Statistics of Chain Polymerizations

The probability of finding an x-mer, or, equivalently, the mole fraction of jc-mers polymerized at some instant of time, is then given by exactly the same expression as that obtained in dealing with condensation polymerizations (Equation 5-19). 

We showed how this equation could be used to obtain expressions for the number and weight average molecular weight in the preceding section. As in step-growth polymerization, we obtain for the polydispersity (Equation 5-20), 

once again, its time for you to do some work. By substituting for p and using the steady-state assumption (if necessary, go back to Chapter 4), show that you obtain the expression for the number average degree of polymerization given by Equation 5-21. 

For anionic polymerizations in protic media, you get the same expressions as those obtained for free radical polymerization with termination by disproportionation (p is still the probability of chain growth, but now 1 -p is the probability of chain transfer). Again, the averages and distributions you can obtain are only valid for low degrees of conversion. For cationic polymerization, there are several types of transfer and termination reactions that occur m most reactions, so you 

Here v is the number of molecules reacted per growing chain. After obtaining an equivalent expression for the weight fraction of x-mers and the number and weight average 

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