Kinetics of sol-to-gel transition in irreversible particulate systems

A comprehensive theory encompassing the kinetics of the sol-to-gel transition is yet to be formulated due to break-down of the mean-field Smoluchowski Equation. Using high temporal-resolution Monte Carlo simulation of irreversible aggregation systems, we show that this transition has three distinct regimes with kinetic exponent z∈1,2 corresponding to aggregation of sol clusters proceeding to the ideal gel point (IGP); z∈2,5.7 for gelation of sol clusters beyond IGP; and z∈2,3.5 for a hitherto unidentified regime involving aggregation of gels when monomer-dense. We further establish universal power-law scaling relationships that connect the kinetics of these three regimes. Improved parameterizations are performed on the characteristic timescale parameters that define each regime.