Higher derivative free energy terms and interfacial curvatures

TL;DR

This paper investigates how higher derivative free energy terms influence the shape of interfaces in phase-separated systems, linking these terms to measurable interfacial curvatures and energies.

Contribution

It demonstrates the explicit connection between higher derivative terms and interfacial curvature contributions in phase separation models.

Findings

Higher derivative terms determine interface shape.

These terms relate directly to mean and Gaussian curvature.

They influence the interfacial free energy explicitly.

Abstract

High derivative terms do not play a major role in field theories because of the associated complexity and inherent difficulty in connecting these terms to physically measurable quantities. A role for higher derivative terms is analyzed for the case of field theories used to describe phase separated systems. In these theories, higher derivative terms are directly connected to an interfacial free energy which contains the mean and the Gaussian curvature and are shown to determine explicitly the shape of the interface.