The predictions of classical theory for the establishment of a network by free-radical polymerization have been tested under conditions for which those predictions should be simple, i.e., short pregel regimes in which the composition and chain length distribution of the primary chains should be nearly invariant and for a nearly equally reactive system (methyl methacrylate/ethylene glycol dimethacrylate). At the moderate to high concentrations of cross-linker used, the classical theory is inapplicable, each of its predictions being disobeyed. Gelation occurs 1-2 orders of magnitude later than predicted, the gel point is relatively insensitive to the amount of cross-linker, the dependence on the primary chain length is weaker than the predicted inverse dependence, and the divergence of the weight-average molecular weight is more consistent with the percolation picture. All of these point to a violation of the mean-field picture, probably through cyclization and (size-dependent) reduction in the reactivity of the pendants.

Relationships have been derived which describe structural development in nonlinear free-radical polymerizations as a function of conversion. The recursive analysis is based on the assumptions of ideal network formation and those assumptions standard in the kinetic analysis of linear free-radical polymerizations. Significant is the fact that changes in average primary chain length (e.g., due to drift or Trommsdorff effect), which in linear systems give rise to large polydispersities, can be accounted for in these relationships. While it is shown that for many systems such rigor is unnecessary in the pregel regime, it is also shown that neglect of such effects in the postgel regime may lead to serious errors. For the case in which monomer depletion is the only source of a changing kinetic chain length, the gel point is observed to be delayed and the network observed to be looser in comparison with the case in which monomer depletion is neglected.

Polymer networks are often formed under conditions for which the history of reaction is important, but nonetheless such nonequilibrium polymerizations may be properly described by statistical methods. This is illustrated for a free-radical polymerization of a diunsaturated monomer subject to firstshell substitution effect. The distinction between first and second double bond reacted leads to long-range correlations which result in coupled integral equations as recursions rather than algebraic relations. The proper consideration of the history of the reaction gives an exact statistical treatment of the evolution of DPW in the pregel regime, a treatment which is compared with various approximations which avoid the complicated mathematics at the cost of not properly maintaining the structural integrity of the polymer.

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