Publisher Correction: Electrically driven three-dimensional solitary waves as director bullets in nematic liquid crystals.

The original version of this article contained an error in the description of Supplementary Movie 7, which incorrectly read 'Collision resulting in annihilation of two solitons. U = 45.1 V, f = 600 Hz, T = 50 °C, d = 8.0 µm. The original movie is taken at the frame rate of 91 fps. The playback speed is 7 fps.' The correct version reads 'Death of a soliton at a dust particle. U = 65.6 V, f = 800 Hz, T = 50 °C, d = 7.7 µm. The original movie is taken at the frame rate of 92 fps. The playback speed is 7 fps.' The HTML has been updated to include a corrected version of the 'Description of Additional Supplementary Files' file.

Electrically driven three-dimensional solitary waves as director bullets in nematic liquid crystals.

Electric field-induced collective reorientation of nematic molecules is of importance for fundamental science and practical applications. This reorientation is either homogeneous over the area of electrodes, as in displays, or periodically modulated, as in electroconvection. The question is whether spatially localized three-dimensional solitary waves of molecular reorientation could be created. Here we demonstrate that the electric field can produce particle-like propagating solitary waves representing self-trapped "bullets" of oscillating molecular director. These director bullets lack fore-aft symmetry and move with very high speed perpendicularly to the electric field and to the initial alignment direction. The bullets are true solitons that preserve spatially confined shapes and survive collisions. The solitons are topologically equivalent to the uniform state and have no static analogs, thus exhibiting a particle-wave duality. Their shape, speed, and interactions depend strongly on the material parameters, which opens the door for a broad range of future studies.

Kerr effect at high electric field in the isotropic phase of mesogenic materials.

The well-known Kerr effect in isotropic fluids consists in the appearance of uniaxial orientational order and birefringence that grows as the square of the applied electric field. We predict and observe that at a high electric field, the Kerr effect displays features caused by the nonlinear dependence of dielectric permittivity on the field-induced orientational order parameter. Namely, the field-induced birefringence grows faster than the square of the electric field and the dynamics of birefringence growth slows down as the field increases. As a function of temperature, the field-induced birefringence is inversely proportional to the departure from an asymptotic critical temperature, but this temperature is no longer a constant (corresponding to the lower limit of the supercooled isotropic phase) and increases proportionally to the square of the electric field.

Direct observation of liquid crystals using cryo-TEM: specimen preparation and low-dose imaging.

Liquid crystals (LCs) represent a challenging group of materials for direct transmission electron microscopy (TEM) studies due to the complications in specimen preparation and the severe radiation damage. In this paper, we summarize a series of specimen preparation methods, including thin film and cryo-sectioning approaches, as a comprehensive toolset enabling high-resolution direct cryo-TEM observation of a broad range of LCs. We also present comparative analysis using cryo-TEM and replica freeze-fracture TEM on both thermotropic and lyotropic LCs. In addition to the revisits of previous practices, some new concepts are introduced, e.g., suspended thermotropic LC thin films, combined high-pressure freezing and cryo-sectioning of lyotropic LCs, and the complementary applications of direct TEM and indirect replica TEM techniques. The significance of subnanometer resolution cryo-TEM observation is demonstrated in a few important issues in LC studies, including providing direct evidences for the existence of nanoscale smectic domains in nematic bent-core thermotropic LCs, comprehensive understanding of the twist-bend nematic phase, and probing the packing of columnar aggregates in lyotropic chromonic LCs. Direct TEM observation opens ways to a variety of TEM techniques, suggesting that TEM (replica, cryo, and in situ techniques), in general, may be a promising part of the solution to the lack of effective structural probe at the molecular scale in LC studies.

Nanosecond electro-optics of a nematic liquid crystal with negative dielectric anisotropy.

We study a nanosecond electro-optic response of a nematic liquid crystal in a geometry where an applied electric field E modifies the tensor order parameter but does not change the orientation of the optic axis (director N ̂). We use a nematic with negative dielectric anisotropy with the electric field applied perpendicularly to N ̂. The field changes the dielectric tensor at optical frequencies (optic tensor) due to the following mechanisms: (a) nanosecond creation of the biaxial orientational order, (b) uniaxial modification of the orientational order that occurs over time scales of tens of nanoseconds, and (c) the quenching of director fluctuations with a wide range of characteristic times up to milliseconds. We develop a model to describe the dynamics of all three mechanisms. We design the experimental conditions to selectively suppress the contributions from the quenching of director fluctuations (c) and from the biaxial order effect (a) and thus, separate the contributions of the three mechanisms in the electro-optic response. As a result, the experimental data can be well fitted with the model parameters. The analysis provides a rather detailed physical picture of how the liquid crystal responds to a strong electric field on a time scale of nanoseconds. The paper provides a useful guidance in the current search for the biaxial nematic phase. Namely, the temperature dependence of the biaxial susceptibility allows one to estimate the temperature of the potential uniaxial-to-biaxial phase transition. An analysis of the quenching of director fluctuations indicates that on a time scale of nanoseconds, the classic model with constant viscoelastic material parameters might reach its limit of validity. The effect of nanosecond electric modification of the order parameter can be used in applications in which one needs to achieve ultrafast (nanosecond) changes in optical characteristics, such as birefringence.

Nanosecond electro-optic switching of a liquid crystal.

Electrically induced reorientation of nematic liquid crystal (NLC) molecules caused by dielectric anisotropy of the material is a fundamental phenomenon widely used in modern technologies. Its Achilles heel is a slow (millisecond) relaxation from the field-on to the field-off state. We present an electro-optic effect in an NLC with a response time of about 30 ns to both the field-on and field-off switching. This effect is caused by the electric field induced modification of the order parameters and does not require reorientation of the optic axis (director).