Elastic modulus formulae for a crosslinked network

The usual formula for the elastic modulus E of a crosslinked highly elastic network E = 3 ρRT/M_c involves molecular weight between crosslinks M_c. It has to be modified by several factors such as the fraction not involved in any external stress and the initial molecular weight distribution. Several correction terms have been proposed. In this paper a fuller calculation is made for two initial molecular weight distributions, uniform and random, to see how far these corrections are valid. Even at high degrees of crosslinking a very significant proportion of the network does not participate in this elastic deformation.

It may appear preferable to relate the elastic modulus E to the number of effective segments between crosslinks, independent of their molecular weight M_cE = 3ρkTQ(1 − s²)p where Q is the number of crosslinked monomer units per unit volume, and (1 − s²)p is a correction factor to allow for segments which are ineffective in an elastic deformation.