ABSTRACT
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 kBT, 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 kBT.
ABSTRACT
The Helmholtz free energy of a constrained supersaturated vapor with a cluster size distribution consisting of clusters of various sizes is modeled as a mixture of hard spheres of various sizes attracting each other. This model naturally takes into account monomer-monomer and monomer-cluster interactions, so it implicitly pertains to nonideal gases, unlike prior work. Based on this model, the expressions for the equilibrium concentration and the formation free energies of clusters in a metastable supersaturated vapor have been derived. These results indicate that the widely used formula, ni = n1exp(-ßΔGi), that computes the formation free energy of a cluster does not work at high supersaturations. As an example, the formation free energies of clusters with Stillinger's physical cluster definition in metastable, highly supersaturated vapors interacting via Lennard-Jones potential are studied using these expressions. Noticeable differences have been found for both the formation free energies of clusters and sizes of the critical clusters computed from our proposed expressions vs those from the formula ni = n1exp(-ßΔGi).
ABSTRACT
In order to improve the sampling of restricted microstates in our previous work [C. Nie, J. Geng, and W. H. Marlow, J. Chem. Phys. 127, 154505 (2007); 128, 234310 (2008)] and quantitatively predict thermal properties of supersaturated vapors, an extension is made to the Corti and Debenedetti subcell constraint algorithm [D. S. Corti and P. Debenedetti, Chem. Eng. Sci. 49, 2717 (1994)], which restricts the maximum allowed local density at any point in a simulation box. The maximum allowed local density at a point in a simulation box is defined by the maximum number of particles Nm allowed to appear inside a sphere of radius R, with this point as the center of the sphere. Both Nm and R serve as extra thermodynamic variables for maintaining a certain degree of spatial homogeneity in a supersaturated system. In a restricted canonical ensemble, at a given temperature and an overall density, series of local minima on the Helmholtz free energy surface F(Nm, R) are found subject to different (Nm, R) pairs. The true equilibrium metastable state is identified through the analysis of the formation free energies of Stillinger clusters of various sizes obtained from these restricted states. The simulation results of a supersaturated Lennard-Jones vapor at reduced temperature 0.7 including the vapor pressure isotherm, formation free energies of critical nuclei, and chemical potential differences are presented and analyzed. In addition, with slight modifications, the current algorithm can be applied to computing thermal properties of superheated liquids.
