The Rouse–Zimm discrete hydrodynamic model is extended to acyclic macromolecules of any topology, and particular attention is devoted to starlike dendrimers and other symmetric cascade structures. As a first approximation, freely rotating models are built for branched structures by means of appropriate choices of topology-dependent stiffness parameters. Relevant dynamic observables (depending on the spectrum of viscoelastic relaxation rates) are studied as functions of local stiffness, of branching topology, and of dendrimer generational growth. The present results show that a moderate increase of local stiffness accounts for the molecular dimensions of dendrimers as previously calculated by Mansfield and Klushin [J. Phys. Chem. 96, 3994 (1992)] by Monte Carlo methods, and reproduces with good precision their results for the intrinsic viscosity (upper-bound calculations). Thus omission of excluded-volume interactions within the present models can be at least partially compensated for by suitable choices of local stiffness parameters, provided that the chain portions between branching points are not very long. In addition, the inaccuracy caused by preaveraging of hydrodynamic interactions (as estimated by computing exact and preaveraged first cumulant of the structure factor) does not seem to obscure the essential conclusions.

The dilute-solution dynamical properties of dendrimers in a good solvent are derived in the framework of the Rouse−Zimm approach. On the basis of a normal-coordinates treatment with preaveraged hydrodynamic interaction, we obtain the spectrum of relaxation times and some dynamical observables such as the viscoelastic complex modulus and the dynamic structure factor with its first cumulant. Since the latter quantity can also be calculated without preaveraging the hydrodynamic interaction, we can assess the accuracy of this approximation. The effect of both the structural symmetry and of the excluded-volume interactions on the intramolecular dynamics is discussed and the qualitative similarities with the effect of local stiffness are pointed out.

The good-solvent expansion of dendrimers is theoretically studied by self-consistent free-energy minimization accounting for all the relevant degrees of freedom. This feature enables a description both of the local conformation and of the overall molecular behavior. Equilibrium and dynamical properties are calculated, in particular the radius of gyration and the viscometric radius (from intrinsic viscosity). The intramolecular swelling is concentrated in the core region, the individual dendra, sub-dendra, etc., being stretched outward with relatively little inter-dendron mixing. Appropriate reduced variables are found for the characteristic radii, which yield a unique master curve for any generation and solvent quality. We also propose an analytical fitting function that permits easy numerical calculation for all cases of interest. The intrinsic viscosity dependence on generation is discussed, including the possible existence of a maximum as experimentally observed in some cases.