Equilibrium constant, polycondensation

The main polymerization method is by hydrolytic polymerization or a combination of ring opening as in (3.11) and hydrolytic polymerization as in (3.12).5,7 9 11 28 The reaction of a carboxylic group with an amino group can be noncatalyzed and acid catalyzed. This is illustrated in the reaction scheme shown in Fig. 3.13. The kinetics of the hydrolytic polyamidation-type reaction has die form shown in (3.13). In aqueous solutions, die polycondensation can be described by second-order kinetics.29 Equation (3.13) can also be expressed as (3.14) in which B is die temperature-independent equilibrium constant and AHa the endialpy change of die reaction5 6 812 28 29 ... 

All reactions involved in polymer chain growth are equilibrium reactions and consequently, their reverse reactions lead to chain degradation. The equilibrium constants are rather small and thus, the low-molecular-weight by-products have to be removed efficiently to shift the reaction to the product side. In industrial reactors, the overall esterification, as well as the polycondensation rate, is controlled by mass transport. Limitations of the latter arise mainly from the low solubility of TPA in EG, the diffusion of EG and water in the molten polymer and the mass transfer at the phase boundary between molten polymer and the gas phase. The importance of diffusion for the overall reaction rate has been demonstrated in experiments with thin polymer films [10]. 

Figure 2.4 Equilibrium constants of esterification and polycondensation as a function of temperature. The data have been published by Yamada and co-workers [23,24], Reimschuessel [21] and Challa [22], or have been calculated by using the commercial process simulator Chemcad (Chemstations)...

Transesterification is the main reaction of PET polycondensation in both the melt phase and the solid state. It is the dominant reaction in the second and subsequent stages of PET production, but also occurs to a significant extent during esterification. As mentioned above, polycondensation is an equilibrium reaction and the reverse reaction is glycolysis. The temperature-dependent equilibrium constant of transesterification has already been discussed in Section 2.1. The polycondensation process in the melt phase involves a gas phase and a homogeneous liquid phase, while the SSP process involves a gas phase and two solid phases. The respective phase equilibria, which have to be considered for process modelling, will be discussed below in Section 3.1. 

In 1959 and 1960, Challa published the first results of quantitative experiments on the poly condensation equilibrium in PET [22, 41, 42], He determined the polycondensation equilibrium constant K at different temperatures and average degrees of polycondensation and found that this parameter depends only slightly on temperature, but increases significantly with increasing degree of polycondensation. The monomer BHET was found not to follow the principle of equal reactivity. 

Later, Fontana [43] performed experiments on transesterification and reinterpreted Challa s results. He concluded that the value of the polycondensation equilibrium constant is close to 0.5, being independent of temperature or degree of polycondensation and that the normal Flory-Schuz distribution does hold in the PET system. In Figure 2.8, the polycondensation equilibrium constant K from different sources [22, 43, 44] is shown as a function of the average degree of polycondensation, Pn. 

With values between 13 and 16, the equilibrium constant is still high enough to regard the formation of DEG from EG to be irreversible in an open industrial system. DEG formation is not only an important side reaction during esterification, polycondensation and glycolysis, but also during distillation of EG and water in the process columns. In particular, the residence time in the bottom reboiler of the last separation column is critical, where the polycondensation catalyst and... 

J Data presented as equilibrium constant K, rate constant (m3 mol-1 min-1) and activation energy Ea (kJmol-1). Reaction orders 2, for esterification, polycondensation and polycondensation of tV 3, for H+ catalyzed reactions 1, for diester group formation and AA degradation. b irrev, irreversible. 

If the equilibrium constant K has a value between 1 and 10, less than a thousandth of the total amount of water formed in the reaction mixture is sufficient to prevent the formation of really high-molecular-weight condensation polymers. Hence it follows that it is extremely important to remove as completely as possible the low-molecular-weight reaction products, for example, water, eliminated during a polycondensation. In principle, these equilibriums are also known in stepwise addition polymerizations (polyaddition) like the back-reactions of urethane groups. Since they mostly occur at higher temperatures only, they can be neglected. 

Elimination of Phenol. The equilibrium constants of the reactions indicated by Reactions 1 and 6 were measured at 275°C to explain the remarkable effect of diphenyl terephthalate in accelerating the PET polycondensation by elimination of phenol (10). 

Under certain conditions, the equilibrium constant for the formation of poly(ethylene terephthalate) (PET) was shown [30] to be 9.6 that is, under the conditions employed the polycondensation reaction coefficient leading to the formation of PET was 9.6 times greater than the rate coefficient for glycolysis of PET. 

In several instances, discussed in more detail later in this section, experimental evidence strongly indicates that the principle of equal reactivity of functional groups is not obeyed for all chain lengths, and that the equilibrium constant may itself be a function of the degree of polycondensation. 

Fig. 6. Equilibrium constant for the polycondensation of bis(2-hydroxyethyl tereph-thalate) as a function of temperature (from ref. 68).

It is obvious from equations (6.12) and (6.13) that the higher the pressure is, the smaller is the equilibrium constant. This is valid for reactions such as thermal cracking, which proceed with a volume increase. It means that a higher pressure leads to an acceleration of polycondensation, alkylation, hydrogenation and other reactions that proceed with a volume decrease. 

Problem 5.10 The equilibrium constant K for the esterification reaction of decamethy-lene glycol and adipic acid is of the order of unity at 110° C. If equimolar amounts of the did and the diacid are used in polycondensation at 110°C, what weight ratio of dissolved water (of condensation) to polymer would correspond to an equilibrium value of 60 at 110°C ... 

If the equilibrium constants are not too large, the polycondensation equilibrium is also actually reached over the usual reaction time scales and yields. In such cases, the equilibrium constants may be related to either the yield in groups or the yield in molecules. 

Thus, the degree of polymerization for self-polycondensation depends on the equilibrium constant and the concentration of available monomer and water at equilibrium. The stoichiometry is also important with foreign polycondensations (see also Section 17.2.2). 

The equilibrium constants for esterifications and transesterifications are generally about 1-10 (Table 17-1). The amidation equilibrium constants are generally higher, but not as high as Schotten-Baumann equilibrium constants. In the latter case, the equilibrium position is not often reached the polycondensation is irreversible. High equilibrium constants have also been reported for cyclopolycondensations. 

Table 17-1. Equilibrium Constants of Various Polycondensations. The Examples 6 and 7 Refer to the First Stage of the Polycondensation to Polyamidic Acids Which Proceeds without Water Elimination...

Further polycondensation is usually prevented, therefore, by the addition of monofunctional compounds that are able to condense and thus act as chain stabilizers or molar mass stabilizers. This stabilization is particularly important with polyamides, since the equilibrium constants are 100 times larger than in polyesters. If the mole fraction of monofunctional compounds is n, the Equation (17-24) is modified to... 

At equilibrium, the net reaction rate is zero, so the equilibrium constant for the polycondensation is given by ... 

The polymerizations shown in Eqs. (2) and (3) actually represent well-known reactions of small molecules, the only distinction being the minimum requirements of difunctionality of each molecule for polymer formation, which makes it possible for the product of each reaction to participate in further reactions. As a rule, the functional groups retain their reactivity regardless of the chain length [11, p. 75], so that these reactions follow the same kinetic rules as for simple molecules however, in contrast to polyaddition reactions, polycondensations suffer from the serious problem of reversibility (e.g., hydrolysis, or depolymerization ) as a result of the possible accumulation of the by-product (e.g., water), and this must be taken into account. In general, because of the unfavorable equilibrium constant for polycondensation reac-... 

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