Rods Near Curved Surfaces and in Curved Boxes

TL;DR

This study investigates how the curvature of surfaces influences the distribution and energy of rigid rods and chains near these surfaces, revealing that surface bending can lower interfacial tension and that shell shape affects rod attraction or repulsion.

Contribution

It provides a detailed analysis of the effects of surface curvature on ideal rigid rods and chains, including partition function calculations for spherical and cylindrical shells.

Findings

Bending surfaces towards rods lowers interfacial tension.

Spherical shells repel rods, cylindrical shells attract them.

Flexibility in chains influences their interaction with curved surfaces.

Abstract

We consider an ideal gas of infinitely rigid rods near a perfectly repulsive wall, and show that the interfacial tension of a surface with rods on one side is lower when the surface bends towards the rods. Surprisingly we find that rods on both sides of surfaces also lower the energy when the surface bends. We compute the partition functions of rods confined to spherical and cylindrical open shells, and conclude that spherical shells repel rods, whereas cylindrical shells (for thickness of the shell on the order of the rod-length) attract them. The role of flexibility is investigated by considering chains composed of two rigid segments.