Static and dynamic heterogeneities in irreversible gels and colloidal gelation

We compare the slow dynamics of irreversible gels, colloidal gels, glasses and spin glasses by analysing the behaviour of the so-called nonlinear dynamical susceptibility, a quantity usually introduced to quantitatively characterize the dynamical heterogeneities. In glasses this quantity typically grows with time, reaches a maximum and then decreases at large times, due to the transient nature of dynamical heterogeneities and to the absence of a diverging static correlation length. We have recently shown that in irreversible gels the dynamical susceptibility is instead an increasing function of time, as in the case of spin glasses, and that it tends asymptotically to the mean cluster size. On the basis of molecular dynamics simulations, we show here that in colloidal gelation where clusters are not permanent, at very low temperature and volume fractions, i.e. when the lifetime of the bonds is much larger than the structural relaxation time, the nonlinear susceptibility has a behaviour similar to that of the irreversible gel, followed, at higher volume fractions, by a crossover towards the behaviour of glass-forming liquids.