Molecular Weight Distribution of Core Cross-Linked Star Polymers

The analytic formulas for the number- and weight-average molecular weights (MWs) of the core cross-linked star polymers (CCSPs) are proposed. In the arm-fi rst method, the number-and weight-average MWs of the arms ((M) over bar (nA) and (M) over bar (wA)) and CCSPs ((M) over bar (n) and (M) over bar (w)) can be determined experimentally. From (M) over bar (nA), (M) over bar (n), and weight fraction of the arms w(A) (or the core, w(C) = 1-w(A)), the number-average number of the arms ((f) over bar (n)) and the number-average core MW ((M) over bar (nC)) can be determined. Because of the correlation between the core MW and the number of the arms, the general solution of (M) over bar (w) for CCSPs presented requires attention to the nature of correlation. When the average and variance of the arm-number distribution are linear function of core MW, the weight-average number of the arms ((f) over bar (w)) and the weight-average core MW ((M) over bar (wC)) can be determined. The approximate estimation method for (f) over bar (w) is also discussed.