Kinetics of polymer synthesis general

In building mathematical models of product formation in a mold it is possible to treat a polymeric material as motionless (or quasi-solid), because the viscosity grows very rapidly with the formation of a linear or network polymer thus, hydrodynamic phenomena can be neglected. In this situation, the polymerization process itself becomes the most important factor, and it is worth noting that the process occurs in nonisothermal conditions. 

A complete description of the process must consist of kinetic equations for all components of the reactive mass, including all fractions of different molecular weights and intermediate and byproducts as well. Such an exact approach is usually superfluous for modelling any real process and should not be applied, because excessive detail actually prevents achievement of the final goal due to overcomplicating of the analysis. Therefore, why correct (necessary and sufficient) choice of the parameters for quantitative estimation is of primary importance in mathematical models of a technological process. 

On these lines, two approaches can be proposed. The first can be applied to the synthesis of linear polymers. In this case, the degree of conversion of a monomer can be chosen as a determining factor. This degree of conversion, p, is expressed as the proportion of a monomer included in macro-molecular chains  

It is evident that at t = 0, p = 0, and after the sufficiently long time, some equilibrium (residual) concentration of the monomer in the reactive medium is maintained. In any practical situation important for technological applications this residual concentration is much less than [M]o and we can assume that p = 1 at t - oo. 

Now we can assume that a polymerization reaction starts at active centers, and that their initial concentration is [A] mol %. Then we can calculate the number-averaged degree of polymerization in the end product as follows 

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