Statistical investigation of the mean size distribution of AB 2/B f type hyperbranched polymer

A statistical method was applied to investigate the number of isomeric structures of hyperbranched polymers formed by the polymerization of an AB(2) type moiety with B-f polyfunctional core moieties (abbreviation as AB(2)/B-f type). By means of the kinetic model described by a Smoluchowski-like coagulation equation, the explicit expressions of z-average mean-square radii of gyration are evaluated as a function of the conversion of functional groups. The numerical calculation shows that the mean size of the AB(2)/B-f type hyperbranched polymers will increase with the increase of the conversion of A groups or the reaction time, furthermore increasing sharply at the end of the reaction. When the reaction is quantitatively completed, the z-average mean-square radii of gyration of AB(2)/B-f type hyperbranched polymers show a maximum. The results are similar to those for star branched polymers, rather than those of hyperbranched polymers made by the AB(f) type monomers without cores; the former had finite values and the latter reached infinite values when the reaction was quantitatively completed. These theoretical analysis conclusions will be important for effectively controlling the mean sizes or the average degrees of hyperbranched polymers by varying the number of the B-f type polyfunctional core moieties in experimental research.