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| : <math> | | : <math> |
| V_{W} \left( x \right) = 8 \pi \epsilon_{sf} \rho_{s} \int_{-\infty}^{-x} {\textrm d z} | | V_{W} \left( x \right) = 8 \pi \epsilon_{sf} \rho_s |
| \left[ \frac{ \sigma^{12}} { 10 z^{10} } | | \left[ - \frac{ \sigma^{12}} { 90 z^{9} } |
| - \frac{\sigma^6 }{ 4 z^4 } \right]; | | + \frac{\sigma^6 }{ 12 z^3 } \right]_{z=-\infty}^{z=-x}; |
| | </math> |
| | |
| | : <math> |
| | V_{W} \left( x \right) = 8 \pi \epsilon_{sf} \rho_s |
| | \left[ \frac{ \sigma^{12}} { 90 x^{9} } |
| | - \frac{\sigma^6 }{ 12 x^3 } \right] |
| </math> | | </math> |
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Revision as of 15:37, 23 March 2007
[EN CONSTRUCCION]
Functional form
The 9-3 Lennard-Jones potential is related to the standard Lennard-Jones potential.
It takes the form:
The minimum value of is obtained at , with
- ,
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 divided in two regions:
- : this region is occupied by a diffuse solid with density composed of 12-6 Lennard-Jones atoms
with paremeters 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 ( I GUESS SO, at least).
The interaction will be:
[TO BE CONTINUED]