Coarse-graining and renormalization group methods for the elucidation of the kinetics of complex nucleation and growth processes

Abstract

We review our work on generalizations of the Becker–Döring model of cluster formation as applied to nucleation theory, polymer growth kinetics and the formation of supramolecular structures in colloidal chemistry. One valuable tool in analysing mathematical models of these systems has been the coarse-graining approximation which enables macroscopic models for observable quantities to be derived from microscopic ones. This permits assumptions about the detailed molecular mechanisms to be tested, and their influence on the large-scale kinetics of surfactant self-assembly to be elucidated. We also summarize our more recent results on Becker–Döring systems, notably demonstrating that cross-inhibition and autocatalysis can destabilize a uniform solution and lead to a competitive environment in which some species flourish at the expense of others, phenomena relevant in models of the origins of life.

Acknowledgements

This paper is dedicated to Professor Mark Child FRS on the occasion of his retirement as Coulson Professor of Theoretical Chemistry at the University of Oxford. We are grateful to P.L. Luisi, A. Eschenmoser, C.D. Bolton and J.R. King for stimulating conversations and contributions over several years towards the development of many of the ideas discussed here. We acknowledge EPSRC grant GR/R94916/01 for funding some of this work.