Numerical investigation of realistic core-shell microgels: Insights on two- and three-body effective interactions

: Core-shell (CS) microgels-comprising a solid core chemically linked to a crosslinked polymer shell-are an important class of stimuli-responsive colloids widely employed for both fundamental and applied studies. Despite extensive experimental investigations, their numerical modeling remains underdeveloped; in particular, a detailed, temperature-resolved insight of their effective interactions is missing. While pairwise descriptions known for standard microgels are expected to be partially extensible to CS-microgels, the effect of the solid core and in turn, the extent and character of many-body contributions remain elusive. To clarify these open issues, this work introduces a computational method to generate realistic CS-microgels at different crosslinker concentrations, accurately reproducing the structure of experimental silica core-poly-N-isopropylacrylamide (pNIPAM) shell microgels at different temperatures across the Volume Phase Transition (VPT) and for different shell-to-core ratios. After validating the model, effective interactions between CS-microgels are calculated, extracting not only two-body interactions but also providing the first quantitative investigation of three-body effects in any microgel system. The present findings show that, albeit small, the latter contributions are non-negligible and exhibit an intriguing sign reversal: while being predominantly attractive at low temperatures, they become repulsive at high ones, nearly canceling out at the VPT. These results reveal a subtle interplay between microgel architecture, temperature and many-body correlations, with direct implications on the design of responsive soft materials and their mutual interactions.