Editing Stockmayer potential
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where: | where: | ||
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> | * <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> | ||
* <math> \Phi(r) </math> is the [[intermolecular pair potential]] between two particles at a distance | * <math> \Phi(r) </math> is the [[intermolecular pair potential]] between two particles at a distance r; | ||
* <math> \sigma </math> is the diameter (length), i.e. the value of <math>r</math> at <math> \Phi(r)=0</math> | * <math> \sigma </math> is the diameter (length), i.e. the value of <math>r</math> at <math> \Phi(r)=0</math> ; | ||
* <math> \epsilon </math> | * <math> \epsilon </math> : well depth (energy) | ||
* <math> \epsilon_0 </math> is the permittivity of the vacuum | * <math> \epsilon_0 </math> is the permittivity of the vacuum | ||
* <math>\mu</math> is the dipole moment | * <math>\mu</math> is the dipole moment | ||
* <math>\theta_1 | * <math>\theta_1,\theta_2 </math> is the inclination of the two dipole axes with respect to the intermolecular axis. | ||
* <math>\phi</math> is the azimuth angle between the two dipole moments | * <math>\phi</math> is the azimuth angle between the two dipole moments | ||
If one defines a reduced dipole moment, <math>\mu^*</math>, such that: | If one defines a reduced dipole moment, <math>\mu^*</math>, such that: | ||
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For this reason the potential is sometimes known as the Stockmayer 12-6-3 potential. | For this reason the potential is sometimes known as the Stockmayer 12-6-3 potential. | ||
==Critical properties== | ==Critical properties== | ||
In the range <math>0 \leq \mu^* \leq 2.45</math> <ref>[http://dx.doi.org/10.1080/00268979400100294 M.E. Van | In the range <math>0 \leq \mu^* \leq 2.45</math> <ref>[http://dx.doi.org/10.1080/00268979400100294 M. E. Van Leeuwe "Deviation from corresponding-states behaviour for polar fluids", Molecular Physics '''82''' pp. 383-392 (1994)]</ref>: | ||
:<math>T_c^* = 1.313 + 0.2999\mu^{*2} -0.2837 \ln(\mu^{*2} +1)</math> | :<math>T_c^* = 1.313 + 0.2999\mu^{*2} -0.2837 \ln(\mu^{*2} +1)</math> | ||
:<math>\rho_c^* = 0.3009 - 0.00785\mu^{*2} - 0.00198\mu^{*4}</math> | :<math>\rho_c^* = 0.3009 - 0.00785\mu^{*2} - 0.00198\mu^{*4}</math> | ||
:<math>P_c^* = 0.127 + 0.0023\mu^{*2}</math> | :<math>P_c^* = 0.127 + 0.0023\mu^{*2}</math> | ||
==References== | ==References== | ||
<references/> | <references/> | ||
'''Related reading''' | '''Related reading''' | ||
*[http://dx.doi.org/10.1016/0378-3812(94)80018-9 M. E. van Leeuwen "Derivation of Stockmayer potential parameters for polar fluids", Fluid Phase Equilibria '''99''' pp. 1-18 (1994)] | *[http://dx.doi.org/10.1016/0378-3812(94)80018-9 M. E. van Leeuwen "Derivation of Stockmayer potential parameters for polar fluids", Fluid Phase Equilibria '''99''' pp. 1-18 (1994)] | ||
*[http://dx.doi.org/10.1103/PhysRevE.75.011506 Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E '''75''' 011506 (2007)] | *[http://dx.doi.org/10.1103/PhysRevE.75.011506 Reinhard Hentschke, Jörg Bartke, and Florian Pesth "Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid", Physical Review E '''75''' 011506 (2007)] | ||
{{numeric}} | {{numeric}} | ||
[[category: models]] | [[category: models]] |