Isotropy - what is it, what is its importance? Which materials are isotropic and which are anisotropic. In this article, we will answer these questions and give you some examples of each of these materials.
Why do pencils write?
Have you ever wondered why pencils write so well? If you try to write on a piece of paper using a computer stylus, then it will not write. So what's the deal with the pencil? The reason is that the pencil is made of a multilayer material called graphite. Each graphite layer has carbon atoms that are strongly bonded to each other. These strong bonds are very difficult to break. On the other hand, the bonds between the graphite layers themselves are very weak, so it is very easy for the layers to slide past each other.
A pencil writes so well because layers of graphite can easily slip past each other and leave a trace of graphite on paper. Carbon atoms are strongly bonded to each other in a layer of graphite, which is strong in some directions and weak in others. Other materials, such as glass, have the same properties in all directions. Therefore, we can classify these materials according to their isotropy.
The concept
The term "isotropy" comes from the Greek words isos ("equal") and tropos ("path") and means uniform in all directions. Isotropic materials, such as glass, show the same material properties in all directions, while anisotropic materials (graphite) show different material properties depending on the direction.
One of the material properties of graphite is strength, but there are other properties that can be considered. For example, thermal conductivity, electrical resistance, and absorption (a measure of how much light a material absorbs).
Isotropic materials
Two common types of isotropic materials are metal and glass. In metals, electrons are separated by many atoms in all directions, so metallic bonds are disoriented. As a result, the properties of metals are often very similar in all directions, which means that metals are usually isotropic.
Vitreous materials are also isotropic. The atoms that make up glass are poorly organized in any direction, so the properties of the material are usually the same in all directions. It is important to remember that even if the material has anisotropic regions, it can be generally isotropic if the anisotropic regions are randomly oriented so that they can cancel each other out.
Isotropy
Isotropy is uniformity in all orientations. The exact definitions depend on the subject area.
- Mathematics. In mathematics, isotropy has several different meanings: isotropic manifolds, isotropic quadratic form, in complex geometry, the line through the origin in the direction of the isotropic vector is an isotropic line, and so on.
- Physics. In quantum mechanics or particle physics, isotropy is one of the properties of elementary particles. When a spinless particle decays, the resulting decay distribution must be isotropic in the rest of the decaying particle frame, regardless of the detailed decay physics. This follows from the rotational invariance of the Hamiltonian, which, in turn, is guaranteed for a spherically symmetric potential. The kinetic theory of gases is also an example of isotropy. It is assumed that the molecules move in random directions and, as a result, there is an equal probability of the molecule moving in any direction. Thus, when there are a lot of molecules in a gas, it is very likely that there will be very similar numbers moving in one direction, like any other, therefore, showing approximate isotropy.
- Hydrodynamics. The fluid flow is isotropic if there is no directional preference (for example, fully developed 3D turbulence).
- Thermal expansion. A solid is called isotropic if the expansion of the solid is equal in all directions when thermal energy is provided to the solid.
- Electromagnetism. An isotropic medium is the same as dielectric constant, the simplest example is free space.
- Optics. Optical isotropy is the presence of the same optical properties in all directions. Individual domain reflection or transmittance is averaged if macroscopic reflection or transmittance is calculated. This can be checked by simply examining, for example, a polycrystalline material under a polarizing microscope with the intersection of polarizers: if the crystallites are greater than the resolution limit, they will be visible.
- Materials Science. When studying the mechanical properties of materials, "isotropy" is the presence of the same property values in all directions. This definition is also used in geology and mineralogy. Glass and metals are examples of isotropic materials. Common anisotropic materials include wood and laminated species such as slate. Isotropic materials are useful because they are easier to shape and their behavior easier to predict. Anisotropic materials can be adapted. For example, fibers in carbon fiber materials and reinforcement in reinforced concrete are designed to withstand stress.
- Cosmology. The big bang theory of the evolution of the universe suggests that space is isotropic. It is also assumed that the space is homogeneous. These two assumptions are collectively known as the Cosmological Principle. Here, homogeneity means that the Universe is the same everywhere, and isotropy means that there is no preferred direction.
- Cell biology. What is isotropy in cell biology? If the properties of the cell wall are more or less the same everywhere, it is called isotropic. The inner part of the cell is anisotropic due to intracellular organelles.
- Physiology. In skeletal muscle cells, the term "isotropic" refers to light bands that contribute to the striped pattern of cells.
- Pharmacology. Although it is well known that the skin is an ideal platform for managing local and systemic drugs, it is a serious barrier to the penetration of most substances.
- Economics and geography. An isotropic region is a region that everywhere has the same properties, for example, the construction required in many types of models.