Martynov Sarkisov: Difference between revisions
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Carl McBride (talk | contribs) m (New page: '''Martynov''' and '''Sarkisov''' proposed an expansion of the Bridge function in terms of basis functions: <math>B(\rho, T, r)= - \sum_{i=1}^\infty A_i (\rho,T) \phi^i (\rho, T, r)</math...) |
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an expansion of the Bridge function in terms of basis functions: | an expansion of the Bridge function in terms of basis functions: | ||
<math>B(\rho, T, r)= - \sum_{i=1}^\infty A_i (\rho,T) \phi^i (\rho, T, r)</math> | :<math>B(\rho, T, r)= - \sum_{i=1}^\infty A_i (\rho,T) \phi^i (\rho, T, r)</math> | ||
where <math>\phi</math> is the chosen basis function and <math>A_i</math> are the coefficients determined from | where <math>\phi</math> is the chosen basis function and <math>A_i</math> are the coefficients determined from | ||
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(1983 Eq.16 Ref. 1) closure in terms of the bridge function, for [[hard sphere]]s, is | (1983 Eq.16 Ref. 1) closure in terms of the bridge function, for [[hard sphere]]s, is | ||
<math>B[\omega(r)]= - A_2 \omega(r_{12})^2 = \sqrt{(1+2\gamma(r))}-\gamma(r) -1</math> | :<math>B[\omega(r)]= - A_2 \omega(r_{12})^2 = \sqrt{(1+2\gamma(r))}-\gamma(r) -1</math> | ||
where <math>\omega(r)</math> is the thermal potential and <math>A_2=1/2</math>. (This closure formed the basis for the | where <math>\omega(r)</math> is the thermal potential and <math>A_2=1/2</math>. (This closure formed the basis for the | ||
Revision as of 12:53, 23 February 2007
Martynov and Sarkisov proposed an expansion of the Bridge function in terms of basis functions:
where is the chosen basis function and are the coefficients determined from thermodynamic consistency conditions. The Martynov-Sarkisov closure is based on the expansion of the Bridge function in powers of the thermal potential.
(1983 Eq.16 Ref. 1) closure in terms of the bridge function, for hard spheres, is
![{\displaystyle B[\omega (r)]=-A_{2}\omega (r_{12})^{2}={\sqrt {(1+2\gamma (r))}}-\gamma (r)-1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/36cd24f0b254c56f94c7bb57e712e81f07721a2b)
where is the thermal potential and . (This closure formed the basis for the Ballone-Pastore-Galli-Gazillo closure for hard sphere mixtures). Charpentier and Jaske (Ref. 2) have observed that the value of differs drastically from 0.5 for temperatures greater than , thus the MS closure is deficient in the supercritical domain.
References
- [MP_1983_49_1495]
- [JCP_2001_114_02284]