Disclination induced wrinkles in freestanding smectic membranes

MATSUMOTO E; VEGA DA; PEZZUTTI A; GARCIA NA; CHAIKIN PM; REGISTER RA

Dublin

Conferencia; 25th International Liquid Crystal Conference - ILCC2014; 2014

The International Liquid Crystal Conference

Non-Euclidean geometry has been shown to be one of the most robust mechanisms used to prescribe the configuration of defects in a crystalline [1] or striped phases [2]. Gaussian curvature can also stabilize more exotic defects, including scars, fractionalized defect charges, and pleats. [3] Likewise, if a two dimensional crystal is allowed to buckle out of the plane, the elastic energy associated with isolated disclinations can be strongly reduced by screening their strain fields through curvature, trading off stretching for bending energy. Depending on the sign of the topological charge, isolated defects can deform the membrane in cone or saddle shape configurations, acting as sources of Gaussian curvature [4]. Therefore, specifying the distribution of disclinations in a flat crystalline membrane aught to determine the geometry of the relaxed three dimensional surface. However, the prohibitively large strain energies associated with isolated disclinations in two dimensional crystals make engineering such a membrane impractical. The relatively low energetic cost of isolated ±1/2 disclinations in smectic membranes makes them appealing as a toy model. We demonstrate that the molecular splay distortions associated with disclinations in a free-standing smectic membrane act as sources of Gaussian curvature, resulting in a pattern of wrinkles in the membrane which form perpendicular to the underlying smectic layers. The wavelength of the wrinkles is dictated by the interplay of the elastic constants. Thus, by dictating the distribution of topological defects, it should possible to control the specific non-Euclidean geometry of the membrane [5]. [1] M. J. Bowick & L. Giomi, Adv. Phys. 58 449 (2009). M. J. Bowick, D. R. Nelson & A. Travesset, Phys. Rev. B 62 8738-8751 (2000).[2] C. D. Santangelo, V. Vitelli, R. D. Kamien & D. R. Nelson, Phys. Rev. Lett. 99, 017801 (2007). R. D. Kamien, D. R. Nelson, C. D. Santangelo & V. Vitelli, Phys. Rev. E 80, 051703 (2009). L. R. G´omez & D. A. Vega, Phys. Rev. E 79, 031701 (2009).[3] A. R. Bausch et al., Science 299, 1716-1718 (2003). W. T. M. Irvine, V. Vitelli & P. M. Chaikin, Nature 468, 947-951 (2010). W. T. M. Irvine, M. J. Bowick & P. M. Chaikin, Nature Materials 11, 948 (2012).[4] H. S. Seung & D. R. Nelson, Phys. Rev. A 38, 1005 (1988). J. M. Park & T. C. Lubensky, J. Phys. I France 6, 493 (1996). A. D. Pezzutti & D. A. Vega, Phys. Rev. E 84, 011123 (2011).[5]E. A. Matsumoto, D. A. Vega, A. D. Pezzutti, N. A. García, P. M. Chaikin & R A. Register. PNAS, 112, 41, 12639 (2015).