Sol-gel transition of loopy polymer networks

During the crosslinking of telechelic polymer chains into a network, the system undergoes a competition between bridging and looping reactions. Looping events not only significantly impact the mechanical properties (e.g. modulus and tearing energy) of the resulting network, but also severely influence the kinetics of the emergence of the giant component (i.e. the gel). While the mechanism by which loops delay the onset of gelation has been largely established, the impact of looping events on the criticality of the sol-gel transition has not been studied as comprehensively. To date, the analogy between gelation and percolation is still largely the standard framework for understanding the gelation process of loopy networks, even though loops introduce irregularities in network topology as well as inhomogeneous rates of bond formation that render the percolation model not directly applicable to the real gelation process. To address this, we utilize a kinetic Monte Carlo simulation that accurately accounts for the loop-bridge competition to numerically track the sol-gel transition. It is found that when looping events are introduced, the criticality of the sol-gel transition can be significantly impacted, as demonstrated by a change in the apparent percolation critical exponents.