General treatment of a kinetic scheme with chain length dependent termination

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Abstract
Without making reference to any special type of the dependence of the rate constant of bimolecular termination kt (m,n) on the chain lengths (m and n) of the two radicals involved universal relations are derived between the basic quantities characteristic of the polymerization kinetics of such a system. In case kt (m,n) can be factorized simple expressions may be obtained also if termination is by recombination. These universal relationships have been successfully tested for a power, law dependence of kt on various means m̄,n̄, kt = kt °(m̄,n̄)−b. Their use provides comfortable access to resolving the kinetic scheme. Thus, for the geometric mean, m̄,n̄ = √mn, in its long chain approximation a complete resolution of a kinetic scheme including chain transfer could be worked out, which is free from any further assumptions. In addition, the numeric results obtained for various means m̄,n̄ are discussed and analyzed with respect to the possibility of obtaining experimental information on which type of mean m̄,n̄ is operative in the bimolecular termination process of free radical polymerization. In a further effort it is shown for some selected examples that any individual functional dependence of kt on m and n will coincide with that for the apparent (i.e. experimentally detectable) termination constant on (average) degree of polymerization of dead polymer, k̄t (P̄), as long as kt is a continuous and monotonous function of m and n.

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