Three eras of micellization

TL;DR

This paper presents a kinetic model describing three distinct eras of micellization, from initial rapid monomer aggregation to equilibrium, using a combination of Becker-Döring, diffusion, and Fokker-Planck equations.

Contribution

It introduces a unified kinetic framework that captures the entire process of micellization through three eras with different dominant mechanisms.

Findings

Initial rapid formation of small clusters

Self-similar growth of nuclei in the second era

Equilibrium distribution achieved in the final era

Abstract

Micellization is the precipitation of lipids from aqueous solution into aggregates with a broad distribution of aggregation number. Three eras of micellization are characterized in a simple kinetic model of Becker-D\"oring type. The model asigns the same constant energy to the $(k-1)$ monomer-monomer bonds in a linear chain of $k$ particles. The number of monomers decreases sharply and many clusters of small size are produced during the first era. During the second era, nucleii are increasing steadily in size until their distribution becomes a self-similar solution of the diffusion equation. Lastly, when the average size of the nucleii becomes comparable to its equilibrium value, a simple mean-field Fokker-Planck equation describes the final era until the equilibrium distribution is reached.