Editing 9-3 Lennard-Jones potential
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The | == Functional form == | ||
The 9-3 Lennard-Jones potential is related to the [[Lennard-Jones model| Lennard-Jones potential]]. | |||
It has the following form: | It has the following form: | ||
: <math> | : <math> | ||
\ | \Phi(r) = \frac{ 3 \sqrt{3}}{ 2} \epsilon \left[ \left( \frac{\sigma}{r} \right)^9 - | ||
\left( \frac{ \sigma }{r} \right)^3 \right]. | \left( \frac{ \sigma }{r} \right)^3 \right]. | ||
</math> | </math> | ||
where <math>\ | where <math>\Phi(r)</math> is the [[intermolecular pair potential]]. | ||
The minimum value of <math> \Phi(r) </math> is obtained at <math> r = r_{min} </math>, with | The minimum value of <math> \Phi(r) </math> is obtained at <math> r = r_{min} </math>, with | ||
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> | |||
* <math> \Phi \left( r_{min} \right) = - \epsilon </math>, | * <math> \Phi \left( r_{min} \right) = - \epsilon </math>, | ||
* <math> \frac{ r_{min} }{\sigma} = 3^{1/6} </math> | * <math> \frac{ r_{min} }{\sigma} = 3^{1/6} </math> | ||
== Applications == | == Applications == | ||
It is commonly used to model the interaction between the particles | It is commonly used to model the interaction between the particles | ||
of a fluid with a flat structureless solid wall | of a fluid with a flat structureless solid wall. | ||
== Interaction between a solid and a fluid molecule == | == Interaction between a solid and a fluid molecule == | ||
Let us consider the space divided in two regions: | Let us consider the space divided in two regions: | ||
Line 54: | Line 56: | ||
- \frac{\sigma^3 }{ 2 x^3 } \right] | - \frac{\sigma^3 }{ 2 x^3 } \right] | ||
</math> | </math> | ||
[[category:models]] | [[category:models]] |