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We have recently shown [Blunt et al., Science 322, 1077 (2008)] that p-terphenyl-3,5,3',5'-tetracarboxylic acid adsorbed on graphite self-assembles into a two-dimensional rhombus random tiling.
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Cohn, H., Kenyon, R., and Propp, J. (2001). A variational principle for domino tilings. J. Am. Math. Soc. 14:297–346; Wilson, D. B. (2004). Mixing times of lozenge tiling and card shuffling Markov chains. Ann. Appl. Prob. 14:274–325
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Bouchaud, J.-P. and Biroli, G. (2004). On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes scenario for the viscosity increase in glasses. J. Chem. Phys. 121:7347Ð7354
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For reviews on dynamic heterogeneity see: Sillescu, H. (1999). Heterogeneity at the glass transition: a review. J. Non-Cryst. Solids, 243:81–108; Ediger, M. D. (2000). Spatially heterogeneous dynamics in supercooled liquids. Annu. Rev. Phys. Chem., 51:99–128; Glotzer, S. C. (2000). Spatially heterogeneous dynamics in liquids: insights from simulation. J. Non-Cryst. Solids, 274:342–355; Andersen, H. C. (2005). Molecular dynamics studies of heterogeneous dynamics and dy- namic crossover in supercooled atomic liquids. Proc. Natl. Acad. Sci. USA 102:6686–6691
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Toninelli, C., Wyart, M., Berthier, L., Biroli, G., and Bouchaud, J. P. (2005). Dynamical susceptibility of glass formers: Contrasting the predictions of theoretical scenarios. Phys. Rev. E, 71:041505–13
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Jack, R. and Garrahan, J. (2005). Caging and mosaic length scales in plaquette spin models of glasses. J. Chem. Phys. 123:164508-13
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Chandler, D., Garrahan, J. P., Jack, R. L., Maibaum, L., and Pan, A. C. (2006). Lengthscale dependence of dynamic four-point susceptibilities in glass formers. Phys. Rev. E, 74:051501–9
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Due to a slight mismatch in the distance between the two end phenyl rings in a TPTC molecule, and that between phenyl rings across a carboxylicÐ-carboxylic hydrogen bond, the tilings of Ref. [ 1 ] are not “ideal” [ 4 ] as there is a small energetic penalty for the parallel tile arrangement. They are “interacting” random tilings [ 8 , 9 ] . This difference in energy is however below the critical value at which such tilings would undergo a Kosterlitz-Thouless (KT) transition to an ordered phase [ 9 ]
Cited in the paper.
Keys, A. S. and Glotzer, S. C. (2007). How do quasicrystals grow? Phys. Rev. Lett. 99:235503–4
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Blunt, M. O., Russell, J. C., Gimenez-Lopez, M. C., Garrahan, J. P., Lin, X., Schroder, M., Champness, N. R., and Beton, P. H. (2008). Random tiling and topological defects in a two-dimensional molecular network. Science, 322:1077–1081
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2008
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Jeng, M., Bowick, M. J., Krauth, W., Schwarz, J. M., and Xing, X. (2008). Vacancy diffusion in the triangular-lattice dimer model. Phys. Rev. E 78:021112Ð12
2008
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Otero, R., Lukas, M., Kelly, R. E. A., Xu, W., Laegsgaard, E., Stensgaard, I., Kan- torovich, L. N., and Besenbacher, F. (2008). Elementary structural motifs in a random network of cytosine adsorbed on a gold(111) surface. Science, 319:312–315
2008
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Stannard A., Blunt M.O., Garrahan J.P. and Beton P.H. (2009). Preprint
2009
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Shokef, Y. and Lubensky, T. C. (2009). Stripes, zigzags, and slow dynamics in buckled hard spheres. Phys. Rev. Lett. 102:048303–4
2009
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