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ScienceWeek
MATERIALS SCIENCE: ON AUXETIC MATERIALS
The following points are made by Ray H. Baughman (Nature 2003 425:667):
1) When compressed in a vise, the sides of a material are expected to bulge. Conversely, stretching is expected to make a material thinner -- as for the rubber band on your desk. Most materials exhibit these dimensional changes in lateral directions to decrease the volume change produced by the applied strain. But materials do exist that expand in at least one lateral direction when stretched. Known as "auxetic" materials, they have recently gone from being rarely recognized to appearing rather commonplace. In fact, much of the crystalline matter in the Universe may be in auxetic phases, from most cubic phases of metals to super-dense crystals thought to comprise the outer crust of neutron stars and the cores of white dwarf stars. These auxetic materials exist across an enormous range of conditions --from near absolute zero and densities of approximately 10^(-15) g/cm^(3) for plasma ion crystals to above 10^(6) K and densities of 10^(11) g/cm^(3) for proposed crystals in stars.
2) The Poisson ratio (defined as -1 times the ratio of lateral to applied elastic strains) describes the behavior of stretched materials -- positive Poisson ratios characterize the expected normal behavior, whereas auxetic materials have a negative value. Although Poisson's ratio for cubic phases must be between -1 and +2, there is no theoretical limitation on this ratio for materials with less internal symmetry. Although few crystals have negative Poisson's ratios for all stretch and lateral directions, such behavior can be obtained for foams of most materials.
3) The behavior of some auxetic materials seems more fitting for Alice's Wonderland than for the real world. After an initial elongation, stretching the porous polytetrafluoroethylene used as artificial arteries generates up to an 11-fold higher relative expansion in one lateral direction. Although the direct effect of a negative Poisson's ratio is to cause an expansion that decreases density during stretching, a small fraction of auxetic crystals actually increase in density when stretched. This behavior is quite rare, but all 13 observed stretch-densified crystals (out of 500 investigated crystals) are auxetic.
4) The answer to this paradox is that very large positive Poisson's ratios are made thermodynamically possible by the existence of negative Poisson's ratios. Indeed, cubic metals that have the most positive Poisson's ratio for one lateral direction also have the most negative Poisson's ratio for the second lateral direction.
5) Auxetic materials could be used as strain amplifiers if the strain-amplification factor (-1 times the Poisson's ratio) is larger in magnitude than one. Strain amplification close to the maximum Poisson's ratio of +2 occurs for cubic phases, and even this small amplification could be useful. However, auxetic materials with lower symmetry can have giant strain amplification factors, for example porous polytetrafluoroethylene has a Poisson's ratio of up to -12, which is about 40 times larger than that for most materials.(1-5)
References (abridged):
1. Baughman, R. H. et al. Science 288, 2018–2022 (2000)
2. Baughman, R. H., Stafström, S., Cui, C. & Dantas, S. O. Science 279, 1522–1524 (1998)
3. Bowick, M., Cacciuto, A., Thorliefsson, G. & Travesset, A. Phys. Rev. Lett. 87, 148103–148106 (2001)
4. Evans, K. E. Adv. Mater. 12, 617–628 (2000)
5. Gibson, L. J. & Ashby, M. Cellular Solids (Pergamon, Oxford,1988)
Nature http://www.nature.com/nature
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ON ELASTIC MEMBRANES
The following points are made by Roderic Lakes (Nature 2001 414:503):
1) Elastic materials deform easily when under strain but return to their original dimensions when the force is removed: they resist changes to both shape and volume. Rubbery materials, which easily change shape but not volume, become notably thinner in cross-section when stretched. This is described by Poisson's ratio, the ratio of transverse contraction to longitudinal extension during stretching. For rubber, Poisson's ratio is close to the theoretical upper limit of 0.5; for most other common materials, the ratio is between 0.25 and 0.35. Because all these materials become thinner when stretched, Poisson's ratio is always positive. The reason for the thinning is that interatomic bonds tend to align when deformed.
2) A negative Poisson's ratio, which requires a transverse expansion (thickening) on stretching, is considered counterintuitive. Indeed, such materials were once thought not to exist or even to be impossible. But materials with negative Poisson's ratio do occur, and have been called "anti-rubber" "auxetic", or "dilational". For example, 2-dimensional honeycomb structures have been developed with "inverted" cells, which unfold when stretched. Regular honeycomb lattices, like most materials, have a positive Poisson's ratio. Similarly, some foam materials with a 3-dimensional microstructure of "inwardly bulging" cells also become fatter when stretched. These foams and honeycombs have such unusual elastic behavior because of nonuniform unfolding or deformation of the microstructure. Such materials are usually tougher and more resilient than most conventional materials.
Nature http://www.nature.com/nature
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