Characteristic temperatures of glassy behaviour in a simple liquid

Localization, Disorder, and Entropy in a Coarse-Grained Model of the Amorphous Solid

We study the role of disorder in producing the metastable states in which the extent of mass localization is intermediate between that of a liquid and a crystal with long-range order. We estimate the corresponding entropy with the coarse-grained description of a many-particle system used in the classical density functional model. We demonstrate that intermediate localization of the particles results in a change of the entropy from what is obtained from a microscopic approach using for sharply localized vibrational modes following a Debye distribution. An additional contribution is included in the density of vibrational states g(ω) to account for this excess entropy. A corresponding peak in g(ω)/ω2 vs. frequency ω matches the characteristic boson peak seen in amorphous solids. In the present work, we also compare the shear modulus for the inhomogeneous solid having localized density profiles with the corresponding elastic response for the uniform liquid in the limit of high frequencies.

Metastable-state dynamics of a liquid: a free-energy landscape study

Using the time dependence of density fluctuations in a supercooled liquid obtained from the solutions of the equations of nonlinear fluctuating hydrodynamics (NFH), the evolution of the system in the free energy landscape is studied. A crossover from a continuous fluid type dynamics to that of hopping between different free energy minima is observed as the liquid is increasingly supercooled. We demonstrate that our results are also in agreement with equilibrium density functional analysis of the same system. The density field obtained in the numerical solution of the NFH equations are further analyzed to introduce complimentary density of voids in the supercooled liquid state and its static and dynamic correlations are computed. The nature of the relaxation of vacancy correlations are observed to be similar to that of the density fluctuations.

Time-dependent correlations in a supercooled liquid from nonlinear fluctuating hydrodynamics

We solve numerically the equations of nonlinear fluctuating hydrodynamics (NFH). A coarse graining of the density field is applied at each time step to avoid instabilities which otherwise plague the algorithm at long times. The equilibrium correlation of the density fluctuations at different times obtained directly from the solutions of the NFH equations are shown here to be in quantitative agreement with corresponding molecular dynamics simulation data. Low-order perturbative treatment of the these NFH equations obtains the mode coupling model. The latter has been widely studied for understanding the slow dynamics characteristic of the supercooled state. A crucial aspect of this theory is a rounded version of a possible ergodic-nonergodic transition in the supercooled liquid at a temperature T(c) between melting point T(m) and the glass transition temperature T(g). In the present work we demonstrate numerically the role of strongly coupled density fluctuations in giving rise to slow dynamics and how the 1/ρ nonlinearity in the NFH equations of motion is essential in restoring the ergodic behavior in the liquid. The relaxation data indicate that at moderate supercooling near T(c), the time temperature superposition holds. The relaxation gets increasingly stretched with increased supercooling. The relaxation time τ shows an initial power-law divergence approaching a transition temperature T(c) generally identified as the mode coupling temperature. From the direct solutions we obtain a value for T(c) much lower than that typically estimated from solution of low-order integral equations of mode coupling theory. This is in agreement with the trend seen in computer simulations.

Free-energy landscape for a tagged particle in a dense hard-sphere fluid

Exploiting the thermodynamic potential functional provided by density functional theory, we determine analytically the free-energy landscape (FEL) in a hard-sphere fluid. The FEL is represented in the three-dimensional coordinate space of the tagged particle. We also analyze the distribution of the free-energy barrier between adjacent basins and show that the most provable value and the average of the free-energy barrier are increasing functions of the density. Since the size of the cooperatively rearranging region (CRR) is also increased as the density is raised [Yoshidome, Phys. Rev. E 76, 021506 (2007)], the present result is consistent with the Adam-Gibbs theory in which the increase of the activation energy is due to the increase of the size of the CRR.

Simulation of an atomistic dynamic field theory for monatomic liquids: freezing and glass formation

We examine a phase field crystal model for simple liquid-solid systems consisting of a free energy functional related to the Ramakrishnan-Yussouff free energy of classical density functional theory and an equation of motion capable of describing long-time-scale behavior in the deeply supercooled regime. The thermodynamics and dynamics of freezing and glass formation in this model system are studied through large-scale three-dimensional Langevin simulations. At low cooling rates bcc crystals are formed by nucleation and growth from the melt. At large cooling rates no clear glass transition is observed, but a kinetically driven first-order transition from supercooled liquid to a disordered glasslike solid does occur. Despite the peculiarities of the transition, the structure and properties of the resulting disordered solid are shown to strongly resemble those of a typical glass. Consequences of pseudocritical behavior and heterogeneity near the liquid spinodal are also discussed.