Droplet condensation in the lattice gas with density functional theory

TL;DR

This paper uses density functional theory to study droplet states in a lattice gas, revealing complex behaviors influenced by lattice discreteness and surface effects, with implications for understanding phase transitions and surface tension.

Contribution

The study applies a fundamental measure theory-based density functional to analyze droplet states in a lattice gas, highlighting effects of lattice discreteness and surface phenomena.

Findings

Sequence of droplet to cylinder to slab transitions observed.

Oscillations and undulations in chemical potential and surface tension behavior.

Large-radius surface tension dominated by 1/R_s^2 term with weak logarithmic correction.

Abstract

A density functional for the lattice gas (Ising model) from fundamental measure theory is applied to the problem of droplet states in three-dimensional, finite systems. Similar to previous simulation studies, the sequence of droplets changing to cylinders and to planar slabs is found upon increasing the average density $\bar\rho$ in the system. Owing to the discreteness of the lattice, additional effects in the state curve for the chemical potential $\mu(\bar\rho)$ are seen upon lowering the temperature away from the critical temperature (oscillations in $\mu(\bar\rho)$ in the slab portion and spiky undulations in $\mu(\bar\rho)$ in the cylinder portion as well as an undulatory behavior of the radius of the surface of tension $R_s$ in the droplet region). This behavior in the cylinder and droplet region is related to washed-out layering transitions at the surface of liquid cylinders and droplets. The analysis of the large-radius behavior of the surface tension $\gamma(R_s)$ gave a dominant contribution $\propto 1/R_s^2$, although the consistency of $\gamma(R_s)$ with the asymptotic behavior of the radius-dependent Tolman length seems to suggest a weak logarithmic contribution $\propto \ln R_s/R_s^2$ in $\gamma(R_s)$. The coefficient of this logarithmic term is smaller than a universal value derived with field-theoretic methods.