Extended Data Fig. 2: POM images of MXene aqueous solutions.

a, At a concentration of 50 mg ml⁻¹, the MXene solution shows a nearly isotropic phase with low birefringence under crossed polarizers. b, At a concentration of 250 mg ml⁻¹, higher birefringence starts to appear. A nematic phase is formed, as clearly indicated from the Schlieren texture shown in the inset. c, d, POM images of the slow-appearing MXene liquid-crystal phase on top of one-dimensional microchannels at two polarizer angles: 45° (c) and 0° (d). Higher birefringence starts to appear when water evaporates, and the resulting nematic liquid-crystal phase of MXene can be well aligned with microchannels. The microchannels used here have the following dimensions: diameter 2 µm, spacing 2 µm and depth 1.5 µm. The Onsager theory of liquid crystals predicts the formation of the liquid-crystal phase as a function of the volume fraction of molecules in a media: low volume fraction gives an isotropic phase, and high volume fraction gives a liquid-crystal phase. The empirical value of the critical volume fraction of liquid-crystal phase formation can be estimated by \(\varphi \approx \frac{4T}{W}\), where Φ is the critical volume fraction, W and T are the width and thickness of the nanosheet, respectively. In our MXene system, Φ is estimated to be around 2 vol%, which is equivalent to about 80 mg ml⁻¹ of MXene nanosheets in aqueous solution. However, because the MXene nanosheets are highly polydisperse in terms of size, and the surface charges differ from system to system, the critical value of Φ could vary in experiments. In this work, we demonstrated the isotropic phase of MXene liquid crystal at around 50 mg ml⁻¹, in good agreement with theory, and we showed the nematic phase of MXene at around 250 mg ml⁻¹. This concentration was chosen to be sufficiently high above the critical value of Φ such that a liquid-crystal phase could be ensured.