Kinetics of polycondensation

Example 8.4 For a second-order, irreversible polycondensation reaction with rate proportional to the concentrations of reactive A and B groups, obtain expressions for conversion and number-average chain length as a function of time for a stoichiometrically equivalent batch. 

Solution. For a second-order reaction, assuming constant volume, 

Separating variables and integrating between the limits when t 0, [A] = [AJ and when t=t and [A] = [A] gives 

Therefore, the number-average chain length increases linearly with time. 

Two cautions are in order about the preceding example. First, by writing an irreversible rate expression, we have assumed that any molecule of condensation is being continuously and efficiently removed from the reaction mass so that there is no depolymerization. Second, not all step-growth reactions are of second order. Some polyesterifications, for example, are catalyzed by their own acid groups and are, therefore, first order in hydroxyl concentration, second order in acid, and third order overall. The rate may also be proportional to the concentration of an added catalyst (usually acids or bases for polycondensations), if used. 

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The kinetics of polycondensation reactions might be expected to be similar to those found in condensation reactions of small molecules (evidence suggests that rate coefficients are independent of polymer size). Polyesterification reactions between dibasic carboxylic acids and glycols can be catalysed by strong acids. In the absence of added catalyst, it has been suggested that the acidic monomer should act as a catalyst, whereupon the rate of reaction should be given by... 

Saunders, J. H. andF. Dobinson, The Kinetics of Polycondensation Reactions, Chap. 7 in Comprehensive Chemical Kinetics, Vol. 15, C. H. Bamford and C. F. H. Tipper, eds., American Elsevier, New York, 1976. 

On this basis the kinetics of polycondensation were worked out a long time ago. The following points are of particular interest ... 

In the case of proteins or nucleic acids we do not have two, but several comonomers furthermore we are not dealing with the simple case of radical polymerization, but with the more complex polycondensation. Very little is known about the kinetics of the copolymerization of polycondensates - for example analysis of ta and re has not been done systematically for amino acids. However, a few general points can still be made on the basis of the general principles of copolymerization. One has been already mentioned that the initial composition of amino acids in the prebiotic soup may not correspond to the amino-acid composition in the chain. Thus, the fact that one given amino acid has a very small frequency of occurrence in protein chains may not necessarily mean that this amino acid was not present under prebiotic conditions the low frequency in the chains can simply be the result of the kinetics of polycondensation. Conversely, the presence of preferred residues or short sequences in protein chains might be due to the interplay of kinetic parameters, and have little to do with the initial biological constraints. 

The kinetics of polycondensation hy nucleophilic aromatic substitution in highly polar solvents and solvent mixtures to yield linear, high molecular weight aromatic polyethers were measured. The basic reaction studied was between a di-phenoxide salt and a dihaloaromatic compound. The role of steric and inductive effects was elucidated on the basis of the kinetics determined for model compounds. The polymerization rate of the dipotassium salt of various bis-phenols with 4,4 -dichlorodiphenylsulfone in methyl sulfoxide solvent follows second-order kinetics. The rate constant at the monomer stage was found to be greater than the rate constant at the dimer and subsequent polymerization stages. 

The kinetics of polycondensation and polyaddition reactions follow the same general scheme, but both differ sharply from the kinetics of addition or chain polymerization. 

Mikitaev, A. K. Korshak, V. V. Musaev, Yu. I. Storozhuk, I. P. Kinetics of polycondensation reaction of disodium salts of bisphenols with 4,4 -DChDPhS. In collection Problems of Physics-chemistry of Polymers. Ed. Mikitaev, A. Zelenev, Yu. Nal chik, KBSU, 1972,4-28. 

The kinetics of polycondensation reactions is similar to that of ordinary condensation reactions. Since the average chain length is related to conversion in linear polycondensation by (9.7), and conversion is given as a function of time by the kinetic expression, x is directly related to the reaction time, and can thus be controlled by limiting the reaction time. Similarly, the time to reach a gel point is related by the rate expression, (9.18) and (9.19). 

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