March 2013
Intermediate to advanced
406 pages
14h 48m
English
Content preview from Perturbation Theories for the Thermodynamic Properties of Fluids and Solids
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356 Perturbation Theories for Fluids and Solids
z
Δz
δ
θ
σ
1
σ
2
FIGURE 10.6 Geometry involved in the derivation of Equation 10.41.
where σ
12
=
1
2
(σ
1
+ σ
2
) and ρ(σ
12
; θ) is the density of the solvent fluid at contact
distance between the large and small spheres. Equation 10.41 reduces to the Asakura–
Oosawa expression (10.37) if the solvent fluid is considered an ideal gas as shown
by Attard (1989b).
On the other hand, Equation 10.41 may be viewed as the local pressure ρ(r)k
B
T
integrated over the area of the exclusion sphere for a sphere of species 2 around a
sphere of species 1. Götzelmann et al. (1998) rewrite Equation 10.41 as
F
d
(
δ
)
=
1
2
πk
B
T
(
σ
1
+σ
2
)
2
π
π
/
2
ρ
(
σ
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