Interpretation of concentration-dependence in aggregation kinetics

Aggregation processes are analyzed by two kinetic models, the random polymerization model and the nucleation-dependent polymerization model. A kinetic equation for the random polymerization model can be derived analytically, revealing the relation between the initial monomer concentration (M]0), the rate constant (k(a)), time (t), the yield of detectable aggregate (F]), and the critical aggregation number (m). However, time-course curves for the nucleation-dependent polymerization model can be obtained by numerical calculation. It is found that lag time (t(d)) and half-time (t1/2) are proportional to M](-1) in the random polymerization model, while t(d) and t1/2 are proportional to M1](-s) (1 < s < n; n is nucleus size) at the lower concentration and are less dependent on M1] at the higher concentration in the nucleation-dependent polymerization model.