Shapes of a liquid droplet in a periodic box

TL;DR

This paper investigates the shape transitions of liquid droplets in a periodic simulation box, developing a theory that predicts morphological changes and matches Monte Carlo data for Lennard-Jones fluids.

Contribution

It introduces a simple theoretical framework for droplet shape transitions in finite systems, extending previous models and validating predictions with simulation data.

Findings

Shape transitions from spherical to cylindrical to slab-like droplets are predicted.

The theory aligns well with Monte Carlo simulation results for Lennard-Jones fluids.

Metastability of complex droplet shapes is discussed and classified.

Abstract

Within the coexistence region between liquid and vapor the equilibrium pressure of a simulated fluid exhibits characteristic jumps and plateaus when plotted as a function of density at constant temperature. These features exclusively pertain to a finite-size sample in a periodic box, as they are washed out in the bulk limit. Below the critical density, at each pressure jump the shape of the liquid drop undergoes a morphological transition, changing from spherical to cylindrical to slab-like as the density is increased. We formulate a simple theory of these shape transitions, which is adapted from a calculation originally developed by Binder and coworkers [{\em J. Chem. Phys.} {\bf 120}, 5293 (2004)]. Our focus is on the pressure equation of state (rather than on the chemical potential, as in the original work) and includes an extension to elongated boxes. Predictions based on this theory well agree with extensive Monte Carlo data for the cut-and-shifted Lennard-Jones fluid. We further discuss on the thermodynamic stability of liquid drops with shapes other than the three mentioned above, like those found deep inside the liquid-vapor region in simulations starting from scratch. Our theory classifies these more elaborate shapes as metastable.