RENORMALIZATION-GROUP THEORY OF INTRAMOLECULAR REACTIONS IN POLYMERIC LIQUIDS

Irreversible intrapolymeric reaction rates kappa are studied using renormalization group methods. We calculate the dependence on the location of two reactive groups along the chain backbone. The form of kappa is determined by the reaction exponent theta = (d + g)/z (d, g and z being respectively the spatial dimension and the correlation hole and dynamical exponents). Unentangled melts (Rouse dynamics, theta < 1) exhibit ''diffusion-controlled'' kinetics: kappa approximate to 1/tau(s) at long times (tau(s) is the relaxation time of the chain segment of length s connecting the groups) with universal prefactors but logarithmic corrections when both groups occupy interior positions. The short time behavior is algebraic. For dilute solutions in good solvents (theta > 1) reactions only weakly perturb equilibrium and even for highly reactive functional groups kappa approximate to s(-v(3+g)) scales as equilibrium contact probabilities where nu is the Flory exponent and the relevant value of g depends on group location. Prefactors are non-universal and time dependence is weak. Theta solvents are marginal (theta = 1): at long times kappa approximate to 1/(tau(s) In s) with logarithmic dependence on time and group reactivity. As for melts, corrections logarithmic in group location arise when both groups are internal.