Vesicles in solutions of hard rods

TL;DR

This paper investigates how solutions of hard rod-like particles influence the surface free energy and equilibrium shapes of vesicles, revealing non-analytical curvature effects and shifts in shape transition boundaries.

Contribution

It introduces a second-order curvature expansion for hard rods near surfaces, showing non-analytical behavior and its impact on vesicle shape transitions.

Findings

Non-analytical curvature dependence of surface free energy

Shift in prolate-oblate transition due to rod solutions

Changes cannot be simplified by rescaling elastic constants

Abstract

The surface free energy of ideal hard rods near curved hard surfaces is determined to second order in curvature for surfaces of general shape. In accordance with previous results for spherical and cylindrical surfaces it is found that this quantity is non-analytical when one of the principal curvatures changes signs. This prohibits writing it in the common Helfrich form. It is shown that the non-analytical terms are the same for any aspect ratio of the rods. These results are used to find the equilibrium shape of vesicles immersed in solutions of rod-like (colloidal) particles. The presence of the particles induces a change in the equilibrium shape and to a shift of the prolate-oblate transition in the vesicle phase diagram, which are calculated within the framework of the spontaneous curvature model. As a consequence of the special form of the energy contribution due to the rods these changes cannot be accounted for by a simple rescaling of the elastic constants of the vesicle as for solutions of spherical colloids or polymers.