Effect of Concentration on Reaction Kinetics in Polymer Solutions

Abstract

We present a theory of irreversible interpolymeric reaction rates k as a function of polymer concentration $ in polymer solutions ranging from dilute through to the melt. At high dilution, kinetics obey mean-field (MF) theory such that k scales as the equilibrium reactive group contact probability. k thus grows with increasing concentration, since the contact probability is enhanced due to screening of excluded volume repulsions: k - 4%/4 whereg is the monomer contact exponent. At large concentrations kinetics are radically different: k = R3/7 then follows a diffusion-controlled (DC) law and decreases with increasing 4 since both coil size R and relaxation rate l/T are diminished. This leads to k - 4418 (unentangled solutions) or k - 4-(6/8+~) (entangled solutions) where y is the entanglement exponent. The transition from MF to DC kinetics happens because the total reaction probability Pduring one coil-coil collision is always an increasing function of $. k is peaked at the transition concentration $**, where Preaches unity for the first time. In agreement with experiment, $** is distinct from the overlap threshold.