Multi-scale relaxation dynamics of arrested patchy particle gels

Patchy particle interactions enable the design of so-called ‘equilibrium gels’, a system where arrest is achieved without an underlying phase separation, resulting in structurally equilibrated gels which do not undergo coarsening-induced aging. Here, we study the multi-scale relaxation dynamics of a model patchy particle gel consisting of nanoparticles linked with end-functionalized polymers by using stopped-flow spectro-photometry, x-ray photon correlation spectroscopy, and linear viscoelastic measurements. We show that, despite the fast dissociation dynamics of an individual polymer linker from the nanoparticle, the relaxation of the system becomes slow and arrested at larger length-scales due to multi-functional associations between the nanoparticles. We show that the nanoscale primary clusters undergo a combination of super-diffusive and diffusive relaxation modes, which is contrasted by the sub-diffusive and stretched-exponential relaxation of the network at the macroscale. We show that the super-diffusive dynamics of the primary clusters are highly intermittent, which supports the interpretation that avalanche dynamics is a general feature associated with the microscopic dynamics of arrested soft materials, irrespective of the material’s route to arrest.