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A network model for the crosslinking of already existing polymer molecules with a so‐called Schulz–Zimm distribution of their molecular weights is presented. It is an extension of previously developed statistical network models applied to the crosslinking of primary polymers with several other molecular weight distributions and with crosslinks of any functionality. The model results in the possibility to obtain more insight into the structure of polymers, especially those with narrow distributions of the molecular weight. In more detail, the model can give a perspective on structural network parameters such as the weight fractions of ideal network, of dangling polymer ends, and of those molecules not connected to the network, i. e., the sol fraction, the number of crosslinks in which a polymer molecule is bound, the functionality of the crosslinks, or the average molar mass of the polymer molecules in between the crosslinks M̄c. Results of calculations are shown for a hypothetical crosslinking process of polymers with various molecular weight distributions. Moreover, the dependency of the network parameters on the polydispersity index and the type of molecular weight distribution is shown. Finally the increase of the functionality of the crosslinks during the ageing process of a 9.9% poly(vinyl chloride) gel as a function of the polydispersity index of the molecular weight distribution is presented.

The cross-linking behavior for a series of solutions of closely related diskotic side-chain polymers, differing in the tails of the mesogens, has been studied. Solubility parameters are used to describe the driving force for the cross-linking behavior in these solutions. Complex formation enthalpies of the physical networks as determined by dynamic rheological measurements in combination with a statistical network model are relatively low. Moreover, with a statistical theory for equilibrium polymers, used by Cates and Candau for slightly similar systems, an average number of disks in a cross-link is calculated. Only two disks appear to be incorporated in the majority of cross-links, whereas most of the disks are in a free state.

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