Equilibria of Bifunctional Polycondensations

Polycondensation reactions are equilibrium reactions. In most polycondensations, the condensation equilibrium is actually reached. Polycondensations usually take place through the elimination of a low-molecular-weight component. The polycondensation of dicarboxylic acids with diols is an example. According to the law of mass action, the concentrations of water, carboxyl, hydroxyl and ester groups are related by 

If carboxyl and hydroxyl groups are not initially present in the same quantities, then the polycondensation can only proceed as far as the total consumption of the functional group that is present at the lowest concentration. To simplify the problem, it is assumed that hydroxyl and carboxyl groups are initially present in equal concentrations (e.g., in the polymerization of hydroxy acids). At equilibrium, the fraction p of functional group pairs is esterified, i.e., there is now a fraction p of ester groups and a fraction 1 — p of hydroxyl and of carboxyl groups, p is the mole fraction of water with respect to the initial molar concentration of OH (or COOH) groups. Equation (17-2) thus becomes 

The sign in front of the square root must be negative, since otherwise p would be greater than 1. 

COOH and OH groups must be present in equivalent concentrations. 

Water can be removed from the polymerization system by thin-layer evaporation, azeotropic distillation with suitable solvents, under vacuum, or by reaction at elevated temperatures. At higher temperatures, however, side reactions tend to occur. The application of vacuum, particularly at low conversions, may remove volatile reactants as well as the water, which destroys the equivalence in the case of different volatilities of the two reactants. The combination of these events is responsible for the fact that there is a limit in the extent to which the equilibrium can be shifted in the direction of polyester. Other reasons are the partial vapor pressure of the water and, considering the macrokinetics (high melt viscosity), the time required for the diffusion of water from the reaction system. 

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