Square colloidal lattices and pair interaction in a binary system of quadrupolar nematic colloids

Spherical colloidal particles with normal and tangential surface director alignment in a nematic liquid crystal induce elastic quadrupoles of opposite signs that attract one another along and perpendicular to the director. We utilize this unique angular profile of the mixed quadrupolar interaction to build 2D crystals with square lattices by laser tweezers.

Figure 1

Schematic drawing of director field around pairs of P (a) and S colloidal particles attracted across (a) and along (b) the nematic director. Microscopic images of $4.32\hspace{0.5em}\mathrm{\mu }\mathrm{m}$ P and S colloidal particles observed in crossed polarizers (indicated by arrows) and in unpolarized light are shown in (c) and (d). Photographs of P-S-P triplets attracted across and along the nematic director are presented in (e) and (f), respectively.

Figure 2

Pair attraction energy (a) of S and P colloids vs. their center-to-center distance $r$. Equilibrium arrangements of the pair for each curve are schematically shown in the inset. The error bars on the curves for each interacting pair account for the variation of data obtained in different experiments for several similar pairs of particles at the same initial separation and all equivalent permutations of each pair. Log-log plots of the attraction force between S and P particles vs. reduced center-to center separation $r/d$ across and along the director are presented in (b) and (c), respectively. Power-law fits (solid lines) are $F_{\mathit{SP}}^{\perp }=19.7/(r/d){}^{6.17}\mathrm{pN}$ and $F_{\mathit{SP}}^{\left|\right|}=36.7/(r/d){}^{5.97}\mathrm{pN}$, respectively. Vertical dashed lines in (b) and (c) mark fitting region boundaries.

Figure 3

Microscopic images of three different 2D binary quadrupolar structures taken under crossed polarizers (left column) and in normal light (middle column) along with their schematic representations (right column).