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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.
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 ...
Using the virial theorem, the velocity dispersion σ can be used in a similar way. Taking the kinetic energy (per particle) of the system as T = 1 / 2 v 2 ~ 3 / 2 σ 2, and the potential energy (per particle) as U ~ 3 / 5 GM / R we can write .
The Axilrod–Teller potential in molecular physics, is a three-body potential that results from a third-order perturbation correction to the attractive London dispersion interactions (instantaneous induced dipole-induced dipole)
Assuming the spacing between two ions is a, the potential in the lattice will look something like this: The mathematical representation of the potential is a periodic function with a period a. According to Bloch's theorem, [1] the wavefunction solution of the Schrödinger equation when the potential is periodic, can be written as:
Given a potential energy function, the radial distribution function can be computed either via computer simulation methods like the Monte Carlo method, or via the Ornstein–Zernike equation, using approximative closure relations like the Percus–Yevick approximation or the hypernetted-chain theory. It can also be determined experimentally, by ...
In 1923, Peter Debye and Erich Hückel reported the first successful theory for the distribution of charges in ionic solutions. [7] The framework of linearized Debye–Hückel theory subsequently was applied to colloidal dispersions by S. Levine and G. P. Dube [8] [9] who found that charged colloidal particles should experience a strong medium-range repulsion and a weaker long-range attraction.
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 ...