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-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 $c_i$, all approaching a limiting value equal to that of the critical nucleus, $c_n$. Continued growth merely increases the range of cluster sizes over which this white distribution applies. A simple expression is qbtain_ed for the flux $\sum_{i=n}^\infty \frac{dc_i}{dt}$, which becomes constant and equal to $(kC - k)c_n$. The monomer uptake increases with time, and is given approximately by $(kC - E)^2c_nt$