Distribution of molecular weight and composition in diblock copolymers

Abstract The distribution of molecular weight (MW) and composition of diblock copolymers is considered theoretically. Assuming that the chain end of each block is coupled randomly, the weight-average MW of the block copolymers is given by Mw = w1 (Mw,1 + Mn,2) + w2 (Mw,2 + Mn,1), irrespective of the shape of the distribution of each block, where wi is the weight fraction, and Mn,i and Mw,i are the number- and weight-average MW of each block. In copolymer chains, the chemical compositions as well as the MWs cannot be identical for all polymers, and there exists a bivariate distribution of MW and composition. When the MW distribution (MWD) of both blocks follows the Schulz-Zimm distribution, the bivariate distribution can be obtained analytically. In addition to the bivariate distribution, the full MWD, the average composition as a function of MW, the composition distribution of copolymers having a specified MW, and the overall composition distribution are obtained. The composition distribution, as well as the average composition, becomes independent of MW under the condition σ1/Mn,1 = σ2/Mn,2, where σ i is a parameter indicating the narrowness of the Schulz-Zimm distribution. The present theoretical analysis provides new insight into the design of diblock copolymers.

Distribution of molecular weight and composition in diblock copolymers Journal Articles