Experimental realization of crossover in shape and director field of nematic tactoids

Spindle-shaped nematic droplets (tactoids) form in solutions of rod-like molecules at the onset of the liquid crystalline phase. Their unique shape and internal structure result from the interplay of the elastic deformation of the nematic and anisotropic surface forces. The balance of these forces dictates that tactoids must display a continuous variation in aspect ratio and director-field configuration. Yet, such continuous transition has eluded observation for decades: tactoids have displayed either a bipolar configuration with particles aligned parallel to the droplet interface or a homogeneous configuration with particles aligned parallel to the long axis of the tactoid. Here, we report the first observation of the continuous transition in shape and director-field configuration of tactoids in true solutions of carbon nanotubes in chlorosulfonic acid. This observation is possible because the exceptional length of carbon nanotubes shifts the transition to a size range that can be visualized by optical microscopy. Polarization micrographs yield the interfacial and elastic properties of the system. Absorbance anisotropy measurements provide the highest nematic order parameter $\left(S=0.79\right)$ measured to date for a nematic phase of carbon nanotubes at coexistence with its isotropic phase.

Figure 1

Nematic tactoids of different configurations formed in a solution of carbon nanotubes in chlorosulfonic acid at 1000 ppm. (a) Polarized optical micrograph showing a collection of tactoids of various size and extinction pattern related to the director-field configuration. Arrows show the orientation of crossed polarizers. Schematic representation of (b) bipolar, with boojum surface defects at the poles, (c) homogenous, and (d) intermediate tactoids characterized by virtual boojums outside of the droplet. $R$ and $r$ denote the major and minor axes of the tactoid, respectively. (e) Optical texture of a bipolar tactoid at the brightest transmission at ${45}^{\circ }$ with respect to the polarizers (top), two dark brushes appearing toward the interface as tactoid is rotated (middle) and a dark cross at the center with bright lobes close to the droplet interface when parallel to either of the polarizers (bottom). (f) Optical texture of a homogeneous tactoid with a uniform change in brightness as it rotates away from ${45}^{\circ }$ (top to bottom). (g) Optical texture of an intermediate tactoid with a nonuniform brightness change (top to bottom) and a low-contrast cross at the center (bottom). All the scale bars are $100\mu \mathrm{m}$.

Figure 2

Experimental (at 1000 ppm) and simulated (at $\Delta n=0.0019)$ polarized micrographs of bipolar, homogenous, and intermediate tactoids as rotated between crossed polarizers. (a) In a bipolar tactoid $\left(R/r=3.0\right)$ the director lines converge on the droplet cusps $\left(\tilde{R}=R\right)$, (b) in a homogenous tactoid $\left(R/r=5.7\right)$ director field lines converge at infinity $\left(\tilde{R}\to \infty \right)$. (c) The intermediate configuration $\left(R/r=3.9\right)$ is a results of a gradual movement of boojums toward the droplet cusps. All the scale bars are $100\mu \mathrm{m}$.

Figure 3

Tactoid size and shape measurements and statistical analysis. (a) Aspect ratio and director field as a function of major axis length of 229 tactoids. The solid black line shows the theoretical prediction with the median bootstrap parameters $\omega =5.6,\lambda =13.9$ $\mu \mathrm{m}$, and ${\gamma }_{33}=1.3$. The dashed line shows the predicted level of bipolarness of the director field described by the relative length of the tactoids and the distance between the virtual boojums. The dotted blue lines show the upper and lower $95\%$ confidence interval on the aspect ratio; see Appendix pp1. (b) Box plots show distribution of the bootstrapped parameters $\omega ,\lambda$, and ${\gamma }_{33}$ with marginal histogram of each parameter. Each box plot is based on fitting the theory to 1000 random resampling of the original data set shown in panel (a). The top and bottom edges of the boxes denote the upper and lower quartiles, solid red lines show the medians, open circles show the outliers, and whiskers show the most extreme points within $1.5$ times of the interquartile range.

Figure 4

Order parameter measurement in tactoids using absorption anisotropy. (a) Optical textures of a CNT tactoid at 3000 ppm obtained between parallel polarizers “P” and “A” with its major axis oriented parallel (top) and perpendicular (bottom) to the polarizers. (b) Optical absorption spectra for nematic phase in solution of CNT in CSA measured at the center of the tactoid [yellow circle in panel (a)].