Fluctuation-Induced Interactions between Rods on a Membrane

TL;DR

This paper investigates how rods embedded in fluctuating surfaces interact through fluctuation-induced forces, revealing a long-range attraction with specific orientational dependencies, relevant for understanding membrane and film behaviors.

Contribution

It provides a theoretical analysis of fluctuation-induced interactions between rods on membranes or films, detailing the distance and orientation dependence of the forces.

Findings

Interaction decays as 1/R^4 with separation

Interaction depends on the surface tension or bending rigidity

Orientation dependence varies with surface type

Abstract

We consider the interaction between two rods embedded in a fluctuating surface. The modification of fluctuations by the rods leads to an attractive long-range interaction between them. We consider fluctuations governed by either surface tension (films) or bending rigidity (membranes). In both cases the interaction falls off with the separation of the rods as $1/R^4$. The orientational part of the interaction is proportional to $\cos^2\left[ \theta_1+\theta_2 \right]$ in the former case, and to $\cos^2\left[ 2\left(\theta_1+\theta_2\right) \right]$ in the latter, where $\theta_1$ and $\theta_2$ are angles between the rods and the line joining them. These interactions are somewhat reminiscent of dipolar forces and will tend to align collections of such rods into chains.