Dynamics of dendrimers and of randomly built branched polymers

We focus on the dynamical properties of dendrimers and of randomly built branched polymers, which allows us to assess theoretically the role of disorder on the relaxation forms. We model the random polymers through a stochastic growth algorithm. Our studies are carried out both in the Rouse and also in the Zimm framework; the latter accounts for hydrodynamic interactions. Moreover, we also mimic the local geometry by imposing conditions on the average values of the angles between neighboring segments. Excluded volume interactions, however, are neglected throughout. The storage $G^{\prime }\mathrm{(\omega )}$ and the loss $G^{″}\mathrm{(\omega )}$ moduli, which we calculate, turn out to depend more on the hydrodynamic and the angular restrictions than on randomness. Furthermore, we find that both the randomness and the angular restrictions slow down the relaxation. Given that $G^{\prime }\mathrm{(\omega ),}$ $G^{″}\mathrm{(\omega )}$ and also $\mathrm{C(t),}$ a function related to the radius of gyration, are all connected to the relaxation function $\mathrm{G(t),}$ a fact which we recall, we also calculate numerically $\mathrm{G(t)}$ and $\mathrm{C(t);}$ moreover we fit, following previous works, $\mathrm{C(t)}$ to stretched-exponential forms. Interestingly, it appears that from all functions considered $\mathrm{G(t)}$ is most sensitive to disorder.