Comment on “Residual multiparticle entropy does not generally change sign near freezing” [ J. Chem. Phys. 128, 161101 (2008) ]

摘要

Doubts on the reliability of a phenomenological criterion originally formulated by Giaquinta and Giunta1 in the context of a detailed analysis of the structural and thermodynamic changes observed in a fluid of hard spheres have been recently raised in relation to the freezing of such a model in spatial dimensions other than two and three.2 The criterion is based on the vanishing of the so-called residual multiparticle entropy (RMPE),1 a quantity defined as the cumulative contribution of more-than-two-particle correlations to the excess entropy (Sex), which can be expressed as an infinite sum of contributions associated with spatially integrated density correlations of increasing order.3,4,5 In the absence of external fields the leading and quantitatively dominant term of the series is the so-called pair entropy (S2) whose calculation solely requires the knowledge of the pair distribution function of the fluid. The only practical, even if indirect, way to determine the RMPE is to compute it as a difference between the excess and pair entropies: ΔS(ρ,T) = Sex(ρ,T)−S2(ρ,T), where ρ is the particle number density and T is the temperature of the fluid.nSince the first explicit observation of a sign change in the RMPE of three-dimensional hard spheres at their freezing point,1 a similar feature has been reported in other pure model fluids6,7,8,9,10,11,12,13,14,15,16 as well as in mixtures,17,18 also in two dimensions.19 In all such cases qualitative (and, often, semiquantitative) congruence between the zero-RMPE loci and the freezing lines was observed along extended thermodynamic paths, traced as a function of temperature, pressure, density, or concentration. Moreover, at variance with other phenomenological one-phase criteria whose applicability is restricted to the freezing transition, the indications provided by the RMPE on the existence and location of an ordering threshold turn out to be significant also in thermodynamic situations where it is two fluid phases that compete, as in the condensation of a gas into a liquid phase11 or in the fluid-fluid phase separation undergone by a binary mixture.20,21,22 The RMPE has been also found to be a sensitive indicator of the onset of even partial ordering processes such as the emergence of mesophases (nematic, smectic) in model liquid crystals23,24,25 or the formation of a hydrogen-bonded network in water.26 In lattice gases27 it further gives interesting clues on other types of transitions such as the infinite-order Kosterlitz and Thouless phase transition.28