Page 110 - Biodegradable Polyesters

88 4 Synthesis, Properties, and Mathematical Modeling of Biodegradable Aliphatic Polyesters

reversible polycondensation reaction was used. Finally, Kostoglou and Bikiaris
[47] presented a simplified model for the esterification of succinic acid/propylene
glycol considering also the effect of the addition of silica nanoparticles on the poly-
merization kinetics.

4.4.2.2 Modeling Approaches
Three modeling approaches can be applied to the esterification reaction kinetics:
the molecular species model, the functional group model, and the overall reaction
model. These are schematically illustrated in Scheme 4.5.

Modeling approaches

Decreasing kinetic parameters needed and computational effort

Overall reaction Functional group Molecular species
models models models

Increasing complexity, physical meaning and information provided

Scheme 4.5 Modeling approaches of the polyesterification reaction kinetics.

The three models differ in their complexity, physical content, and in the degree
of information they produce, following a decreasing order in all features from the
first to the third model. The molecular species models are based on population
mass balances of all the species present in the reactor, including oligomers with
various degrees of polymerization. They are the most realistic but they are very
complex and depend on a large number of kinetic parameters with direct physical
meaning. They are capable of predicting the complete molecular weight distribu-
tion. The functional group models are considerably simpler from a mathematical
point of view; they use parameters with more abstract physical meaning, and pre-
dict a limited amount of information on the reaction mixture. Finally, the overall
reaction model assumes a global reaction between reactants leading directly to the
products through a generalized rate expression with parameters having no direct
physical meaning but identified (as the rate expression itself) from the experimen-
tal results. The choice of the appropriate model depends on the specific problem
examined.

4.4.2.3 Modeling Using the Functional Group Approach

Reaction Mechanism In this section, the polymer segment approach, which is in
the framework of functional group approaches is presented [38]. The model is