Linear viscoelastic spectra of soft particulate gels: master curve and physical origin of the fractal constitutive behavior

We investigate the connection between the load-bearing network structure in soft particulate gels and their linear 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 broad relaxation spectra, microscopic dynamics, and mechanics consistent with several observations in colloidal and protein gels. The main ingredients of the model are short-range attractive interactions and bending stiffness for the inter-particle bonds. Using the OWCh protocol we analyze the shape of the frequency-dependent dynamic modulus G*(ω) and its dependence on the gel connectivity and on the preparation protocol. We show that, over a wide range of network connectivities, the viscoelastic response of different gels can be captured in a unique master curve compactly described in terms of a fractional constitutive model. The master curve provides new insight into how fractal remnants of the gelation process at the onset of rigidity can determine the linear viscoelastic behavior of soft particulate gels.