Polycondensation Kinetics: 5. Time-Dependent Composition of Sol and Gel Phases

Time-dependent concentrations of n-mers P(n, t) have been found by numerically solving rate equations for a system containing a finite number N of monomers from 32 to 1024 at the initial point of time t = 0, where chain growth is limited, n ≤ N, and the total mass of the phases is conserved before and after the gel point. It has been shown that the property of dynamic self-similarity of clusters with different values of N suggests that Ps(n, N, t > T0) = P(n, N, T0) in the sol and Pg(n, N, t > T0) = P(n, N, T0) − Ps(n, N, t) in the gel. The increase in the gel mass is due to the polycondensation flux from the sol resulting in the formation of loose clusters followed by aging, when the gel transforms into a dense globule with an average length of 〈n〉 ~ N and a loose shell 〈n〉 ~ N1/2. The times of these transformations have been found.