Fomin potential - Revision history

Carl McBride: Removed extra rhs parenthesis

2014-01-24T12:39:26Z

Removed extra rhs parenthesis

← Older revision		Revision as of 14:39, 24 January 2014
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	:<math>		:<math>
	\Phi_{12}\left( r \right) = \left( \frac{d}{r} \right)^n + \lambda_0 + \sum_{i=1}^{i=i_{max}} \lambda_i \tanh ( k_i (r-\sigma_i )))		\Phi_{12}\left( r \right) = \left( \frac{d}{r} \right)^n + \lambda_0 + \sum_{i=1}^{i=i_{ \mathrm{max} }} \lambda_i \tanh ( k_i (r-\sigma_i ))
	</math>		</math>

Fomin314 at 11:27, 24 January 2014

2014-01-24T11:27:08Z

← Older revision		Revision as of 13:27, 24 January 2014
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	:<math>		:<math>
	\Phi_{12}\left( r \right) = \left( \frac{d}{r} \right)^n + \lambda_0 \sum_{i=1}^{i=~~imax~~} \lambda_i \tanh ( k_i (r-\sigma_i )))		\Phi_{12}\left( r \right) = \left( \frac{d}{r} \right)^n + \lambda_0 + \sum_{i=1}^{i=i_{max}} \lambda_i \tanh ( k_i (r-\sigma_i )))
	</math>		</math>

Fomin314 at 11:25, 24 January 2014

2014-01-24T11:25:41Z

← Older revision		Revision as of 13:25, 24 January 2014
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	The '''Fomin potential''' ~~is given by~~ <ref>[http://dx.doi.org/10.1063/1.2965880 Yu. D. Fomin, N. V. Gribova, V. N. Ryzhov, S. M. Stishov, and Daan Frenkel "Quasibinary amorphous phase in a three-dimensional system of particles with repulsive-shoulder interactions", Journal of Chemical Physics '''129''' 064512 (2008)]</ref> (Eq. 2):		The '''Fomin potential''' was firstly introduced as <ref>[http://dx.doi.org/10.1063/1.2965880 Yu. D. Fomin, N. V. Gribova, V. N. Ryzhov, S. M. Stishov, and Daan Frenkel "Quasibinary amorphous phase in a three-dimensional system of particles with repulsive-shoulder interactions", Journal of Chemical Physics '''129''' 064512 (2008)]</ref> (Eq. 2):

	:<math>		:<math>
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	where <math> \Phi_{12}\left( r \right) </math> is the [[intermolecular pair potential]], <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math> is the distance between site 1 and site 2, <math>n=14</math> and <math>k_0=10</math>. <math>d</math> is the diameter of the hard core, <math>\sigma_s</math> is the width of the repulsive shoulder, <math>\epsilon</math> is the height of the shoulder. As such, this model can be viewed as a softened [[square shoulder model]].		where <math> \Phi_{12}\left( r \right) </math> is the [[intermolecular pair potential]], <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math> is the distance between site 1 and site 2, <math>n=14</math> and <math>k_0=10</math>. <math>d</math> is the diameter of the hard core, <math>\sigma_s</math> is the width of the repulsive shoulder, <math>\epsilon</math> is the height of the shoulder. As such, this model can be viewed as a softened [[square shoulder model]].

			Later it was generalized to the form <ref>[http://dx.doi.org/10.1063/1.3530790 Yu. D. Fomin, E. N. Tsiok and V. N. Ryzhov, "Complex phase behavior of the system of particles with smooth potential with repulsive shoulder and attractive well", Journal of Chemical Physics '''134''' 044523 (2011)]</ref> :

			:<math>
			\Phi_{12}\left( r \right) = \left( \frac{d}{r} \right)^n + \lambda_0 \sum_{i=1}^{i=imax} \lambda_i \tanh ( k_i (r-\sigma_i )))
			</math>

			By varying coefficients <math> \lambda_i </math> one can add repulsive shoulders or attractive wells to the potential.
	==References==		==References==
	<references/>		<references/>
	[[category: models]]		[[category: models]]

Carl McBride: New page: The '''Fomin potential''' is given by [http://dx.doi.org/10.1063/1.2965880 Yu. D. Fomin, N. V. Gribova, V. N. Ryzhov, S. M. Stishov, and Daan Frenkel "Quasibinary amorphous phase in a...

2009-08-03T10:09:09Z

New page: The '''Fomin potential''' is given by <ref>[http://dx.doi.org/10.1063/1.2965880 Yu. D. Fomin, N. V. Gribova, V. N. Ryzhov, S. M. Stishov, and Daan Frenkel "Quasibinary amorphous phase in a...

New page

The '''Fomin potential''' is given by <ref>[http://dx.doi.org/10.1063/1.2965880 Yu. D. Fomin, N. V. Gribova, V. N. Ryzhov, S. M. Stishov, and Daan Frenkel "Quasibinary amorphous phase in a three-dimensional system of particles with repulsive-shoulder interactions", Journal of Chemical Physics '''129''' 064512 (2008)]</ref> (Eq. 2):

:<math>
\Phi_{12}\left( r \right) = \left( \frac{d}{r} \right)^n + \frac{\epsilon}{2} (1 - \tanh ( k_0 (r-\sigma_s )))
</math>

where <math> \Phi_{12}\left( r \right) </math> is the [[intermolecular pair potential]], <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> is the distance between site 1 and site 2, <math>n=14</math> and <math>k_0=10</math>. <math>d</math> is the diameter of the hard core, <math>\sigma_s</math> is the width of the repulsive shoulder, <math>\epsilon</math> is the height of the shoulder. As such, this model can be viewed as a softened [[square shoulder model]].
==References==
<references/>
[[category: models]]