Linking self-assembly, rheology, and gel transition in attractive colloids

We propose a microscopic framework based on nonequilibrium statistical mechanics to connect the microscopic level of particle self-assembly with the macroscopic rheology of colloidal gelation. The method is based on the master kinetic equations for the time evolution of the colloidal cluster size distribution, from which the relaxation time spectrum during the gelation process can be extracted. The relaxation spectrum is a simple stretched-exponential for irreversible diffusion-limited colloidal aggregation gelation, with a stretching exponent d(f)/3, where d(f) is the mass fractal dimension. As opposed to glassy systems, the stretched-exponential relaxation does not result from quenched disorder in the relaxation times, but from the self-assembly kinetics in combination with the fractal character of the process. As the master kinetic equations for colloidal aggregation do not admit bond-percolation solutions, the arrest mechanism is driven by the interconnection among fractal clusters when excluded volume becomes active, i.e., at sufficiently high packing of clusters. The interconnections between rigid clusters decrease the soft modes of the system and drive a rigidity-percolation transition at the cluster level. Using the Boltzmann superposition principle, the creep and the full rheological response can be extracted for both irreversible and thermoreversible colloidal aggregation. In the case of thermoreversible gelation, the attraction energy is finite and plays the role of the control parameter driving a nonequilibrium phase transition into a nonequilibrium steady-state ( the gel). A power-law spectrum coexisting with a stretched-exponential cut-off is predicted leading to power-law rheology at sufficiently high frequency. Our theory is in good agreement with experimental data of different systems published by other authors, for which no theory was available. (C) 2014 The Society of Rheology.