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The `!Stockmayer potential`! is a mathematical model for representing the interactions between pairs of `F33f`_`[atoms`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Atoms]`_`f or `F33f`_`[molecules`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Molecules]`_`f. It is defined as a `F33f`_`[Lennard-Jones potential`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Lennard-Jones_potential]`_`f with a point `F33f`_`[electric dipole moment`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Electric_dipole_moment]`_`f.

A Stockmayer liquid consists of a collection of spheres with point dipoles embedded at the centre of each. These spheres interact both by Lennard-Jones and dipolar interactions. In the absence of the point dipoles, the spheres face no rotational friction and the translational dynamics of such LJ spheres have been studied in detail. This system, therefore, provides a simple model where the only source of rotational friction is dipolar interactions.`:cite-ref-1[`F5bf`_`[1`#cite-note-1]`_`f]

The interaction potential may be written as

V ( r ) = 4 ε ε 12 [ ( σ σ 12 r ) 12 − − ( σ σ 12 r ) 6 ] − − ξ ξ ( μ μ 1 μ μ 2 r 3 ) {\\displaystyle V(r)=4\\varepsilon _{12}\\left[\\left({\\frac {\\sigma _{12}}{r}}\\right)^{12}-\\left({\\frac {\\sigma _{12}}{r}}\\right)^{6}\\right]-\\xi \\left({\\frac {\\mu _{1}\\mu _{2}}{r^{3}}}\\right)}

where the parameters ε ε 12 {\\displaystyle \\varepsilon _{12}} and σ σ 12 {\\displaystyle \\sigma _{12}} are related to `F33f`_`[dispersion`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Van_der_Waals_force]`_`f strength and particle size respectively, just as in the `F33f`_`[Mie potential`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Mie_potential]`_`f or `F33f`_`[Lennard-Jones potential`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Lennard-Jones_potential]`_`f, which is the source of the first term, μ μ i {\\displaystyle \\mu _{i}} is the `F33f`_`[dipole moment`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Electric_dipole_moment]`_`f of species i {\\displaystyle i} , and ξ ξ {\\displaystyle \\xi } is a parameter describing the relative orientation of the two dipoles, which may vary between -2 and 2.`:cite-ref-2[`F5bf`_`[2`#cite-note-2]`_`f]

>>References

`:cite-note-1`!1.`! `F0af`_`[↑`#cite-ref-1]`_`f `:citerefbagchijana2010`aBagchi, Biman; Jana, Biman (2010), "Solvation dynamics in dipolar liquids", `*Chem. Soc. Rev.`* (in German), vol. 39, no. 6, pp. 1936–1954, `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1039/b902048a, `F33f`_`[PMID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=PMID_(identifier)]`_`f 20502796

`:cite-note-2`!2.`! `F0af`_`[↑`#cite-ref-2]`_`f `:citerefmasonmonchick1962`aMason, E. A.; Monchick, L. (1962-05-15). "Transport Properties of Polar-Gas Mixtures". `*The Journal of Chemical Physics`*. `!36`! (10): 2746–2757. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1063/1.1732363. `F33f`_`[ISSN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISSN_(identifier)]`_`f 0021-9606.

1. M. E. Van Leeuwe "Deviation from corresponding-states behaviour for polar fluids", Molecular Physics `!82`! pp. 383-392 (1994)

2. Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E `!75`! 011506 (2007)

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