Effect of the excluded volume on specific rate of combination reactions between polymer radicals

The specific rate k_D for reaction between polymer radicals is formulated when the potential of average force on the basis of the excluded volume affects the motion of the polymer radicals. This rate is given by \documentclass{article}\pagestyle{empty}\begin{document}$ k_D = Fk_S \left( {{\rm with}\ {F} = \sum\limits_{s = 0}^\infty {{{ ‐ 2(\alpha ^2 ‐ 1)]} \mathord{\left/ {\vphantom {{ ‐ 2(\alpha ^2 ‐ 1)]} {(s + 1)^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern‐\nulldelimiterspace} 2}} }}} \right. \kern‐\nulldelimiterspace} {(s + 1)^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern‐\nulldelimiterspace} 2}} }}} } \right) $\end{document} where k_S is specific rate of reaction between radical chain ends and α is the average expansion of the polymer arising from the long-range effects. The effect of the excluded volume reduces k_D. F depends on the degree of polymerization of the polymer radical when α ≠ 1. These results are discussed in terms of the experimental data for very low polymer concentrations.