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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138 Perturbation Theories for Fluids and Solids
g
0
r
i
+r
2
=
3
N
i
0
2πNρ
r
3
i+1
−r
3
i
, (6.33)
g
1
r
i
+r
2
=−
3
j
N
i
N
j
0
−
N
i
0
N
j
0
u
∗
1
r
j
2πNρ
r
3
i+1
−r
3
i
. (6.34)
For the particular case of the SW potential, u
∗
i
(r) =−1 within the well 0 < x ≤ λ,
where x = r/σ, and the expressions for the terms F
n
simplify to (Alder et al. 1972)
F
1
Nk
B
T
=−
M
0
N
, (6.35)
F
2
Nk
B
T
=−
1
2
1
N
(
M −
M
0
)
2
0
, (6.36)
F
3
Nk
B
T
=−
1
6
1
N
(
M −
M
0
)
3
0
, (6.37)
F
4
Nk
B
T
=−
1
24
1
N
(
M −
M
0
)
4
0
−3
(
M −
M
0
)
2
2
0
, (6.38)
and so on, where M is the number of pairs separated a distance x ≤ λ of each
other. Expressions (6.29) through (6.38) can be evaluated from computer simu-
lation in the reference HS system. Such
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