Effect of initiation and transfer rates on molecular size distribution in dianionic polymers

Abstract

The problem of molecular size distribution in dianionic polymerization in which a polymer chain can add monomers on both ends is investigated. The initiation rate is considered finite and chain transfer through the monomer is operative. Exact expressions for the size distribution are obtained by solving the differential rate equations of Pepper. The result is a large number of series whose poor convergence renders it practically useless for numerical computations for long chains. However, the expressions for the number average chain length and the weight average chain length are obtained in a closed form. Next, we employ the continuum approach for deducing expressions for various quantities. The size distribution function is obtained in a closed form while the results for the averages show only minor differences from the exact ones. We then consider the kinetic scheme given by Moacanin and Rembaum for another class of dianionic polymerization and derive results using the exact as well as the continuum approach. The kinetic schemes give rise to polymers which differ appreciably in their statistical character. Some features of the size distribution in the two cases are brought out. Finally, we analyze the experimental results of Pepper on the dianionic polymerization of vinyl mesitylene by sodium naphthalene in tetrahydrofurane and estimate the relative values of the initiation and transfer rates to explain the experimental trend.