Mie potential

The Mie potential is an intermolecular pair potential, i.e. it describes the interactions between particles on the atomic level. The Mie potential is one of the most simple, yet most powerful pair potentials, which describes both repulsive and dispersive interactions of atoms and molecules. The Mie potential is written as^[1]

${\displaystyle V_{\mathrm {Mie} }(r)=C\,\varepsilon \left[\left({\frac {\sigma }{r}}\right)^{n}-\left({\frac {\sigma }{r}}\right)^{m}\right],~~~~~~(1)}$

with

${\displaystyle C={\frac {n}{n-m}}\left({\frac {n}{m}}\right)^{\frac {m}{n-m}}}$ .

In Eq. (1), ${\displaystyle r}$ is the distance between two particles, ${\displaystyle \varepsilon }$ is the dispersion energy, and ${\displaystyle \sigma }$ indicates the distance of ${\displaystyle V=0}$ . The parameter ${\textstyle \sigma }$ is usually referred to as 'size of the particle'. The parameters ${\textstyle n}$ and ${\textstyle m}$ characterize the shape of the potential: ${\textstyle n}$ describes the character of the repulsion and ${\textstyle m}$ describes the character of the attraction.

The Mie potential is attributed to the German physician Gustave Mie.^[2] The Mie potential is the generalized case of the Lennard-Jones (LJ) potential – the probably most frequently used pair potential.^[3][4] Hence, the LJ potential has ${\textstyle n=12}$ and ${\textstyle m=6}$ in Eq. (1). The attractive exponent ${\textstyle m=6}$ is physically justified by the London dispersion,^[5] whereas no justification for a certain value for the repulsive exponent is known. The repulsive steepness parameter ${\textstyle n}$ has a significant influence on the modelling of thermodynamic derivative properties, e.g. the compressibility and the speed of sound. Therefore, the Mie potential is presently considered the more sophisticated intermolecular potential than the more simple Lennard-Jones potential. The Mie potential is used today in state-of-the-art force fields in molecular modeling. Mostly, the attractive exponent is thereby chosen to be ${\textstyle m=6}$, whereas the repulsive exponent is used as an adjustable parameter during the model fitting.

Thermophysical properties of the Mie potential have been frequently studied in the past decades, e.g. its virial coefficients,^[6] interfacial^[7] and vapor-liquid equilibrium^[8][9] properties.

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