Closed form results for shape transitions in lipid monolayer domains

TL;DR

This paper derives closed form solutions for integrals related to shape transitions in lipid monolayer domains, simplifying stability analysis and providing explicit formulas for critical domain sizes under Coulomb interactions.

Contribution

It presents a novel closed form evaluation of integrals in lipid domain stability analysis, extending previous work and enabling easier computation of stability thresholds.

Findings

Closed form expressions for integrals in domain stability analysis.

Simplified formulas for critical domain radii under Coulomb interactions.

Asymptotic behaviors characterized in various limits.

Abstract

Isolated domains in lipid monolayers exhibit shape transitions as a consequence of the competing effects of line tension and long-range dipolar interactions. Nontrivial integrals ultimately arise in instability analysis calculations of these domains. In this work we present a closed form evaluation of such integrals in terms of associated Legendre functions. Our approach is motivated by and extends the work of J. M. Deutch and F. E. Low (J. Phys. Chem., 1992, 96, 7097-7101). Our closed form solutions lead to simpler analytic expressions for stability thresholds, which are easier to evaluate explicitly. Relevant asymptotic behavior is calculated in various limits of interest. For the case of Coulomb interactions, a general closed form expression is obtained for the critical domain radii.