Abstract

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.

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