Anisotropic substance

Kneubuhl, F.K. and Natterer, B. 1961. Paramagnetic resonance intensity of anisotropic substances and its influence on line shapes. Helvetica Physica Acta 34 710-717. 

Liquid crystal polymers (LCP) are polymers that exhibit liquid crystal characteristics either in solution (lyotropic liquid crystal) or in the melt (thermotropic liquid crystal) [Ballauf, 1989 Finkelmann, 1987 Morgan et al., 1987]. We need to define the liquid crystal state before proceeding. Crystalline solids have three-dimensional, long-range ordering of molecules. The molecules are said to be ordered or oriented with respect to their centers of mass and their molecular axes. The physical properties (e.g., refractive index, electrical conductivity, coefficient of thermal expansion) of a wide variety of crystalline substances vary in different directions. Such substances are referred to as anisotropic substances. Substances that have the same properties in all directions are referred to as isotropic substances. For example, liquids that possess no long-range molecular order in any dimension are described as isotropic. 

Polarimetry is defined as the quantitative measurement of a change in the direction of the vibration of plane-polarized light during its passage through an optically anisotropic substance or its solution33. 

B. Bleaney, Electron spin resonance intensity in anisotropic substances. Proc. Phys. Soc. (Lond.), 1960, 75, 621-623. 

Measurement of magnetic anisotropy can be performed by single crystal magnetometry methods. A particularly sensitive way to do this is by cantilever torque magnetometry where the crystal is mounted on an upper plate (the cantilever), fixed at one end, above a lower metallic plate. When a magnetic field is applied to an anisotropic substance it experiences a torque T given by the cross product T = M x H... 

In 1973 Labes et ah 8,9) synthesized crystalline bundles of impure (SN)a. flbers. Although the S N atomic ratio was 1 1, the material contained 5.48% impurity (4.93% 0, 0.42% H, and 0.13% C). However, metallic-like conductivity was observed in directions parallel to the (SN), flbers, and this increased sharply with decrease in temperature. Six different samples had conductivities at room temperature of 10, 89, 230, 640, 1470, and 1730 ohm" cm" Since the electrical conductivity of an anisotropic substance can be affected enormously by even traces of impurities, we decided that it was most important to attempt to synthesize analytically pure crystals of (SN). and to examine the physical and chemical properties of the material. Only in this way would it be possible to determine whether the metallic-like properties reported for (SN). (8, 9) were characteristic of the pure material. 

As has been shown previously by us [3] and independently by Tarasov [4], an allowance for the regularity of elastic wave propagation in crystals gives a Debye-type expression in which the exponent is one (n — 1) for one-dimensional structures (filaments), two (n = 2) for laminar structures, and three (n = 3) for isotropic space structures. In all the intermediate cases, the exponent n will have an intermediate value. However, in contrast to Tarasov, we did not consider the behavior of filaments or layers and their interaction with each oiher, but the special features of occupation by figurative points corresponding to the excitation of vibrations in the phase k space of anisotropic substances. 

Compensator n. An anisotropic substance of known retardation superimposed on the field of view with its vibration directions 45° from the vibration directions of the polarizer and analyzer. When an anisotropic particle is positioned so its slow component is parallel to the slow component of the compensator, the retardations are added. When the particle and compensator slow components are perpendicular, the retardations are subtracted. Compensator retardations may be fixed or variable. 

In anisotropic substances, e.g. a non-cubic single crystal, the magnetic moment M depends on the direction and on the magnitude of the magnetic field strength H and Eq. (2) has to be replaced by... 

The major sources of error in using the unsteady-state charts are the inadequate data on the density, heat capacity, and thermal conductivity of the foods and the prediction of the convective coefficient. Food materials are irregular anisotropic substances, and the physical properties are often difficult to evaluate. Also, if evaporation of water occurs on chilling, latent heat losses can affect the accuracy of the results. 

Just as the polarisation and the electric field do not in general point in the same direction in an anisotropic material, the cirrrent density and electric field are not necessarily colhnear in an anisotropic substance, a mnst therefore be a tensor quantity and... 

Because the relative permittivity of an anisotropic substance is different for electric fields in different directions, the index of refraction for light polarised with its electric field in different directions is also different. This optical phenomenon is called birefringence, and since we are discussing linearly polarised light, it should really be called linear birefringence. In a nematic hquid crystal, this means that light polarised... 

In the anisotropic bodies case, the cohesion forces between the constituent particles discontinuously vary with the direction, with maximum and minimum intensity values in the neighboring directions, but with the same value on the parallel directions. As a result, the vectorial physical properties of the anisotropic substance, especially those related to the cohesion, will depend on the direction. 

Birefringence Optical phenomena of anisotropic substances quantitatively measured as the difference between the refractive indices of the substances. 

---