Functional Theory Of Inhomogeneous Liquids Research Articles

Density functional theory of inhomogeneous liquids. IV. Squared-gradient approximation and classical nucleation theory

The squared-gradient approximation to the modified-core Van der Waals density functional theory model is developed. A simple, explicit expression for the SGA coefficient involving only the bulk equation of state and the interaction potential is given. The model is solved for planar interfaces and spherical clusters and is shown to be quantitatively accurate in comparison to computer simulations. An approximate technique for solving the SGA based on piecewise-linear density profiles is introduced and is shown to give reasonable zeroth-order approximations to the numerical solution of the model. The piecewise-linear models of spherical clusters are shown to be a natural extension of classical nucleation theory and serve to clarify some of the nonclassical effects previously observed in liquid-vapor nucleation. Nucleation pathways are investigated using both constrained energy-minimization and steepest-descent techniques.

Density functional theory of inhomogeneous liquids. III. Liquid-vapor nucleation

The process of nucleation of vapor bubbles from a superheated liquid and of liquid droplets from a supersaturated vapor is investigated using the modified-core van der Waals model density functional theory [J. F. Lutsko, J. Chem. Phys. 128, 184711 (2008)]. A novel approach is developed whereby nucleation is viewed as a transition from a metastable state to a stable state via the minimum free energy path, which is identified using the nudged elastic-band method for exploring free energy surfaces. This allows for the unbiased calculation of the properties of sub- and super-critical clusters, as well as of the critical cluster. For Lennard-Jones fluids, the results compare well to simulation and support the view that at low to moderate supersaturation nucleation proceeds smoothly rather than via spinodal-like instabilities as has been suggested recently. The possibility that the nucleation barrier vanishes at high supersaturation is, however, not ruled out.

Density functional theory of inhomogeneous liquids. II. A fundamental measure approach

Previously, it has been shown that the direct correlation function for a Lennard-Jones fluid could be modeled by a sum of that for hard-spheres, a mean-field tail, and a simple linear correction in the core region constructed so as to reproduce the (known) bulk equation of state of the fluid [Lutsko, J. Chem. Phys. 127, 054701 (2007)]. Here, this model is combined with ideas from the fundamental measure theory to construct a density functional theory for the free energy. The theory is shown to accurately describe a range of inhomogeneous conditions including the liquid vapor interface, the fluid in contact with a hard wall, and a fluid confined in a slit pore. The theory gives quantitatively accurate predictions for the surface tension, including its dependence on the potential cutoff. It also obeys two important exact conditions: That relating the direct correlation function to the functional derivative of the free energy with respect to density and the wall theorem.

Density functional theory of inhomogeneous liquids. I. The liquid-vapor interface in Lennard-Jones fluids

A simple model is proposed for the direct correlation function (DCF) for simple fluids consisting of a hard-core contribution, a simple parametrized core correction, and a mean-field tail. The model requires as input only the free energy of the homogeneous fluid, obtained, e.g., from thermodynamic perturbation theory. Comparison to the DCF obtained from simulation of a Lennard-Jones fluid shows this to be a surprisingly good approximation for a wide range of densities. The model is used to construct a density functional theory for inhomogeneous fluids which is applied to the problem of calculating the surface tension of the liquid-vapor interface. The numerical values found are in good agreement with simulation.