Editing Martynov Sarkisov
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'''Martynov''' and '''Sarkisov''' proposed | '''Martynov''' and '''Sarkisov''' proposed | ||
an expansion of the | 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> | ||
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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 | ||
[[thermodynamic consistency]] conditions. | [[thermodynamic consistency]] conditions. | ||
The Martynov-Sarkisov | The Martynov-Sarkisov closure is based on | ||
the expansion of the | 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 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 | ||
[[Ballone-Pastore-Galli- | [[Ballone-Pastore-Galli-Gazillo]] closure for hard sphere mixtures). | ||
Charpentier and Jaske | Charpentier and Jaske (Ref. 2) have | ||
observed that the value of <math>A_2</math> differs drastically from 0.5 for temperatures | observed that the value of <math>A_2</math> differs drastically from 0.5 for temperatures | ||
greater than <math>T^*\approx 2.74</math>, thus the Martynov-Sarkisov closure is deficient in the supercritical domain. | greater than <math>T^*\approx 2.74</math>, thus the Martynov-Sarkisov closure is deficient in the supercritical domain. | ||
==References== | ==References== | ||
#[http://dx.doi.org/10.1080/00268978300102111 G. A. Martynov; G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics '''49''' 1495-1504 (1983)] | |||
#[http://dx.doi.org/10.1063/1.1332808 I. Charpentier and N. Jakse "Exact numerical derivatives of the pair-correlation function of simple liquids using the tangent linear method", Journal of Chemical Physics '''114''' pp. 2284-2292 (2001)] | |||
doi:10.1063/1.1332808 | |||
#[JCP_2001_114_02284] | |||
#[JCP_1993_99_03926] | |||
#[JCP_1999_110_03961] | |||
[[ | #[JCP_2001_114_09496] | ||