Swollen and collapsed phases in polymer networks under tension

Athermal polymer networks under tension display a discontinuous transition between a high- and a low-density phase at a sufficiently low cross-link/entanglement density. At a fixed temperature, a critical cross-link density is found above which the system is stable at all tensions. Approaching the critical cross-link density and tension, the bulk modulus of the system is seen to vanish resulting in auxetic behavior (i.e., negative Poisson ratio). We present a model of athermal networks which assumes affine deformation of network junction and independent network strands. We rigorously treat the nonlinear hardening of chain strands upon deformation and account for monomer repulsion with Wertheim's TPT1 theory. Our model quantitatively agrees with simulation data at low density and predicts the existence of a phase transition ending at a critical cross-link 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 this system. We draw parallels with the volume phase transition (VPT) occurring at a critical solvent quality in gels.