Angular Dependence of Scattered Light from Hyperbranched Structures in a Good Solvent. A Fractal Approach

The neglect of excluded volume interaction in light scattering from randomly branched macromolecules leads to misinterpretation of the angular dependence. With a space correlation function of general fractal behavior γ(r) = Ae -( r /ξ)/(r/ξ)3- d Feltoft et al. (Phys. Rev. B 1986, 33, 269) derived the corresponding particle scattering factor P(q R g) of the angular dependence of scattered light, where q = (4πn 0/λ 0) sin θ/2 is the value of the scattering vector, R g is the radius of gyration, and ξ is a correlation length which is correlated to R g. Complete agreement between theory and three sets of chemically different randomly branched clusters was obtained (Macromolecules 1997, 30, 2365) with a fractal dimension of d = 1.76 (renormalization group theory: d RG = 1.70). In the present contribution, the Feltoft et al. approach is extended to hyperbranched and star-branched macromolecules. In contrast to randomly branched samples these structures are not selfsimilar objects. However, the angular dependence of these structures are well described by two different correlation lengths, ξ DB and ξ lin. The central part of the angular dependence is represented by a generalized Debye−Bueche space correlation function with correlation length ξ DB, the asymptotic regime of large q R g by that for polydisperse linear chains with correlation length ξ lin. The theory is applied to partially degraded amylopectins. A considerably higher branching density was found from the experimental data with perturbed than unperturbed chains. The remaining deviations from literature data are attributed to the neglect of chain stiffness and heterogeneity in branching.