Kinetics of intermolecular reactions in dilute polymer solutions and unentangled melts

Irreversible intermolecular reaction rates k in dilute polymer solutions and unentangled melts are studied as a function of time, molecular weight, and location of reactive groups along the polymer backbones. As for intramolecular reactions, the kinetics are determined by the reaction exponent 0 (3 + g) / z, where z and g are, respectively, the dynamical and excluded volume “correlation hole ” exponents. Using scaling arguments, we show that k is driven to either mean-field (MF) or diffusion-controlled (DC) behavior, the short time rate k ( t) being driven by increasing time, the long time rate k, by increasing chain length N. In parallel, detailed renormalization-group (RG) calculations of k are presented. The RG transformation drives the kinetics to either a DC or MF fixed point in correspondence to the scaling picture. In good solvents, dilute solutions (6> 1) exhibit intrinsically MF reaction kinetics, irrespective of group reactivity. k is so weakened by intercoil excluded volume repulsions that the DC limit does not exist. Thus k- N-”g (v is the Flory exponent) scales as the equilibrium contact probability and for interior groups is related to the statistics of three-arm and four-arm star molecules. At small times k ( t) exhibits only a weak time dependence. In contrast, unentangled melts (Rouse dynamics) are intrinsically DC (8 < 1) and k ( t) - tl/*, k, - N-1/2 as derived by previous workers. We obtain crossover results describing the ”trajectory ” from MF to DC for moderately long chains. In 9 solvents (0 = 1) kinetics are marginal and characterized by logarithmic dependencies k ( t) - l/ln t and k, - l/ln N. For reacting polymers of very different lengths k is dominated by the smallest chain in all cases. I.