Modeling of Complex Polycondensation Reactions

Many processes at low temperature and in homogeneous phase can nevertheless be analyzed through the methods described in Section 3.4.4, as they now stand. 

Rate equations allowing the prediction of concentrations of reactive groups, including more complex molecular fragments (monads, dyads and so on) from mass balance equations are established in Section 3.4.2 for irreversible reactions or systems with at most FSSEs if reversible reactions exist. Stoichiometric coefficients are introduced in order to obtain a fairly general formalism, later exploited in Section 3.4.4. 

Prediction of molecular weight distributions for reversible, linear, alternating polycondensation is discussed in Section 3.4.5. Mathematical difficulties grow considerably in the presence of SSSEs. There seems to be no alternative to Monte Carlo methods for dealing with reversible nonlinear polycondensations or even linear polycondensations where more than two kinds of bonds are present. 

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The monomer feed is converted into Polyamide-6 by polycondensation and polyaddition reactions [930]. This reaction step can be realized by a complex reactor which can be modeled as a sequence of stirred tank and plug-flow reactors. An exemplary model flowsheet comprising two reactors (CSTR) with an intermediate water separation (Split) is shown in Fig. 5.20. Such a model of the reaction section can be analyzed by means of Polymers Plus, an extension of Aspen Plus for handling polymer materials [513]. 

This example illustrates several difficulties encountered in modeling reversible polycondensation reactions with substitution effects. A major problem is the possible change in the nature of bonds because another bond connecting a different unit has been destroyed. There is no closed set of rate equations in terms of the concentrations of functional groups [AXA], [BYB], [Zp], [Z j, [Zb], and [Zp], even with the help of the two stoichiometric restrictions [X] = [AXA] - - [Zp] + [Za] + [Zp] and [Y] = [BYB] - - [Z ] -I- [Zp] + [Zp]. Introduction of more complex chemical entities does not alleviate the problem. 

The chemical structure of the polymers was confirmed by NMR and elemental analysis, and spectroscopically characterized in comparison with monodisperse low molecular weight model compounds. Scheme 5 outlines the approach to the model compounds. Model compounds 31-34 were synthesized by complexation of the ruthenium-free model ligands 29/30 with 3/4. The model ligands were synthesized in toluene/diisopropylamine, in a similar fashion as the polycondensation using Pd(PPh3)4 and Cul as catalyst (Sonogashira reaction) [34,47-49]. 

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