A roadmap for mathematical modeling

Comprehensive polymerization models may be used by scientists and engineers to reduce the time required to develop new polymer products and advanced production processes for their manufacture as well as to optimize existing processes. 

In addition to the material and energy balances presented above, a roadmap for modeling will now be provided, describing basic steps in the modeling (computer simulation) exercise and linking them to key references in the literature, followed 

Classical sources of modeling information and mathematical models (material/mass balances for species, energy balances and population balances for radicals and (dead) polymer molecules) can be found in texts by Biesenberger and Sebastian [92] and Dotson et al. [ 127], and in the classical paper by Ray [54]. 

Bulk and solution (and several suspension and precipitation polymerization systems) can be modeled as homogeneous single-phase systems, or using a monomer-rich and a polymer-rich phase. The level of model sophistication and detail depends upon the intended use of the model. By their nature, these mathematical models are semi-mechanistic or semi-empirical , indicating that they are based on polymerization mechanisms with the inevitable use of certain (often many) parameters. 

Translated into computer code, these model equations are solved numerically (with the appropriate initial and/or boimdary conditions). They are then combined with experimental data for parameter estimation, sensitivity studies and investigation (corroboration) of model trends. 

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