Minimal Model of Solitons in Nematic Liquid Crystals

Solitons in liquid crystals have generated considerable interest. Several hypotheses of varying complexity have been advanced to explain how they arise, but consensus has not emerged yet about the underlying forces responsible for their formation or their structure. In this work, we present a minimal model for solitons in achiral nematic liquid crystals, which reveals the key requirements needed to generate them in the absence of added charges. These include a surface inhomogeneity, consisting of an adsorbed particle capable of producing a twist, flexoelectricity, dielectric contrast, and an applied ac electric field that can couple to the director’s orientation. Our proposed model is based on a tensorial representation of a confined liquid crystal, and it predicts the formation of “butterfly” structures, quadrupolar in character, in regions of a slit channel where the director is twisted by the surface imperfection. As the applied electric field is increased, solitons (or “bullets”) become detached from the wings of the butterfly, and then propagate rapidly throughout the system. The main observations that emerge from the model, including the formation and structure of butterflies, bullets, and stripes, as well as the role of surface inhomogeneity and the strength of the applied field, are consistent with experimental findings presented here for nematic LCs confined between two chemically treated parallel plates.

Figure 1

Simulated system: (a) the electric field is applied perpendicular to the confining walls, which impart parallel anchoring and (b) a hemispherical particle is placed on the bottom boundary. (c) The PE particle (indicated by a black circle) in the LC film confined between two ${\mathrm{C}}_{16}\mathrm{SH}$ SAM surfaces. (d),(e) The particle nucleates a stationary quadrupolar distortion when an electric field (300 Hz, 40 V) is applied; (d) bright-field image, (e) imaged under crossed polarizers. Scale bars $50\mathrm{\mu }\mathrm{m}$. The results of simulations of the butterfly structure are consistent with the experimental observations. Experimentally, it is observed that the butterfly remains stable in the vicinity of the particle. (f) Polscope image showing the LC director profiles within a stationary butterfly. Scale bar $30\mathrm{\mu }\mathrm{m}$. (g) In simulations, polarized light shows the butterfly in the region of the hemisphere with a $1\mathrm{\mu }\mathrm{m}$ size, and (h) the orientation of the director matches the experimental observation.

Figure 2

(a) Experimental observation of bullet release from a butterfly. (b) Corresponding simulation results show the creation of a butterfly in the region above the particle, and the repeated ejection of bullets that move with uniform speed. (c) Free energy as a function of simulation time; the energy increases until a bullet becomes detached from the butterfly, at which point the energy drops slightly before another bullet is ejected. Each colored region corresponds to the ejection of a new bullet. (d) Landau–de Gennes, elastic and flexoelectric, and surface energy contribution, respectively. (e) The dielectric energy exhibits a small increase throughout the entire process. (f) The surface energy is 2 orders of magnitude smaller than the other contributions to the free energy; it increases with each bullet that is formed.

Figure 3

State diagram delineating regions where different structures are observed as a function of the normalized frequency and intensity of the electric field. We show the director’s corresponding theoretical and experimental images under cross polarizers, respectively; starting from low intensity, we observe a cross pattern above the particle. After increasing the intensity, a butterfly is observed and bullets are generated in a narrow region of frequency. Stripes are observed for a high-intensity field over a wide range of frequencies. The system enters a chaotic regime when the electric field is even stronger.