Gaussian overlap model: Difference between revisions
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The '''Gaussian overlap model''' was developed by Bruce J. Berne and Philip Pechukas <ref>[http://dx.doi.org/10.1063/1.1677837 | The '''Gaussian overlap model''' was developed by Bruce J. Berne and Philip Pechukas <ref>[http://dx.doi.org/10.1063/1.1677837 Bruce J. Berne and Philip Pechukas "Gaussian Model Potentials for Molecular Interactions" Journal of Chemical Physics '''56''' pp. 4213-4216 (1972)]</ref> and is given by Eq. 3 in the aforementioned reference: | ||
:<math>\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</math> | :<math>\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</math> | ||
where <math>n=2</math>, <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math> \epsilon(\mathbf{u}_1,\mathbf{u}_2) </math> and <math>\sigma (\mathbf{u}_1,\mathbf{u}_2, \hat{\mathbf{r}})</math> are angle dependent strength and range parameters, and <math>\hat{\mathbf{r}}</math> is a unit vector. Not long after the introduction of the Gaussian overlap model Stillinger <ref>[http://dx.doi.org/10.1063/1.432891 Frank H. Stillinger "Phase transitions in the Gaussian core system", Journal of Chemical Physics '''65''' pp. 3968-3974 (1976)]</ref> proposed a stripped-down version of the model, known as the '''Gaussian core model'''. Note that as <math>n \rightarrow \infty</math> | where <math>n=2</math>, <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math> \epsilon(\mathbf{u}_1,\mathbf{u}_2) </math> and <math>\sigma (\mathbf{u}_1,\mathbf{u}_2, \hat{\mathbf{r}})</math> are angle dependent strength and range parameters, and <math>\hat{\mathbf{r}}</math> is a unit vector. Not long after the introduction of the Gaussian overlap model Stillinger <ref>[http://dx.doi.org/10.1063/1.432891 Frank H. Stillinger "Phase transitions in the Gaussian core system", Journal of Chemical Physics '''65''' pp. 3968-3974 (1976)]</ref> proposed a stripped-down version of the model, known as the '''Gaussian core model'''. For <math>n=4</math> a [[Soft cluster crystal phase]] has been observed. For Note that as <math>n \rightarrow \infty</math> | ||
this potential becomes the [[penetrable sphere model]]. | this potential becomes the [[penetrable sphere model]]. | ||
==Equation of state== | ==Equation of state== | ||
: | <ref>[http://dx.doi.org/10.1063/1.1531611 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)]</ref> | ||
==Virial coefficients== | ==Virial coefficients== | ||
: | <ref>[http://dx.doi.org/10.1142/S0129183199000279 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)]</ref> | ||
==Phase diagram== | ==Phase diagram== | ||
The phase diagram of the Gaussian-core model has been calculated by Prestipino et al.<ref>[http://dx.doi.org/10.1103/PhysRevE.71.050102 Santi Prestipino, Franz Saija, and Paolo V. Giaquinta "Phase diagram of the Gaussian-core model", Physical Review E '''71''' 050102 (2005)]</ref> while the solid-liquid phase equilibria has been calculated by Mausbach et al <ref>[http://dx.doi.org/10.1063/1.3256004 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)]</ref> using the [[GWTS algorithm]]. | The phase diagram of the Gaussian-core model has been calculated by Prestipino et al.<ref>[http://dx.doi.org/10.1103/PhysRevE.71.050102 Santi Prestipino, Franz Saija, and Paolo V. Giaquinta "Phase diagram of the Gaussian-core model", Physical Review E '''71''' 050102 (2005)]</ref> while the solid-liquid phase equilibria has been calculated by Mausbach et al <ref>[http://dx.doi.org/10.1063/1.3256004 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)]</ref> using the [[GWTS algorithm]]. | ||
==Shear viscosity== | ==Shear viscosity== | ||
<ref>[http://dx.doi.org/10.1063/1.3273083 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)]</ref> | <ref>[http://dx.doi.org/10.1063/1.3273083 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)]</ref> | ||
==Isotropic-nematic phase transition== | |||
<ref>[http://dx.doi.org/10.1063/1.4981887 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)]</ref>. | |||
==References== | ==References== | ||
<references/> | <references/> | ||
| Line 18: | Line 20: | ||
*[http://dx.doi.org/10.1021/j100238a030 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)] | *[http://dx.doi.org/10.1021/j100238a030 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)] | ||
*[http://dx.doi.org/10.1080/00268978900101841 Tomas Boublik "The gaussian overlap model again", Molecular Physics '''67''' pp. 1327-1336 (1989)] | *[http://dx.doi.org/10.1080/00268978900101841 Tomas Boublik "The gaussian overlap model again", Molecular Physics '''67''' pp. 1327-1336 (1989)] | ||
*[http://dx.doi.org/10.1063/1.3429354 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)] | |||
*[http://dx.doi.org/10.1063/1.3559678 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)] | |||
*[http://dx.doi.org/10.1063/1.3609277 Atsushi Ikeda and Kunimasa Miyazaki "Thermodynamic and structural properties of the high density Gaussian core model", Journal of Chemical Physics '''135''' 024901 (2011)] | |||
*[http://dx.doi.org/10.1063/1.3615949 Atsushi Ikeda and Kunimasa Miyazaki "Slow dynamics of the high density Gaussian core model", Journal of Chemical Physics '''135''' 054901 (2011)] | |||
*[https://doi.org/10.1063/1.5013644 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)] | |||
[[Category: Models]] | [[Category: Models]] | ||
[[Category: liquid crystals]] | |||
Latest revision as of 12:23, 30 January 2018
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 , is the intermolecular pair potential, and 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 a Soft cluster crystal phase has been observed. For Note that as this potential becomes the penetrable sphere model.
Equation of state[edit]
Virial coefficients[edit]
Phase diagram[edit]
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[edit]
Isotropic-nematic phase transition[edit]
[8].
References[edit]
- ↑ 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)