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_c, and the ideal mean field prediction for the gel point, p_c,id, is a function of the average number of cross-links per pervaded volume of a network strand, P, and thus, exhibits an explicit dependence on junction functionality, f. In contrast, the amount of intramolecular 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_c – p_c,id. Therefore, p_c – p_c,id cannot be predicted from intramolecular reactions and vice versa in contrast to a long standing proposal in the literature. Instead, the main contribution to p_c – p_c,id for P > 1 arises from the extra bonds needed to bridge the gaps between giant molecules separated in space and scales roughly ∝ (P – 1)^-1/2. Further corrections to scaling are due to nonideal reaction kinetics, composition fluctuations, and incompletely screened excluded volume, which are discussed briefly.