness of the interactions, as well as expectations from earlier results. We rationalize our results by considering the full form of the Adam-Gibbs relation, which requires, in addition to the temperature dependence of the configuration entropy, knowledge of the high temperature activation energies ino rder to determine fragility. We show that consideration of the scaling of the high temperature activation energy with the liquid density, analyzed in recent studies, provides a partial rationalization of the observed behavior

Glass Transition in Supercooled Liquids with Medium Range Crystalline Order

The origins of rapid dynamical slow down in glass forming liquids in the growth of static length scales, possibly associated with identifiable structural ordering, is a much debated issue. Growth of medium range crystalline order (MRCO) has been observed in various model systems to be associated with glassy behaviour. Such observations raise the question about the eventual state reached by a glass former, if allowed to relax for sufficiently long times. Is a slowly growing crystalline order responsible for slow dynamics? Are the molecular mechanisms for glass transition in liquids with and without MRCO the same? If yes, glass formers with MRCO provide a paradigm for understanding glassy behaviour generically. If not, systems with MRCO form a new class of glass forming materials whose molecular mechanism for slow dynamics may be easier to understand in terms of growing crystalline order, and should be approached in that manner, even while they will not provide generic insights. In this study we perform extensive molecular dynamics simulations of a number of glass forming liquids in two dimensions and show that the static and dynamic properties of glasses with MRCO are different from other glass forming liquids with no predominant local order. We also resolve an important issue regarding the so-called Point-to-set method for determining static length scales, and demonstrate it to be a robust, order agnostic, method for determining static correlation lengths in glass formers

The role of structure and entropy in determining differences in dynamics for glass formers with different interaction potentials

We present a study of two model liquids with different interaction potentials, exhibiting similar structure but significantly different dynamics at low temperatures. By evaluating the configurational entropy, we show that the differences in the dynamics of these systems can be understood in terms of their thermodynamic differences. Analyzing their structure, we demonstrate that differences in pair correlation functions between the two systems, through their contribution to the entropy, dominate the differences in their dynamics, and indeed overestimate the differences. Including the contribution of higher order structural correlations to the entropy leads to smaller estimates for the relaxation times, as well as smaller differences between the two studied systems