Molecular dynamics simulation study of self-diffusion for penetrable-sphere model fluids

Abstract

Molecular dynamics simulations are carried out to investigate the diffusion behavior of penetrable-sphere model fluids characterized by a finite energy barrier ϵ. The self-diffusion coefficient is evaluated from the time-dependent velocity autocorrelation function and mean-square displacement. Detailed insights into the cluster formation for penetrable spheres are gained from the Enskog factor, the effective particle volume fraction, the mean free path, and the collision frequency for both the soft-type penetrable and the hard-type reflective collisions. The simulation data are compared to theoretical predictions from the Boltzmann kinetic equation and from a simple extension to finite ϵ of the Enskog prediction for impenetrable hard spheres (ϵ→∞). A reasonable agreement between theoretical and simulation results is found in the cases of ϵ∗ ≡ ϵ/k(B)T=0.2, 0.5, and 1.0. However, for dense systems (packing fraction ϕ>0.6) with a highly repulsive energy barrier (ϵ∗ = 3.0), a poorer agreement was observed due to metastable static effects of clustering formation and dynamic effects of correlated collision processes among these cluster-forming particles.

Communication: Generalizing Rosenfeld's excess-entropy scaling to predict long-time diffusivity in dense fluids of Brownian particles: From hard to ultrasoft interactions

“…trends in the long-time molecular dynamics of particles with bounded, penetrable-sphere interactions. 37 Another promising, albeit more heuristic, approach for predicting the dynamic properties of soft-particle fluids is a recently proposed generalization 21 of the excess-entropy scaling method of Rosenfeld. 38,39 Here, excess entropy s ex refers to the difference between the entropy per particle of the fluid and that of an ideal gas of particles with the same number density ρ.…”

[N]pT Monte Carlo simulations of the cluster-crystal-forming penetrable sphere model

“…This distinction between the high and low T regime also has a dynamical signature. 16,18 Collisions between particles can be divided in two types: soft refractive collisions, in which a particle goes through another, and hard reflective collisions, in which particles elastically bounce back from each other. At temperatures T 0.3 from molecular dynamics simulations 18 or T 0.25-0.5 from an Enskog-type theoretical analysis, 16 the first collision type is highly suppressed because the particle momenta are low, and the collision frequency of the second type is as high as in hard spheres.…”

“…Its properties have been explored by density functional theory (DFT), cell theory, kinetic theory, and basic simulations. [14][15][16][17][18] To complement these two systems, Mladek et al have introduced the generalized exponential model of index n (GEM-n), with a pair potential that scales with distance r like exp (− r n ), to interpolate between the GCM (n = 2) and the PSM (n = ∞). 19 Since then, a number of additional dynamic and thermodynamic studies have looked at the exotic properties of this class of models.…”

Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties

“…In the ϵ → 0 limit, the interactions are completely ideal. The PS model has been extensively studied analytically and through simulation [23][24][25][26][27][28][29] as it provides for a simple theoretical model describing the anomalous structural and dynamical behavior observed in soft-matter systems. Systems governed by bounded interactions can give rise to an interesting phase behavior in which completely repulsive pairwise interactions give rise to multiple occupancy lattice geometries in the formation of "cluster crystals."…”

“…10,17,[29][30][31] In molecular dynamics (MD) simulations of the PS model, Santos and coworkers observed anomalous dynamical properties due to this clustering behavior. 26 While the CG procedure has been shown to be an effective method for modeling structural properties, 2,3 the timescale acceleration of dynamical observables is a known problem. 32 Several methodologies including dissipative particle dynamics 33 and multi-particle collision dynamics 34,35 have been applied to control thermal fluctuations, and thus the respective time-scale of dynamical evolution through the construction of renormalized solvent-solute interactions.…”