Effect of the excluded volume on specific rate of combination reactions between polymer radicals |
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Authors: | Katsukiyo Ito |
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Abstract: | The specific rate kD 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} = sumlimits_{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 kS 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 kD. 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. |
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