Relative reaction probabilities in polymer-polymer reactions, 1. Investigations with Monte-Carlo model chains

Pairs of chains taken from ensembles of five-way cubic lattice chains (athermal or theta) were analysed for the (relative) probability of contact formation between specified segments belonging to different chains within this pair. This probability may be taken as a measure of the rate constant which characterizes bimolecular polymer-polymer reactions which occur between active sites attached to or localized at these segments, relative to the reaction between the same active sites, if these were not bound to the polymer chains. It turns out that the (expected) effect which results from the interaction between the chains as a whole (external shielding) is of comparatively small extent and is fairly independent of chain length. The much more important contribution, however, is made by a novel phenomenon which — exhibiting a strong dependence on chain length n — is responsible for an “internal” shielding: the compatible pair configurations (i. e. those which are free of intermolecular intersections) are characterized by largely increased segment-segment distances. As a consequence, the probability of contact formation is much lower than it would be expected from a convolution of the (mutually independent) radial distributions of the segments participating in contact formation. The overall shielding factor K can be represented as a product of the fairly independent contributions of external (K_G) and internal (K_w) shielding. The overall chain length dependence is described by a power law K = Dn^d, where the exponent d depends on whether two (Type I contacts), one (Type II) or no endsegment at all (Type III) is involved in contact formation. For athermal chains the exponents are d = ?0,16 (Type I), d = ?0,30 (Type II), and d = ?0,50 (Type III), the pre-factor being of the order of unity throughout. Θ-systems roughly show the same general characteristics as the athermal ones, however, to a lesser extent. Thus, neither shielding nor its chain length dependence vanish, the exponents being about ?0,06 (Type I), ?0,1 (Type II), and ?0,2 (Type III), respectively.