Kinetics of Step Polymerization

Consider the polyesterification of a diacid and a diol to illustrate the general form of the kinetics of a typical step polymerization. Simple esterification is a well-known acid-catalyzed reaction and polyesterification follows the same course [Otton and Ratton, 1988 Vancso-Szmercsanyi and Makay-Bodi, 1969]. The reaction involves protonation of the carboxylic acid, 

In the above equations and / are used to indicate all acid or alcohol species in the 

Equation 2-15 is inconvenient in that the concentration of protonated carboxylic groups is not easily determined experimentally. One can obtain a more convenient expression for Rp by substituting for C(OH)2 from the equilibrium expression 

Two quite different kinetic situations arise from Eq. 2-17 depending on the identity of HA, that is, on whether a strong acid such as sulfuric acid orp-toluenesulfonic acid is added as an external catalyst. 

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Yet another possiblity for the nonlinearity in the low conversion region is the decrease in the volume of the reaction mixture with conversion due to loss of one of the products of reaction (water in the case of esterification). This presents no problem if concentration is plotted against time as in Eq. 2-20. However, a plot of 1/(1 — p j2 against time (Eq. 2-22) has an inherent error since the formulation of Eq. 2-21 assumes a constant reaction volume (and mass) [Szabo-Rethy, 1971]. Elias [1985] derived the kinetics of step polymerization with correction for loss of water, but the results have not been tested. It is unclear whether this effect alone can account for the nonlinearity in the low conversion region of esterification and polyesterification. 

The kinetics of step polymerizations other than polyesterification follow easily from those considered for the latter. The number of different general kinetic schemes encountered in actual polymerization situations is rather small. Polymerizations by reactions between the... 

In order to obtain a kinetic expression for the overall rate of polymerization, it is necessary to assume that both kp and kt are independent of the size of the radical. [This assumption is inherent in Eqs. (6.15) through (6.18).] It may be recalled that the same type of assumption was also employed in deriving the kinetics of step polymerization (Chapter 5). There is, however, ample experimental evidence which indicates that although radical reactivity depends on molecular size, the effect of the size vanishes after the dimer or trimer [Ij. 

Step polymerizations are usually carried out with nearly stoichiometric amounts (i.e., equal moles) of the two reacting functional groups and Eqs. (5.15) and (5.19) are then applicable. The kinetics of step polymerizations with nonstoichiometric amounts of the groups can also be treated (liin and Yu, 1978) in a similar way, though the final rate expressions are quite different (see Problem 5.5). 

Gandhi, K. S. and Babu, S. V. (1978) Kinetics of step polymerization with unequal reactivities, AIChEJ 25,268. 

The assumption of equal reactivity of functional groups also greatly simplifies the kinetics of step polymerization since a single rate constant applies to each of the step-wise reactions. It is usual to define the overall rate of reaction as the rate of decrease in the concentration of one or other of the functional groups, i.e. in general terms for equimolar stoichiometry... 

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