Cracks and Topological Defects in Lyotropic Nematic Gels

We report on the effects of the coupling of nematic order and elasticity in anisotropic lyotropic gels consisting of large nematic domains of surfactant coated single wall carbon nanotubes embedded in a cross-linked $N$-isopropyl acrylamide polymer matrix. We observe the following striking features: (i) undulations and then cusping of the gel sidewalls, (ii) a nematic director field that evolves as the gel sidewalls deform, (iii) networks of surface cracks that are orthogonal to the nematic director field, and (iv) fissures at the sidewall cusps and associated topological defects that would not form in liquid nematics.

Figure 1

(a)–(c) A summary of the evolution of the physical properties of the nematic gels with time before and after shrinking. The gel sidewalls remained flat for a few minutes to several hours after the gels have shrunk (a). Undulation of the gel sidewalls developed within a few hours to 1 day (b). We also observed surface cracks [dark lines in (b)]. The undulations eventually gave rise to sidewall cusps, indicated by an arrow in (c). (d)–(e) Fissures developed at the sidewall cusp and propagated along the $X$ axis into the sample and along the $Z$ axis the entire thickness of the gel, indicated by an arrow in (d). Radial $+1$ defect is clearly visible $36\mu \mathrm{m}$ (d) and $51\mu \mathrm{m}$ (e) along the $Z$ axis into the sample.

Figure 2

The four bright lobes of the defects rotated counterclockwise with a counterclockwise rotation of the crossed polarizers suggesting the defects are $+1$. The SWNT orientation and the director field around the $+1$ defects were radial (shown schematically on right).

Figure 3

Birefringence images and sketches of the director field in gels during undulations but before cusping [(a) and (b)] and after cusping [(c) and (d)].

Figure 4

(a) Surface cracks develop in the nematic gels after 4 hours to 1 day. (b) Overlaying the director field on the crack pathways, we find that the surface cracks are orthogonal to the director field. The crack pathways also suggest the presence of a $-1/2$ defect at region $\mathbf{A}$.