Sign Change of Poisson's Ratio for Carbon Nanotube Sheets

Abstract

Most materials shrink laterally like a rubber band when stretched, so their Poisson's ratios are positive. Likewise, most materials contract in all directions when hydrostatically compressed and decrease density when stretched, so they have positive linear compressibilities. We found that the in-plane Poisson's ratio of carbon nanotube sheets (buckypaper) can be tuned from positive to negative by mixing single-walled and multiwalled nanotubes. Density-normalized sheet toughness, strength, and modulus were substantially increased by this mixing. A simple model predicts the sign and magnitude of Poisson's ratio for buckypaper from the relative ease of nanofiber bending and stretch, and explains why the Poisson's ratios of ordinary writing paper are positive and much larger. Theory also explains why the negative in-plane Poisson's ratio is associated with a large positive Poisson's ratio for the sheet thickness, and predicts that hydrostatic compression can produce biaxial sheet expansion. This tunability of Poisson's ratio can be exploited in the design of sheet-derived composites, artificial muscles, gaskets, and chemical and mechanical sensors.

Negative Poisson's Ratio Behavior Induced by an Elastic Instability

“…Moreover, several geometries and mechanisms have been proposed to achieve negative values for the Poisson's ratio, including foams with reentrant structures [1] , hierarchical laminates [12] , polymeric and metallic foams [13] , microporous polymers [14] , molecular networks [15] and manybody systems with isotropic pair interactions [16] . Negative Poisson's ratio effects have also been demonstrated at the micron scale using complex materials which were fabricated using soft lithography [17] and at the nanoscale with sheets assemblies of carbon nanotubes [18] .…”

Modelling negative linear compressibility in tetragonal beam structures

“…During this orthorhombic phase, a small NLC was present between 8 and 90kbars. The possibility of Carbon nanotube sheets exhibiting NLC has also been investigated using analytical derivations Hall et al, 2008). Several naturally occurring NLC structures have also been discovered.…”

Negative Poisson’s ratios in metal nanoplates

“…W hen stretched, materials with a negative Poisson's ratio become thicker in the direction perpendicular to the original force [1][2][3][4][5][6][7][8][9][10][11] . Materials exhibiting such counterintuitive behaviour, known as auxetics, are of great interest not only because they are rare, but also because of their numerous potential applications in various fields, such as the design of fasteners 12 , prostheses 13 , pizeocomposites 14,15 , filters 16 , earphones 17 , seat cushions 18,19 and superior dampers 20 .…”

“…Materials with negative Poisson's ratios have been extensively studied since Lakes 1 reported a negative Poisson's ratio in a reentrant foam structure. Reentrant foam structure is an example of 'structural networks' [2][3][4][5][21][22][23] that manifest a negative Poisson's ratio, whereas their components at the molecular or microscale level have positive Poisson's ratios. Among structural networks are molecular networks 3 , hierarchical structures 4 , composites 5 and hinged structures 22,23 .…”