Lennard-Jones potential

The simplest intermolecular interactions are observed between two molecules of a monatomic gas, such as argon. The essential features are a strong hard-core repulsion, along with a weak attraction at somewhat larger distances, with the attractive part varying in strength as the inverse sixth power of the separation of the two particles, r. The essential features are approximated quite well by a Lennard-Jones potential, which can be written in two equivalent forms:

E(LJ) = 4 epsilon [(sigma/r)12 - (sigma/r)6]

E(LJ) = (a/r)12 - (b/r)6

Simpler Approximations

Two simpler, discontinuous potential energy functions capture some of the features seen in the continuous Lennard-Jones potential.

When models of polymers are constructed on lattices of various kinds, the chains often are allowed to interact with one another by one of these two discontinuous potentials, due to the discretization of configurational space on the lattice.

Lorentz/Berthelot Mixing Rules

For the interaction of heteroatomic pairs, the effective values of sigma and epsilon are calculated from those for the homoatomic pairs using the Lorentz-Berthelot mixing rules: arithmetic mean for sigma, geometric mean for epsilon.

sigmaAB = (1/2)(sigmaAA + sigmaBB)

epsilonAB = (epsilonAAepsilonBB)1/2

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July 2, 1999
Wayne L. Mattice: wlm@polymer.uakron.edu