Sabine Enders

Calculation of surface properties of pure fluids using density gradient theory and SAFT-EOS

Abstract The Cahn–Hilliard theory was combined with three equations of state (EOS) (the Peng–Robinson (PR), the Sanchez–Lacombe (SL) lattice fluid model, and the original Statistical Associating Fluid Model) in order to describe both the phase behaviour and the surface properties of different types of molecules, namely nonpolar substances (n-alkanes and aromatic compounds), alcohols and water. Experimental surface tensions for nonpolar compounds could be correlated accurately and comparably by all EOS, adjusting one temperature-independent influence parameter. Despite the limitation in the critical region, the Statistical Association Fluid Theory (SAFT)-EOS successfully predicts the saturated liquid density and the degree of hydrogen bonding for methanol. The implementation of the SAFT-EOS into the Cahn–Hilliard framework leads to a useful possibility to calculate surface tensions which are in satisfactory agreement with experimental data, if the temperature-independent influence parameter was fitted to experimental surface tensions. The non-ideal behaviour of water is reflected in its phase behaviour and also in its surface tension. Some noticeable improvements of the association model 4C (four association sites) over the model 3B (three association sites) are found for the calculation of liquid–vapour equilibrium, the monomer concentration and the surface tension of water. Unfortunately, the SAFT-approach for associating compounds did not generally result in accurate calculations, especially near the critical region. Under comparable conditions the SAFT-EOS gives better surface tensions of water at low temperatures than the Associated-Perturbed-Anisotropic-Chain Theory (APACT)-EOS. At high temperatures, the opposite behaviour was observed.

Phase behaviour of hyperbranched polymers in demixed solvents

Hyperbranched polymers have attracted increased interest because of their tunable properties, which are affected by their architecture and a wide range of different functional groups. Many applications of hyperbranched polymers have been proposed based on their liquid–liquid phase behaviour. In recent years, the Lattice Cluster Theory (LCT) has been used to consider the impact of the architecture on the phase behaviour of hyperbranched polymers. In the theoretical framework of the LCT, the chain architecture is included in the Helmholtz energy, so all derived properties are influenced by polymer architecture. Until now, the application of the LCT in the field of hyperbranched polymers has been limited to ternary systems composed of one polymer with an arbitrary chain structure, one trimer and one solvent. This paper aims to extend the LCT to a ternary system that includes two polymers with an arbitrary chain structure and one solvent occupying one lattice site. In contrast to previous studies, the ternary system consists of Boltorn H20 + butan-1-ol + water, where all of the binary subsystems show demixing behaviour. Whereas experimental data are reported in the literature for the binary subsystems Boltorn H20 + water and butan-1-ol + water, no experimental information is available for the binary subsystem Boltorn H20 + butan-1-ol. Therefore, the phase behaviour of this subsystem was measured using the visual method. The paper discusses the possibility of predicting the ternary phase behaviour with the LCT in combination with the modified Wertheim theory based on knowledge of the phase behaviour of the corresponding binary subsystems. To verify the theoretical results, the ternary phase equilibria at constant temperature were also measured. In addition, the dependence of the thermodynamic properties on the special production lot of the commercially available Boltorn H20 is discussed.

Prediction of Interfacial Tensions between Demixed Ternary Mixtures

Abstract The interfacial tension between demixed liquids has a large impact on the mass transfer over the phase boundary. In this paper a special version of the density-gradient theory for ternary systems, where the grand thermodynamic potential is calculated using the Koningsveld–Kleintjens model, is suggested. This approach allows the prediction of the interfacial tensions of practical important ternary systems based on information of the binary subsystems. In order to verify this idea two ternary systems showing only one miscibility gap, namely water + butan-1-ol + ethanol and water + acetone + toluene, were selected. The predicted interfacial tensions were very close to the experimental data taken from the literature and to own experimental data obtained by spinning drop measurements. Both systems differ in the enrichment behavior. Whereas ethanol will be enriched in the interface to a small amount, the enrichment of acetone is much more pronounced.

Influence of different alcohols on the swelling behaviour of hydrogels

The swelling equilibrium of cross-linked poly(N-isopropylacrylamide) (PNIPAAm) hydrogels in alcohol solutions as a function of temperature, alcohol concentration, kind of alcohol (C1OH–C3OH) and gel properties was investigated experimentally. Additionally, the swelling degree as a function of the alcohol concentration was modelled with the UNIQUAC-Free Volume model in combination with the Phantom Network theory. The experiments show that, in pure water, the transition temperature is between 303.15 and 308.15 K depending on the properties of the gel and hence on the polymerization conditions. The transition from a swollen to a shrunken state is caused by the polymeric network and the change of polymer chain localization. In a system with hydrogel + water + alcohol, the swelling degree decreases with increasing alcohol concentration until the shrunken state is reached and increases again by further addition of alcohol at constant temperature. With increasing carbon number of the alcohols, the transition from a swollen to a shrunken state and vice versa shifts to lower concentrations at constant temperature. The use of the UNIQUAC-Free Volume model with Phantom Network theory leads to results in good agreement with the experimental data.

