Molecular weights, number average between crosslinks

One way to specify molecular size is by the length of the end-to-end vector r (Fig. 3.6) that runs from the start to the end of an isolated chain, or between the crosslinks at the end of a network chain. The molecule is assumed to be unstressed, so its equilibrium shape has end-to-end vector tq. The average length of to will be calculated for a polymer with a C—C single bond backbone of a particular molecular weight. The average is over a large number of similar chains, and over a period of time. 

Mc number average molecular weight between crosslinks... 

In both equations, Dw is the solute diffusion coefficient in pure water, rs is the molecular radius of the solute, ls is its characteristic size, Vw is the water free volume, Mc is the molecular weight between crosslinks in the amorphous phase, Mn is the number average molecular weight of the polymer before crosslinking, M is the minimum value of Mc below which the solute cannot diffuse, 4>(V) is the free volume function mentioned earlier, and k3 is a constant. 

Figure 15.8 2H NMR spectra obtained in a randomly crosslinked, deuterated PB network. Precursor chain molecular weight 115700 g.mol"1, 1.2% crosslink agent, the average molecular weight between junctions is 27400 g.mol 1 (as determined by swelling experiments) or 11600 g.mol"1 (elastic measurements). The smooth curves are fits with a most probable distribution of chain lengths with number average molecular weight Mc = 11600 and with non-Gaussian chain statistics...

The number of repeating units between crosslinks, N, a parameter appearing in equation (1), can be simply defined as the jratio of the number average molecular weight between crosslinks, Mc, to the average molecular weight of the clusters, Mq. 

M number average molecular weight o network chain between the crosslinks by stress relaxation. 

Swelling experiments and stress-strain measurements are widely used to estimate the crosslinking density in liquid-crystalline networks [101,106-108], For ideal rubbers with tetrafunctional crosslinks, these techniques allow the evaluation of the number average molecular weight between crosslinks [104, 105]. 

Based on the amount of bromine reacted, th number average molecular weight between two crosslink sites (M ) in PPO was 17,000. The theoretical of the crosslinked polystyrene was 7,260. 

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