Gaussian overlap model
The Gaussian overlap model was developed by Bruce J. Berne and Philip Pechukas [1] and is given by Eq. 3 in the aforementioned reference:
![{\displaystyle \Phi _{12}(\mathbf {u} _{1},\mathbf {u} _{2},\mathbf {r} )=\epsilon (\mathbf {u} _{1},\mathbf {u} _{2})\exp \left[{\frac {-r}{\sigma (\mathbf {u} _{1},\mathbf {u} _{2},{\hat {\mathbf {r} }})}}\right]^{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/06dd600d91f1c00673ec1724076f3ff8697d992a)
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 n=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}(r)} 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 \epsilon(\mathbf{u}_1,\mathbf{u}_2) } 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 \sigma (\mathbf{u}_1,\mathbf{u}_2, \hat{\mathbf{r}})} are angle dependent strength and range parameters, and is a unit vector. Not long after the introduction of the Gaussian overlap model Stillinger [2] proposed a stripped-down version of the model, known as the Gaussian core model. 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 n=4} a Soft cluster crystal phase has been observed. For Note that as 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 n \rightarrow \infty} this potential becomes the penetrable sphere model.
Equation of state
Virial coefficients
Phase diagram
The phase diagram of the Gaussian-core model has been calculated by Prestipino et al.[5] while the solid-liquid phase equilibria has been calculated by Mausbach et al [6] using the GWTS algorithm.
Shear viscosity
Isotropic-nematic phase transition
[8].
References
- ↑ Bruce J. Berne and Philip Pechukas "Gaussian Model Potentials for Molecular Interactions" Journal of Chemical Physics 56 pp. 4213-4216 (1972)
- ↑ Frank H. Stillinger "Phase transitions in the Gaussian core system", Journal of Chemical Physics 65 pp. 3968-3974 (1976)
- ↑ Enrique de Miguel and Elvira Martín del Río "Equation of state for hard Gaussian overlap fluids", Journal of Chemical Physics 118 pp. 1852-1858 (2003)
- ↑ Ssu-Li Huang and Venkat R. Bhethanabotla "Virial coefficients for the hard Gaussian overlap model", International Journal of Modern Physics C 10 pp. 361-374 (1999)
- ↑ Santi Prestipino, Franz Saija, and Paolo V. Giaquinta "Phase diagram of the Gaussian-core model", Physical Review E 71 050102 (2005)
- ↑ Peter Mausbach, Alauddin Ahmed, and Richard J. Sadus "Solid-liquid phase equilibria of the Gaussian core model fluid", Journal of Chemical Physics 131 184507 (2009)
- ↑ Alauddin Ahmed, Peter Mausbach, and Richard J. Sadus "Strain-rate dependent shear viscosity of the Gaussian core model fluid", Journal of Chemical Physics 131 224511 (2009)
- ↑ G. Rickayzen and D. M. Heyes "Isotropic-nematic phase transition of uniaxial variable softness prolate and oblate ellipsoids", Journal of Chemical Physics 146, 164505 (2017)
Related reading
- P. A. Monson and K. E. Gubbins "Equilibrium properties of the Gaussian overlap fluid. Monte Carlo simulation and thermodynamic perturbation theory" Journal of Physical Chemistry 87 pp. 2852-2858 (1983)
- Tomas Boublik "The gaussian overlap model again", Molecular Physics 67 pp. 1327-1336 (1989)
- Lindsey Ann Shall and S. A. Egorov "Structural and dynamical anomalies of a Gaussian core fluid: A mode-coupling theory study", Journal of Chemical Physics 132 184504 (2010)
- Peter Mausbach and Richard J. Sadus "Thermodynamic properties in the molecular dynamics ensemble applied to the Gaussian core model fluid", Journal of Chemical Physics 134 114515 (2011)
- Atsushi Ikeda and Kunimasa Miyazaki "Thermodynamic and structural properties of the high density Gaussian core model", Journal of Chemical Physics 135 024901 (2011)
- Atsushi Ikeda and Kunimasa Miyazaki "Slow dynamics of the high density Gaussian core model", Journal of Chemical Physics 135 054901 (2011)
- Manoj Kumar Nandi and Sarika Maitra Bhattacharyya "Analysis of the anomalous mean-field like properties of Gaussian core model in terms of entropy", Journal of Chemical Physics 148 034504 (2018)