Reacting polymers with highly correlated initial conditions

We propose and theoretically study an experiment designed to measure short- time polymer reaction kinetics ill melts or dilute solutions. The photolysi s of groups centrally located along chain backbones, one group per chain, c reates pairs of spatially highly correlated macroradicals. We calculate tim e-dependent rate coefficients kappa (t) governing their first-order recombi nation kinetics, which are novel on account of the far-from-equilibrium ini tial conditions. In dilute solutions (good solvents) reaction kinetics are intrinsically weak, despite the highly reactive radical groups involved. Th is leads to a generalised mean-field kinetics in which the rate of radical density decay -n(overdot) similar to S(t), where S(t) similar to t(-(1+g/3) ) is the equilibrium return probability for 2 reactive groups, given initia l contact. Here g approximate to 0.27 is the correlation hole exponent for self-avoiding chain ends. For times beyond the longest coil relaxation time tau, -n(overdot) similar to S(t) remains true, but center of gravity coil diffusion takes over with rms displacement of reactive groups x(t) similar to t(1/2) and S(t) similar to 1/x(3)(t). At the shortest times (t less than or similar to 10(-6) s), recombination is inhibited due to spin selection rules and we find n(overdot) similar to S(t). In melts, kinetics are intrin sically diffusion-controlled, leading to entirely different rate laws. Duri ng the regime limited by spin selection rules, the density of radicals deca ys linearly, n(0) - n(t) similar to t. At longer times the standard result -n(overdot) similar to dx(3)(t)/dt (for randomly distributed ends) is repla ced by n(overdot) - d(2)x(3)(t)/dt(2) for these correlated initial conditio ns. The long-time behavior, t > tau has the same scaling form in time as fo r dilute solutions.