n - PATh :.: Process and Product Applied Thermodynamics research ...

Modeling
The equation of state is written in terms of the Helmholtz free energy. The different
microscopic contributions that control the macroscopic properties of the fluid are explicitly
considered when building the theory. The residual Helmholtz free energy for an
n-component mixture of associating chain molecules can be expressed as a sum of three
terms: a reference term, A ref , including the repulsive and the attractive energies, a chain
Figure III.1a.Two-dimensional view of a
homonuclear nonassociating Lennard-Jones chain
with equal segment sizes and dispersive energies
(Blas and Vega, 1998a).
Figure III.1b.Two-dimensional view of the
homonuclear associating chain. The large circles
represent the Lennard-Jones cores and the small
circle is an associating site (Blas and Vega,
1998a)
Figure III.1c. Perturbation scheme for the formation of a molecule within the SAFT formalism. (a) An
initial system of reference particles is combined to form linear chains (b). To these chain molecules,
association sites are added, which allow them to bond among themselves (c), (Muller and Gubbins, 2001)
term, A chain , and a perturbation term, A assoc , which explicitly takes into account the
contribution due to the association,
A
res
= A − A
ideal
= A
ref
+ A
chain
( mρ,
T,
σ , ε ) + A ( ρ,
T,
x , σ , ε , m )
assoc
αi
β j αi
β j
( ρ,
T,
x , σ , ε , ε , k ) + ....
i
i
i
i
i
i
i
+
(III.3)
where ρ is the (chain) molecular density, T the absolute temperature, and xi the
composition of species i in the mixture. Molecular parameters are m, the number of
spherical segments forming a chain molecule, and the diameter σ and dispersive energy ε
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