Structure properties of dextran. 3. Shrinking factors of individual clusters

Size exclusion chromatography in combination with multiangle laser light scattering and viscometry was applied for the study of the branched structures of commercial dextrans. Shrinking factors g = R-g,i(branch)2/R-g,i(linear)2 and g' = [eta](i,branch)/[eta](i.linear) were calculated, where the radii of gyration of pullulan were taken as the reference for the derivation of g, For the calculation of the g' factor, a reference curve was constructed by linear extrapolation of the low molar mass dextran data toward higher molar masses. A power law behavior g' = g(eta)(b) was found with exponent b(eta) = 0.71 +/- 0.05 which is slightly larger than 0.60 as was estimated by Kurata et al. and found with endlinked polystyrene star molecules. The combination of both shrinking factors also allowed us to estimate the Flory draining parameter Phi as a function of molar mass and of g, respectively. The Phi factor was found to increase with the number of branching points of the macromolecules. A quantitative estimation of the number of branching points is possible for randomly branched materials by applying the Zimm-Stockmayer relationship. For a good fit the equation had to be modified by changing the asymptotic power from -0.5 to -0.72. The branching unit was found to have a molar mass of 29 000 g/mol, which corresponds for hyperbranched chains to a chain length of about 90 monomer units between two branching points. The effect of incomplete fractionation is discussed.