Fig. 9

Examples of spherical multipole moments of composite nematic colloids. The value of \(q_{l1}^x\) was calculated for selected simulated composite nematic colloids and chain particle comprising of two equal spheres. a Colloidal particle with homeotropic boundary conditions centered at r_a below the origin induces a quadrupolar distortion of n(r), commonly known as a Saturn ring configuration. b Corresponding graph shows constant quadrupole coefficient at all displacements d_i, other multipoles have extreme or zero at d_i = −r_a, corresponding to the geometrical center of the spherical colloid. c Spherical colloidal particle with conic anchoring at angle α = 20° centered at r_a below the origin. d Plot shows that quadrupolar coefficient is constant at all d_i, whereas other coefficients higher then 16-pole are zero when center of the interpolation sphere coincides with geometrical center d_i = d_a. e Composite colloidal particle at r_a below the origin with d_b = 0, r_b = 2r_a/5 and conic anchoring at angle α = 60°. f Quadrupolar coefficient is constant regardless the position of the interaction sphere, whereas higher multipole moments show complex variations even at the geometrical center. Geometrical centers of the composite colloids are depicted with red dashed line. g Chain colloid with homeotropic anchoring on the surfaces induces two Saturn rings. h The director field shows strong quadrupolar and hexadecapolar, and weak 64-polar contribution. Higher multipoles are zero in the geometrical center of a composite chain colloid. i Chain colloid with tangential anchoring induces strong neck defect and two boojums at the poles. j The director field shows strong hexadecapole, quadrupole and 64-pole, whereas higher multipoles are zero in the geometrical center. The location of the geometrical center of the colloid is depicted with red dashed line (at d_i = 0)