Kinetic models of J-aggregation of polymethine dyes

Several models are considered to describe the kinetics of J-aggregation of polymethine dyes in solution. The scaling model is applicable only for irreversible aggregation. It uses a stretched exponential function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ e^{ - (kt)^n } $$\end{document} to fit the kinetic curve and provides only scant information on the mechanism of J-aggregation involving monomers. The model of random polymerization is applied only for irreversible aggregation. However, it can be used for description of the early aggregation stages. The nucleation-dependent polymerization model, which is used to describe the growth of J-aggregate, consists of reversible nucleation and irreversible aggregation steps. However, fitting the calculated curves to the experimental ones is rather difficult. The model of autocatalysis is most appropriate for describing the kinetics of J-aggregation occurring via both monomers and dimers. The best fitting results are obtained assuming the time dependence of the rate constant as k(t) = k0 + kc(kct)n.