Signatures of auxeticity in microgels at low and ultralow crosslinker concentration

Auxetic behavior, characterized by a negative Poisson's ratio, is a counterintuitive mechanical response exhibited, among other systems, by certain polymer networks. Here, through in silico simulations we investigate the mechanical response of thermoresponsive microgels across the volume phase transition upon varying crosslinker concentration down to ultralow conditions, a regime so far unexplored. After refining the method to estimate the elastic moduli based on equilibrium shape fluctuations for the challenging case of ULCs, which are very sparse networks with rather anisotropic shape, we are able to show the onset of auxetic behavior near the volume phase transition for microgels with crosslinker concentration of ~ 1%. In addition, we find that ULC microgels exhibit a slightly negative Poisson's ratio across the whole swollen regime. Further examining the auxetic response within the inner region of the network, we also demonstrate that, for ULC microgels, this extends at all length scales, suggesting that it is an intrinsic property of the weakly connected polymer network. The present findings should likely stimulate novel experimental investigations, aiming to measure the Poisson's ratio of individual low and ultralow crosslinked microgels, to verify these intriguing numerical predictions.