Rouse dynamics of a dendrimer model in the Theta condition

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 tau(D) = 6G2(G) zeta/k, the second time is approximately tau(s) = 5.8 zeta/k, and the third time is approximately tau(r) = tau(e) = 2(G+1)zeta/k, where zeta 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.