Theory of electrostriction of liquid-crystalline blue phases I and II

Abstract

For the cubic lattices of the liquid-crystalline blue phases I and II electrostriction has been observed recently, i.e., a distortion of the crystal by an electric field in quadratic order. Here we investigate the characterizing fourth-order electrostriction tensor. Because electrostriction results from a competition between electric and elastic forces, the tensor is the quotient of the elasto-optic and the elastic tensor. The latter are derived from the Landau-de Gennes theory of phase transitions in liquid crystals within the model of rigid helices and are expressed as functionals of the alignment tensor for the undistorted system. Comparison is made with experimental data. The limit ations of the model of rigid helices are discussed.In the liquid-crystalline blue phases I and 11 (BP I and 11) the molecular axes align to form a periodic long-range orientational order. The unit cell is cubic and contains about 10 7 molecules. Standard methods of crystallography, such as Bragg reflection and Kossel diagrams, have b een applied to investigate this periodic structure with light in the visible range. Under the influence of a weak electric field, shifts in the Kossel diagrams and of the wavelengths of the Bragg peaks have been observed [1][2][3][4]. The variations are due to a distortion of the unit cell by the electric field. The process is called electrostriction; its characteristic measurable quantity is the fourth-order electrostriction tensor R.For the description of the orientational order of theCharacteristic parameters are the chirality ~e, the reduced temperature t, and the wave number qc of the cholesteric helix. By £ij 1 we denote the components of the Levi-Civita tensor. j E contains the simplest S0(3) invariant, which can be constructed by Q and E. Q0is the homogeneous part (k = 0) of the order p a rameter. Symmetry makes it vanish in the cubic blue phases. The coefficient 8 includes proportionality factors both between the order parameter and the anisotropic part of 44 molecules the traceless and symmetric alignment tensor Q is used , which is approximately proportional to the anisotropic part of the dielectric tensor (5]. The tensor field Q(r) is expanded into a Fourier series where the Fourier coefficients are written in a spherical tensor basis {Mm(k)} (6]:The free enthalpy of blue phases in an applied homoge neous electric field E is composed of the free enthalpy jLG according to Landau-de Gennes theory and an electric free ent halpy jE . It is expressed in scaled units [7] :(1) the dielectric tensor as well as between the applied electric field and the internal electric field. This fact can b e proven by comparing jE with the electric-field term of the Maxwell theory.The quantity, which is measured in field experiments and which is therefore defined on a macroscopic scale, is the electrostriction tensor R . It consists of an elastic and an electric part. In this paper we develop an analytical mesoscopic theory by expressing both contributions to 2752

Dendron‐Stabilized Liquid Crystalline Blue Phases with an Enlarged Controllable Range of the Photonic Band for Tunable Photonic Devices

“…The deformation behavior of BP lattices under electric fields resulting from a competition between elastic force and electric force has been theoretically reported; it is described as a difference of free‐energy change (Δ F BP ) between an initial state ( F 0 ) and an excited state at a critical point of electric field‐induced BP–N* transition ( F BP‐N *) 91–98. However, the correlation between the temperature change and the shift range in BPs has never been discussed.…”

Polymer‐stabilized blue phases: promising mesophases for a new generation of liquid crystal displays

“…Field-induced phase transitions and the continuous deformation of the superstructure (electrostriction) [52,[78][79][80][81][82][83] lead to color changes under the influence of an electric field ( Fig. 2(d)).…”

Thermodynamics of blue phases in electric fields

“…[8]). At the same time, these theories were also unable to account for anomalous electrostriction of BPI [6,16,17]. Recent simulations have shown that these shortfalls are a drawback of the approximations employed, and not of the underlying Landau -de Gennes mean field free energy [18].…”