THEORY OF INTRAMOLECULAR REACTIONS IN POLYMERIC LIQUIDS

We calculate irreversible intramolecular reaction rates k(t) between two reactive groups attached to a flexible polymer chain. Results are derived using scaling arguments; in addition, a detailed renormalization-group treatment is developed which justifies and extends the scaling results. Asymptotically, reaction kinetics are either ''diffusion-controlled'' (DC) or ''law of mass action' (LMA) as determined by a characteristic exponent, theta, depending only on the class of polymer-solvent system. For unentangled melts (Rouse dynamics) of sufficiently long chains k(t) is of DC form for cyclization (case 1), and for one end and one deeply internal group (case 2): the long time rate k(infinity) is-proportional-to 1/tau(s) (tau(s) is-the relaxation time of the chain segment of length s connecting the groups), while at short times k(t) is-proportional-to t-1/4. When both groups are deeply internal (case 3), k(infinity) suffers logarithmic corrections. For dilute solutions in good solvents k(t) is so weakened by excluded-volume repulsions that laws of mass action apply (LMA) even for very reactive groups; a diffusion-controlled limit does not exist. Case i is governed by the ith correlation hole exponent of des Cloizeaux (i = 1, 2, 3) and k(t) has only weak time dependence. THETA solvents are marginal (on the DC/LMA boundary), and k(t) collects logarithmic corrections in time, group location, and chain length.