Synopsis
The differential equations governing the molecular weight distribution (MWD) in step-growth polymerization are coupled and nonlinear and a large number of them must be solved simultaneously to keep the truncation error low. In this work, these equations have been decoupled so that they can be solved sequentially. The solution of these is independent of the truncation error and there is considerable saving of computation time. To demonstrate the efficiency of the algorithm, the formation of polyethylene terephthalate (PET) in batch reactors with ethylene glycol evaporating has been analyzed. The feed to the reactor is taken as polymer with its oligomers present according to the Flory's distribution. The effect of pressure and temperature of the reactor on the progress of polymerization has been modelled and evaluated. The amount of ethylene glycol distilled, the concentrations of the first five oligomers Q1 to Q5, the number average chain length, and the polydispersity index of the polymer have been determined. It is shown that the reduced pressure and increased temperature reduce the concentration of the condensation product in the reaction mass, thus pushing the polymerization in the forward direction. Lastly the CPU time on Dec 1090 using this algorithm is only 0.40 s compared to about 10 min for similar computations using other existing methods.