Mean spherical approximation: Difference between revisions

Revision as of 15:17, 20 June 2007

The Lebowitz and Percus mean spherical approximation (MSA) (1966) (Ref. 1) closure is given by

c(r)=-\beta \omega (r),~~~~r>\sigma .

The Blum and Høye mean spherical approximation (MSA) (1978-1980) (Refs 2 and 3) closure is given by

{\rm {g}}_{ij}(r)\equiv h_{ij}(r)+1=0~~~~~~~~r<\sigma _{ij}=(\sigma _{i}+\sigma _{j})/2

and

c_{ij}(r)=\sum _{n=1}{\frac {K_{ij}^{(n)}}{r}}e^{-z_{n}r}~~~~~~\sigma _{ij}<r

where $h_{ij}(r)$ and $c_{ij}(r)$ are the total and the direct correlation functions for two spherical molecules of i and j species, $\sigma _{i}$ is the diameter of 'i species of molecule. Duh and Haymet (Eq. 9 Ref. 4) write the MSA approximation as

g(r)={\frac {c(r)+\beta \Phi _{2}(r)}{1-e^{\beta \Phi _{1}(r)}}}

where $\Phi _{1}$ and $\Phi _{2}$ comes from the Weeks-Chandler-Anderson division of the Lennard-Jones potential. By introducing the definition (Eq. 10 Ref. 4)

\left.s(r)\right.=h(r)-c(r)-\beta \Phi _{2}(r)

one can arrive at (Eq. 11 in Ref. 4)

B(r)\approx B^{\rm {MSA}}(s)=\ln(1+s)-s

The Percus Yevick approximation may be recovered from the above equation by setting $\Phi _{2}=0$ .

Thermodynamic consistency

See Ref. 5.

References

@@ Line 23: / Line 23: @@
-where <math>\Phi_1</math> and <math>\Phi_2</math> comes from the [[WCA division]] of the [[Lennard-Jones model | Lennard-Jones]] potential.
+where <math>\Phi_1</math> and <math>\Phi_2</math> comes from the
+[[Weeks-Chandler-Anderson perturbation theory | Weeks-Chandler-Anderson division]]
+of the [[Lennard-Jones model | Lennard-Jones]] potential.
 By introducing the definition  (Eq. 10 Ref. 4)

Mean spherical approximation: Difference between revisions

Revision as of 15:17, 20 June 2007

Thermodynamic consistency

References

Navigation menu

Search