Development of an EOS based on lattice cluster theory for pure components

In many industrial applications, like tissue fabric production, osmotic separation, but also tissue engineering in medical laboratories, the knowledge of polymer behaviour is of vital importance. This behaviour is partially well known, but often the underlying mechanisms are not understood to a degree, which would make a prediction of polymer behaviour possible based on short and long chain branching, as well as general architecture. The Lattice Cluster Theory (LCT) of Freed and co-workers makes it possible to describe the influence of molecules’ architecture on the free energy of mixtures containing them. As possible functional groups (e.g. acidic groups) or permanent dipole or multi-pole moments are not accounted for by the LCT, this article will deal with linear and branched alkanes in order to test its applicability on the calculation of thermodynamic properties of these common compounds. To model the influence of pressure on phase behaviour, the LCT is transformed to a lattice gas equation of state. As is usual in lattice gas theories, the influence of free volume, and hence density will be modelled by the introduction of a non-interacting species of the size of one lattice site (hole). This approach yields the Lattice Cluster Theory Equation of State (LCT-EOS). The LCT-EOS pure component parameters are fit to the experimental data of several n-alkanes. Using only these parameters, fit to linear alkanes, the vapour pressure of a branched alkane is predicted accurately.

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► A new equation of state is developed based on lattice cluster theory.
► The equation can be used for various isomers with equal pure-component parameters.
► Vapour pressures of different alkane-isomers having 7 carbon atoms are calculated.
► The theoretical results show a very good agreement with experimental data.