Fig. 3. Theoretical predictions of bipolar LC microparticle internal ordering and attractive interaction energies.

(A to C) Director profiles in the x-z plane of a bipolar LC microparticle calculated numerically for tangential surface anchoring energies of 64.5 μN/m (A), 6.2 μN/m (B), and 0.6 μN/m (C). (D and E) Attractive interaction energy calculated using Eq. 1 either by (solid lines) integrating over all volume elements of a bipolar microparticle with intermediate (W = 6.2 μN/m) tangential anchoring or by (dashed lines) approximating LC ordering at the surface nearest the probe colloid as representative of the entire volume, at various angles of incidence (β) at a surface-to-surface separation, d, of 3 nm (D) and at various surface-to-surface separations above the pole (β = 0°) (E). (D) Inset: Illustration showing the angle of incidence, β. (E) Inset: Illustration showing location of probe colloid as surface-to-surface separation is varied. (F) Calculated average director angle, α^eff, sampled by a probe colloid as a function of β and a separation of 10 nm from the surface of the bipolar microparticle. (Solid lines) Results are shown for surface anchoring energies of 64.5 μN/m (orange), 6.2 μN/m (blue), and 0.6 μN/m (gold). The corresponding effective Hamaker constant for interaction energies calculated according to Eq. 1 (dashed lines) for surface anchoring energies of 64.5 μN/m (red), 6.2 μN/m (cyan), and 0.6 μN/m (black) is also shown. (F) Inset: Illustration of LC ordering near a probe colloid and the angle, α, between a probe colloid and the local LC director.