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Gibaud T, Kaplan CN, Sharma P, et al. Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes. Proc Natl Acad Sci U S A. 2017;114(17):E3376-E3384doi: 10.1073/pnas.1617043114.
Gibaud, T., Kaplan, C. N., Sharma, P., Zakhary, M. J., Ward, A., Oldenbourg, R., Meyer, R. B., Kamien, R. D., Powers, T. R., & Dogic, Z. (2017). Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes. Proceedings of the National Academy of Sciences of the United States of America, 114(17), E3376-E3384. https://doi.org/10.1073/pnas.1617043114
Gibaud, Thomas, et al. "Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes." Proceedings of the National Academy of Sciences of the United States of America vol. 114,17 (2017): E3376-E3384. doi: https://doi.org/10.1073/pnas.1617043114
Gibaud T, Kaplan CN, Sharma P, Zakhary MJ, Ward A, Oldenbourg R, Meyer RB, Kamien RD, Powers TR, Dogic Z. Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes. Proc Natl Acad Sci U S A. 2017 Apr 25;114(17):E3376-E3384. doi: 10.1073/pnas.1617043114. Epub 2017 Apr 14. PMID: 28411214; PMCID: PMC5410790.
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Proc Natl Acad Sci U S A. 2017 Apr 25;114(17):E3376-E3384. doi: 10.1073/pnas.1617043114. Epub 2017 Apr 14.

Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes.

Proceedings of the National Academy of Sciences of the United States of America

Thomas Gibaud, C Nadir Kaplan, Prerna Sharma, Mark J Zakhary, Andrew Ward, Rudolf Oldenbourg, Robert B Meyer, Randall D Kamien, Thomas R Powers, Zvonimir Dogic

Affiliations

  1. The Martin Fisher School of Physics, Brandeis University, Waltham, MA 02454.
  2. Université de Lyon, Ens de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France.
  3. John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138.
  4. Department of Physics, Indian Institute of Science, Bangalore 560012, India.
  5. Program in Cellular and Molecular Medicine, Boston Children's Hospital, Boston, MA 02115.
  6. Marine Biological Laboratory, Woods Hole, MA 02543.
  7. Department of Physics, Brown University, Providence, RI 02912.
  8. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104.
  9. School of Engineering, Brown University, Providence, RI 02912.
  10. The Martin Fisher School of Physics, Brandeis University, Waltham, MA 02454; [email protected].

PMID: 28411214 PMCID: PMC5410790 DOI: 10.1073/pnas.1617043114

Abstract

In the presence of a nonadsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one-rod-length-thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study elasticity of fluid sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes composed of a mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit, disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cusp-shaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime, the cusp defects have repulsive interactions, but away from this limit we measure effective long-ranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration, and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes.

Keywords: Gaussian curvature; chirality; liquid crystals; membranes; self-assembly

Conflict of interest statement

The authors declare no conflict of interest.

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