Exact solution of the Percus Yevick integral equation for hard spheres: Difference between revisions
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The exact solution for the [[Percus Yevick]] integral equation for hard spheres | The exact solution for the [[Percus Yevick]] integral equation for [[hard spheres]] | ||
was derived by M. S. Wertheim in 1963 | was derived by M. S. Wertheim in 1963 Ref. 1 (See also Ref. 2) | ||
(and for mixtures by in Lebowitz 1964 | (and for mixtures by in Lebowitz 1964 Ref. 3). | ||
The direct correlation function is given by ( | The direct correlation function is given by (Ref. 1 Eq. 6) | ||
:<math>C(r/R) = - \frac{(1+2\eta)^2 - 6\eta(1+ \frac{1}{2} \eta)^2(r/R) + \eta(1+2\eta)^2\frac{(r/R)^3}{2}}{(1-\eta)^4}</math> | :<math>C(r/R) = - \frac{(1+2\eta)^2 - 6\eta(1+ \frac{1}{2} \eta)^2(r/R) + \eta(1+2\eta)^2\frac{(r/R)^3}{2}}{(1-\eta)^4}</math> | ||
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==References== | ==References== | ||
#[PRL_1963_10_000321] | |||
#[JMP_1964_05_00643] | |||
#[PR_1964_133_00A895] |
Revision as of 13:24, 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 (\cite{PRL_1963_10_000321} Eq. 7)
Everett Thiele (1963 \cite{JCP_1963_39_00474}) 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]