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265183 Prediction of Thermodynamic Properties for Structural Isomers by Use of the Lattice Cluster Theory Equation of State for Pure Compounds

__K. Langenbach__ and S. Enders

E-mail : Kai.Langenbach@tu-berlin.de

**Key words:** equation of state, lattice cluster
theory, pure components, physical properties prediction

During the last years there have been great advances in the calculation of phase diagrams with physically based equations of state (e.g. PC-SAFT[1]). In their development the occurring energetic effects caused by interactions between different or similar functional groups where in the main focus. The application of these equations of state for isomers require pure-component parameters for every isomer, which are sometimes very hard to obtain, because only limiting amount of experimental data are available. However, for complex molecules, like polymers or biomolecules, the architecture has a large impact on the thermodynamic properties and the involved phase behavior.

On the other hand Freed and co-workers developed the Lattice Cluster Theory[2], which allows the description of a molecule's architecture directly in the thermodynamic potentials. This is possible, using a cluster expansion of the partition function that incorporates a molecule's structure through a set of combinatorial numbers describing its united-atom architecture. This theory admitted the description of several architecture dependent phase equilibria (e.g. demixing equilibria of hyper-branched polymers in pure and mixed solvents[3]). In this application; however, the lattice is introduced incompressible. Following a proposal by Freed et al.[4], the lattice can be made compressible by the introduction of void lattice sites, thereby allowing the derivation of an equation of state. This course of action allows the development of an equation of state (LCT-EOS) with two adjustable parameters for a pure substance, i.e. the size of a lattice site and the interaction energy between two non-void sites. It can be shown that the LCT-EOS is capable of calculating small differences between the vapor pressures of isomers (e.g. n-heptane and 2,3-dimethyl pentane) with the same set of pure-component parameters.

This contribution
deals with the presentation of the new LCT-EOS, with the calculation of the
architectural coefficients for arbitrary structures from graph theory and with possible
parameterizations of the theory. Furthermore, the calculated vapor pressures, the
saturation densities and heats of vaporization for several alkanes, differing
in chain length and in isomerism, are discussed and compared with experimental
data from literature.

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