Exact solution of the Percus Yevick integral equation for hard spheres: Difference between revisions
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and ''R'' is the hard sphere diameter. | and ''R'' is the hard sphere diameter. | ||
The equation of state is (Ref. | The equation of state is (Ref. 1 Eq. 7) | ||
:<math>\beta P \rho = \frac{(1+\eta+\eta^2)}{(1-\eta)^3}</math> | :<math>\beta P \rho = \frac{(1+\eta+\eta^2)}{(1-\eta)^3}</math> | ||
Everett Thiele (1963 | Everett Thiele (1963 Ref. 4}) also studied this system, | ||
resulting in (Eq. 23) | resulting in (Eq. 23) | ||
Line 45: | Line 45: | ||
#[JMP_1964_05_00643] | #[JMP_1964_05_00643] | ||
#[PR_1964_133_00A895] | #[PR_1964_133_00A895] | ||
#[JCP_1963_39_00474] |
Revision as of 13:26, 23 February 2007
The exact solution for the Percus Yevick integral equation for hard spheres 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 R 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
- [PRL_1963_10_000321]
- [JMP_1964_05_00643]
- [PR_1964_133_00A895]
- [JCP_1963_39_00474]