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Conformations of Crumpled Sheet Polymers

Published online by Cambridge University Press:  15 February 2011

David R. Nelson
David R. Nelson*
Affiliation:
Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138
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Flexible sheet polymers or “membranes” can be regarded as two-dimensional generalizations of linear polymer chains, for which there is a vigorous theoretical and experimental literature. Flexible membranes should exhibit even more richness and complexity, for two basic reasons. The first is that important geometric concepts like intrinsic curvature, orientability and genus, which have no direct analogue in linear polymers, appear naturally in discussions of two-dimensional macromolecules. Our understanding of the interplay between these concepts and the statistical mechanics of surfaces is still in its infancy. [1] The second reason is that surfaces can exist in a variety of different phases. The possibility of a two-dimensional shear modulus in planar membranes shows that we must distinguish between solids and liquids when these objects are allowed to crumple into three dimensions. Hexatic membranes, with extended six-fold bond orientational order, provide yet another important possibility. All three phases have quite distinctive properties. [2, 3] There are no such sharp distinctions for linear polymer chains.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 272: Symposium O – Chemical Processes in Inorganic Materials: Metal and Semiconductor Clusters , 1992 , 301
Copyright
Copyright © Materials Research Society 1992

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References

REFERENCES

1. For recent reviews, see the articles in Statistical Mechanics of Membranes and Surfaces, edited by Nelson, D.R., Piran, T. and Weinberg, S. (World Scientific, Singapore) 1989, and R. Lipowsky, Nature 349, 475 (1991).Google Scholar
2. Peliti, L. and Leibler, S., Phys. Rev. Lett. 54, 1690 (1985).Google Scholar
3. Nelson, D.R. and Peliti, L., J. Phys. France 48, 1085 (1987).Google Scholar
4. Hwa, T., Kokufuta, E. and Tanaka, T., Phys. Rev. A 44, 2235 (1991); X. Wen et. al. Nature 335, 426 (1992).Google Scholar
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6. Toner, J., Phys. Rev. Lett. 64, 1741 (1990); G. Gomper and D.M. Kroll, J. Phys. I France 1, 1411 (1991).Google Scholar
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8. For diffraction from flat phase, see Abraham, F.F. and Nelson, D.R., Science 249, (1990).Google Scholar