Relationship between kinetic chain length and radical polymerization rate

In the copolymerization of monomers M₁ and M₂ which form polymer radicals of chain length n of N¹_n with electron on a M₁ type and N²_n with one on a M₂ type, it is assumed that the specific rates of termination between N¹_n and N¹_n and N¹_s, N¹_n and N²_s, and N²_n and N²_s are k_α(ns)^?a, k_β(ns)^?a, and k_γ(ns)^?a, respectively, where k_α, k_β, and k_γ are the rate constants of reaction between segment radicals in the respective termination, and a is constant. The relation between kinetic chain length n? and polymerization rate R_p is derived as: 1/n? = 1/n?₀ + const. (R_p)^A(a), where n?₀ is the kinetic chain length of the polymer formed by transfer and A (a) is unity (predominance of transfer) and 1/(1–2a) (no transfer). In the copolymerization between methyl methacrylate (M₁) and styrene (M₂) at 60°C, when R_p → 0, k_r12/k₁₂ + k_r21/k₂₁ = 5.9× 10^?5 is obtained, where k_r12 and k_r21 are the rate constants of transfer of N¹ to M₂ and N² to M₁, and k₁₂ and k₂₁ are the rate constants of propagation of N¹ to M₂ and N² to M₁. In the absence of transfer, the a value is found to be 0.065 ± 0.008, from the relation between n? and R_p, regardless of the monomer composition. Such a value is also estimated by setting b = 0.72 in a = 0.153 (2b–1), where b is the constant in the Mark-Houwink equation. Further, the value of k_β is found to be 1.18 × 10⁹l./mole-sec, which is comparable with the diffusion-controlled rate of reaction between small molecules. The rate of reaction between segment radicals is fivefold larger than the polymer-polymer termination when transfer predominates.