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Elusive torque sensed by liquid crystals

Almost half a century ago, it was predicted that the confinement of quantum fluctuations could induce mechanical rotation — the Casimir torque. This prediction has now been confirmed using liquid crystals.
Slobodan Žumer is in the Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, and the Jožef Stefan Institute, 1000 Ljubljana, Slovenia.
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Quantum physics tells us that empty space is filled with fluctuating electromagnetic fields. If two metal plates are positioned close to each other, the quantum fluctuations between the plates differ from those outside the plates, producing a force that pushes the plates closer together. This phenomenon is known as the Casimir effect. In 1972, it was suggested1 that quantum fluctuations could also generate a turning effect, called a torque, if the metal plates were replaced by materials that are optically anisotropic — that is, their optical properties, sensed by a light beam, depend on the beam’s direction. Writing in Nature, Somers et al.2 report experimental evidence for this Casimir torque through the twisting of liquid crystals. The discovery paves the way for the development of complex micrometre- and nanometre-scale mechanical devices.

Following the prediction of the Casimir effect between two ideal metal plates3, the concept was extended to real materials, such as conventional metals and electrical insulators known as dielectrics4. The Casimir effect can be explained by a restriction in the quantum and thermal fluctuations that can exist between the boundaries of two materials, leading to a weak attractive force. This force is maximal if the confining boundaries are identical, and is smaller — or can even be repulsive — if the boundaries differ in their electrical properties or shape5.

Because of the weakness of the Casimir force and its strong dependence on confining boundaries, it was nearly 50 years before solid experimental confirmation of the Casimir effect was realized6. Concurrently, it became clear that the concept of fluctuation-induced interactions, arising from confined fluctuating electromagnetic fields, could be generalized to other confined fields in different areas of physics. Examples of such fields include sound waves and capillary waves (ripples).

Other fluidic systems that have fluctuation-induced interactions include ‘critical’ fluids7 and liquid crystals8. In the latter, the molecular ordering associated with different crystal phases — such as cholesteric, nematic and smectic phases — and, in particular, the anchoring of liquid crystals to surfaces can lead to diverse behaviour of Casimir-like forces9. It is also worth mentioning examples beyond condensed-matter systems, such as confined gravitational waves10.

The realization that altering the properties of the confining boundaries changes the ensuing Casimir force was naturally followed by the idea that breaking the symmetry of physical properties of confining surfaces or objects could lead to the emergence of the Casimir torque5. More than four decades ago, a theory was developed1 to describe the Casimir torque between two solid, optically anisotropic crystals that are in close proximity to each other. This theory was subsequently improved and extended to more-complex systems such as layered media12, and many experiments were proposed. Nevertheless, it is only now, with the work of Somers and colleagues, that the existence of the Casimir torque has been convincingly proved.

The authors’ groundbreaking experiment was based on the idea12 of replacing one of the two solid crystals with a nematic liquid crystal. The liquid crystal was fixed on one side, and was exposed to the nearby solid crystal, which was free to rotate, on the other side (Fig. 1). The liquid crystal had two roles: first as an optically anisotropic material, and second as a torque sensor.

The Casimir torque, although weak, forced the average orientation of molecules in the nematic liquid crystal along a direction that11 characterizes the solid crystal, known as its optical axis. This produced a twisted deformation that spread through the whole of the liquid crystal. Somers et al. detected the deformation by its effect on the intensity of light that was passed through a polarizer, the two crystals and a second polarizer called the analyser (Fig. 1). This clever experimental set-up allowed the authors to determine the dependence of the Casimir torque on the distance between the crystals, for four different solid crystals.

Figure 1 | Measurement of the Casimir torque. Somers et al.2 have demonstrated that a solid crystal can cause the average orientation of molecules in a ‘nematic’ liquid crystal to twist (from angle θ1 to angle θ2), owing to a phenomenon known as the Casimir torque (orange arrow). The authors detected light that passed from a source through a polarizer, the two crystals and a second polarizer called an analyser. The thickness (t) of the liquid crystal was much larger than both the distance (d) between the crystals and the wavelength of the light. The authors selected a particular value for θ1 and the orientations of the polarizers, and varied the solid crystal’s optical axis — a direction in the crystal along which the speed of propagating light is independent of the light’s polarization. They determined θ2 from the intensity of the transmitted light, and measured the Casimir torque using the value of θ2 and the known elastic properties of the liquid crystal.

Liquid crystals offer great potential because of their large response to weak external electric fields and other perturbations. Their best-known application is in liquid-crystal displays (LCDs). A less-known application is their use as sensor elements. Temperature sensors based on the temperature sensitivity of light reflection from cholesteric liquid crystals have been used for decades. By contrast, chemical sensors based on the adsorption of molecules on liquid-crystal surfaces, particularly for sensing biological molecules, have been developed only in the past decade. Somers and colleagues’ sensor for the Casimir torque is the latest example of a sensor in which a minuscule torque is determined using the elasticity of a liquid crystal, rather than by conventional mechanical means.

One remaining question is whether the measured Casimir torque could be enhanced. Much progress has been made in the optimization of nematic liquid crystals for displays and photonic applications, and so it would be worth exploring whether a liquid crystal is available that has more-optimal properties than has the crystal used by the authors. In addition to increasing the torque, such a liquid crystal would need to be more easily twisted than the one used here.

It is also possible that the torque sensor could be made from a cholesteric liquid crystal. Such a crystal selectively reflects circularly polarized light that has a polarization rotating in the same direction as the crystal’s intrinsically twisted structure. The Casimir torque would further twist, or untwist, the cholesteric crystal’s structure, affecting the selective light reflection in a way that should be detectable.

The successful observation of the Casimir torque by Somers et al. is a key contribution to fundamental physics that also has broad implications. The evolution of microscale mechanical and electromechanical devices has already reached to below the micrometre scale, and needs to take into account quantum phenomena and the effects of thermal and quantum fluctuations. Therefore, the development of nanoscale mechanical and electromechanical systems must take into account the Casimir force and torque, or even directly use these phenomena13.

Building on the current work, Casimir-like effects that can occur because of thermal fluctuations should be examined in many confined systems, including gases, conventional liquids, critical liquids, colloidal dispersions, polymers and liquid crystals. This could enable these systems to be used in complex micro- and nanoscale fluidic devices.

Nature 564, 350-351 (2018)

doi: 10.1038/d41586-018-07744-9

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