Entropic surfaces such as fluctuating 2D membranes are predicted to have desirable mechanical properties when unstressed, including a negative Poisson’s ratio. We present measurements of the strain-dependent Poisson ratio of self-avoiding membranes. We show that finite size membranes with free boundary conditions in fact have a positive Poisson ratio due to spontaneous non-zero mean curvature, which can be suppressed with an explicit bending rigidity in agreement with literature. Applying longitudinal strain to this system suppresses this mean curvature and entropic out-of-plane fluctuations, resulting in a negative Poisson’s above a critical strain, with Poisson ratios significantly more negative than the zero-strain limit for infinite sheets. We find that this auxetic behavior persists to surprisingly high strains (over 20% for the smallest surfaces), and finite size effects are actually desirable in producing a surface with a negative Poisson ratio over a wide range of strains. These results give clues to designing surfaces with a tunable negative Poisson ratio by using materials with a set amount of initial applied strain or adjusting the surface rigidity.
