Spatially heterogeneous dynamics and locally arrested density fluctuations from first principles

Abstract

We present a first-principles formalism for studying dynamical heterogeneities in glass-forming liquids. Based on the non-equilibrium self-consistent generalized Langevin equation theory, we were able to describe the time-dependent local density profile during the particle interchange among small regions of the fluid. The final form of the diffusion equation contains both the contribution of the chemical potential gradient written in terms of a coarse-grained density and a collective diffusion coefficient as well as the effect of a history-dependent mobility factor. With this diffusion equation, we captured interesting phenomena in glass-forming liquids such as the cases when a strong density gradient is accompanied by a very low mobility factor attributable to the denser part: in such circumstances, the density profile falls into an arrested state even in the presence of a density gradient. On the other hand, we also show that above a certain critical temperature, which depends on the volume fraction, any density heterogeneity relaxes to a uniform state in a finite time, known as equilibration time. We further show that such equilibration time varies little with the temperature in diluted systems but can change drastically with temperature in concentrated systems.

Boson and two-dimensional cluster model composed of quenching disorder eigenvalues and eigenvectors in the glass transition

“…The positively charged particles (M + -Ps) of all HSMs in a z-axial soft matrix are located at the equipotential singularities of 1/16, and all negatively charged electrons of all HSMs are located at point p-p * of n = 0, and their average position is at the bottom of the potential well with z = 0.. Each CI-boson has 16 CEPs with different repulsion energies in the z-direction, which may be of microscopic origin for the potential energy landscape 39,40 (iv) CI-boson has heterogeneity. Density heterogeneity or kinetic heterogeneity is also a hot topic about glass state 41,42 . which can be attributed to the heterogeneity of the distribution of CI-bosons.…”

Perspective: New directions in dynamical density functional theory

“…Montañez-Rodríguez et al [151] studied diffusion on spherical surfaces. The nonequilibrium self-consistent generalized Langevin equation [152], an extension of DDFT, was applied to arrested density fluctuations by Lira-Escobedo et al [153,154]. Density fluctuations were also modeled using an adiabatic approximation by Szamel [155].…”