Molecular weight development in non-linear step-growth polymerization

3 Molecular weight development in non-linear step-growth polymerization 

To further explore the development of branched polymer networks and the formation of gel molecules, consider a mixture of two bifunctional monomers (AA, BB) and a trifunctional monomer (A3). Under certain conditions, molecules in this type of system can form 

To make predictions about the onset of gelation, Flory considered the conditions under which there will be a finite probability that any chain element, picked at random from the reaction mixture, occurs as part of an infinite network. He also introduced the branching coefficient, a, defined as the probability that a particular functional group belonging to a branch unit leads (via bifiinctional imits) to another branch unit. 

Assuming equal reactivities of aU functional groups, the following variables can be defined  

the probability that the A group of a branch unit (denoted A in the chain above) is connected to the sequence of units shown is Pa[Pb(1 - P )PaYPbP. This probability is derived by multiplying the probabilities for the following independent events  

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