Dynamic equivalence between atomic and colloidal liquids

Abstract

We show that the kinetic-theoretical self-diffusion coefficient of an atomic fluid plays the same role as the short-time self-diffusion coefficient DS in a colloidal liquid, in the sense that the dynamic properties of the former, at times much longer than the mean free time, and properly scaled with DS, will be indistinguishable from those of a colloidal liquid with the same interaction potential. One important consequence of such dynamic equivalence is that the ratio DL/DS of the long-time to the short-time self-diffusion coefficients must then be the same for both, an atomic and a colloidal system characterized by the same inter-particle interactions. This naturally extends to atomic fluids a well-known dynamic criterion for freezing of colloidal liquids [Phys. Rev. Lett. 70, 1557(1993]. We corroborate these predictions by comparing molecular and Brownian dynamics simulations on the hard-sphere system and on other soft-sphere model systems, representative of the "hard-sphere" dynamic universality class. One of the fundamental challenges in understanding the relationship between dynamic arrest phenomena in colloidal systems [1], and the glass transition in simple glass-forming atomic liquids [2], is to determine the role played by the underlying (Brownian vs. Newtonian) microscopic dynamics. It is a widespread notion that colloidal systems constitute a mesoscopic analog of atomic systems regarding the relationship between inter-particle forces and macroscopic properties [3,4]. The molecular dynamics simulation of an atomic liquid, for example, is expected to yield the same equilibrium phase diagram, and a similar dynamic arrest scenario, as the Brownian dynamics simulation of a colloidal liquid, when referring to the same model system [5,6]. Important questions, however, remain unanswered, even at normal liquid states, far from the neighborhood of the conditions for dynamic arrest. For example, while it is well-known that monodisperse Brownian liquids will freeze when the longtime self-diffusion coefficient D L reaches about 0.1×D S , with D S being the short-time self-diffusion coefficient ("Löwen's dynamic freezing criterion" [7]), no analogous criterion has been identified for the corresponding atomic liquids.In the attempt to develop the extension to atomic liquids, of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [8], we have discovered that a well-defined long-time dynamic equivalence between atomic and colloidal liquids emerges upon the identification of the kinetic-theoretical self-diffusion coefficient D 0 of an atomic fluid [9], as the analog of the short-time self-diffusion coefficient D S of a colloidal liquid. In this short communication we describe the physical foundations of this extended SCGLE theory, which also constitute the physical basis of the referred dynamic equivalence. One of the most important manifestations of the latter is that the ratio D * ≡ D L /D S must then be the same for an atomic and a colloidal system characterized by the same inter-par...

Non-equilibrium theory of arrested spinodal decomposition

“…where the phenomenological cut-off wave-vector k c depends on the system considered. Since in this paper we are only interested in semi-quantitative trends, here we adopt the value k c = 1.305(2π/σ) = 8.2/σ, determined in a calibration procedure involving simulation data of the hard-spheres system [41].…”

Isomorphs, hidden scale invariance, and quasiuniversality

“…• Different IPL systems' close similarities with respect to structure and dynamics, similarities that extend to all other Roskilde-simple liquids [47][48][49][50][51][52][53][54][55][56][57][58][59][60].…”

Explaining why simple liquids are quasi-universal

“…An early hint of dynamic quasi-universality was provided by Rosenfeld who in 1977 showed that the diffusion constant is an almost universal function of the excess entropy (the entropy minus that of an ideal gas at the same temperature and density) [6]. This finding did not attract a great deal of attention at the time, but the last decade has seen renewed interest in excess-entropy scaling [7,8] and, more generally, in the striking similarities of the structure and dynamics of many simple model liquids [9][10][11][12][13][14]. Thus Heyes and Branka and others have documented that inverse power-law (IPL) systems with different exponents have similar structure and dynamics [9,11,[20][21][22][23], Medina-Noyola and coworkers have established that quasi-universality extends to the dynamics for Newtonian as well as Brownian equations of motion [10,13,14], Scopigno and co-workers [21] have documented HS-like dynamics in liquid gallium studied by quasi-elastic neutron scattering, and Liu and coworkers have suggested a mapping of a soft-sphere system's dynamics to that of the HS system [12].…”