Dynamic structure of thermoreversible colloidal gels of adhesive spheres -art. no. 051402

The dynamic structure factor f(q,t) of suspensions of adhesive colloidal sp heres has been characterized as a function of temperature over the volume f raction range 0.010< <phi> <0.075. Below a critical temperature that is vol ume fraction dependent, the suspensions underwent an abrupt, reversible tra nsition in dynamic structure. Below their gel points suspensions became non ergodic, and the time decay of f(q,t) was arrested by as many as five decad es. Static light scattering demonstrated that the adhesive spheres formed a fractal cluster gel structure. A recent model of the dynamics of fractal c lusters [A. H. Krall and D. A. Weitz, Phys. Rev. Lett. 80, 778 (1998)] was applied to extract the temperature and volume fraction dependence of the ch aracteristic decay times of f(q,t). Immediately above the gel temperature a single stretched exponential decay of f(q,t) was observed. The temperature dependence of the decay time was <tau>(alpha) similar to epsilon (-1.15+/- 0.06), where epsilon = (T - T-gel)/T-gel, and T-gel is the gelation tempera ture. The argument of the stretched exponential decay p decreased monotonic ally as the temperature was lowered toward the gel point, until, at gelatio n, p similar to0.5. Below the gel temperature, an initial stretched exponen tial decay of f(q,t) was followed by a plateau. Finally, at long rimes, an additional exponential decay of the gel f(q,t) was observed. By applying th e fractal cluster dynamics model, it was found that the initial decay time, tau (beta)similar to epsilon (-1.00+/-0.07). The plateau in f(q,t) was due to an upper bound of the mean-squared displacement of gel segments, denote d delta (2). The typical magnitude of delta (2) was not much greater than t he square of the particle radius. The data showed delta (2) similar to epsi lon (-1.05+/-0.07). The additional exponential decay at long times, tau (ga mma), depended only weakly on epsilon. Its dependence on the scattering vec tor was tau (gamma)similar toq(-0.53+/-0.06). The argument of the stretched exponential decay of the gel f(q,t) and volume fraction dependence of tau (beta) and delta (2) indicate that the spatial scaling of the gel complianc e is consistent with the gel network bonds possessing angular rigidity. The epsilon dependence of the characteristic times tau (alpha) and tau (beta) could not be fully explained by the fractal duster dynamics model. The long rime decay of f(q,t) exhibited behavior that differed from that recently r eported for dilute gels of aqueous colloidal polystyrene [Cipelletti et al, Phys. Rev. Lett. 84, 2275 (2000)]. We hypothesize that the long-time decay in f(q,t) of the gels studied here is due to rare bond disaggregation proc esses that occur because of the relatively weak interaction between the adh esive spheres (DeltaE(min)/kT similar to 10) of the thermoreversible gel.