Role of entropy in the thermodynamic evolution of the time scale of molecular dynamics near the glass transition

Abstract

In this paper, we investigate how changes in the system entropy influence the characteristic time scale of the system molecular dynamics near the glass transition. Independently of any model of thermodynamic evolution of the time scale, against some previous suppositions, we show that the system entropy S is not sufficient to govern the time scale defined by structural relaxation time τ. In the density scaling regime, we argue that the decoupling between τ and S is a consequence of different values of the scaling exponents γ and γ(S) in the density scaling laws, τ=f(ρ(γ)/T) and S=h(ρ(γ(S))/T), where ρ and T denote density and temperature, respectively. It implies that the proper relation between τ and S requires supplementing with a density factor, u(ρ), i.e., τ=g(u(ρ)w(S)). This meaningful finding additionally demonstrates that the density scaling idea can be successfully used to separate physically relevant contributions to the time scale of molecular dynamics near the glass transition. The relation reported by us between τ and S constitutes a general pattern based on nonconfigurational quantities for describing the thermodynamic evolution of the characteristic time scale of molecular dynamics near the glass transition in the density scaling regime, which is a promising alternative to the approaches based as the Adam-Gibbs model on the configurational entropy that is difficult to evaluate in the entire thermodynamic space. As an example, we revise the Avramov entropic model of the dependence τ(T,ρ), giving evidence that its entropic basis has to be extended by the density dependence of the maximal energy barrier for structural relaxation. We also discuss the excess entropy S(ex), the density scaling of which is found to mimic the density scaling of the total system entropy S.

Adam-Gibbs model in the density scaling regime and its implications for the configurational entropy scaling

“…Thus, the configurational entropy seems to be sufficient to govern the structural relaxation of supercooled liquids without any contributions from additional factors. For comparison, we have very recently established 41 that such an exclusive impact is not made on the structural relaxation by the total system entropy S and the excess entropy S ex (defined as the difference between the total system entropy and the entropy of an ideal gas at the same density and temperature), although both S and S ex obey the density scaling law. For S and S ex , the values of the scaling exponents have been found by us to be considerably different from that valid for τ α of a given glass former, and consequently the different values of the scaling exponents rationalize the decoupling observed by us between τ α and S (or S ex ) and imply that the relation between τ α and S (or S ex ) requires supplementing with an additional density factor 41 .…”

“…For comparison, we have very recently established 41 that such an exclusive impact is not made on the structural relaxation by the total system entropy S and the excess entropy S ex (defined as the difference between the total system entropy and the entropy of an ideal gas at the same density and temperature), although both S and S ex obey the density scaling law. For S and S ex , the values of the scaling exponents have been found by us to be considerably different from that valid for τ α of a given glass former, and consequently the different values of the scaling exponents rationalize the decoupling observed by us between τ α and S (or S ex ) and imply that the relation between τ α and S (or S ex ) requires supplementing with an additional density factor 41 . In this context, our findings reported herein become especially useful for further investigations, because they suggest a way to formulate an optimal model of the thermodynamic evolution of the time scale of molecular dynamics of supercooled liquids, which is expected to be able to take a form of a single variable function of the configurational entropy S C or the scaling variable TV γ in the power law density scaling regime.…”

“…(2) . This discrepancy can be argued 8 41 by considerably different values of the density scaling exponent for the dynamic quantities and the total system entropy, which have been established for real glass formers.…”

Communication: Studies of the Lennard-Jones fluid in 2, 3, and 4 dimensions highlight the need for a liquid-state 1/d expansion

“…27 from 2014. After that paper was written, it became clear that Roskilde (R) simple systems [29][30][31][32][33][34][35][36][37][38][39][40][41][42] -those with R > 0.9-are characterized by approximately obeying the following condition:…”

Thermodynamic consequences of the kinetic nature of the glass transition

“…It is worth noting that the universal character of the equivalent equations (5)–(7) , can be extended beyond the assumed case of the dependence . Considering the density scaling laws for and (discussed later for and in the Supplementary Information for ), we have very recently argued 34 that the structural relaxation time can be in general a volume-entropy function . Then, equation (5) also remains valid as shown in Supplementary Information .…”