Résumé
We perform a comparative simulation study of the dynamical properties of ultrasoft particles in cluster phases. We focus on the generalized exponential model (GEM), a prototypical model for ultrasoft colloids, such as dendrimers and microgels. In the GEM of order n, particles interact through the potential u(r) = exp [−(r/σ)^n ], where σ and are length and energy scales, respectively. For n > 2 the GEM displays crystalline phases with multiply-occupied sites, i.e., it forms cluster crystals. We present extensive simulation results on the hopping dynamics of the GEM with n = 4 in the fcc cluster phase and report the first simulation evidence of cluster glasses in a bidisperse version of the model. The dynamics of the model in the fcc cluster phase is investigated through a combination of molecular dynamics (MD), Brownian dynamics (BD) and Monte Carlo (MC) simulations. We study the activated dynamics of particles as they hop from site to site in the cluster structure, and analyze the statistics of jump events. We find that the diffusion mechanism depends sensitively on the microscopic dynamics. In MD simulations particles can jump over several cluster site in a correlated fashion, leading to a broad distribution of jump lengths P_jump (r). In MC and BD simulations, by contrast, particles hop only to nearest neighbor sites. The underlying distributions of jump lengths affect the long time dynamics of the particles, giving rise, for instance, to qualitatively different shapes of the van Hove correlation functions. We attribute these differences to the suppression of momentum correlation in the two stochastic methods. The agreement between MC and BD simulations support the view that MC dynamics effectively incorporate solvent effects in a simulation of model colloids. We then extend our investigations to a binary mixture of particles with n = 4 and size ratio σ_11/σ_22 = 1.4, simulated over a wide range of densities. As the fluid is slowly quenched from high T, we observe the formation of stable clusters, whose centers of mass eventually arrest into a disordered configuration. The location of the cluster glass transition does not depend sensitively on the quench rate and is associated to a fragile-to-strong crossover in the T-dependence of the partial diffusion coefficients. In the cluster glass, particles hop from cluster to cluster. Unlike in cluster crystals, however, long range jumps are suppressed in MD simulations due to the disorder of the underlying cluster structure. We attribute the ability to form amorphous cluster phases to the size bidispersity of the particles. Clusters formed at low T are mostly homo-coordinated, leading to an effective binary mixture of clusters. This, in turn, frustrates crystallization of the clusters' centers of mass. This interpretation is supported by the comparison with a variant of the model with continuous size polydispersity. Our observations thus suggest a viable route to cluster glass formation in a more ample class of colloidal fluids, such as systems with competing interactions.