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

Modeling
polymers and their mixtures, surfactants and micellar systems, liquid crystals, liquid
immiscible mixtures, water and electrolytes, and fluids in which intramolecular bonding is
important.
It is important to notice that in order to obtain an equation that is simple to use, the
TPT-1 theory assumes some approximations that can limit the level of accuracy obtained
when the theory is applied. The first-order theory gives a good approximation for the
configurational properties of linear chains (Muller and Gubbins, 1993), even up to the
infinite-length limit. However, TPT-1 does not make a distinction with regard to bond
angles within a molecule. This means that the first-order theory implies conformality
between branched and linear isomers of the same number of segments. For instance, the
theory assumes that a n-alkane has the same reduced EoS as a neo-alkane (Pàmies, 2003).
One can overcome this situation by using the second-order or higher levels of the theory,
which accounts for the simultaneous bonding of more then two molecules. However, each
level of approximation requires the corresponding structural information for the fluid,
which, most of the times is not available (Muller and Gubbins, 1993).
Another important aspect is that for attractive flexible chains, the Wertheim
formalism does not take into account the intramolecular attraction, and therefore, the
predicted low-density limit is unrealistic (Johnson et al., 1994). No coil-up of the chains is
accounted for at low temperatures, and phase diagrams of these fluids are inaccurate; at
higher densities, intramolecular effects are effectively counterbalanced by intermolecular
interactions, and these considerations are less important. Applications to ring structures
also require particular modifications to the theory (Filipe et al., 1997). New approaches to
overcome this problem are being proposed as is the case of the PC-SAFT model from
Gross and Sadowski (Gross and Sadowski, 2001) who used a hard-chain reference with a
Barker-Henderson-type perturbation (Barker and Henderson, 1967a and 1967b) to account
for the attraction of these chains (as opposed to adding the perturbation on the segment
level).
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