Segmental Diffusion Models Including Excluded Volume and Gaussian Chain Statistics

Segmental Diffusion Models Including Excluded Volume and Gaussian Chain Statistics 

A second model with segmental diffusion as the rate-determining step has been introduced by Mahabadi and O Driscoll [100]. Although it shows great similarity to the model of Horie, Mita and Kambe [111], it has some specific and improved features (i) it predicts the termination rate coefficient for all possible i-j combinations (instead of only i-i) and (ii) it also includes a physically more correct relation for the linear expansion coefficient Mahabadi and O Driscoll [100], have pointed out that the correlation that Horie et al. used to descibe a was inconsistent with literature data. 

Mahabadi and O Driscoll s starting point was somewhat different to the one used by Horie et al. The microscopic rate coefficient for bimolecular termination was now expressed as the product of (i) the rate coefficient for translational diffusion and (ii) the probability of reaction, both being dependent upon the separation distance between the two polymer coils. This reaction probability was supposed to be determined by the rate coefficient of segmental diffusion of the chain ends (Smoluchowski model [202]) and the time available for a termination reaction. The latter parameter effectively cancels out the influence of the translational diffusion coefficient, making the process only dependent upon the rate of segmental diffusion. The final equation that Mahabadi and O Driscoll obtained for k was simplified for practical purposes and expressed as a product of two functions  

Beside the efforts of Horie et al. and Mahabadi and O Driscoll, many other models have appeared incorporating the excluded volume effect. Among others, contributions have been made by Ito [112], Doi [210], Morawetz [211] and O Shaughnessy et al. [58-60, 120, 184]. The last group considered the reaction kinetics of polymer solution under dilute (and 

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