EFFECT OF CONCENTRATION ON REACTION-KINETICS IN POLYMER-SOLUTIONS

We present a theory of irreversible interpolymeric reaction rates k as a function of polymer concentration phi 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 approximately phi3g/4 where g is the monomer contact exponent. At large concentrations kinetics are radically different: k almost-equal-to R3/tau then follows a ''diffusion-controlled'' (DC) law and decreases with increasing phi since both coil size R and relaxation rate 1/tau are diminished. This leads to k approximately phi-5/8 (unentangled solutions) or k approximately phi-(5/8+gamma)(entangled solutions) where gamma is the entanglement exponent. The transition from MF to DC kinetics happens because the total reaction probability P during one coil-coil collision is always an increasing function of phi. k is peaked at the transition concentration phi**, where P reaches unity for the first time. In agreement with experiment, phi** is distinct from the overlap threshold.