Self-assembly of skyrmion-dressed chiral nematic colloids with tangential anchoring

Abstract

We describe dipolar nematic colloids comprising mutually bound solid microspheres, three-dimensional skyrmions, and point defects in a molecular alignment field of chiral nematic liquid crystals. Nonlinear optical imaging and numerical modeling based on minimization of Landau-de Gennes free energy reveal that the particle-induced skyrmions resemble torons and hopfions, while matching surface boundary conditions at the interfaces of liquid crystal and colloidal spheres. Laser tweezers and videomicroscopy reveal that the skyrmion-colloidal hybrids exhibit purely repulsive elastic pair interactions in the case of parallel dipoles and an unexpected reversal of interaction forces from repulsive to attractive as the center-to-center distance decreases for antiparallel dipoles. The ensuing elastic self-assembly gives rise to colloidal chains of antiparallel dipoles with particles entangled by skyrmions.

Defect topologies in chiral liquid crystals confined to mesoscopic channels

“…15 More recently, quite a bit of experimental and theoretical interest has been devoted to study torons and other soliton-like structures. [16][17][18][19][20] These rather complex structures are created and stabilized in external laser fields.…”

Topology and self-assembly of defect-colloidal superstructure in confined chiral nematic liquid crystals

“…Similar to chiral magnets [27][28][29], chiral nematic liquid crystals (CNLCs) are capable of hosting stable nonsingular topologically nontrivial particlelike solitonic field configurations in the molecular alignment field, i.e. in the director field n(r) describing patterns of long molecular axis orientation in these calamitic nematic systems [30][31][32][33][34][35][36][37]. These twisted solitonic director structures include both two-dimensional (2D) skyrmions in the form of double-twisted tubes of n(r), also called "baby skyrmions" [33], and three-dimensional skyrmions, such as torons and hopfions comprising double twist tori, i.e.…”

“…closed loops of double-twist cylinders of n(r) [34,35]. Given that the nematic ground state manifold RP 2 is a sphere with all antipodal points identified [36], these 2D and 3D skyrmions are labeled by elements of the second and third homotopy groups, π 2 (RP 2 )=Z, and π 3 (RP 2 )=Z, respectively [35][36][37]. They have been experimentally realized in confinement-unwound CNLC cells with perpendicular surface boundary conditions and cell thickness comparable to the equilibrium cholesteric pitch [34,35,37], the distance over which n(r) in the ground state CNLC twists around the helical axis by 2π.…”

“…Given that the nematic ground state manifold RP 2 is a sphere with all antipodal points identified [36], these 2D and 3D skyrmions are labeled by elements of the second and third homotopy groups, π 2 (RP 2 )=Z, and π 3 (RP 2 )=Z, respectively [35][36][37]. They have been experimentally realized in confinement-unwound CNLC cells with perpendicular surface boundary conditions and cell thickness comparable to the equilibrium cholesteric pitch [34,35,37], the distance over which n(r) in the ground state CNLC twists around the helical axis by 2π. Since the transition from uniform to solitonic n(r) of the skyrmions is discontinuous in nature, the common approaches of generating such solitons involve focused laser beams [33][34][35], phase transitions [33], and hydrodynamic instabilities [33], which can transform the initial confinement-unwound homeotropic director field to that with individual solitons or their arrays.…”

“…Since the transition from uniform to solitonic n(r) of the skyrmions is discontinuous in nature, the common approaches of generating such solitons involve focused laser beams [33][34][35], phase transitions [33], and hydrodynamic instabilities [33], which can transform the initial confinement-unwound homeotropic director field to that with individual solitons or their arrays. Recent studies of cholesterics confined to a thin layer, where homeotropic surface boundary conditions stabilize unwound homogenous director field, indicated that colloidal microspheres with tangential surface boundary conditions can lead to stable or metastable 3D and 2D skyrmionic solitons [37]. The individual particles are dressed and multiple particles are entangled by the looped double-twist cylinders of n(r) occurring to minimize the overall free energy of the constrained CNLC [33].…”