Connecting Elasticity and Effective Interactions of Neutral Microgels: The Validity of the Hertzian Model

Abstract

An important open problem in materials science is whether a direct connection\nexists between single-particle elastic properties and the macroscopic bulk\nbehavior. Here we address this question by focusing on the archetype of soft\ncolloids: thermoresponsive microgels. These colloidal-sized polymer networks\nare often assumed to interact through a simple Hertzian potential, a classic\nmodel in linear elasticity theory. By developing an appropriate methodology,\nthat can be generalized to any kind of soft particle, we are able to calculate\nall the elastic moduli of non-ionic microgels across their volume phase\ntransition (VPT). Remarkably, we reproduce many features seen in experiments,\nincluding the appearance of a minimum of the Poisson's ratio close to the VPT.\nBy calculating the particle-particle effective interactions and the resulting\ncollective behavior, we find that the Hertzian model works well up to moderate\nvalues of the packing fraction.\n