(511c) Persistently Auxetic Materials (PAMs): Engineering the Poisson Ratio of 2D Self-Avoiding Membranes Under Conditions of Non-Zero Anisotropic Strain

Authors: 
Govind Rajan, A., Massachusetts Institute of Technology
Ulissi, Z., Massachusetts Institute of Technology
Strano, M. S., Massachusetts Institute of Technology
Entropic surfaces represented by fluctuating 2D membranes are predicted to have desirable mechanical properties when unstressed, including a negative Poissonâ??s ratio (â??auxeticâ? behavior). Herein, we present calculations of the strain-dependent Poisson ratio of self-avoiding 2D membranes demonstrating desirable auxetic properties over a range of mechanical strain. Finite size membranes with unclamped boundary conditions have positive Poissonâ??s ratio due to spontaneous non-zero mean curvature, which can be suppressed with an explicit bending rigidity in agreement with prior findings. Applying longitudinal strain along a singular axis to this system suppresses this mean curvature and the entropic out-of-plane fluctuations, resulting in a new, molecular scale mechanism for realizing a negative Poissonâ??s ratio above a critical strain, with values significantly more negative than the previously observed zero-strain limit for infinite sheets. We find that auxetic behavior persists over surprisingly high strains of more than 20% for the smallest surfaces, with desirable finite size scaling producing surfaces with negative Poissonâ??s ratio over a wide range of strains. These results promise the design of surfaces and composite materials with tunable Poissonâ??s ratio by pre-stressing platelet inclusions or controlling the surface rigidity of a matrix of 2D materials.