Estimation of molecular weight distribution based on chain length dependence of termination rate

When a chain length dependence of polymer‐polymer termination is given by kt,ns = const. (n−2a + s−2a) where n and s are the chain lengths for the polymer radicals and a is parameter, an instantaneous weight fraction of the non‐reacting polymers is derived as: where h and k̄ are the kinetic parameters, p is a parameter depending on a, and pn is instantaneous number‐average chain length. Such a weight fraction corresponds to the experimental one over a wide range of conversion in the polymerization of styrene. On the scope of this correspondence, the polymer‐polymer termination rate is estimated as: k̄t = 8πR0D1/100 ( = 4πRsDs) where R0 is reaction radius between monomer radicals and D1 is the diffusion coefficient of the monomer; Rs is reaction radius between segment radicals with n ≅ 100 and Ds is the diffusion coefficient of the segment. The Fujita‐Doolittle theory applies to such a rate. Further, the rate also yields 1.5 × 1071./mole‐sec, which is the observable extent at conversions less than 0.2.