Statistical treatment of polymerization problems

Historically, polymerization problems were initially treated using statistical methods. This is because they have the advantage of simplicity when dealing with simple polymerization problems. In using such approaches, a certain amount of intuition is necessary. For example, consider the case of a step-growth homopolymerization of a, co-amino-caproic acid to make nylon 6. This reaction can be schematically represented by 

Complete knowledge of the chain length distribution is available if, Pj, the fraction of (or probability of having formed) polymer molecules containing j monomer residues, is known. If p is the a priori probability that a single addition of monomer to the growing chain is made, then it is quite clear that a 

One of the fundamental questions in batch polymerizations of this type is how to let the reaction go to obtain the distribution given by equation (3.84). This procedure cannot answer such a question, or related questions such as the time evolution of the distribution To deal with this it is necessary to identify 

Statistical methods which have been used to treat polymerization problems can be grouped into three categories direct, formal Markov chain theory, and recursive approaches. They differ in detail and objectives but all contain the underlying assumption that polymerization follows Markovian statistics. 

To explain the method, consider a reaction mixture of any number of types of monomers. The total number of difunctional monomers is given by so the total is IN. These include all types in the ratio 1 rj Tj Tj, etc. Clearly the 

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