Modified Lennard-Jones model: Difference between revisions
Carl McBride (talk | contribs) m (Typo confirmed.) |
Carl McBride (talk | contribs) (Added a recent publication (Virial coefficients)) |
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<math>C_3 = -68.069 \epsilon</math> <ref>Note: due to a typographical error in the original ms, in Table I <math>C_3</math> appears to be positive. </ref>. | <math>C_3 = -68.069 \epsilon</math> <ref>Note: due to a typographical error in the original ms, in Table I <math>C_3</math> appears to be positive. </ref>. | ||
<math>C_4 = −0.0833111261\epsilon</math> | <math>C_4 = −0.0833111261\epsilon</math> | ||
and <math>C_5 = 0.746882273 \epsilon</math>. | and <math>C_5 = 0.746882273 \epsilon</math>. | ||
==Virial coefficients== | |||
The [[Virial equation of state|virial coefficients]] up to the seventh order have been calculated for the range of temperatures <math>k_BT/\epsilon = 0.3-70</math> <ref>[http://dx.doi.org/10.1063/1.4882896 M. V. Ushcats "Modified Lennard-Jones model: Virial coefficients to the 7th order", Journal of Chemical Physics '''140''' 234309 (2014)]</ref>. | |||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: models]] | [[category: models]] | ||
Revision as of 12:42, 23 June 2014
The modified Lennard-Jones model is given by (Eq. 2 [1]):
- 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}(r) = \left\{ \begin{array}{ll} 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{12}- \left( \frac{\sigma}{r}\right)^6 \right] + C_1 & r \leq 2.3 \sigma \\ C_2 \left(\frac{\sigma}{r} \right)^{12} + C_3 \left(\frac{\sigma}{r} \right)^{6} + C_4 \left(\frac{r}{\sigma} \right)^{2} + C_5 & 2.3 \sigma < r < 2.5 \sigma\\ 0 & 2.5 \sigma \leq r \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 C_1 = 0.016132 \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 C_2 = 3136.6 \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 C_3 = -68.069 \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 C_4 = 0.083312 \epsilon} 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 C_5 = 0.74689\epsilon} . These parametrs are chosen so that the function 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}(r)} , as well as the first derivative, is continuous both 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 = 2.3\sigma} 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 r = 2.5\sigma} . These parameters have recently been recalculated with greater precision by Asano and Fuchizaki [2], leading to 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 C_1 = 0.0163169237\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 C_2 = 3136.5686 \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 C_3 = -68.069 \epsilon} [3]. 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 C_4 = −0.0833111261\epsilon} 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 C_5 = 0.746882273 \epsilon} .
Virial coefficients
The virial coefficients up to the seventh order have been calculated for the range of temperatures 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 k_BT/\epsilon = 0.3-70} [4].
References
- ↑ Jeremy Q. Broughton and George H. Gilmer "Molecular dynamics investigation of the crystal–fluid interface. I. Bulk properties", Journal of Chemical Physics 79 pp. 5095-5104 (1983)
- ↑ Yuta Asano and Kazuhiro Fuchizaki "Phase diagram of the modified Lennard-Jones system", Journal of Chemical Physics 137 174502 (2012)
- ↑ Note: due to a typographical error in the original ms, in Table I appears to be positive.
- ↑ M. V. Ushcats "Modified Lennard-Jones model: Virial coefficients to the 7th order", Journal of Chemical Physics 140 234309 (2014)
