Fig. 2

Angular and radial dependence of colloidal interactions. a Free energy as a function of α for different inter-particle separations d/R for θ_e = 90° for two particles (R = 200 nm) confined in a uniform LC channel (h = 3.6 μm). The inset plot shows the dependence of α^* on the colloidal separation d. b Vector field of forces between two colloidal particles for d/R = 2.6 and 3.2, derived from the spatial gradient of free energy. The far-field director is denoted by n₀. c Evolution of free energy as a function of α with different θ_e (d/R = 2.4). The inset plot shows the dependence of α^* on colloidal separation d. d, e Evolution of free energy as a function of α for different d/R with θ_e = 45°. f Dependence of attraction on d/R for particles with θ_e = 45°, 90°, and θ_e = 0°, along α = 70°, 30°, and 65°. The dashed line is a least-squares fit of colloidal pair-interactions. The coefficients are (b₂ = −0.0088, b₄ = −0.0144, b₆ = −0.0004), (b₂ = −0.0496, b₄ = −0.0089, b₆ = −0.0005), (b₂ = 0.1001, b₄ = −0.0105, b₆ = 0.0009) for colloids with θ_e = 45°, 90°, and θ_e = 0°, respectively