Termination rate constants in radical polymerization

A rate constant is generally derived by using Fick's equation corresponding to the spherical interdiffusion of particles. By using this rate constant, chain and primary radical termination rate constants can be approximated to rate constants for the bimolecular reactions between two radical chain ends, and primary radical and radical chain end, respectively. The former is given by k_s = 8πN_LD_sL_s exp { ? L_s/R_s} × 10^?3 1./mole-sec. The latter is given by k_si = 4πN_L(D_s + D_i)L_si exp { ? L_si/R_si} × 10^?3 1./mole-sec. Here, N_L is Avogadro's number; D_s and D_i are the diffusion constants of radical chain end and primary radical, respectively; L_s and L_si are, respectively, the distances between two radical chain ends and between a primary radical and a radical chain end at a thermal energy equal to the coulombic energy of interaction of the net charges; and R_s and R_si are, respectively, the average distances between two radical chain ends and primary radical on a collision.