9-3 Lennard-Jones potential

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The 9-3 Lennard-Jones potential is related to the Lennard-Jones potential. It has the following form:

where is the intermolecular pair potential and . The minimum value of is obtained at , with

  • ,


It is commonly used to model the interaction between the particles of a fluid with a flat structureless solid wall or vice versa (Ref. 1).

Interaction between a solid and a fluid molecule[edit]

Let us consider the space divided in two regions:

  • : this region is occupied by a diffuse solid with density composed of 12-6 Lennard-Jones atoms

with parameters and

Our aim is to compute the total interaction between this solid and a molecule located at a position . Such an interaction can be computed using cylindrical coordinates.

The interaction will be:


  1. Farid F. Abraham and Y. Singh "The structure of a hard-sphere fluid in contact with a soft repulsive wall", Journal of Chemical Physics 67 pp. 2384-2385 (1977)