We introduce a microscopically realistic model of a physical gel and use computer simulations to study its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a critical point, a gelation line determined by geometric percolation, and an equilibrium gel phase unrelated to phase separation. The global structure of the gel is homogeneous, but the stress is only supported by a fractal network. The gel dynamics is highly heterogeneous and we propose a theoretical model to quantitatively describe dynamic heterogeneity in gels. We elucidate several differences between the dynamics of gels and that of glass formers.

We show that finite-range alternatives to the standard long-range BKS pairpotential for silica might be used in molecular dynamics simulations. We studytwo such models that can be efficiently simulated since no Ewald summation isrequired. We first consider the Wolf method, where the Coulomb interactions aretruncated at a cutoff distance r_c such that the requirement of chargeneutrality holds. Various static and dynamic quantities are computed andcompared to results from simulations using Ewald summations. We find very goodagreement for r_c ~ 10 Angstroms. For lower values of r_c, the long--rangestructure is affected which is accompanied by a slight acceleration of dynamicproperties. In a second approach, the Coulomb interaction is replaced by aneffective Yukawa interaction with two new parameters determined by a forcefitting procedure. The same trend as for the Wolf method is seen. However,slightly larger cutoffs have to be used in order to obtain the same accuracywith respect to static and dynamic quantities as for the Wolf method.

We use a standard Monte Carlo algorithm to study the slow dynamics of a binary Lennard-Jones glass-forming mixture at low temperature. We find that the Monte Carlo approach is by far the most efficient way to simulate a stochastic dynamics since the relaxation is about 10 times faster than in Brownian dynamics and about 30 times faster than in stochastic dynamics. Moreover, the average dynamical behaviour of the system is in quantitative agreement with that obtained using Newtonian dynamics, apart from at very short times where thermal vibrations are suppressed. We show, however, that dynamic fluctuations quantified by four-point dynamic susceptibilities do retain a dependence on the microscopic dynamics, as recently predicted theoretically.

We study theoretically and numerically a family of multipoint dynamic susceptibilities that quantify the strength and characteristic length scales of dynamic heterogeneities in glass-forming materials. We use general theoretical arguments (fluctuation-dissipation relations and symmetries of relevant dynamical field theories) to relate the sensitivity of averaged two-time correlators to temperature and density to spontaneous fluctuations of the local dynamics. Our theoretical results are then compared to molecular dynamics simulations of the Newtonian, Brownian, and Monte Carlo dynamics of two representative glass-forming liquids, a fragile binary Lennard-Jones mixture, and a model for the strong glass-former silica. We justify in detail the claim made by Berthier [Science 310, 1797 (2005)] that the temperature dependence of correlation functions allows one to extract useful information on dynamic length scales in glassy systems. We also discuss some subtle issues associated with the choice of microscopic dynamics and of statistical ensemble through conserved quantities, which are found to play an important role in determining dynamic correlations. (C) 2007 American Institute of Physics.