%0 Book Section %1 statphys23_0519 %A Schröder-Turk, G.E. %A Ellison, L.J. %A Michel, D. %A Cleaver, D.J. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K bicontinuous crystals gyroid liquid materials nanocrystalline networks phase self-assembly statphys23 topic-7 transition %T The morphology of the Gyroid ($Ia3d$) phase in self-assemblies of hard pear-shaped particles %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=519 %X Purely entropic self-assemblies of pear-shaped particles, interacting by hard-wall repulsion only, have recently been shown to assemble into the bicontinuous triply-periodic Gyroid structure of symmetry $Ia3d$ 1. This phase is well-known in lyotropic liquid crystals where a lipid or surfactant bilayer separating two intertwined labyrinthine domains forms as a consequence of the chemical interaction between amphibilic molecules and water. In the latter case, the bilayer mid-surface is required, by symmetry, to be the minimal Gyroid surface described by Schoen; fluctuations of the molecules around this surface correspond to the thickness variations of the bilayer, and are small relative to the thickness of the labyrinthine domains. For these pear-shaped particles, however, there is no a priori reason to expect a minimal surface partition, and fluctuations of the particle position around the surface are not restricted to be small. In this talk we report on a morphological analysis of the simulation results of ref. 1 using the medial surface concept 2. We demonstrate the validity of a description of this system with reference to the minimal Gyroid surface: the particle positions have a typical distance to the minimal Gyroid surface with small fluctuations, and there is a clear correlation between the directional vectors of the pear-shaped particles and the normal directions of the Gyroid surface. This analysis provides morphological data with which to clarify how entropy alone can lead to this ordered phase. It is also a necessary precursor to an analysis of defect formation in this intricate phase, necessary to an understanding of the topological transitions that characterize the structural transformation from a smectic bilayer arrangement to the Gyroid. 1) L.J. Ellison, D.J. Michel, F. Barmes, D.J. Cleaver, Phys. Rev. Letts, 97, 237801 (2006)\\ 2) G.E. Schröder-Turk, A. Fogden, S.T. Hyde, Eur. Phys. J. B, 54, 509(2006)

@incollection{statphys23_0519, abstract = {Purely entropic self-assemblies of pear-shaped particles, interacting by hard-wall repulsion only, have recently been shown to assemble into the bicontinuous triply-periodic Gyroid structure of symmetry $Ia\overline{3}d$ [1]. This phase is well-known in lyotropic liquid crystals where a lipid or surfactant bilayer separating two intertwined labyrinthine domains forms as a consequence of the chemical interaction between amphibilic molecules and water. In the latter case, the bilayer mid-surface is required, by symmetry, to be the minimal Gyroid surface described by Schoen; fluctuations of the molecules around this surface correspond to the thickness variations of the bilayer, and are small relative to the thickness of the labyrinthine domains. For these pear-shaped particles, however, there is no a priori reason to expect a minimal surface partition, and fluctuations of the particle position around the surface are not restricted to be small. In this talk we report on a morphological analysis of the simulation results of ref. [1] using the medial surface concept [2]. We demonstrate the validity of a description of this system with reference to the minimal Gyroid surface: the particle positions have a typical distance to the minimal Gyroid surface with small fluctuations, and there is a clear correlation between the directional vectors of the pear-shaped particles and the normal directions of the Gyroid surface. This analysis provides morphological data with which to clarify how entropy alone can lead to this ordered phase. It is also a necessary precursor to an analysis of defect formation in this intricate phase, necessary to an understanding of the topological transitions that characterize the structural transformation from a smectic bilayer arrangement to the Gyroid. 1) L.J. Ellison, D.J. Michel, F. Barmes, D.J. Cleaver, Phys. Rev. Letts, 97, 237801 (2006)\\ 2) G.E. Schr\"oder-Turk, A. Fogden, S.T. Hyde, Eur. Phys. J. B, 54, 509(2006)}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Schr\"oder-Turk, G.E. and Ellison, L.J. and Michel, D. and Cleaver, D.J.}, biburl = {https://www.bibsonomy.org/bibtex/2128dc6ab1de90c8e8ee2be85fd4d863c/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {cc1d76c79a45268f8557ad31d15d5f09}, intrahash = {128dc6ab1de90c8e8ee2be85fd4d863c}, keywords = {bicontinuous crystals gyroid liquid materials nanocrystalline networks phase self-assembly statphys23 topic-7 transition}, month = {9-13 July}, timestamp = {2007-06-20T10:16:22.000+0200}, title = {The morphology of the Gyroid ($Ia\overline{3}d$) phase in self-assemblies of hard pear-shaped particles}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=519}, year = 2007 }