Editing 9-3 Lennard-Jones potential
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The | [EN CONSTRUCCION] | ||
It | == Functional form == | ||
The 9-3 Lennard-Jones potential is related to the [[Lennard-Jones model|standard Lennard-Jones potential]]. | |||
It takes the form: | |||
: <math> | : <math> | ||
V(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> | ||
The minimum value of <math> V(r) </math> is obtained at <math> r = r_{min} </math>, with | |||
The minimum value of <math> | |||
* <math> | * <math> V \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: | ||
* <math> x < 0 </math>: this region is occupied by a ''diffuse'' solid with density <math> \rho_s </math> composed of 12-6 [[Lennard-Jones model|Lennard-Jones]] atoms | * <math> x < 0 </math>: this region is occupied by a ''diffuse'' solid with density <math> \rho_s </math> composed of 12-6 [[Lennard-Jones model|Lennard-Jones]] atoms | ||
with | with paremeters <math> \sigma_s </math> and <math> \epsilon_a </math> | ||
Our aim is to compute the total interaction between this solid and a molecule located at a position <math> | Our aim is to compute the total interaction between this solid and a molecule located at a position <math> x > 0 </math>. | ||
[TO BE CONTINUED] | |||