Polymerization with Freezing
E. Ben-Naim and P.L. Krapivsky
Irreversible aggregation processes involving reactive and frozen
clusters are investigated using the rate equation approach. In
aggregation events, two clusters join irreversibly to form a larger
cluster, and additionally, reactive clusters may spontaneously
freeze. Frozen clusters do not participate in merger events.
Generally, freezing controls the nature of the aggregation process,
as demonstrated by the final distribution of frozen clusters. The
cluster mass distribution has a power-law tail, $F_k\sim
k^{-\gamma}$, when the freezing process is sufficiently
slow. Different exponents, $\gamma=1$, $3$ are found for the
constant and the product aggregation rates, respectively. For the
latter case, the standard polymerization model, either no gels, or a
single gel, or even multiple gels may be produced.
source,
ps,
pdf