Combined Description of the Equation of State and Diffusion Coefficient of Liquid Water Using a Two-State Sanchez–Lacombe Approach

Abstract

Water is one of the most important compounds on Earth, yet its material properties are still poorly understood. Here, we use a recently developed two-state, two-(time)scale (TS2) dynamic mean-field model combined with the two-state Sanchez–Lacombe (SL) thermodynamic theory in order to describe the equation of state (density as a function of temperature and pressure) and diffusivity of liquid water. In particular, it is shown that in a relatively wide temperature and pressure range (160 K < T < 360 K; 0 < P < 100 MPa), density and self-diffusion obey a special type of dynamic scaling, similar to the “τTV” scaling of Casalini and Roland, but with the negative exponent γ. The model predictions are consistent with experimental data. The new equation of state can be used for various process models and generalized to include multicomponent mixtures.

Unifying Physical Framework for Stretched-Exponential, Compressed-Exponential, and Logarithmic Relaxation Phenomena in Glassy Polymers

“…If one is to use the TZ equation to describe the volume, enthalpy, or stress relaxation in polymeric glass-formers, the question arises: what is the physical meaning of the parameters used in this equation, and how they can be tied to other material properties (preferably the equilibrium ones)? Here, we demonstrate that the TZ relaxation equation can be derived in a straightforward way within the “two-state, two-(time)­scale” (TS2) framework recently proposed by Ginzburg et al − Within this framework, the “fast” state variable, ψ (the “solid” state fraction), relaxes on the time scale of the Johari–Goldstein beta-relaxation time, τ β . The “slow” state variable, ν (the lattice “occupancy”; [1 – ν] is the fractional free volume), relaxes on the time scale of the alpha-relaxation time, τ α , which, in turn, depends on ψ.…”