Chain-length-dependent termination rate processes in free-radical polymerizations. 1. Theory

Kinetic modeling of free radical polymerization of styrene initiated by the bifunctional initiator 2,5-dimethyl-2,5-bis(2-ethyl hexanoyl peroxy)hexane

“…A constant k t dependent on the chain length would give a better result. For long chains, the termination would be smaller than for small active chains due to a restricted mobility [37][38][39][40][41][42], which leads to an increase of the mass molecular weight and the polydispersity.…”

A Theoretical Description of a Method for Model-Independent Determination of Bimolecular Chain-Length-Dependent Free-Radical-Termination Rate Coefficients

“…[9][10][11][12][13][14][15][16] Unfortunately, the assumptions used in these derivations were not validated and the choice for a particular chain-length-dependent termination model can at least be called questionable. In the numerical approach, [17][18][19][20][21][22][23][24] which has become available with the increasing speed of computers, these simplifications are not made and all possible termination events between macroradicals of different sizes are accounted for. Although this approach is physically more correct, one still needs to assume a chain-length-dependent termination model, among them the harmonic mean model, 14 the geometric mean model, [14][15][16]25,26 and the Smoluchowski model 27 with chain-length-dependent diffusion coefficients.…”

“…Although this approach is physically more correct, one still needs to assume a chain-length-dependent termination model, among them the harmonic mean model, 14 the geometric mean model, [14][15][16]25,26 and the Smoluchowski model 27 with chain-length-dependent diffusion coefficients. 17,20 (In the numerical approach only the latter two have been used, [17][18][19][20][21][22][23][24] sometimes in combination with a chain-length-independent residual termination model. [17][18][19] ) Besides, the discriminative value of this numerical procedure does not seem to be very significant as only one experimental parameter (〈k t 〉 or overall polymerization rate, etc.)…”

“…17,20 (In the numerical approach only the latter two have been used, [17][18][19][20][21][22][23][24] sometimes in combination with a chain-length-independent residual termination model. [17][18][19] ) Besides, the discriminative value of this numerical procedure does not seem to be very significant as only one experimental parameter (〈k t 〉 or overall polymerization rate, etc.) is available from an experiment for comparison and for justification of the termination model used, while an almost infinite number of parameters were used as input for the model.…”

“…To reduce the CPU time needed to simulate a TR-SP-PLP experiment, coarse graining was applied in all calculations in a fashion similar to that described by Russell et al 17 Small radicals of different chain lengths were all treated as kinetic nonequivalent individual species and were consequently assigned to different grains. For radicals, however, with somewhat larger chain lengths, species of different lengths were simply lumped together and the average chain length was taken as the measure of the kinetic chain length of all species in that specific grain.…”