Isotropic substance

Given these differences between rigid and flexible conduit, let us examine the differences between steel and RTR pipe, both of which are, of course, flexible conduits. First, steel pipe is by definition constructed from a material, steel, that for our purposes is a homogeneous isotropic substance. Therefore, steel pipe can be considered to have the same material properties in all directions that is, it is equally strong in both the hoop and longitudinal directions [Fig. 4-2(b)]. 

In general, there are three kinds of moduli Young s moduli E, shear moduli G, and bulk moduli K. The simplest of all materials are isotropic and homogeneous. The distinguishing feature about isotropic elastic materials is that their properties are the same in all directions. Unoriented amorphous polymers and annealed glasses are examples of such materials. They have only one of each of the three kinds of moduli, and since the moduli are interrelated, only two moduli are enough to describe the elastic behavior of isotropic substances. For isotropic materials... 

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. 

This description of antennas may seem more appropriate to a discussion of radio or television waves. We must realize, however, that at the molecular level dipoles behave exactly like antennas. Since molecules are made up of charged parts, a dipole moment /x is induced by the electric field of the radiation in any material through which radiation passes. In this discussion, the dipole moment equals the product of the effective charge displaced by the field and its distance of separation from the opposite charge. In SI, pi has units C m. We consider isotropic materials characterized by a polarizability a. As the name implies, this property measures the ease with which charge separation —polarity —is induced in a molecule by an electric field. For isotropic substances, the dipole moment and the field are related by the expression... 

Often for solids, linear thermal expansion coefficients, a, = (1 /L) x (.9L/dT)P, are tabulated. For an isotropic substance (the same in all directions), we can relate aL to the volumetric thermal expansion coefficient, defined in Eq. (8), by considering a cube with V = L ... 

I. The dielectric constants and conductivities of mixtures composed of isotropic substances. Ann. Phys. (Leipzig) 24, 636-664 (1935) 665-679 (1935)... 

A second reason why even isotropic substances may only virtually disappear is due to dispersion. We have all seen dispersion at work when a beam of white light is split into a rainbow of colors by a prism. The dispersion of the liquid is rarely the same as the solid. Therefore, although one wavelength of light may match up, others will not, and there will be faint color fringes around the edge... 

Using (2.1.4), the coil energy for isotropic substances simplifies to... 

For relatively small electric fields in isotropic substances P = ) E, where is the electric susceptibility. If the medium is made up of N atoms (or ions) per unit volume, the polarization is P = N wherep is the average dipole moment per atom. The polarizability a can be defined as p = ctE , where is the local field at the position of the atom. Using the Lorentz method to calculate the local field one finds ... 

The simplest theory of diffusion in isotropic substances is based on the assumption that the rate of transfer between diffusing molecules through unit cross-section area is proportional to the concentration gradient ... 

In ferromagnetic materials there exists a volume anomaly AVo at absolute zero. For an isotropic substance the magnetic energy is related through the equation... 

Here, B is called the magnetic induction and M is the (induced) magnetic moment per unit volume or the magnetization. In general, B, H, and M of Eq. (1) are vector quantities. If we consider an isotropic substance, M depends only on H and is independent of direction... 

Bruggeman DAG (1935) Calculation of various physics constants in heterogenous substanees I. Dielectricity constants and conductivity of mixed bodies from isotropic substances. Annalen Der Physik 24(7) 636... 

Elastic modulus is a quantitative measure of the stiffness or rigidity of a material. For example, for homogeneous isotropic substances in tension, the strain (e) is related to the applied stress (o) by the equation E = o/e, where E is defined as the elastic modulus. A similar definition of shear modulus (g) applies when the strain is shear. 

One of best illustrations of how polarized li t interacts with solid samples is found in the forensic analysis of glass. As shown in the figure, polarized li t is not altered by an isotropic substance such as gjass, and under crossed polars, the field... 

In 1875, J. Kerr observed that if a transparent isotropic substance is placed in a stationary electric field, it becomes optically anitotropic and doubly reflecting because the electric field tends to bring about a definite orientation of the molecules. 

Birefringence - The light is transmitted with equal velocities in an isotropic substance. In anisotropic materials, molecular structure is such that the transmission vibration varies as a funetion of direction. A material is optically anisotropic when its refractive index depends on direetion. Birefringence is calculated as the dififerenee inreirae-tive index in two selected perpendieular direetions. 

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