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Purely entropic self-assembly of the bicontinuous Ia3̅d gyroid phase in equilibrium hard-pear systems

Philipp W. A. Schönhöfer, Laurence J. Ellison, Matthieu Marechal, Douglas J. Cleaver, Gerd E. Schröder-Turk
Published 16 June 2017.DOI: 10.1098/rsfs.2016.0161
Philipp W. A. Schönhöfer
School of Engineering and Information Technology, Mathematics and Statistics, Murdoch University, 90 South Street, Murdoch, Western Australia 6150, AustraliaInstitut für Theoretische Physik I, Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
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Laurence J. Ellison
Materials and Engineering Research Institute, Sheffield Hallam University, Sheffield S1 1WB, UK
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Matthieu Marechal
Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
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  • For correspondence: matthieu.marechal@fau.de
Douglas J. Cleaver
Materials and Engineering Research Institute, Sheffield Hallam University, Sheffield S1 1WB, UK
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  • For correspondence: D.J.Cleaver@shu.ac.uk
Gerd E. Schröder-Turk
School of Engineering and Information Technology, Mathematics and Statistics, Murdoch University, 90 South Street, Murdoch, Western Australia 6150, Australia
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Abstract

We investigate a model of hard pear-shaped particles which forms the bicontinuous IaEmbedded Imaged structure by entropic self-assembly, extending the previous observations of Barmes et al. (2003 Phys. Rev. E 68, 021708. (doi:10.1103/PhysRevE.68.021708)) and Ellison et al. (2006 Phys. Rev. Lett. 97, 237801. (doi:10.1103/PhysRevLett.97.237801)). We specifically provide the complete phase diagram of this system, with global density and particle shape as the two variable parameters, incorporating the gyroid phase as well as disordered isotropic, smectic and nematic phases. The phase diagram is obtained by two methods, one being a compression–decompression study and the other being a continuous change of the particle shape parameter at constant density. Additionally, we probe the mechanism by which interdigitating sheets of pears in these systems create surfaces with negative Gauss curvature, which is needed to form the gyroid minimal surface. This is achieved by the use of Voronoi tessellation, whereby both the shape and volume of Voronoi cells can be assessed in regard to the local Gauss curvature of the gyroid minimal surface. Through this, we show that the mechanisms prevalent in this entropy-driven system differ from those found in systems which form gyroid structures in nature (lipid bilayers) and from synthesized materials (di-block copolymers) and where the formation of the gyroid is enthalpically driven. We further argue that the gyroid phase formed in these systems is a realization of a modulated splay-bend phase in which the conventional nematic has been predicted to be destabilized at the mesoscale due to molecular-scale coupling of polar and orientational degrees of freedom.

Footnotes

  • One contribution of 17 to a theme issue ‘Growth and function of complex forms in biological tissue and synthetic self-assembly’.

  • © 2017 The Author(s)
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6 August 2017
Volume 7, issue 4
Interface Focus: 7 (4)
  • Table of Contents
Theme issue ‘Growth and function of complex forms in biological tissue and synthetic self-assembly’ organized by Stephen T. Hyde, Gerd E. Schröder-Turk, Myfanwy E. Evans and Bodo D. Wilts

Keywords

self-assembly
computer simulations
entropy
gyroid
triply periodic minimal surfaces
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Purely entropic self-assembly of the bicontinuous Ia3̅d gyroid phase in equilibrium hard-pear systems
Philipp W. A. Schönhöfer, Laurence J. Ellison, Matthieu Marechal, Douglas J. Cleaver, Gerd E. Schröder-Turk
Interface Focus 2017 7 20160161; DOI: 10.1098/rsfs.2016.0161. Published 16 June 2017
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Research article:

Purely entropic self-assembly of the bicontinuous Ia3̅d gyroid phase in equilibrium hard-pear systems

Philipp W. A. Schönhöfer, Laurence J. Ellison, Matthieu Marechal, Douglas J. Cleaver, Gerd E. Schröder-Turk
Interface Focus 2017 7 20160161; DOI: 10.1098/rsfs.2016.0161. Published 16 June 2017

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  • Article
    • Abstract
    • 1. Introduction
    • 2. Phase diagram
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    • 4. Conclusion
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