New formulation of the lattice cluster theory equation of state for multi-component systems

The molecular structure or short chain branching of chemical compounds is known to have a strong impact on their thermodynamic behaviour. For example the vapour pressure of isomeric alkanes is increased with branching, but also the behaviour of more complex species and mixtures of them can be quite sensitive to molecular architecture. Usually, thermodynamic properties like equilibria or densities are modelled by the use of equations of state, of which the physically based ones, like the Statistical Associating Fluid Theory (SAFT) family have become popular in the past two decades due to their ability to accurately describe a rich variety of thermodynamic properties. However, these theories are not capable of including branching effects on an a priori basis. Recent advances in the application of lattice cluster theory have shown that this theory is capable of describing isomeric effects for pure alkane isomers, namely the rising vapour pressures with stronger branching. The description of these effects is extended here to multi-component systems, while retaining the simple functional form of a series expansion. Moreover, the original theory is simplified using some graph invariants, without loosing any thermodynamic information.