Onset of criticality in hyper-auxetic polymer networks

Andrea Ninarello,Emanuela Zaccarelli,José Ruiz-Franco

doi:10.1038/s41467-022-28026-z

Andrea Ninarello, Emanuela Zaccarelli + Show 1 more

Open Access

https://doi.org/10.1038/s41467-022-28026-z

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Abstract

Against common sense, auxetic materials expand or contract perpendicularly when stretched or compressed, respectively, by uniaxial strain, being characterized by a negative Poisson’s ratio ν. The amount of deformation in response to the applied force can be at most equal to the imposed one, so that ν = − 1 is the lowest bound for the mechanical stability of solids, a condition here defined as “hyper-auxeticity”. In this work, we numerically show that ultra-low-crosslinked polymer networks under tension display hyper-auxetic behavior at a finite crosslinker concentration. At this point, the nearby mechanical instability triggers the onset of a critical-like transition between two states of different densities. This phenomenon displays similar features as well as important differences with respect to gas-liquid phase separation. Since our model is able to faithfully describe real-world hydrogels, the present results can be readily tested in laboratory experiments, paving the way to explore this unconventional phase behavior.

Highlights

Against common sense, auxetic materials expand or contract perpendicularly when stretched or compressed, respectively, by uniaxial strain, being characterized by a negative Poisson’s ratio ν
We start by calculating the elastic properties of diamond networks (Diam) for different values of the crosslinker concentration c for negative pressures starting from P = 0
For each studied state point, we independently evaluate three moduli: the bulk modulus K is obtained from equilibrium NPT runs, whereas the Young modulus Y and the Poisson’s ratio ν are estimated from strainstress simulations, as described in the Methods section

Summary

Introduction

Auxetic materials expand or contract perpendicularly when stretched or compressed, respectively, by uniaxial strain, being characterized by a negative Poisson’s ratio ν. Pioneering evidence of a negative Poisson’s ratio has been reported for these systems close to the so-called Volume Phase Transition[15–17]: in this case, a variation in temperature changes the affinity of the polymer to the solvent, favoring monomer-monomer aggregation, in full analogy with the gas-liquid critical point, but with the additional constraint of network connectivity. Another thermodynamic parameter that influences the network properties without affecting monomeric interactions is pressure, or tension. Numerical efforts have been able to realize fully-connected, disordered networks with arbitrary density and crosslinker concentrations[24,25]

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Results

Conclusion