A new pathway for the re-equilibration of micellar surfactant solutions

Micellar surfactant solutions are generally assumed to undergo restructuring via stepwise monomer loss following a dilution. This process is captured by the Becker-Döring equations, an infinite-dimensional system of ordinary differential equations for the concentration of each aggregate in solution....

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Bibliographic Details
Published in:Soft matter 2013-01, Vol.9 (3), p.853-863
Main Authors: Griffiths, I. M, Breward, C. J. W, Colegate, D. M, Dellar, P. J, Howell, P. D, Bain, C. D
Format: Article
Language:English
Subjects:
Aggregates
Breaking down
Differential equations
Mathematical models
Micelles
Monomers
Pathways
Surfactants
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Summary:Micellar surfactant solutions are generally assumed to undergo restructuring via stepwise monomer loss following a dilution. This process is captured by the Becker-Döring equations, an infinite-dimensional system of ordinary differential equations for the concentration of each aggregate in solution. We reveal certain classes of surfactants, such as the non-ionic family C n E m , for which the predicted re-equilibration times via stepwise monomer loss are far greater than those observed experimentally. We investigate two alternative pathways for re-equilibration, first allowing for micelles to break down into two aggregate fragments rather than stepwise monomer release, and secondly by allowing aggregates to merge together to form large super-micelles that exceed the size of a proper micelle. While the former shows no discernible difference in the predicted time to re-equilibration, the latter provides an alternative pathway to re-equilibration: the formation of unstable super-micelles that break down to proper micelles via a cascade of stepwise monomer release. The new theory is shown to describe the re-equilibration of any surfactant system, with the conventional Becker-Döring theory forming a subset of the model that describes the behaviour of a small range of surfactant systems with high critical micelle concentrations and low aggregation numbers. The pathway proposed provides an essential mechanistic route to equilibrium. Evolution of monomer concentration, X 1 , to the CMC ( X 1 = 1) with time illustrating the effect of allowing super-micelle formation.
ISSN:1744-683X
1744-6848
DOI:10.1039/c2sm27154k