Capturing Structure and Morphology in Responsive Microgels: From Intrinsic Free Energy to Collective Behavior

We develop a coarse-grained theoretical and computational framework based on responsive effective pair potentials to describe the compression behavior of core-shell microgels in a good solvent. Our approach accounts for the intrinsic morphological heterogeneity of the particles by decomposing the total free energy into core and shell contributions, each governed by a Flory-Rehner-type model with distinct mechanical properties. Mechanical equilibrium between both regions is imposed to capture the swelling behavior self-consistently. Interparticle interactions are modeled using a four-component, size-dependent multi-Hertzian pair potential that incorporates the differential mechanical response and compressibility of the core and shell. The model parameters are determined by fitting to dynamic light scattering measurements of PNIPAM microgels across a range of temperatures spanning the lower critical solution temperature, thus, capturing the thermoresponsive swelling behavior. The model also provides variation of the core size upon thermal or mechanical collapse of the microgels. Monte Carlo simulations are then performed to investigate the collective properties of concentrated suspensions, including size distribution, effective packing fraction, structural organization, and phase behavior as a function of compression. Our results demonstrate that both the intrinsic particle softness and responsiveness, as well as their heterogeneous internal structure, play a crucial role in determining the microstructure and thermodynamic state of dense microgel systems.