A cholesteric liquid crystal (CLC) formed by chiral molecules represents a self-assembled one-dimensionally periodic helical structure with pitch $p$ in the submicrometer and micrometer range. Because of the spatial periodicity of the dielectric permittivity, a CLC doped with a fluorescent dye and pumped optically is capable of mirrorless lasing. An attractive feature of a CLC laser is that the pitch $p$ and thus the wavelength of lasing $\overline{\lambda }$ can be tuned, for example, by chemical composition. However, the most desired mode to tune the laser, by an electric field, has so far been elusive. Here we present the realization of an electrically tunable laser with $\overline{\lambda }$ spanning an extraordinarily broad range (>100 nm) of the visible spectrum. The effect is achieved by using an electric-field-induced oblique helicoidal (OH) state in which the molecules form an acute angle with the helicoidal axis rather than align perpendicularly to it as in a field-free CLC. The principal advantage of the electrically controlled CLC_OH laser is that the electric field is applied parallel to the helical axis and thus changes the pitch but preserves the single-harmonic structure. The preserved single-harmonic structure ensures efficiency of lasing in the entire tunable range of emission. The broad tuning range of CLC_OH lasers, coupled with their microscopic size and narrow line widths, may enable new applications in areas such as diagnostics, sensing, microscopy, displays, and holography. Significance Liquid-crystal lasers based on micrometer-scale self-organization of organic molecules into the so-called cholesteric liquid crystal are simple to manufacture; they are small in size and low in cost and power consumption. Their potential applications range from sensing and imaging to informational displays and miniature “lab-on-a-chip” devices. We report a cholesteric structure used as the laser’s resonator cavity that enables a continuous real-time tuning of the emitted wavelength in a very broad range by applying an electric field. The structure is heliconical, with the molecules rotating around a helical axis and being tilted toward this axis. The electric field controls the tilt and the pitch, thus changing the wavelength by at least 100 nm.

(E)-4-Fluoro-cinnamaldehyde malononitrile ((E)-4FCM) is a new phenylbutadiene derivative that undergoes a [2+2] photocycloaddition in the crystal form. Optical absorption and proton nuclear magnetic resonance (¹H-NMR) measurements demonstrate that the solid-state (E)-4FCM photodimerization is a negative photochromic reaction that proceeds to 97% completion. The large geometry change and full conversion allow bulk crystals of (E)-4FCM to show strong photosalient effects when exposed to 405 nm ultraviolet light. When (E)-4FCM nanowires are grown in an anodic alumina oxide (AAO) template, they maintain a high degree of crystallinity and orientation, as determined by X-ray diffraction measurements. When illuminated, (E)-4FCM nanowire bundles exhibit a rapid expansion, during which they spread by as much as 300% in the lateral direction. This lateral expansion is at least partially due to a photoinduced crystal expansion along the diameter of the nanowires. When (E)-4FCM nanowires are confined inside the AAO template, the photoinduced expansion can be harnessed to deform the template, causing it to bend under UV light irradiation. The bending motion due to 2.0 mg of 4FCM in a template can cause the template to bend by up to 1.0 mm and lift up to 200 g. These results represent a significant improvement in work output relative to previous composite actuator membranes based on diarylethene photochromes.

The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase transition, it does not provide a realistic equation of state in that the pressure remains finite for arbitrarily high densities. In this work, we derive a mean field density functional form of the Helmholtz free energy for nematics with hard core repulsion. In addition to predicting the isotropic-nematic transition, the model provides a more realistic equation of state. The energy landscape is much richer, and the orientational probability distribution function in the nematic phase possesses a unique feature—it vanishes on a nonzero measure set in orientation space.

Binary mixtures of liquid crystals whose constituent molecules are not cylindrically symmetric are considered. For a mixture consisting of biaxial molecules with ${\mathit{D}}_{2\mathit{h}}$ symmetry, two tensor order parameters are required to specify the orientational order of each component. Using mean-field theory, expressions for the free energy of the mixture and the orientational order parameters are obtained as functions of temperature. In the geometric-mean approximation, the parameters of the theory are ratios of anisotropic interaction strengths, which can be determined from measurements on the pure components. The theoretical predictions are compared with recent experimental results of ${}_{}{}^2{}_{}{}^{}\mathrm{NMR}$ measurements on the binary mixture of the liquid-crystal 2-fluorenyl-4’-tetradecyloxy-benzoate-${\mathit{d}}_9$ (${\mathrm{FLOC}}_{14}$) and p-xylene-${\mathit{d}}_{10}$ (p-Xy).

The St. Petersburg paradox provides a simple paradigm for systems that show sensitivity to rare events. Here, we demonstrate a physical realization of this paradox using tensile fracture, experimentally verifying for six decades of spatial and temporal data and two different materials that the fracture force depends logarithmically on the length of the fiber. The St. Petersburg model may be useful in a variety fields where failure and reliability are critical.