Multimerization: Association and aggregation. XIII. Concentration dependence of apparent average molecular weights of a poly‐disperse associating polymer in a theta solvent

Abstract

Abstract Analytical expressions are derived for the concentration dependences of different apparent average ( n , w , z ) molecular weights for two types (end‐to‐end and segment‐to‐segment) of open association of polymolecular unimers. The open association is defined as an association leading to an unlimited number of multimer species. The type of association depends upon the number of associogenic sites per unimer molecule: for the end‐to‐end type this number is constant, whereas for the segment‐to‐segment type it is proportional to the degree of polymerization of the unimer. For the end‐to‐end association, a simple relation exists between the polydispersity ( M̄ r ) w /( M̄ r ) n of the mul‐timer and the association number r and the polymolecularity ( M̄ I ) w /( M̄ I ) n of the unimers: ( M̄ r ) w /( M̄ r ) n = 1 + r −1 [( M̄ I ) w /( M̄ I ) n − 1]. The z ‐average and higher averages of the r ‐mers may be lower than the corresponding averages of the unimers. In the theta‐state, ( M̄ n ) app,Θ and ( M̄ w ) app,Θ are linear functions of c /( M̄ n ) app,Θ , whereas a more complicated relation exists for the apparent higher averages. For the segment‐to‐segment association, both ( M̄ w ) app,Θ and ( M̄ z ) app,Θ are linear function of the weight concentration c , whereas no closed expression could be found for ( M̄ n ) app,Θ . For the polydispersities of multimers one finds ( M̄ I ) z /( M̄ r ) w = 1 + r −1 [( M̄ I ) z /( M̄ I ) w − 1], and, in the special case of a Schulz‐Zimm distribution of unimer molecular weights, ( M̄ r ) n /( M̄ r ) w = 1 + r −1 [( M̄ I ) n /( M̄ I ) w − 1].