Harmonic repulsion potential: Difference between revisions
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==References== | ==References== | ||
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;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]] | ||
Latest revision as of 10:31, 25 September 2017
The Harmonic repulsion potential, designed for studies of polymer micelles, dendrimers, and colloidal particles, is given by ([1] Eq. 2):
- 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 \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. }
where 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 \Phi_{12}\left( r \right) } is the intermolecular pair potential, 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 := |\mathbf{r}_1 - \mathbf{r}_2|} is the distance between site 1 and site 2. 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} represents a length scale 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} an energy. For example, for 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=20} the potential looks like
Phase diagram[edit]
The phase diagram in the pressure-temperature plane has been calculated by Zhu and Lu [2].
See also[edit]
References[edit]
- ↑ 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)
- ↑ You-Liang Zhu and Zhong-Yuan Lu "Phase diagram of spherical particles interacted with harmonic repulsions", Journal of Chemical Physics 134 044903 (2011)
- Related reading