The non-ideal preparation state of polymer (model) networks

We show that the phantom modulus can be split into two major contributions: the cycle rank of the active network structure and a correction resulting from non-ideal chain conformations at the instance of cross-linking. The correction contains several contributions related to loop formation, an effective repulsion between network junctions, and an excess strain of chains that develops towards the end of the reactions, if reaction partners become sparse. This challenges the text-book assumption that network strands are incorporated into the network with the same conformations as a free chain inside the reaction container. Our results are relevant for developing a better understanding of rubber elasticity and its dependence on the network formation process.