In colloidal gels, attractive interactions among suspended colloids drive a thermodynamic instability that promotes aggregation, arresting in a space spanning network structure possessing unique mechanical properties. Commonly, phase separation is induced by the addition of non-adsorbing polymer to a suspension of repulsive colloids by the well-known depletion interaction. Such depletion gels are ubiquitous in industrial processes and products where fine solids are dispersed in polymer solutions, including agrochemicals, consumer care products, and pharmaceuticals. In applications, the rheology of a gel is its principle material property of interest, including its elasticity and yielding.
At low volume fractions and strong interaction energies between particles, colloidal gels are effectively modeled as fractal flocs formed through diffusion-controlled kinetic processes, which pack together to span the sample. The flocs are the principal load bearing units of the gel and theories connecting the floc architecture to the gel modulus remain a state-of-the-art description. Yet, there exists no definitive micro-structural theory for the elasticity of colloidal gels formed via arrested phase separation, which occurs at higher volume fractions and lower strengths of interaction. What are the fundamental structural units imparting elasticity to the network, and what physical principles govern their formation?
We use a recent model depletion gel that enables the rheology, structure, and particle interactions to be measured in concert . As the attractive strength between particles increases, the gel elastic modulus increases, but that this change cannot be accounted for by the immediate increase in bond stiffness between particles and clusters alone derived from the depletion interaction energy. The modulus is, however, consistent with an increasing number of cluster-cluster contacts. Based on the cluster model of gel rheology, two principal length scales emerge: at the particle level, the internal cluster structure becomes less dense with increasing attractive strength, and extends from the attractive glass line of colloids with short range attraction into the lower density gel region, similar to recent studies of protein gels , but in contrast to prior studies of suspensions that rely solely on imaging the microstructure . However, the size of the clusters, the length scale over which stress is transmitted during elastic deformation, does not depend on the magnitude of the attractive strength; its origin remains an open question. These results confirm that there is an intimate connection between the gelation of colloids with short-range attraction and phase separation. Remarkably, the cluster gel model gives consistent results for depletion gels that span a range of length scales and chemistries, but otherwise capture the same relative range of attraction and interaction strengths .