On one-dimensional nucleation and growth of "living" polymers II. Growth at constant monomer concentration

Abstract

An analytical solution is given for the kinetics of reversible homogeneous one-dimensionalgrowth, assuming that all association rate constants have the same value k, that all dissociation rate constants are likewise equal to and that the monomer concentration has a constant value, C. Such growth tends to generate a maximally polydisperse ("white") distribution of cluster concentrations ci all approaching a limiting value equal to that of the critical nucleus, ci. Continued growth merely increases the range of cluster sizes over which this white distribution applies. A simple expression is obtained for the flux ε_i=n^∞dc/dt}, which becomes constant and equal to (→kC -→ k)c_n. The monomer uptake increases with time, and is given approximately by (kC -K)²c_nt.