Network Physics and emergence of elasticity in colloidal gels: mechanical perspectiv

Colloidal gels exhibit a range of rate- and time-dependent rheological behavior that are classified as thixotropic elaso-visco-plastic. This complex rheology arises from the colloidal phase dynamics, and specifically, the evolution of a particulate microstructure that forms due to attractive interactions between different particles. These forces result in thermoreversible bonds, which in turn result in space-spanning networks that govern the mechanics of colloidal gels. What is clear is that particle-level bonds give rise to clusters at the mesoscale, and that elasticity in these gels arises from a percolated network at the macroscale. Thus, understanding the physics of this particulate network is the key to controlling and designing gels with desirable properties. Thus, we borrow well-established concepts from network science to interrogate and characterize the particulate network in attractive colloidal gels. We associate each colloidal particle to a vertex, and each inter-particle bond to an edge; we then proceed to the analysis of the networks of bonds, completely unaware of the spatial coordination of the particles, and to reveal structural signatures both at local and global scales. We employ network science tools to identify colloidal clusters and coarse grain the network further. The cluster networks from gels of different energy potential show distinct features and a simple spring network made out of the clusters made was found to recover the mechanics of our colloidal gel, suggesting that the appropriate length scale for a network analysis is set by the cluster size rather than individual particles. Finally, we show that network resilience analysis made possible using a Girvan-Newman criterion shows similar features to those from the elasticity of the spring network when strength of attraction between colloids is varied.