9-3 Lennard-Jones potential: Difference between revisions
| Line 24: | Line 24: | ||
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 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 paremeters <math> \sigma_s </math> and <math> \epsilon_a </math> | with paremeters <math> \sigma_s </math> and <math> \epsilon_a </math> | ||
Revision as of 12:55, 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:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V(r) = \frac{ 3 \sqrt{3}}{ 2} \epsilon \left[ \left( \frac{\sigma}{r} \right)^9 - \left( \frac{ \sigma }{r} \right)^3 \right]. }
The minimum value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V(r) } is obtained at Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r = r_{min} } , with
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V \left( r_{min} \right) = - \epsilon } ,
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 divided in two regions:
- : this region is occupied by a diffuse solid with density Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_s } composed of 12-6 Lennard-Jones atoms
with paremeters Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma_s } and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon_a }
Our aim is to compute the total interaction between this solid and a molecule located at a position Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x > 0 } .
[TO BE CONTINUED]