Emergence of rigidity, microscopic rearrangements and viscoelastic response in soft particle gels

We have investigated the connection between the structural and mechanical heterogeneities of soft particulate gels and their viscoelastic spectrum in a 3-D microscopic numerical model, using large scale simulations with Optimally Windowed Chirp (OWCh) signals. In the model, particles spontaneously self-assemble into disordered, stable porous networks (even at low volume fractions) that feature extended relaxation spectra, microscopic dynamics, and mechanics consistent with several observations in colloidal and protein gels. To recapitulate the basic features of the particle contacts in those systems, the main ingredients of the model are short-range attractive interactions and bending stiffness for the inter-particle bonds. We have analyzed the emergence of rigidity, the shape of the frequency-dependent dynamic modulus G*(ω) and its dependence on the gel connectivity, and the distribution of microscopic non-affine rearrangements the network experiences under small-amplitude oscillatory deformation. We show how the viscoelastic response of different gels can be captured in a unique master curve through a fractional constitutive model and discuss how the underlying microscopic dynamical processes determine the rheological response.