# Stockmayer potential

The **Stockmayer potential** consists of the Lennard-Jones model with an embedded point dipole. Thus the Stockmayer potential becomes (Eq. 1 ^{[1]}):

where:

- is the intermolecular pair potential between two particles at a distance
- is the diameter (length), i.e. the value of at
- represents the well depth (energy)
- is the permittivity of the vacuum
- is the dipole moment
- and are the angles associated with the inclination of the two dipole axes with respect to the intermolecular axis.
- is the azimuth angle between the two dipole moments

If one defines a reduced dipole moment, , such that:

one can rewrite the expression as

For this reason the potential is sometimes known as the Stockmayer 12-6-3 potential.

## Critical properties[edit]

In the range ^{[2]}:

## Bridge function[edit]

A bridge function for use in integral equations has been calculated by Puibasset and Belloni ^{[3]}.

## References[edit]

- ↑ W. H. Stockmayer "Second Virial Coefficients of Polar Gases", Journal of Chemical Physics
**9**pp. 398-402 (1941) - ↑ M.E. Van Leeuwen "Deviation from corresponding-states behaviour for polar fluids", Molecular Physics
**82**pp. 383-392 (1994) - ↑ Joël Puibasset and Luc Belloni "Bridge function for the dipolar fluid from simulation", Journal of Chemical Physics
**136**154503 (2012)

**Related reading**

- Frank M. Mourits, Frans H. A. Rummens "A critical evaluation of Lennard–Jones and Stockmayer potential parameters and of some correlation methods", Canadian Journal of Chemistry
**55**pp. 3007-3020 (1977) - M. E. van Leeuwen "Derivation of Stockmayer potential parameters for polar fluids", Fluid Phase Equilibria
**99**pp. 1-18 (1994) - Osvaldo H. Scalise "On the phase equilibrium Stockmayer fluids", Fluid Phase Equilibria
**253**pp. 171–175 (2007) - Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E
**75**011506 (2007) - Jun Wang , Pankaj A. Apte , James R. Morris and Xiao Cheng Zeng "Freezing point and solid-liquid interfacial free energy of Stockmayer dipolar fluids: A molecular dynamics simulation study", Journal of Chemical Physics
**139**114705 (2013)