On the ripening of vesicle dispersions

We analyze the ripening process where, in a dispersion of vesicles, amphiphile monomers diffuse between vesicles of different sizes, leading to a change in the size distribution. Since, typically, vesicles are not under tension, the driving force for the process comes from the curvature energy. With the conventional expansion of the curvature energy density, g,, to harmonic order we find that the free energy change on adding a monomer is independent of vesicle radius. The monomer exchange is then a purely random process. By introducing corrections to the harmonic curvature energy, either by expanding g,, to fourth order in the curvatures, or by a term logarithmic in the vesicle size, one obtains a driving force for ripening. Depending on the correction, different scenarios are predicted. The fourth-order correction and a negative logarithmic correction term result in a ripening toward unimodal vesicle distribution around the mean vesicle size of the initial distribution. For a positive logarithmic correction term, on the other hand, the ripening by itself should result in the formation of many small vesicles and a few very big ones. The rate of the monomer redistribution is primarily determined by the magnitude of the thermodynamic driving force and by the monomer solubility. For vesicles formed by single chain surfactants we estimate that the size redistribution should occur at a measurable rate, providing an opportunity to experimentally study which correction to the leading curvature energy is most significant.