In our world today, the majority of all substances exist in one of the three most well known phases: liquids, solids, and gases. The main idea that allows us to distinguish between the 3 phases is the intermolecular forces that exist between particles.
In a solid, it is well known that the particles are “packed” closely together, which equivalently means that there exists a large amount of intermolecular forces. Similarly, liquids are essentially particles that have an average amount of intermolecular forces between the particles. Finally, by observation, gases have little to no intermolecular forces between them. This follows the properties of an ideal gas as the intermolecular forces in an ideal gas are considered negligible. In regular chemistry, these intermolecular forces can be divided into three types of forces, depending on whether there exists momentary interactions between particles, or there exists a permanent electrostatic attraction between the particles. The three are known as Dipole-Dipole, Hydrogen Bonding, and London Dispersion forces. Quantum mechanics further explore the relationship between electrons and the substance’s physical property, allowing many interesting theory to develop. Amongst those theories, one of them is band theory, which is based on the molecular orbital theory. Several other states of matter other than the common solid, liquid, and gas is also introduced.
The electronic band structure of a solid describes the ranges of energy that a solid may have, known as energy bands, and the ranges of energy that a solid may not have, known as energy gaps. The band theory models many of the physical properties of solids, such as electrical resistivity and optical absorption. In a way, band theory is a general version of molecular orbital theory. Molecular orbital theory
Figure 2. A basic band theory diagram. As the band gap increases, the solid’s conductivity decreases.
describes the behaviors of a single atom in a molecule, like the probability of the electron’s position and energy. These behaviors are often approximated by combining atomic orbitals. The atomic orbital describes the quantum mechanical behavior of an electron in an atom and the probability of the electron’s position and energy.
The electrons in an individual atom occupy atomic orbitals, forming a discrete set of energy levels. When several atoms are brought together to form a molecule, the atomic orbitals became molecular orbitals with different energy levels.
According to Pauli’s exclusion effect, electrons that are in an atom or molecule must have different quantum numbers. Quantum numbers are a representation of different atomic orbitals. In other words, the electrons in a molecule must have different atomic orbitals. Since atomic orbitals are directly related to energy levels, the electrons must have different energy levels as well. As a result, the number of the molecular orbitals is proportional to the number of valence electrons. In the case where there is a large number of atoms (OVER 9000, more like 10^20) brought together to form a solid, the differences between each individual discrete energy level becomes negligible. Thus continuous bands of energy begin to form. However, some intervals of energy contain no orbitals no matter how many atoms are congregated. This creates band gaps, which are important for semi-conductors and insulators.
When a liquid or gas is heated beyond its critical point it becomes what is known as a “superfluid” Superfluidity is when the matter behaves like a fluid with zero viscosity; it appears to exhibit the ability to self-propel and travel in a way that defies the forces of gravity and surface tension. The critical point is the temperature at which no pressure will be able to reliquify or recondense the material. Put simply, a superfluid is a vapor that can flow. You can see this demonstrated in this video of superfluid helium.
Bose-Einstein condensate is a state of matter that occurs at extremely low temperatures, near absolute zero. At such a temperature, the kinetic energy of the material’s molecules will be extremely low, and the slow motion allows some of the more bizarre aspects of quantum mechanics to occur. For example, when the temperature of Helium-4 goes below 4.2 K it condenses into a liquid, and at below 2.17 K, it exhibits a number of strange behaviors as a result of becoming a superfluid. A superfluid in a beaker will form a film that crawls up the walls, over the top, and down the sides until the beaker is emptied. Another interesting effect is quantised vorticity. Vorticity, in fluid dynamics, describes the local spinning motion of a fluid near some point, as would be seen by an observer located at that point and traveling along with the fluid. In a rotating container of He-4, a vortex can form in the middle, with fluid moving around in a circle, much like a water vortex around a plughole in a bath. The difference is that only certain fluid velocities are allowed. At a given distance from the vortex center there is a minimum velocity, then twice that velocity, then three times, etc. No velocities between these values are permitted, so the vortices are said to be quantized.