On the liquid-glass transition line in monatomic Lennard-Jones fluids

Abstract

A thermodynamic approach to derive the liquid-glass transition line in the reduced temperature vs reduced density plane for a monatomic Lennard-Jones fluid is presented. The approach makes use of a recent reformulation of the classical perturbation theory of liquids [M. Robles and M. López de Haro, Phys. Chem. Chem. Phys. 3, 5528 (2001)] which is at grips with a rational function approximation for the Laplace transform of the radial distribution function of the hard-sphere fluid. The only input required is an equation of state for the hard-sphere system. Within the Mansoori-Canfield/Rasaiah-Stell variational perturbation theory, two choices for such an equation of state, leading to a glass transition for the hard-sphere fluid, are considered. Good agreement with the liquid-glass transition line derived from recent molecular dynamic simulations [Di Leonardo et al., Phys. Rev. Lett. 84, 6054(2000)] is obtained.

Theoretical scheme for the shear viscosity of Lennard-Jones fluids

“…This fact was used in Ref. 10 to predict a liquid-glass transition line by solving the equation d 3 ͑ * , T * ͒ /6= g , in a MC/RS perturbation scheme. Therefore, in principle the transition line can be translated to the * − T * or * − * spaces.…”

Impact of elastic heterogeneity on the propagation of vibrations at finite temperatures in glasses

“…We have used periodic boundary conditions in cubic simulation boxes of size L, such that the number density isρ = N/L 3 = 1.015. Atρ, the melting and glass-transition temperatures are T m ≃ 1.0 and T g ≃ 0.4 [51], respectively. In order to access the relevant small wave vector (q) region relevant here, we have considered N = 4000 to 1000188, corresponding to L = 15.80 to 99.…”

Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids

“…(119) it may well happen that, once Z s has been chosen, there exists a certain packing fraction η g above which α is no longer positive. This may be interpreted as an indication that, at the packing fraction η g where α vanishes, the system ceases to be a fluid and a glass transition in the HS fluid occurs [74][75][76]. Expanding (113) in powers of s and using Eq.…”

“…Similarly, admitting that there is a glass transition in the HS fluid at the packing fraction η g ≃ 0.56 [128], one can now determine the location of the liquid-glass transition line for the LJ fluid in the (ρ, T ) plane from the simple relationship (π/6)ρσ 3 0 (ρ, T ) = η g . With a proper choice for Z HS , it has been shown [76,129,130] that the critical point, the structure, and the phase diagram (including a glass transition) of the LJ fluid may be adequately described with this approach.…”