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

An analytical solution is given for the kinetics of reversible homogeneous one-dimensional growth, assuming that all association rate constants have the same value k, that all dissociation rate constants are likewise equal to k, 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, cn. Continued growth merely increases the range of cluster sizes over which this white distribution applies. A simple expression is obtained for the flux sigma infinity i = n dci/dt, which becomes constant and equal to (kC - k)cn. The monomer uptake increases with time, and is given approximately by (kC - k)2cnt.