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

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