Growth in systems of vesicles and membranes

TL;DR

This paper presents a theoretical model describing the growth process of membranes and vesicles in supersaturated solutions, highlighting differences from classical droplet growth theories and exploring conditions for vesicle formation.

Contribution

It introduces a coupled system of equations for membrane and vesicle growth, accounting for curvature and edge energy effects, and analyzes their solutions under various initial conditions.

Findings

Membranes nucleate and grow, then close to form vesicles beyond a critical size.

The model predicts growth dynamics consistent with experimental parameters.

Differences from classical droplet growth theories are elucidated.

Abstract

We present a theoretical study for the intermediate stages of the growth of membranes and vesicles in supersaturated solutions of amphiphilic molecules. The problem presents important differences with the growth of droplets in the classical theory of Lifshitz-Slyozov-Wagner, because the aggregates are extensive only in two dimensions, but still grow in a three dimensional bath. The balance between curvature and edge energy favours the nucleation of small planar membranes, but as they grow beyond a critical size they close themselves to form vesicles. We obtain a system of coupled equations describing the growth of planar membranes and vesicles, which is solved numerically for different initial conditions. Finally, the range of parameters relevant in experimental situations is discussed.