Mie potential

The Mie potential was proposed by Gustav Mie in 1903 . It is given by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r) = \left( \frac{n}{n-m}\right) \left( \frac{n}{m}\right)^{m/(n-m)} \epsilon \left[ \left(\frac{\sigma}{r} \right)^{n}- \left( \frac{\sigma}{r}\right)^m \right] }

where:

• $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r) } is the intermolecular pair potential between two particles at a distance r;
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } is the value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} at Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi(r)=0}  ;
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon }  : well depth (energy)

Note that when $n=12$ and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m=6} this becomes the Lennard-Jones model.

The location of the potential minimum is given by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r_{min} = \left( \frac{n}{m} \sigma^{n-m} \right) ^ {1/(n-m)} }

Second virial coefficient

The second virial coefficient and the Vliegenthart–Lekkerkerker relation .

References

Related reading

• Pedro Orea, Yuri Reyes-Mercado, Yurko Duda "Some universal trends of the Mie(n,m) fluid thermodynamics", Physics Letters A 372 pp. 7024-7027 (2008)
• N.S. Ramrattan, C. Avendaño, E.A. Müller and A. Galindo "A corresponding-states framework for the description of the Mie family of intermolecular potentials", Molecular Physics 113 pp. 932-947 (2015)