Modeling of Polymerization Schemes

Methods for predicting molecular weight distributions at chemical equUibrium and for irreversible polycondensations are presented with some detail below see Sections 3.4.3 and 3.4.4. 

Applicability of statistical-probabilistic methods far from chemical equilibrium cannot be guaranteed, and the kinetic approaches described in Sections 3.4.4 and 3.4.5 are a better choice. 

Use of statistical-probabilistic methods for describing polycondensations started with Flory, who used them to compute the equilibrium chain length distribution of linear systems and later was able to predict gelation conditions for multifunctional monomers. Stockmayer [7] could extend this method to the computation of chain length distributions and average molecular weights of nonlinear polymers. 

Gordon [20, 28] recognized that nonlinear polymers in the absence of intramolecular reaction can be described by a Galton-Watson branching process. Relatively complex chemical systems, presenting substitution effects, became tractable, and even some properties of polymer networks relevant to rubber elasticity theory [29] and average radius of gyration [30] as well as other polymer properties [31-33] could be computed. 

Alternative approaches to Gordon s branching theory have later been developed, mainly the so-called recursive method [34, 35], which is in a number of ways simpler to understand and use, but lacks the power of the older theory in many situations. 

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