Thermodynamic and structural properties of the high density Gaussian core model

Abstract

We numerically study thermodynamic and structural properties of the one-component Gaussian core model at very high densities. The solid-fluid phase boundary is carefully determined. We find that the density dependence of both the freezing and melting temperatures obey the asymptotic relation, log T f , log T m ∝ −ρ 2/3 , where ρ is the number density, which is consistent with Stillinger's conjecture. Thermodynamic quantities such as the energy and pressure and the structural functions such as the static structure factor are also investigated in the fluid phase for a wide range of temperature above the phase boundary. We compare the numerical results with the prediction of the liquid theory with the random phase approximation (RPA). At high temperatures, the results are in almost perfect agreement with RPA for a wide range of density, as it has already been shown in the previous studies. In the low temperature regime close to the phase boundary line, although RPA fails to describe the structure factors and the radial distribution functions at the length scales of the interparticle distance, it successfully predicts their behaviors at longer length scales. RPA also predicts thermodynamic quantities such as the energy, pressure, and the temperature at which the thermal expansion coefficient becomes negative, almost perfectly. Striking ability of RPA to predict thermodynamic quantities even at high densities and low temperatures is understood in terms of the decoupling of the length scales which dictate thermodynamic quantities from the interparticle distance which dominates the peak structures of the static structure factor due to the softness of the Gaussian core potential.

Mean-field dynamic criticality and geometric transition in the Gaussian core model

“…(A1)). Indeed, we found S(k → 0) ≈ 10 −6 at the temperatures we studied [26]. Furthermore, χ 2 ρ in Eq.…”

“…The crystallization kinetics is very slow and virtually negligible in our simulations [23,24]. We note that the density is much higher than ρ ≈ 0.24, the re-entrant melting density of GCM [26][27][28]. In the low density limit, the GCM approaches asymptotyically the three-dimensional hard sphere model [21].…”

“…In the following, we will use σ, 10 −6 ǫ, and 10 −6 ǫ/k B as units of the length, energy, and temperature, respectively. We focus on supercooled fluids along the isochore ρ = 2.0, for which the thermodynamically stable state is the BCC crystal (for T < 8.2) [23,26]. The crystallization kinetics is very slow and virtually negligible in our simulations [23,24].…”

Generalized Langevin equations for a driven tracer in dense soft colloids: construction and applications

“…In the same line of reasoning, one could wonder whether glassy effects could come into play upon lowering the density even more. Indeed it has been observed that in soft systems, the melting transition and the glass transition are re-entrant, meaning that one can observe the melting of the crystal or of the glass upon densifying the system [38,47,48]. The perturbative expansion that we use here is likely to be valid only at even higher densities, since only non-perturbative calculations such as Mode-Coupling Theory have so far been able to capture glassy behaviors in the dynamics [49,50].…”

Hyperuniform states of matter

“…The Gaussian-core model (GCM), in which particles interact with a a purely repulsive Gaussian pair potential, v 2 (r) = exp[−(r/σ) 2 ], was introduced by Stillinger [364] as a simple model to mimic effective pair interactions between the centers of mass of two polymer chains. Since then, the GCM has been investigated by many groups [363,[365][366][367]. Zachary, Stillinger and Torquato [363] studied the liquid states of this model in R d in various approximations and arbitrary dimensions.…”