Exact solution of the Percus Yevick integral equation for hard spheres: Difference between revisions
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The equation of state is (Ref. 1 Eq. 7) | The equation of state is (Ref. 1 Eq. 7) | ||
:<math>\beta P \rho = \frac{(1+\eta+\eta^2)}{(1-\eta)^3}</math> | :<math>\frac{\beta P}{\rho} = \frac{(1+\eta+\eta^2)}{(1-\eta)^3}</math> | ||
Everett Thiele (1963 Ref. 4}) also studied this system, | Everett Thiele (1963 Ref. 4}) also studied this system, |
Revision as of 16:42, 4 April 2011
The exact solution for the Percus Yevick integral equation for the hard sphere model was derived by M. S. Wertheim in 1963 Ref. 1 (See also Ref. 2) (and for mixtures by in Lebowitz 1964 Ref. 3). The direct correlation function is given by (Ref. 1 Eq. 6)
where
and is the hard sphere diameter. The equation of state is (Ref. 1 Eq. 7)
Everett Thiele (1963 Ref. 4}) also studied this system, resulting in (Eq. 23)
where (Eq. 24)
and
and
and where .
The pressure via the pressure route (Eq.s 32 and 33) is
and the compressibility route is
References
- M. S. Wertheim "Exact Solution of the Percus-Yevick Integral Equation for Hard Spheres", Physical Review Letters 10 321 - 323 (1963)
- M. S. Wertheim "Analytic Solution of the Percus-Yevick Equation", Journal of Mathematical Physics, 5 pp. 643-651 (1964)
- J. L. Lebowitz, "Exact Solution of Generalized Percus-Yevick Equation for a Mixture of Hard Spheres", Physical Review 133 pp. A895 - A899 (1964)
- Everett Thiele "Equation of State for Hard Spheres", Journal of Chemical Physics, 39 pp. 474-479 (1963)