Abstract
Ordinary crystals are characterized by long-range translational order in all three dimensions. In lower-dimensional systems, in contrast, translational order is destroyed through the ‘Landau–Peierls instability’ — displacements from periodic ordering due to thermal fluctuations whose amplitude increases with the size of the system1,2,3,4. This effect is well known for layered systems ordered in one dimension, such as surfactant membranes5,6, smectic (layered) liquid crystals7 and liquid crystalline polymers8, which form ordered stacks of fluid monolayers. Smectic liquid-crystal polymers can be weakly crosslinked to form percolating elastomeric networks that still allow mobility on a molecular scale9,10. In these smectic elastomers, fluctuations of the fluid layers are coupled to distortions of the underlying network, and are therefore energetically penalized11, even though the network of crosslinks has a random nature and thus no three-dimensional translational order. Here we present a high-resolution X-ray diffraction study of a smectic elastomer that reveals the effects of crosslinking on long-range ordering. We find that the introduction of a random network of crosslinks enhances the stability of the layered structure against thermal fluctuations and suppresses the Landau–Peierls instability so as to induce ‘one-dimensional’ long-range ordering at length-scales up to several micrometres.
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References
Landau, L. D. in Collected Papers of L. D. Landau (ed. ter Haar, D.) 193–216 (Gordon & Breach, New York, (1965)).
Peierls, R. E. Bemerkung über Umwandlungstemperaturen. Helv. Phys. Acta Suppl. 7, S81–S83 (1934).
Chaikin, P. M. & Lubensky, T. C. Principles of Condensed Matter Physics (Cambridge Univ. Press, New York, (1995)).
de Gennes, P. G. & Prost, J. The Physics of Liquid Crystals 2nd edn (Clarendon Press, Oxford, (1993)).
Safinya, C. R. et al. Steric interactions in a model multimembrane system: a synchrotron X-ray study. Phys. Rev. Lett. 57, 2718–2721 (1986).
Sirota, E., Smith, G. S., Safinya, C. R., Plano, R. J. & Clark, N. A. X-ray scattering studies of aligned, stacked surfactant membranes. Science 242, 1406–1409 (1988).
Als-Nielsen, J. et al. Observation of algebraic decay of positional order in a smectic liquid crystal. Phys. Rev. B22, 312–320 (1980).
Nachaliel, E., Keller, E. N., Davidov, D. & Boeffel, C. Algebraic dependence of the structure factor and possible anharmonicity in a high resolution X-ray study of a side-group polymeric liquid crystal. Phys. Rev. A43, 2897–2902 (1991).
Zentel, R. Liquid crystalline elastomers. Angew. Chem. Adv. Mater. 101, 1407–1415 (1989).
Finkelmann, H., Benne, J. & Semmler, K. Smectic liquid crystal elastomers. Macromol. Symp. 96, 169–174 (1995).
Terentjev, E. M., Warner, M. & Lubensky, T. C. Fluctuations and long-range order in smectic elastomers. Europhys. Lett. 30, 343–348 (1995).
Caillé, A. Remarques sur la diffusion des rayons X dans les smectiques. C. R. Acad. Sci. Paris B274, 891–893 (1972).
Warren, B. E. X-ray Diffraction (Addison-Wesley, Reading, (1969)).
de Gennes, P. G. in Polymer Liquid Crystals (eds Ciferri, A., Krigbaum, W. R. & Meyer, R. B.) 115–132 (Academic, New York, (1982)).
Mitchell, G. R., Davis, F. J. & Guo, W. Strain-induced transitions in liquid-crystal elastomers. Phys. Rev. Lett. 71, 2947–2950 (1993).
Krivoglaz, M. Theory of X-ray and Thermal Neutron Scattering by Real Crystals (Plenum, New York, (1969)).
Zentel, R. & Benalia, M. Stress-induced orientation in lightly crosslinked liquid-crystalline side-group polymers. Makromol. Chem. 188, 665–674 (1987).
Kaganer, V. M., Ostrovsky, B. I. & de Jeu, W. H. X-ray scattering in smectic liquid crystals: from ideal- to real-structure effects. Phys. Rev. A44, 8158–8166 (1991).
Olmsted, P. D. & Terentjev, E. M. Mean-field nematic-smectic-A transition in a random polymer network. Phys. Rev. E53, 2444–2453 (1996).
Blatter, G., Feigelíman, M. V., Geshkenbein, V. B., Larkin, A. I. & Vinokur, V. M. Vortices in high temperature superconductors. Rev. Mod. Phys. 66, 1125–1380 (1994).
Terentjev, E. M. Non-uniform deformations and molecular random fields in liquid crystalline elastomers. Macromol. Symp. 117, 79–88 (1997).
Acknowledgements
We thank E. M. Terentjev for discussions, E. Gebhard for assistance in sample preparation, and J. Commandeur for technical support. This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie [Foundation for Fundamental Research on Matter (FOM)] with support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Netherlands Organization for the Advancement of Research (NWO)]. W.d.J. acknowledges additional support from a NATO collaborative research grant.
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Wong, G., de Jeu, W., Shao, H. et al. Induced long-range order in crosslinked ‘one-dimensional’ stacks of fluid monolayers. Nature 389, 576–579 (1997). https://doi.org/10.1038/39271
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DOI: https://doi.org/10.1038/39271
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