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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230 Perturbation Theories for Fluids and Solids
where z is the coordination number of the lattice, so that the FH insertion probability
is (Dickman and Hall 1986)
p
(
φ
)
=
(
1 −φ
)(
1 −φ
0
)
n−1
=
(
1 −φ
)
n
1 −
2φ
z
1 −
1
n
1−n
. (8.61)
Introducing this probability into Equation 8.57 yields
Z =
n
φ
z
2
ln
1 −
2φ
z
1 −
1
n
−ln
(
1 −φ
)
. (8.62)
8.4.2 EXTENSION OF THE FLORY AND FLORY–HUGGINS THEORIES TO
CONTINUOUS SPACE
The Flory and FH theories were extended by Dickman and Hall (1986) to
continuous-space fluids. In this case, the osmotic EOS (Equation 8.57) takes the
form
Z = 1 − ln p
(
η
)
+
1
η
η
0
ln p
η
dη
, (8.63)
where
η = ρ
n
v
n
is the packing fraction of the chains with number density ...
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