Dipolar colloids in nematostatics: Tensorial structure, symmetry, different types, and their interaction

Abstract

We formulate a numerical method for predicting the tensorial linear response of a rigid, asymmetrically charged body to an applied electric field. This prediction requires calculating the response of the fluid to the Stokes drag forces on the moving body and on the countercharges near its surface. To determine the fluid's motion, we represent both the body and the countercharges using many point sources of drag known as stokeslets. Finding the correct flow field amounts to finding the set of drag forces on the stokeslets that is consistent with the relative velocities experienced by each stokeslet. The method rigorously satisfies the condition that the object moves with no transfer of momentum to the fluid. We demonstrate that a sphere represented by 1999 well-separated stokeslets on its surface produces flow and drag force like a solid sphere to one-percent accuracy. We show that a uniformly-charged sphere with 3998 body and countercharge stokeslets obeys the Smoluchowski prediction [1] for electrophoretic mobility when the countercharges lie close to the sphere. Spheres with dipolar and quadrupolar charge distributions rotate and translate as predicted analytically to four percent accuracy or better. We describe how the method can treat general asymmetric shapes and charge distributions. This method offers promise as a way to characterize and manipulate asymmetrically charged colloid-scale objects from biology (eg. viruses) and technology (eg. self-assembled clusters).

Transport of particles in liquid crystals

“…The ring structure can be stabilized in a thin cell of thickness close to 2 R 34 , for relatively small R or for relatively weak anchoring strength 35 , under a high electric or magnetic field 36,37 . Besides the configurations shown in Fig.1, more complex structures, including twisted ones, around particles of various shapes have been considered, see, for example, [38][39][40][41][42][43] and references therein. Figure 2 shows the optical microscopy textures of a sphere with normal anchoring and accompanying hyperbolic hedgehog and its modification by a strong alternating current (AC) electric field.…”

“…If the sphere spins at a distance h   from the wall, the velocity gradient between the wall and the sphere is much steeper (and thus the viscous stress is larger) than in the rest of the space, Fig.18, so there is a force pushing the sphere along the wall, perpendicular to the axis of spinning. By balancing the torques and forces acting on the Quincke rotator near the wall, one finds the velocity of translation in the direction perpendicular to both the applied electric field and the spinning axis 60 , , the velocities might be very high, (40)(41)(42)(43)(44)(45)(46)(47)(48)(49)(50) V/μm . In smectic A samples with air bubbles, the particles are strongly trapped in the meniscus region, at the grain boundary separating the regions of differently tilted smectic layers.…”

Active Shape-Morphing Elastomeric Colloids in Short-Pitch Cholesteric Liquid Crystals

“…An interesting interplay between symmetries of distortions in n(r) and χ(r) can be noticed when comparing like-shaped particles introduced into nematic and cholesteric LC, respectively, as we discuss in the supplementary material [38]. Furthermore, since four types of pure and many hybrid elastic dipoles in nematic LCs can be identified using a tensorial description based on different symmetries of elastic distortions [11], we extend this description to CLCs and then further classify elastic dipoles obtained in our experiments in the supplementary material [38,39]. In both nematic and cholesteric LCs, LCE colloids rotate to minimize elastic energy of the surrounding n(r) or χ(r) in response to changes of particle shape (Video 1 in [38]) and even the simplest non-reciprocal dynamic morphing of the shape results in a directional locomotion (Video 2 in [38]).…”

“…Along with symmetry considerations, this brings about an expansion into multipole series and electrostatic analogies between long-distance colloidal interactions and that of multipoles in electrostatics [1][2][3][4][5][6][7][8][9][10][11]36]. The ground state in a CLC is strongly twisted and a direct parallel with the homogeneous nematic ground state is impossible because homogeneity of the ground state is a prerequisite of the symmetry-based considerations [11]. However, a similar approach for cholesterics is prompted by the de Gennes-Lubensky model [36], which describes a short-pitch CLC in terms of the director χ normal to cholesteric layers.…”

“…Shape of particles dictates colloidal self-assembly [3,[7][8][9][10][11][12][13][14][15] and may enable practical utility of these fascinating LC-colloidal systems. Although complex-shaped particles can be fabricated using photolithography [3,6], two-photon polymerization [10], nanocrystal growth [8], and wet chemical synthesis [7,9], these approaches provide nematic dispersions of non-responsive particles with no means for altering their shape, alignment, locomotion, and self-assembly [3,[5][6][7][8].…”