Confinement Effect on Interparticle Potential in Nematic Colloids

We studied the confinement effect on the interaction force in nematic liquid crystal colloids with spherical particles inducing planar anchoring. Using magneto-optical tweezers, we measured the spatial dependence of the quadrupolar structural interparticle force over 4 orders of magnitude. For small separations, the interparticle potential follows the power law, whereas for separations larger than the sample thickness, it decreases exponentially with the decay length proportional to the sample thickness. Experimental results are reproduced by using the Landau–de Gennes free-energy minimization approach.

Figure 1

(a) Schematic top view of the system. The LC-mediated force ${\overrightarrow{F}}_{\mathrm{LC}}$ was balanced by the magnetic force ${\overrightarrow{F}}_m$, achieved by a rotating magnetic field $\overrightarrow{B}$. Note the orientation of the nonperturbed director $\overrightarrow{n}$. (b) The sample thickness $h$ was obtained by measuring the projection $a$. (c) Top view of the actual beads. (d) Two beads in contact that were used for determining the sample thickness. The difference in size is because only one bead is in the focal plane of the microscope. $D=4.4\mu \mathrm{m}$.

Figure 2

Logarithmic plot of the interparticle potential as a function of normalized bead separation $x/D$ for two cell thicknesses $h$. For small $x/D$, the data are fitted using power law function (solid lines) and for larger $x/D$, exponential function is used (dashed lines). The inset shows interparticle force $F$ as a function of $x/D$ for sample $A$. Experimental errors are of the size of the symbols.

Figure 3

Logarithmic plot of the numerically obtained interparticle potential as a function of normalized bead separation $x/D$ for three different sample thicknesses $h$. For small $x/D$, the data are fitted using power law function (solid lines) and for larger $x/D$, exponential function is used (dashed lines).