# Zur Entwicklung von Zustandsgleichungen aus Gittermodellen

- Development of equations of state based on lattice models

Heggen, Roland; Lucas, Klaus (Thesis advisor)

*Aachen : Publikationsserver der RWTH Aachen University (2007)*

Dissertation / PhD Thesis

Aachen, Techn. Hochsch., Diss., 2006

Abstract

More and more areas of daily life depend primarily on material and energy conversions. Without electrical or chemically bound energy as well as technically converted materials, modern life today is no longer conceivable. Most materials and the most common energy sources are often not directly usable for today's needs in their naturally occurring form. They must be transformed to suit the desired application. Here, it is of great interest to work as effectively as possible, i.e. with little consumption of resources and energy. With a suitable design of chemical plants, natural resources can be preserved while simultaneously reaching higher economic efficiency. A very large and important part of material transformation takes place in the liquid and gaseous states. Here, phase equilibria play a decisive role. With the applied separation processes, such as extraction, rectification, absorption and crystallization, which are important in the chemical industry, differences of the various materials in the different phases are used for the separation of substances. In order to be able to realize these material transformations in technically relevant magnitude, it is necessary to know about the material systems used and to describe them. To avoid lengthy and expensive experiments for each mixture and each composition, it is of great importance to derive the mixture chracteristics from the characteristics of pure materials. A possibility to determine material properties exists in the use of equations of state. They establish functional connections between the thermodynamic variables of state. Thus, equations of state are used to describe the characteristics of fluids, fluid mixtures, and solids. With respect to thermodynamics it is usually distinguished between caloric and thermal equations of state. However, they are connected via general relations between the variables of state. The group of thermal equations of state takes a special role, since particularly for these models many variants were developed in the past. With this type of equation of state the variables of state p, v, T as well as the amount of material n are set in relationship to each other. The most common example for this might be the ideal gas law. Within this group it is again differentiated between the cubic equations of state with its most well-known representative the van der Waals equation as well as the non-cubic equations of state. For the latter the virial equation should be mentioned as the most prominent representative. Within this work an alternative of the non-cubic equations of state is considered. Thus, an equation of state for pure materials and mixtures, based on the lattice model for fluids, is derived. In the past lattice equations of state were introduced in literature, with the pretension to differ substantially from the already existing ones. Within this dissertation it is shown that these alleged differences dissolve after introducing uniform boundary conditions. The presented equations of state can consequently all be reduced to a unique form. A substantial characteristic, which interconnects all these equations, is the statistic independence of certain molecule characteristics, what leads to the so-called quasi-chemical approximation or, in the more general case, to the Free Segment Approximation. The introduced lattice equation of state can exist in different degrees of detail. In the simplest form it only models spherical model molecules with an isotropic surface. After introduction of extensions concerning molecule geometry as well as concerning the intermolecular reciprocal effects, it can also treat structured molecule types with different interacting surface segments. Within this context the designation multi-segment lattice equation of state was introduced. This multi-segment lattice equation of state is subsequently examined by computer-assisted adjustment calculations for simple model substances. For the execution of these optimization calculations it was necessary to develop appropriate program systems or adapt already existing ones, which permit the application to a lattice equation of state concerning the necessary equilibrium computations.

Institutions

- Chair and Institute of Technical Thermodynamics [412110]

### Identifier

- URN: urn:nbn:de:hbz:82-opus-18565
- RWTH PUBLICATIONS: RWTH-CONV-123381