An Analysis of the Gel Point of Polymer Model Networks by Computer Simulations

The gel point of end-linked model networks is determined from computer simulation data. It is shown that the difference between the true gel point conversion, $p_{\text{c}}$, and the ideal mean field prediction for the gel point, $p_{\text{c,id}}$, is a function of the average number of cross-links per pervaded volume of a network strand, $P$, and thus, contains an explicit dependence on junction functionality $f$. On the contrary, the amount of intra-molecular reactions at the gel point is independent of $f$ in a first approximation and exhibits a different power law dependence on the overlap number of elastic strands as compared to the gel point delay $p_{\text{c}}-p_{\text{c,id}}$. Therefore, $p_{\text{c}}-p_{\text{c,id}}$ cannot be predicted from intra-molecular reactions and vice versa in contrast to a long standing proposal in literature. Instead, the main contribution to $p_{\text{c}}-p_{\text{c,id}}$ for $P>1$ arises from the extra bonds (XB) needed to bridge the gaps between giant molecules separated in space and scales roughly $\propto\left(P-1\right)^{-1/2}$. Further corrections to scaling are due to non-ideal reaction kinetics, composition fluctuations, and incompletely screened excluded volume, which are discussed briefly.