Department of Chemical Engineering, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, United States.
ACS Nano. 2016 Aug 23;10(8):7542-9. doi: 10.1021/acsnano.6b02512. Epub 2016 Jul 18.
Entropic surfaces represented by fluctuating two-dimensional (2D) membranes are predicted to have desirable mechanical properties when unstressed, including a negative Poisson's ratio ("auxetic" 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 Poisson'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 molecular-scale mechanism for realizing a negative Poisson'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 Poisson's ratio over a wide range of strains. These results promise the design of surfaces and composite materials with tunable Poisson's ratio by prestressing platelet inclusions or controlling the surface rigidity of a matrix of 2D materials.
当不受应力时，由涨落二维（2D）膜表示的熵表面预计具有理想的机械性能，包括负泊松比（“负泊松比”行为）。在此，我们提出了自回避 2D 膜的应变相关泊松比的计算，该膜在一定的机械应变范围内表现出理想的负泊松比性能。具有无约束边界条件的有限尺寸膜由于自发的非零平均曲率而具有正泊松比，这可以通过与先前发现一致的显式弯曲刚度来抑制。将纵向应变沿奇异轴施加到该系统中会抑制这种平均曲率和熵的面外涨落，从而在高于临界应变的情况下实现负泊松比的分子级机制，其值比以前观察到的无限片的零应变极限明显更负。我们发现，对于最小的表面，令人惊讶的是，在超过 20%的高应变下，仍然存在负泊松比行为，并且通过预加载血小板夹杂物或控制二维材料基质的表面刚度，可以产生具有宽应变范围的负泊松比表面。这些结果有望通过预拉伸血小板夹杂物或控制二维材料基质的表面刚度来设计具有可调泊松比的表面和复合材料。
