Numerical or direct integration and other approximate methods

1 Numerical or direct integration and other approximate methods 

As already noted, a polymerization reaction is described by an infinite set of species mass balance equation. The difficulties encountered in the numerical integration of this set of rate equations are most apparent by looking at a simple example. 

The rate constant kj refers to the jth propagation step on a chain. The material balances for the various polymer species in a batch reactor then result in an 

Since there are no termination reactions and all the growth chains are created at t = 0, it is obvious that the number of polymer molecules remains constant. This is verified by summing equations (3.13) and (3.14) for all j. The result is 

So LPj = Iq, The number of growing polymer molecules is equal to the number of initiator molecules added to the reaction mixture. 

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