Surface termination in chain reactions and the interaction with homogeneous termination

Abstract

Three aspects of chain termination at surfaces have been discussed. First, formulae have been developed for the surface termination constant for efficient and inefficient surfaces, as well as for surfaces of intermediate efficiency, in plane, cylindrical and spherical vessels. These formulae can conveniently be applied to the interpretation of experimental results. Secondly, the interaction between surface termination and linear homogeneous termination has been examined in circumstances where the surface termination alone would give a non-uniform distribution of chain centres across the vessel. Explicit formulae have been developed for plain, cylindrical and spherical vessels, which show that the surface termination constant is increased considerably above the value in the absence of homogeneous termination because of the more uniform profile of chain-centre concentration imposed by the homogeneous termination. The increase is most marked when the contribution from surface termination is relatively small, but the effect can increase the total rate of termination by as much as 15% for plane vessels and 20% for spherical vessels. Thirdly, the interaction has been examined in cylindrical vessels by numerical integration for the case of mutual homogeneous destruction of chain centres, since no simple explicit formulae can be developed, and increases of up to 20% in the total termination rate have been found.