Abstract
We report the results of recent investigations on the statistical mechanics of membranes with in-plane crystalline or hexatic order1. Our motivation was to understand the interplay between thermally excited shape fluctuations (undulations) and degrees of freedom associated with the internal ordering of the membrane. The more usual membranes, in particular those described by the Helfrich2 free energy, are fluid in the sense that the molecules forming them freely and quickly rearrange to comply with shape fluctuations. As a consequence, it becomes possible to describe them as geometrical surfaces, whose free energy depends only on their shape.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. R. Nelson and L. Peliti, J. Physique (in press).
W. Helfrich, Z. Naturforsch. 28c, 693 (1973).
W. Helfrich, J. Physique 46, 1263 (1985).
L. Peliti and S. Leibler, Phys. Rev. Lett. 56, 1690 (1985).
P.-G. de Gennes and C. Taupin, J. Phys. Chem. 86, 2294 (1982).
See e.g. J. Fröhlich, in Applications of Field Theory to Statistical Mechanics, edited by L. Garrido, Lecture Notes in Physics, 216 (Berlin: Springer, 1985 ).
Y. Kantor, M. Kardar and D. R. Nelson, Phys. Rev. Lett. 57, 791 (1986) and Phys. Rev. B (in press).
Y. Kantor and D. R. Nelson, unpublished.
D. R. Nelson and B. I. Halperin, Phys. Rev. B19, 2457 (1979); see also D. R. Nelson, Phys. Rev. B27, 2902 (1983).
F. David and E. Guitter, unpublished.
L. Landau and E. M. Lifshitz, Theory of Elasticity (New York: Pergamon, 1970), secs. 11–15.
S. Ami and H. Kleinert, Phys. Lett. Al20, 207 (1987).
L. H. Mitchell and A.K. Head, J. Mech. Stat. Solids 9, 131 (1961).
E. Sackmann, this workshop.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Peliti, L., Nelson, D.R. (1987). Elasticity of Crystalline and Hexatic Membranes. In: Meunier, J., Langevin, D., Boccara, N. (eds) Physics of Amphiphilic Layers. Springer Proceedings in Physics, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83202-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-83202-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-83204-8
Online ISBN: 978-3-642-83202-4
eBook Packages: Springer Book Archive