Arrested fluid-fluid phase separation in depletion systems: Implications of the characteristic length on gel formation and rheology

We investigate the structural, dynamical, and rheological properties of colloid-polymer mixtures in a volume fraction range of phi=0.15-0.35. Our systems are density-matched, residual charges are screened, and the polymer-colloid size ratio is similar to 0.37. For these systems, the transition to kinetically arrested states, including disconnected clusters and gels, coincides with the fluid-fluid phase separation boundary. Structural investigations reveal that the characteristic length, L, of the networks is a strong function of the quench depth: for shallow quenches, L is significantly larger than that obtained for deep quenches. By contrast, L is for a given quench depth almost independent of phi; this indicates that the strand thickness increases with phi. The strand thickness determines the linear rheology: the final relaxation time exhibits a strong dependence on phi, whereas the high frequency modulus does not. We present a simple model based on estimates of the strand breaking time and shear modulus that semiquantitatively describes the observed behavior.