Nucleation of liquid droplets in a fluid with competing interactions

Abstract

Using a simple density functional theory (DFT) the height of the free energy barrier for forming a droplet of the liquid phase from the metastable gas phase is determined for a model colloidal fluid exhibiting competing interactions. The pair potential has a hard core of diameter σ, is attractive Yukawa at intermediate separations, and is repulsive Yukawa at large separations. It is found that even a very weak long-range repulsive tail in the pair potential has a profound effect on nucleation: increasing the amplitude of the repulsive Yukawa tail reduces significantly the free energy barrier height and therefore increases the liquid droplet nucleation rate. The method introduced for calculating the droplet density profile and free energy employs a fictitious external potential to stabilize a liquid droplet of the desired size, i.e. with a given excess number of particles. For the critical droplet, corresponding to an extremum of the grand potential, this fictitious potential is everywhere zero. The decay of the droplet density profiles into the bulk gas is examined. For a range of nucleation state points the DFT predicts exponentially damped, long wavelength oscillatory decay for systems exhibiting long-range repulsion, contrasting sharply with the monotonic decay found when the pair potential has only an attractive Yukawa piece. The changes in nucleation properties found for small amplitudes of the repulsive Yukawa tail reflect the propensity of the fluid to form modulated structures such as clusters or stripes.

Keywords:

• nucleation
• free energy barrier
• colloids
• competing interactions
• gas–liquid phase separation
• density functional theory

Acknowledgements

It is a pleasure to dedicate this contribution to Luciano Reatto – a hugely influential figure in the theory of liquids. He and Davide Pini inspired both of us to investigate the structural properties and phase behaviour of mermaid models. We are grateful for their insight and for guiding us to many of the problems, and the solutions, that we addressed in recent years. AJA acknowledges the support of RCUK.