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Diagram showing the ionic concentration and potential difference as a function of distance from the charged surface of a particle suspended in a dispersion medium. Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface.
The Lennard-Jones potential is a simple model that still manages to describe the essential features of interactions between simple atoms and molecules: Two interacting particles repel each other at very close distance, attract each other at moderate distance, and eventually stop interacting at infinite distance, as shown in the Figure.
Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency ...
One may also consider an empty [clarification needed] irregular lattice, in which the potential is not even periodic. [1] The empty lattice approximation describes a number of properties of energy dispersion relations of non-interacting free electrons that move through a crystal lattice. The energy of the electrons in the "empty lattice" is the ...
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions. The theorem is named after the Swiss physicist Felix Bloch, who discovered the theorem in 1929. [1] Mathematically, they are written [2]
This model explains the origin of the electronic dispersion relation, but the explanation for band gaps is subtle in this model. [2]: 121 The second model starts from the opposite limit, in which the electrons are tightly bound to individual atoms. The electrons of a single, isolated atom occupy atomic orbitals with discrete energy levels.
The delta potential is the potential = (), where δ(x) is the Dirac delta function. It is called a delta potential well if λ is negative, and a delta potential barrier if λ is positive. The delta has been defined to occur at the origin for simplicity; a shift in the delta function's argument does not change any of the following results.
The Hamaker constant provides the means to determine the interaction parameter C from the vdW-pair potential, w ( r ) = − C r 6 . {\displaystyle w(r)={\frac {-C}{r^{6}}}.} Hamaker's method and the associated Hamaker constant ignores the influence of an intervening medium between the two particles of interaction.