Birefringence external fields

The Lorentz-Lorenz equation can be used directly to model the birefringence of a solution of rigid rod molecules subject to an orienting, external field. Figure 7.2 shows a representative molecule, which is modeled as having a uniaxial polarizability of the form... 

The frequency of the external field in other experiments [138,140,141] was chosen within the interval axB >1> coxD/a, which, given cr 1 andeviscous fluids such as glycerol. For the weak-field probing, a negative stationary and negligible oscillating birefringence had been predicted and confirmed. With the aid of our Eqs. (4.362) and (4.363), this is immediately recovered in the form... 

One sees that on taking the first term of the expansion, an optical birefringence (236) dependent on the square of the external field is obtained in accordance with Kerr s law. 

Birefringence of Dipolar Anisotropically Polarizable Microsystems. In the general case of microsystems which are dipolar and at the same time anisotropically polarizable in an external field E, the reorientation function for the Kerr effect is given by equation (233). Graphs of this reorientation function are shown in Figure 13 against the parameter Xi at parametrical values of X = X ln for = 1,4,9,16,25, 36,. 

The radial configuration occurs when the liquid crystal molecules are anchored with their long axes perpendicular to the droplet wall (Figure 3B). The radial droplet is not birefringent. Application of an external field switches the radial droplet to an axial configuration. As with the bipolar case the films switch from scattering to transparent upon application of an electric field if np=n0. 

The birefringence in external electric and magnetic fields (the Kerr and Cotton-Mouton effects) can be explained by the anisotropy of the properties of the medium that is due to either the orientation of anisotropic molecules in the external field (the Langevin-Bom mechanism) or the deformation of the electric or magnetic susceptibilities by this field, i.e., to hyperpolarizabilities (Voight mechanism). The former mechanism is effective for molecules that are anisotropic in the absence of the field and... 

The selection rules allow us to choose the systems in which the orien-. tational mechanism of birefringence is effective. On the other hand, the explicit form of the temperature dependence Anor(/3) is of no less interest. Its general investigation for any external field and for arbitrary molecular... 

Electro-optic effects refer to the changes in the refractive index of a material induced by the application of an external electric field, which modulates their optical properties [61, 62], Application of an applied external field induces in an optically isotropic material, like liquids, isotropic thin films, an optical birefringence. The size of this effect is represented by a coefficient B, called Kerr constant. The electric field induced refractive index difference is given by... 

The steady-state dichroic ratio of liquid crystalline solutions of PBLG (Fig. 3) increases with external field strength and the a mptotic value is 4.5—4.7, regardless of the polymer concentration for completely birefringent solutions 23). It may be safe to say that all the polymer molecules are parallel or neady parallel within molecular aggregates 31). Therefore, the value of 7 for the particle is tentatively assumed... 

When an electric field is applied to the liquid crystalline solution of polypeptide, the proton signal of a solvent molecule such as methylene bromide or methylene chloride splits into a doublet however, the center signal is still observed in the initial position, even in the steady state (Fig. 7). The origin of the splitting wfll be mentioned in Section V, and let us pay attention only to this center signal here. This signal corresponds to disordered solvent molecules which are free from the action of molecular fields caused by the oriented molecular clusters. These free solvent molecules are more in evidence in the ratio in less concentrated (but fuUy birefringent) liquid crystalline solution. When measured soon after the removd of the external field (the... 

The induced birefringence is a function of the polarizabilities and the extent of alignment of the resultant dipole moments // of the particles in the solution by the external field E. Under the assumption that interparticle interaction is negligible (dilute solutions) and the energy of interaction U between E and fi is less than the thermal energy kT, the following expressions can be derived [3] for the low-field limit ... 

We find an increase in the transition temperature linear in Ve, and a continuous second order transition above a certain critical external field. The external field can cause ordering in the isotropic phase (fig. 5), As an application, the magnetic birefringence in a isotropic liquid crystalline polymer melt has been calculated and good agreement with measurements of Haret is found. 

Polymer solutions are isotropic at equilibrium. If there is a velocity gradient, the statistical distribution of the polymer is deformed from the isotropic state, and the optical property of the solution becomes anisotropic. This phenomena is called flow birefringence (or the Maxwell effect). Other external fields such as electric or magnetic fields also cause birefringence, which is called electric bire ingence (or Kerr effect) and magnetic birefiingence (Cotton-Mouton effect), respectively. 

Secondly, due to the large molecular anisotropy, rodlike polymers are much more easily oriented by an external field and show large birefringence. This enables us to use electric or magnetic birefringence as a practical tool to study the rotational motion of these polymers. ... 

The preconditions for the use of polymer liquid crystals in display applications are that they exhibit bulk optical properties dependent on the molecular orientation in the mesophase and that this orientation may be altered on application of an external field. In this chapter we shall be concerned with electric or optical fields only. The particular optical property, i.e. (a) the birefringence, (b) the dichroism or (c) the scattering power, defines the display construction in terms of the use of polarized (a and b) or non-polarized (b and c) light, whereas the ability to switch from one orientation to another depends on the anisotropic electric permittivity and the orientational elastic constants. The dynamics of the induced orientation will depend, additionally, on the viscosity constants of the material. 

The optical-field-induced Freedericksz transition for a twist deformation by a normally incident laser beam in a planar-aligned nematic liquid crystal is studied. The Euler equation for the molecular director and the equations describing the evolution of the beam polarization in the birefringent medium are solved simultaneously in the small-perturbation limit. The stability of the undistorted state is investigated. An alternate series of stable and unstable bifurcations is found. This phenomenon has no analog in the Freedericksz transition induced by dc electric and magnetic external fields. 

Electric field is also expected as an effective external field to drive finite and fast deformation in LCEs, because, as is well known for low molecular mass LCs (LMM-LCs), an electric field is capable of inducing fast rotation of the director toward the field direction [6]. This electrically driven director rotation results in a large and fast change in optical birefringence that is called the electro-optical (EO) effect. The EO effect is a key principle of LC displays. Electrically induced deformation of LCEs is also attractive when they are used for soft actuators a fast actuation is expected, and electric field is an easily controlled external variable. However, in general, it is difficult for LCEs in the neat state to exhibit finite deformation in response to the modest electric fields accessible in laboratories. Some chiral smectic elastomers in the neat state show finite deformation stemming from electroclinic effects [7,8], but that is beyond the scope of this article we focus on deformation by director rotation. 

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