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 15:42, 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

  1. M. S. Wertheim "Exact Solution of the Percus-Yevick Integral Equation for Hard Spheres", Physical Review Letters 10 321 - 323 (1963)
  2. M. S. Wertheim "Analytic Solution of the Percus-Yevick Equation", Journal of Mathematical Physics, 5 pp. 643-651 (1964)
  3. J. L. Lebowitz, "Exact Solution of Generalized Percus-Yevick Equation for a Mixture of Hard Spheres", Physical Review 133 pp. A895 - A899 (1964)
  4. Everett Thiele "Equation of State for Hard Spheres", Journal of Chemical Physics, 39 pp. 474-479 (1963)