Termination processes in free radical polymerization, 4. The evaluation of an analytical expression relating the bimolecular rate constant of termination to the length of the two radicals involved

Abstract

Quite a number of independent observations, which have been collected during the last decade, have raised considerable doubt about the concept of a chain length independent rate constant of termination in free radical polymerization. The evaluation of the experiments carried out with the SIP (spatial intermittent polymerization) reactor designed by O'Driscoll and Mahabadi1*2), for instance, has led to apparent rate constants of termination in styrene or methyl methacrylate polymerization which decrease when the polymerization conditions (at constant temperature and monomer concentration) are varied favouring the formation of a higher molecular weight polymer. These findings have been cast into the phenomenological equation kt a P -b kt (apparent) rate constant of bimolecular termination between growing radical chains P number average degree of polymerization of the polymer formed From the data given in the work of O'Driscoll and Mahabadil.z) values in the range from 0,15 to 0,25 can be evaluated for the exponent b3), the upper limit values referring to the bulk polymerization of styrene, the lower ones to the bulk polymerization of methyl methacrylate. Another argument against the chain length independence of kt can be derived from the papers of Yasukawa et aL4-@, in which the authors demonstrated that the experimental moleculai weight distribution of polystyrene from bulk polymerization is in better agreement with the theoretical one, if tentatively a chain length dependence of the type x, y = lengths (degrees of polymerization) of the two individual chain radicals taking part in the bimolecular termination process

Termination in Dilute‐Solution Free‐Radical Polymerization: A Composite Model

“…Considering first the experimental values of e, they are in impressive agreement with what theory predicts for the case of the termination rate being controlled by the rate of chainend encounter of overlapping macroradical coils: as has been pointed out, [12] regardless of whether the system is 'weakly reactive' [13,14] (i.e., few chain-end encounters result in reaction) or 'strongly reactive' [12] (i.e., all chainend encounters result in reaction), e % 0.16 in good solvent is predicted. [12][13][14] This provides a persuasive argument for accepting this mechanism of -and with it this e value fordilute solution termination between macroradical coils.…”

“…Considering all the experimental [2][3][4][5][6][7] and theoretical [12][13][14] evidence outlined above, one must conclude that for termination of long radicals e L % 0.16 (corresponding to the best data of Table 1), although we recognize that this value will depend somewhat on the monomer, temperature [24] and solvent quality. [25] Hence e L ¼ 0.16 will be used in the calculations of this paper.…”

“…[12][13][14] This provides a persuasive argument for accepting this mechanism of -and with it this e value fordilute solution termination between macroradical coils. Nevertheless, one is entitled to wonder why this chainlength dependence has not been observed in studying processes which should mimic the termination reaction.…”

“…[30] While the numerical methods of this paper could be used to do calculations for any variation of e with i, for simplicity Termination in Dilute-Solution Free-Radical Polymerization: A Composite Model we will restrict ourselves to our ''two-e'' model. We do this for two reasons: (1) Because we feel that our model, which is a simple ''composite'' model in that it includes the ideas of both center-of-mass diffusion [19,31] and chain-end encounter, [12][13][14] may capture the essence of the real situation, even if not the complete detail. In particular, it seems extremely likely to us that e is higher for small chains than for long chains.…”

SP–PLP–EPR Investigations into the Chain‐Length‐Dependent Termination of Methyl Methacrylate Bulk Polymerization

“…Values around 0.16 are predicted for a l , that is for segmentaldiffusion controlled k t . [4][5][6] A series of k 1;1 t and k 0 t parameters, see Equation (1), as well as power-law exponents a s and a l that meet the theoretical predictions, has already been measured. [7][8][9][10][11][12][13] Three techniques have primarily been used for these experiments.…”