Dynamics of Glass Forming Liquids with Randomly Pinned Particles

It is frequently assumed that in the limit of vanishing cooling rate, the glass transition phenomenon becomes a thermodynamic transition at a temperature $T_{K}$. However, with any finite cooling rate, the system falls out of equilibrium at temperatures near $T_g(>T_{K})$, implying that the very existence of the putative thermodynamic phase transition at $T_{K}$ can be questioned. Recent studies of systems with randomly pinned particles have hinted that the thermodynamic glass transition may be observed in simulations and experiments carried out for liquids with randomly pinned particles. This expectation is based on the results of approximate calculations that suggest that the temperature of the thermodynamic glass transition increases as the concentration of pinned particles is increased and it may be possible to equilibrate the system at temperatures near the increased transition temperature. We test the validity of this prediction through extensive molecular dynamics simulations of two model glass-forming liquids in the presence of random pinning. We fit the temperature-dependence of the structural relaxation time to the Vogel-Fulcher-Tammann form that predicts a divergence of the relaxation time at a temperature $T_{VFT}$ and identify this temperature with the thermodynamic transition temperature $T_K$. We find that $T_{VFT}$ does not show any sign of increasing with increasing concentration of pinned particles. The main effect of pinning is found to be a rapid decrease in the kinetic fragility of the system with increasing pin concentration. Implications of these observations for current theories of the glass transition are discussed.Comment: submitted to scientific repor

Growing length and time scales in glass forming liquids

We study the growing time scales and length scales associated with dynamical slow down for a realistic glass former, using computer simulations. We perform finite size scaling to evaluate a length scale associated with dynamical heterogeneity which grows as temperature decreases. However, relaxation times which also grow with decreasing temperature, do not show the same kind of scaling behavior with system size as the dynamical heterogeneity, indicating that relaxation times are not solely determined by the length scale of dynamical heterogeneity. We show that relaxation times are instead determined, for all studied system sizes and temperatures, by configurational entropy, in accordance with the Adam-Gibbs relation, but in disagreement with theoretical expectations based on spin-glass models that configurational entropy is not relevant at temperatures substantially above the critical temperature of mode coupling theory. The temperature dependence of the heterogeneity length scale shows significant deviations from theoretical expectations, and the length scale one may extract from the system size dependence of the configurational entropy has much weaker temperature dependence compared to the heterogeneity length scale at all studied temperatures. Our results provide new insights into the dynamics of glass-forming liquids and pose serious challenges to existing theoretical descriptions

Short-time β\beta-relaxation in glass-forming liquids is cooperative in nature

Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. The short-time $\beta$-relaxation is generally attributed to spatially local processes involving the rattling motion of a particle in the transient cage formed by its neighbors. Using molecular dynamics simulations for three model glass-forming liquids, we show that the $\beta$-relaxation is actually cooperative in nature. Using finite-size scaling analysis, we extract a growing length-scale associated with $\beta$-relaxation from the observed dependence of the $\beta$-relaxation time on the system size. Remarkably, the temperature dependence of this length scale is found to be the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time $\alpha$-relaxation regime. These results show that the conventional interpretation of $\beta$-relaxation as a local process is too simplified and provide a clear connection between short-time dynamics and long-time structural relaxation in glass-forming liquids

Vanishing of configurational entropy may not imply an ideal glass transition in randomly pinned liquids

Ozawa et. al [1] presented numerical results for the configurational entropy density, $s_c$, of a model glass-forming liquid in the presence of random pinning. The location of a "phase boundary" in the pin density ($c$) - temperature ($T$) plane, that separates an "ideal glass" phase from the supercooled liquid phase, is obtained by finding the points at which $s_c(T,c) \to 0$. According to the theoretical arguments by Cammarota et. al. [2], an ideal glass transition at which the $\alpha$-relaxation time $\tau_\alpha$ diverges takes place when $s_c$ goes to zero. We have studied the dynamics of the same system using molecular dynamics simulations. We have calculated the time-dependence of the self intermediate scattering function, $F_s(k,t)$ at three state points in the $(c-T)$ plane where $s_c(T,c) \simeq 0$ according to Ref. [1]. It is clear from the plots that the relaxation time is finite [$\tau_\alpha \sim \mathcal{O}(10^6)]$ at these state points. Similar conclusions have been obtained in Ref.[3] where an overlap function was used to calculate $\tau_\alpha$ at these state points

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

Block Analysis for the Calculation of Dynamic and Static Length Scales in Glass-Forming Liquids

We present {\it block analysis}, an efficient method to perform finite-size scaling for obtaining the length scale of dynamic heterogeneity and the point-to-set length scale for generic glass-forming liquids. This method involves considering blocks of varying sizes embedded in a system of a fixed (large) size. The length scale associated with dynamic heterogeneity is obtained from a finite-size scaling analysis of the dependence of the four-point dynamic susceptibility on the block size. The block size dependence of the variance of the $\alpha$-relaxation time yields the static point-to-set length scale. The values of the obtained length scales agree quantitatively with those obtained from other conventional methods. This method provides an efficient experimental tool for studying the growth of length scales in systems such as colloidal glasses for which performing finite-size scaling by carrying out experiments for varying system sizes may not be feasible.Comment: 5 pages, 3 figure

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

Signatures of Dynamical Heterogeneity in the Structure of Glassy Free-energy Minima

From numerical minimization of a model free energy functional for a system of hard spheres, we show that the width of the local peaks of the time-averaged density field at a glassy free-energy minimum exhibits large spatial variation, similar to that of the ``local Debye-Waller factor'' in simulations of dynamical heterogeneity. Molecular dynamics simulations starting from a particle configuration generated from the density distribution at a glassy free-energy minimum show similar spatial heterogeneity in the degree of localization, implying a direct connection between dynamical heterogeneity and the structure of glassy free energy minima.Comment: 5 pages, 5 figure