Equilibrium Polycondensations with Several Monomers

These computations assume there is some way of predicting how molecular fragments (usually monads, unless higher-order substitution effects have to be tackled) are mutually connected. More specifically, it is necessary to know the distributions of the numbers of bonds connecting the fragments, for each kind of fragment. In fact, one may need only some of the moments of the aforementioned distributions for making a few calculations. 

A kinetic method may be used for this prediction, but mainly as a means to avoid solving equations derived from mass action laws for concentrations of fragments. This has been one of our motivations for presenting the formahsm in Section 3.4.2. 

Each directed bond Z is supposed to start a pendent chain Vi(xz,XA) with counts of end groups and directed bonds x and xz, respectively. Notice that the molecular graphs have to be considered as digraphs, otherwise xz would be meaningless it would be impossible to know the counts of the monomer units according to their chemical nature. 

All isomeric trees with the same counts of groups are lumped into the same chemical species leading to vector count distributions with Nza = Nz + Na independent variables. 

Vectors of dummy Laplace variables sa and Sz will be associated with the counts of unreacted groups and directed bonds. Variables s and Sz will be often ranged 

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