Computer-simulation studies of kinetic gelation

Computer simulations are performed to study kinetic gelation on a simple cubic lattice. Two models are considered: (1) irreversible gelation in which the monomers and microgels attempt to react with their neighboring particles with a certain probability (${\mathrm{p}}_{\mathrm{b}}$) and (2) reversible gelation in which the bonds are broken with a certain probability (${\mathrm{p}}_{\mathrm{r}}$). The growth of the extent of reaction (i.e., the concentration of the bonds grown), volume fraction of the gel, weight average degree of polymerization, and the correlation length are studied as a function of ${\mathrm{p}}_{\mathrm{b}}$ and ${\mathrm{p}}_{\mathrm{r}}$. We observe that (i) the concentration of bonds grows nonlinearly with time. (ii) The critical gel time (${\mathrm{t}}_{\mathrm{c}}$) increases nonlinearly on increasing the degree of reversibility, ${\mathrm{p}}_{\mathrm{r}}$, while the critical concentration (${\mathrm{p}}_{\mathrm{c}}$) at the gel point is insensitive to ${\mathrm{p}}_{\mathrm{b}}$ and ${\mathrm{p}}_{\mathrm{r}}$. (iii) For large ${\mathrm{p}}_{\mathrm{r}}$, our data suggest that the sol-to-gel transition may be nonuniversal.