Formation free energies of clusters at high supersaturations

Estimating metastable thermodynamic properties by isochoric extrapolation from stable states

The description of metastable fluids, those in local but not global equilibrium, remains an important problem of thermodynamics, and it is crucial for many industrial applications and all first order phase transitions. One way to estimate their properties is by extrapolation from nearby stable states. This is often done isothermally, in terms of a virial expansion for gases or a Taylor expansion in density for liquids. This work presents evidence that an isochoric expansion of pressure at a given temperature is superior to an isothermal density expansion. Two different isochoric extrapolation strategies are evaluated, one best suited for vapors and one for liquids. Both are exact for important model systems, including the van der Waals equation of state. Moreover, we present a simple method to evaluate all the coefficients of the isochoric expansion directly from a simulation in the canonical ensemble. Using only the properties of stable states, the isochoric extrapolation methods reproduce simulation results with Lennard-Jones potentials, mostly within their uncertainties. The isochoric extrapolation methods are able to predict deeply metastable pressures accurately even from temperatures well above the critical. Isochoric extrapolation also predicts a mechanical stability limit, i.e., the thermodynamic spinodal. For water, the liquid spinodal pressure is predicted to be monotonically decreasing with decreasing temperature, in contrast to the re-entrant behavior predicted by the direct extension of the reference equation of state.

Formation free energy of an i-mer at spinodal

In statistical mechanics, the formation free energy of an i-mer can be understood as the Gibbs free energy change in a system consisting of pure monomers after and prior to the formation of the i-mer. For molecules interacting via Lennard-Jones potential, we have computed the formation free energy of a Stillinger i-mer [F. H. Stillinger, J. Chem. Phys. 38, 1486 (1963)] and a ten Wolde-Frenkel (tWF) [P. R. ten Wolde and D. Frenkel, J. Chem. Phys. 109, 9901 (1998)] i-mer at spinodal at reduced temperatures from 0.7 to 1.2. It turns out that the size of a critical Stillinger i-mer remains finite and its formation free energy is on the order of k_BT, and the size of a critical tWF i-mer remains finite and its formation free energy is even higher. This can be explained by Binder's theory [K. Binder, Phys. Rev. A 29, 341 (1984)] that for a system, when approaching spinodal, if the Ginzburg criterion is not satisfied, a gradual transition will take place from nucleation to spinodal decomposition, where the free-energy barrier height is on the order of k_BT.