Harmonic repulsion potential - Revision history

Carl McBride: Added a recent publication

2017-09-25T09:31:17Z

Added a recent publication

← Older revision		Revision as of 11:31, 25 September 2017
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	==References==		==References==
	<references/>		<references/>
			;Related reading
			*[http://dx.doi.org/10.1063/1.5002536 V. A. Levashov "Crystalline structures of particles interacting through the harmonic-repulsive pair potential", Journal of Chemical Physics '''147''' 114503 (2017)]

	[[category: models]]		[[category: models]]

Carl McBride: Added some internal links

2011-01-26T11:05:30Z

Added some internal links

← Older revision		Revision as of 13:05, 26 January 2011
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	The '''Harmonic repulsion potential''' is given by (<ref>[http://dx.doi.org/10.1103/PhysRevLett.103.245701 Ning Xu, Thomas K. Haxton, Andrea J. Liu, and Sidney R. Nagel "Equivalence of Glass Transition and Colloidal Glass Transition in the Hard-Sphere Limit", Physical Review Letters '''103''' 245701 (2009)]</ref> Eq. 2):		The '''Harmonic repulsion potential''', designed for studies of [[Polymers \|polymer]] [[micelles]], [[dendrimers]], and [[Colloids \|colloidal particles]], is given by (<ref>[http://dx.doi.org/10.1103/PhysRevLett.103.245701 Ning Xu, Thomas K. Haxton, Andrea J. Liu, and Sidney R. Nagel "Equivalence of Glass Transition and Colloidal Glass Transition in the Hard-Sphere Limit", Physical Review Letters '''103''' 245701 (2009)]</ref> Eq. 2):

	:<math>		:<math>

Carl McBride: Added internal link to plot of potential

2011-01-26T10:43:34Z

Added internal link to plot of potential

← Older revision		Revision as of 12:43, 26 January 2011
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	</math>		</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>\sigma</math> represents a length scale and <math>\epsilon</math> an energy.		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>\sigma</math> represents a length scale and <math>\epsilon</math> an energy. For example, for <math>\epsilon=20</math> the potential looks like

			:[[Image:harmonic_sphere.png\|500px]]
	==Phase diagram==		==Phase diagram==
	The [[Phase diagrams \|phase diagram]] in the [[Phase diagrams: Pressure-temperature plane \| pressure-temperature plane]] has been calculated by Zhu and Lu <ref>[http://dx.doi.org/10.1063/1.3548886 You-Liang Zhu and Zhong-Yuan Lu "Phase diagram of spherical particles interacted with harmonic repulsions", Journal of Chemical Physics '''134''' 044903 (2011)]</ref>.		The [[Phase diagrams \|phase diagram]] in the [[Phase diagrams: Pressure-temperature plane \| pressure-temperature plane]] has been calculated by Zhu and Lu <ref>[http://dx.doi.org/10.1063/1.3548886 You-Liang Zhu and Zhong-Yuan Lu "Phase diagram of spherical particles interacted with harmonic repulsions", Journal of Chemical Physics '''134''' 044903 (2011)]</ref>.

Carl McBride: Created page with "The '''Harmonic repulsion potential''' is given by ([http://dx.doi.org/10.1103/PhysRevLett.103.245701 Ning Xu, Thomas K. Haxton, Andrea J. Liu, and Sidney R. Nagel "Equivale..."

2011-01-26T10:25:25Z

Created page with "The '''Harmonic repulsion potential''' is given by (<ref>[http://dx.doi.org/10.1103/PhysRevLett.103.245701 Ning Xu, Thomas K. Haxton, Andrea J. Liu, and Sidney R. Nagel "Equivale..."

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The '''Harmonic repulsion potential''' is given by (<ref>[http://dx.doi.org/10.1103/PhysRevLett.103.245701 Ning Xu, Thomas K. Haxton, Andrea J. Liu, and Sidney R. Nagel "Equivalence of Glass Transition and Colloidal Glass Transition in the Hard-Sphere Limit", Physical Review Letters '''103''' 245701 (2009)]</ref> Eq. 2):

:<math>
\Phi_{12}\left( r \right) =
\left\{ \begin{array}{lll}
\frac{\epsilon}{2} (1-r/\sigma)^{2} & ; & r < \sigma \\
0 & ; & r \geq \sigma
\end{array} \right.
</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>\sigma</math> represents a length scale and <math>\epsilon</math> an energy.
==Phase diagram==
The [[Phase diagrams |phase diagram]] in the [[Phase diagrams: Pressure-temperature plane | pressure-temperature plane]] has been calculated by Zhu and Lu <ref>[http://dx.doi.org/10.1063/1.3548886 You-Liang Zhu and Zhong-Yuan Lu "Phase diagram of spherical particles interacted with harmonic repulsions", Journal of Chemical Physics '''134''' 044903 (2011)]</ref>.
==See also==
*[[Hertzian sphere model]]
==References==
<references/>
[[category: models]]