  An important open problem in materials science is whether a direct connection
exists between single-particle elastic properties and the 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 non-ionic microgels across their volume phase
transition (VPT). Remarkably, we reproduce many features seen in experiments,
including the appearance of a minimum of 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.
