Hard rectangles near curved hard walls: tuning the sign of the Tolman length

TL;DR

This study combines analytic, simulation, and density functional methods to analyze how the Tolman length's sign can be tuned for hard rectangles near curved walls, revealing its dependence on density and aspect ratio.

Contribution

It introduces a comprehensive approach to determine the curvature correction of interfacial tension for anisotropic particles near curved boundaries, highlighting tunable sign change of the Tolman length.

Findings

The Tolman length changes sign at a finite density.

Aspect ratio influences the sign and magnitude of the Tolman length.

Curvature and density jointly affect interfacial tension corrections.

Abstract

Combining analytic calculations, computer simulations, and classical density functional theory we determine the interfacial tension of orientable two-dimensional hard rectangles near a curved hard wall. Both a circular cavity holding the particles and a hard circular obstacle surrounded by particles are considered. We focus on moderate bulk densities (corresponding to area fractions up to 50 percent) where the bulk phase is isotropic and vary the aspect ratio of the rectangles and the curvature of the wall. The Tolman length, which gives the leading curvature correction of the interfacial tension, is found to change sign at a finite density, which can be tuned via the aspect ratio of the rectangles.