The book intends to give a state-of-the-art overview of flexoelectricity, a linear physical coupling between mechanical (orientational) deformations and electric polarization, which is specific to systems with orientational order, such as liquid crystals. Chapters written by experts in the field shed light on theoretical as well as experimental aspects of research carried out since the discovery of flexoelectricity. Besides a common macroscopic (continuum) description the microscopic theory of flexoelectricity is also addressed. Electro-optic effects due to or modified by flexoelectricity as well as various (direct and indirect) measurement methods are discussed. Special emphasis is given to the role of flexoelectricity in pattern-forming instabilities. While the main focus of the book lies in flexoelectricity in nematic liquid crystals, peculiarities of other mesophases (bent-core systems, cholesterics, and smectics) are also reviewed. Flexoelectricity has relevance to biological (living) systems and can also offer possibilities for technical applications. The basics of these two interdisciplinary fields are also summarized.

Abstract : A positive nematic liquid crystal (5CB) sample is confined in cylindrical cells under strong or weak axial anchoring boundary conditions when a radial nonuniform low-frequency electric field is applied and the flexoelectric effect is taken into account. Based on the Frank elastic free energy, the surface energy of the Rapini–Papoular approximation, the polarization free energy and the flexoelectric free energy caused by electric field, we obtain the free energy density of the nematic and solve the corresponding Euler–Lagrange equation numerically. We investigate the director distribution, the critical voltage and the critical exponent of nematic liquid crystal in cylindrical cells. It follows that the critical exponent is the classical one. It is also shown that the critical voltage in the system is affected by the flexoelectric effect, the geometric effect and radial weak anchoring effect on the cylindrical surfaces. A new type of director transition caused by the flexoelectric effect, the dielectric coupling effect and the radial weak anchoring effect is found.

Flexoelectricity in liquid crystals is thought to be due to a coupling between dielectric properties and shape anisotropy of the molecules and described by the fiexoelectric coefficients el and e3. Two experiments are needed to measure el and e3 and it is usual to measure the difference (el - e3) and the sum (el + e3) and then calculate el and e3· The first experiment to measure the difference (el - e3) uses a TN structure with an in-plane applied electric field. Due to the dielectric coupling, the director aligns with the electric field and due to the fiexoelectric effect, the director tilts out of plane. This tilt is measured optically using two laser beams at oblique incidence, e.g. 45°. Using a theoretical model the experimental data is fitted and the difference (el - e3) extracted. The second experiment to measure the sum (el + e3) uses a Pi cell. Applying an ac voltage the transmission through the device is a repeating oscillating signal which contains 1st and 2nd harmonics. The 1st harmonic corresponds to the fiexoelectric effect and the 2nd harmonic to the dielectric effect. Using a lock-in amplifier, the harmonics were measured and the sum (el + e3) extracted using a theoretical model to fit the experimental data. Unfortunately, the data proved the experiment to be unreliable and another method was developed, which uses a BAN cell. The third experiment uses simple pulses in a BAN cell and also measures the sum (el + e3). The big disadvantage of the BAN cell is an internal voltage, which is created by the homeotropic alignment layer and the fiexoelectric polarisation. The internal voltage has the same effect on the director profile as the fiexoelectric effect, which is a big problem in measuring fiexoelectricity. Using a material, which is non ionic and has no fiexoelectricity, the internal bias could be measured and taken into account. Applying short de pulses of opposite sign, the fiexoelectric effect can be observed by the optical response and can be measured. Using these experiments, a number of investigation are being carried out such as the correlation between fiexoelectricity and the molecular structure, ions, elastic properties, molecular orientation, dielectric anisotropy 6E, and order parameter S. The results showed that fiexoelectricity only depends on ions and dielectric properties which was very interesting and surprising at the same time.