Mean spherical approximation

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

c (r) = - β ω (r), r > σ .

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

g_{i j} (r) \equiv h_{i j} (r) + 1 = 0 r < σ_{i j} = (σ_{i} + σ_{j}) / 2

and

c_{i j} (r) = \sum_{n = 1} \frac{K_{i j}^{(n)}}{r} e^{- z_{n} r} σ_{i j} < r

where $h_{i j} (r)$ and $c_{i j} (r)$ are the total and the direct correlation functions for two spherical molecules of i and j species, $σ_{i}$ 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) + β Φ_{2} (r)}{1 - e^{β Φ_{1} (r)}}

where $Φ_{1}$ and $Φ_{2}$ comes from the WCA division of the Lennard-Jones potential. By introducing the definition (Eq. 10 Ref. 4)

s (r) = h (r) - c (r) - β Φ_{2} (r)

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

B (r) \approx B^{M S A} (s) = \ln (1 + s) - s

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

References

Mean spherical approximation

References

Navigation menu

Search