9-3 Lennard-Jones potential

[EN CONSTRUCCION]

Functional form

The 9-3 Lennard-Jones potential is related to the standard Lennard-Jones potential.

It takes the form:

$V(r)=\frac{3\sqrt{3}}{2}ϵ[{(\frac{\sigma }{r})}^9-{(\frac{\sigma }{r})}^3].$

The minimum value of $V(r)$ is obtained at $r=r_{min}$, with

• $V(r_{min})=-ϵ$,

• $\frac{r_{min}}{\sigma }=3^{1/6}$

Applications

It is commonly used to model the interaction between the particles of a fluid with a flat structureless solid wall.

Interaction between a solid and a fluid molecule

Let us consider the space dividen in two regions:

• $x<0$: this region is occupied by a diffuse solid with density ${\rho }_s$ composed of Lennard-Jones atoms

with paremeters ${\sigma }_s$ and ${ϵ}_a$

[to be continued]