Theory of the Increase in Rigidity of Rubber during Cure

The rigidity of rubber, considered as a network of flexible molecules with Gaussian configuration functions, can be calculated for a particular sample if one is given a complete description of the molecular network or certain types of statistical description. In particular, it is sufficient to know the distribution of lengths and vector‐mean extensions of the segments of the network, or only the latter distribution if it is of Gaussian form. The assumption that the vector‐mean extensions have a Gaussian distribution corresponds to a similar postulate in the theory of Wall, and has been applied to a simplified network theory by Flory. In the complete theory it leads to calculation of the same proportionality between the rigidity of the material and the number Ga of segments, per unit volume, in the ``active'' part of the molecular network. However, consideration of the process of cure shows that this assumption cannot be expected to be correct, though it does lead to results of the right order of magnitude...