Equilibrium Fluid-Crystal Interfacial Free Energy of Bcc-Crystallizing Aqueous Suspensions of Polydisperse Charged Spheres

TL;DR

This study analyzes the interfacial free energy in charged colloidal suspensions during crystallization, revealing its dependence on polydispersity and entropy, and providing estimates for equilibrium values.

Contribution

It introduces a simple extrapolation scheme to estimate equilibrium interfacial free energy from non-equilibrium data in charged colloids.

Findings

Interfacial free energy decreases with increasing polydispersity.

Values are on the order of a few kBT and not correlated with electrostatic parameters.

Interfacial free energy correlates linearly with entropy of freezing.

Abstract

The interfacial free energy is a central quantity in crystallization from the meta-stable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from this data effective non-equilibrium values for the interfacial free energy between the emerging bcc-nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory. A strictly linear increase of the interfacial free energy was observed as a function of increased meta-stability. Here, we further analyze this data for five aqueous suspensions of charged spheres and one binary mixture. We utilize a simple extrapolation scheme and interpret our findings in view of Turnbull's empirical rule. Our first estimates for the reduced interfacial free energy, $\sigma_{0,bcc}$, between coexisting equilibrium uid and bcc-crystal phases are on the order of a few $k_BT$. Their values are not correlated to any of the electrostatic interaction parameters but rather show a systematic decrease with increasing size polydispersity and a lower value for the mixture as compared to the pure components. At the same time, $\sigma_0$ also shows an approximately linear correlation to the entropy of freezing. The equilibrium interfacial free energy of strictly monodisperse charged spheres may therefore be still greater.