How to calculate crosslinking density of the rubber and Molecular weight between crosslinks in NR, SBR, etc..
I shall answer by giving the easiest example:
For sulfur-crosslinked natural rubber (N.R), my students used to determine the crosslinking density or the percentage of sulfur incorporated by dividing the number of moles of sulfur used initially on the number of moles of N.R which in turn is found by dividing the mass of N.R on the mass of the CRU "constitutional repeating unit" of N.R which is isoprene , as you know. Note that all sulfur is used up as if it is a limiting reactant.
I must add that the famous Ebonite "which is black -usually- polished hard rubber" is N.R that has been vulcanized by using 30-35% sulfur for preferably one hour or more .
how to calculate VR-volume fraction of the vulcanizate in the swollen sample.
I measured the molecular mass between cross-links Mc of epoxy via DMA here: 10.1002/polb.24077
However, the standard formula of the rubber-elasticity theory should work much better for rubber: 3E = rho R T / Mc
Here, E is the Young's modulus at Temperature T, R is the universal gas constant, and rho is the rubber's density.
A relatively lesser known but more quantitative method is time-domain double quantum NMR. For NR, you can get Mc, i.e. MW between crosslinks but for SBR, you get a paramter which is directly related. 10.1021/ma4026064 (see the title figure)
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