Branched conformational properties of macromolecules in close relation to chemical synthesis. II. Influence of excluded volume interactions.

The description of perturbed particle conformations needs as a prerequisite the algorithm of unperturbed chains which is outlined in Paper I [J. Chem. Phys. 143, 114906 (2015)]. The mean square segment length ⟨r(2)(n)⟩=b(2)n(2ν) with ν = 0.588 for linear chains in a good solvent is used as an approximation also for branched samples. The mean square radius of gyration is easily derived, but for the hydrodynamic, the segment distribution by Domb et al. [Proc. Phys. Soc., London 85, 624 (1965)] is required. Both radii can analytically be expressed by Gamma functions. For the angular dependence of scattered light, the Fourier transform of the Domb distribution for self-avoiding random walk is needed, which cannot be obtained as an analytical function and was derived by numerical integration. The summation over all segment length in the particle was performed with an analytic fit-curve for the Fourier transform and was carried out numerically. Results were derived (i) for uniform and polydisperse linear chains, (ii) or f-functional randomly branched polymers and their monodisperse fractions, (iii) for random A3B2 co-polymers, and (iv) for AB2 hyper-branched samples. The deviation of the Gaussian approximation with the variance of ⟨r(2)(n)⟩=b(2)n(2ν) slightly overestimates the excluded volume interaction but still remains a fairly good approximation for region of qR(g) < 10.