Phase Transitions of Polymer Networks under Tension

Recent simulations have demonstrated that dry, cross-linked polymer networks under tension display all the features of the volume phase transition occurring in solvent-swollen gels, including (hyper-)auxetic behavior. Here, we present a quantitative model of crosslinked polymer networks which assumes affine, isotropic deformation of network junctions and independent network strands. We rigorously treat the nonlinear hardening of chain strands upon deformation by using an extensible freely jointed chain model and account for monomer interactions with perturbation theory. Our model quantitatively agrees with simulation data at low density and predicts the existence of a phase transition ending at a critical crosslink density. We demonstrate that a network with Hookean/Gaussian strands is not able to hold an arbitrary tension, highlighting the importance of nonlinear hardening in stabilizing three-dimensional networks under isotropic deformation. Our approach allows to study the generic features of volume instabilities in cross-linked polymers and uncovers the central role of the cross-link fraction in determining the stability envelope.