Polyesterification uncatalyzed reaction

The derivation (Sec. 2-2b) of the kinetics of catalyzed polyesterification assumes that the catalyzed reaction is much faster than the uncatalyzed reaction, that is, k 3> k. This assumption is usually valid and therefore one can ignore the contribution by the uncatalyzed polyesterification to the total polymerization rate. For example, k is close to two orders of magnitude larger than k for a typical polyesterification. For the atypical situation where k is not negligible relative to k , the kinetic expression for [M] or Xn as a function of reaction time must be derived [Hamann et al., 1968] starting with a statement of the polymerization rate as the sum of the rates of the catalyzed and uncatalyzed polymerizations ... 

Comparison of Fig. 5.2 with Fig. 5.1 shows that the catalyzed polyesterification is significantly faster than the uncatalyzed reaction. Simila, there is much greater rate of increase of the degree of polymerization (see p. 330) with reaction time in the catalyzed polyesterification (Fig. 5.2) relative to the uncatalyzed reaction (Fig. 5.1). Catalyzed polyesterification is therefore economically more feasible. 

Derive an expression for the relationship between the extent of reaction, p, and time, t, in an uncatalyzed polyesterification. Show all the integrations explicitly ... 

Rel. (2.3.11) correlates the value for DP with the initial monomer concentration, rate constant k and the time of reaction t. Similar theory can be developed for reactions that are of first order in one reactant and of second order in the other reactant (such as for the case of uncatalyzed polyesterification reactions). 

The rate constants obtained by the above method for uncatalyzed polyesterification of adipic acid with different glycols are shown in Table 5.2. The Arrhenius parameters A and E of the equation k — Aexp —E/RT) are also presented in Table 5.2 for those reactions that have been studied kinetically at more than one temperature. Note that the concentration units of the rate constants are in terms of moles per kilogram, which is a more convenient measure of concentration than the usual moles per liter because the volume of the system decreases significantly due to reaction. 

Figure 5.1 Plot of Eq. (5.30) for the later stages of uncatalyzed polyesterification of adipic acid and 1,10-decamethylene glycol (Problem 5.1). (Note that the reaction time of zero corresponds to 82% conversion of the original COOH groups present.)...

By combining Eq. (5.38) with Eqs. (5.30) and (5.34), the dependence of the molecular weight on reaction time for catalyzed and uncatalyzed polyesterifications, respectively, is obtained as shown by... 

Problem 5.8 Show that in the high conversion region, for uncatalyzed polyesterification is proportional to and that for catalyzed polyesterification is proportional to t, where t is the reaction time. 

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