On the predictions and limitations of the Becker-Döring model for reaction kinetics in micellar surfactant solutions

I M Griffiths; C D Bain; C J W Breward; D M Colegate; P D Howell; S L Waters

doi:10.1016/j.jcis.2011.04.074

On the predictions and limitations of the Becker-Döring model for reaction kinetics in micellar surfactant solutions

J Colloid Interface Sci. 2011 Aug 15;360(2):662-71. doi: 10.1016/j.jcis.2011.04.074. Epub 2011 Apr 27.

Authors

I M Griffiths¹, C D Bain, C J W Breward, D M Colegate, P D Howell, S L Waters

Affiliation

¹ Mathematical Institute, University of Oxford, OX1 3LB, UK. ian.griffiths@maths.ox.ac.uk

PMID: 21571292
DOI: 10.1016/j.jcis.2011.04.074

Abstract

We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker-Döring system of equations, using realistic expressions for the reaction constants fit to results from Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, substituting a large system of ordinary differential equations for a partial differential equation in two independent variables: time and aggregate size. Numerical solutions demonstrate that re-equilibration occurs in two distinct stages over well-separated timescales, in agreement with experiment and with previous theories. We conclude by exposing a limitation in the Becker-Döring theory for re-equilibration of surfactant solutions.