We studied the dependence of the dynamic properties on the generation G of a star-burst dendrimer model. The Rouse approximation for the mobility matrix was used for simplicity. We categorized all normal-mode displacements and considered various time-dependent correlation functions and the intrinsic viscosity. We determined three different time scales corresponding to (1) the diffusion of the center of mass through a distance equal to the dendrimer size, (2) the relaxation of the position of the center of mass relative to the central core monomer, and (3) the rotational and internal elastic motions of the molecule. These relaxation times depend differently on the generation G for large G:  the first time is approximately τD = 6G2 G ζ/k, the second time is approximately τs = 5.8ζ/k, and the third time is approximately τr = τe = 2 G +1ζ/k, where ζ is the friction coefficient for a single monomer and k = 3k B T/a 2 with k B being the Boltzmann constant, T the temperature, and a the average distance between the monomers. A linear dependence of the intrinsic viscosity on the generation was also found. These findings form the basis for further generalization of the theory to include hydrodynamic and excluded-volume interactions in order to model the actual systems more realistically.

We report the calculation of autocorrelation relaxation times, intrinsic viscosity, and the diffusion coefficient of a starburst dendrimer model, using both the preaveraging and variational-bound techniques. The model includes hydrodynamic effects, represented by the Rotne-Prager interaction, as well as excluded-volume repulsion, represented by a hard-core potential. Analytical derivations of the main formulae used in the paper are all explicitly given, and Monte Carlo simulations are used to carry out the thermodynamic average.

A dendrimer is a hyperbranched macromolecule that is grown from a central core generation by generation. We demonstrate through Monte Carlo simulations of a dendrimer model in two dimensions that when the terminal monomers and the interior monomers interact through an effective Flory-Huggins parameter , an angularly dependent domain structure forms in the molecule for sufficiently large . Based on the simulation data, we further show that the formation of the domain pattern is a smooth crossover, not a phase transition, from a mixed structure.