Prediction of Interfacial Tension of Binary Mixtures

Abstract The PCP-SAFT is applied in the density gradient theory for prediction of the surface tension of mixture containing a component having a dipole or a quadrupole moment. The surface tension of mixture can be predicted very close to experimental data taken from the literature.

Solubility calculations of branched and linear amino acids using lattice cluster theory

In this work, the activity coefficients and the solubility of amino acids in water were calculated using the lattice cluster theory (LCT) combined with the extended chemical association lattice model allowing self-association as well as cross-association. This permits the study of the influence of the amino acids structure on the thermodynamic properties for the first time. By the used model, the activity coefficient and solubilities of the investigated fourteen amino acids (glycine, alanine, γ-aminobutyric acid, dl-valine, dl-threonine, dl-methionine, l-leucine, l-glutamic acid, l-proline, hydroxyproline, histidine, l-arginine, α-amino valeric acid) could be described in good accordance with experimental data. In the case of different α-amino acids, but different hydrocarbon chains, the same interaction energy parameter can be used within the LCT. All studied amino acids could be modelled using the same parameter for the description of the amino acid association properties. The formed cross-associates contain more amino acids than expressed by the overall mole fraction of the solution. Moreover, the composition of the cross-associates depends on temperature, where the amount of amino acids increases with increasing temperature.

Solid–liquid equilibria of crystalline and semi-crystalline monodisperse polymers, taking into account the molecular architecture by application of the lattice cluster theory

In this work, an old theory for the melting of linear, semi-crystalline polymers, developed by Flory in 1949, is rediscovered and extended to branched polymers. The extension is realised by the incorporation of the lattice cluster theory, which is able to model polymers with an arbitrary architecture. The final working equation describing the melting of a branched semi-crystalline polymer can be solved for the melting temperature analytically. This new equation permits the theoretical investigation of different impact factors on the melting temperature in the case of branched semi-crystalline polymer, for instance the influence of molecular weight on the structural variables that describe the crystalline state. It could be shown that the extension leads to a better description of experimental data for the melting of high-density polyethylene taken from the literature than the original equation of linear semi-crystalline polymers. However, the comparison with experimental data makes it clear that the incorporation of polydispersity in the theoretical framework is needed.

Cross-association of multi-component systems

The design and optimization of equipment in chemical industry (e.g. heat exchanger) and also process simulations require the knowledge of physical properties of mixtures, for instance the involved phase equilibria, enthalpies and the heat capacities. Most experimental data on these properties exists for pure compounds (e.g. water) and for binary mixtures (e.g. water ethanol). The database is however, very limited for mixtures of more than two species. Physically sound equations of state, like the Perturbed-Chain Statistical Associating Theory (PC-SAFT) have been used successfully to provide information about these thermodynamic properties for a wide variety of substances including systems of associating and non-associating or systems of associating and cross-associating species. One of the main challenges using this Wertheim-type equation of state is the mathematically implicit form of the underlying nonlinear system of equations, if association occurs. This article provides in depth information about our recently developed fast and stable algorithm to solve this system of equations numerically for multi-component systems, as well as a new method to find good initial values for the numerical algorithm. Furthermore, the numerical results are compared to experimental data on several properties of interest and found to be in good to excellent agreement.

Theory of Random Copolymer Fractionation in Columns

Random copolymers show polydispersity both with respect to molecular weight and with respect to chemical composition, where the physical and chemical properties depend on both polydispersities. For special applications, the two-dimensional distribution function must adjusted to the application purpose. The adjustment can be achieved by polymer fractionation. From the thermodynamic point of view, the distribution function can be adjusted by the successive establishment of liquid–liquid equilibria (LLE) for suitable solutions of the polymer to be fractionated. The fractionation column is divided into theoretical stages. Assuming an LLE on each theoretical stage, the polymer fractionation can be modeled using phase equilibrium thermodynamics. As examples, simulations of stepwise fractionation in one direction, cross-fractionation in two directions, and two different column fractionations (Baker–Williams fractionation and continuous polymer fractionation) have been investigated. The simulation delivers the distribution according the molecular weight and chemical composition in every obtained fraction, depending on the operative properties, and is able to optimize the fractionation effectively.

Modelling of adsorption isotherms of isomers using density functional theory

ABSTRACT For the separation of components having very similar vapour pressures, adsorption may be a promising separation method leading to products with a high purity. Especially, the separation of alkanes having the same molecular mass, but differ in the molecule architecture is very challenging and very important in petroleum refining. The adsorption isotherms of pure components and binary mixtures are calculated with the density functional theory, in which the thermodynamic properties are expressed as functionals of the spatially varying density, in combination with an equation of state based on the lattice cluster theory (LCT-EOS), which is originally developed by Freed and co-workers. The LCT-EOS allows to take the branching of the molecules directly into account without any additional fitting parameter. This theoretical framework can be employed for the calculation of the density profiles of pure components and partial density profiles in the case of mixtures within the narrow pores. The integration of these profiles leads to the adsorption isotherm. The obtained adsorption isotherms show that adsorption can be a promising technology for the separation of isomers having very similar boiling point, however further optimisation is required.