Superposition of Liquid–Liquid and Solid–Liquid Equilibria of Linear and Branched Molecules: Ternary Systems

Abstract

Oiling-out is an unwanted phenomenon during crystallization processes since it influences the product properties negatively and should, therefore, be avoided. To reduce the time of process development, thermodynamic modeling is usually applied. In the course of fitting model parameters, thermodynamic data of the present molecules are required. In case of branched molecules these thermodynamic data are often not available. To overcome this limitation, a methodology, which allows for the prediction of liquid–liquid equilibria (LLE) of binary systems containing branched molecules was developed recently. The developed methodology was applied in this contribution in order to predict the superposition of ternary LLE and solid–liquid equilibria (SLE) of the system n-hexadecane + 2,2,4,4,6,8,8-heptamethyl­nonane + ethanol. To consider the influence of the molecular architecture on phase equilibria, the lattice cluster theory in combination with the chemical association lattice model was applied. The prediction of the ternary phase equilibria was based on the binary subsystems. It could be shown that the ternary LLE and the ternary SLE can be predicted in very good agreement with experimental data using the same set of model parameters. All model parameters were fitted using only binary LLE data of linear alkanes dissolved in ethanol. Neither binary experimental data of the branched alkane nor ternary ones were used for parameter fitting.

Liquid–Liquid Equilibrium and Interfacial Tension of Hexane Isomers–Methanol Systems

“…Since alcohols are highly polar components, which show self-association, LCT was combined with the chemical association lattice model (CALM) in order to account for the self-association of the alcohol. The predicted LLE of Goetsch et al , agreed very well with experimental data for binary systems containing a branched alkane dissolved in an alcohol as well as for the ternary systems composed of a linear alkane, a branched alkane, and an alcohol.…”

“…Hereby, z stands for the lattice coordination number, while ε/ k B T is the dimensionless interaction energy of nearest neighbor segments. The lattice coordination number was set to z = 6 according to former publications ,, and the interaction energy ε reads as where ε AA , ε BB , and ε AB are the interaction energies between two segments of type AA , BB , and AB , respectively. The LCT is written in terms of segment fractions, which can be calculated by eq . …”

“…The lattice cluster theory, originally derived by Freed and co-workers, − is a thermodynamic model considering the molecular architecture using architecture parameters, which are determined by the chemical structure. Goetsch et al , developed a methodology based on Lattice Cluster Theory (LCT) in order to predict binary and ternary LLE of systems containing branched molecules. They investigated different mixtures of alkanes and alcohols.…”

Adsorption Isotherms of Liquid Isomeric Mixtures

“…The lattice coordination number z was chosen to be 6 in accordance with earlier publications. , ε/ k B T is defined as …”

“…The lattice cluster theory (LCT) developed by Freed and co-workers − directly considers the molecular architecture within the Helmholtz free energy, where the molecular architecture is defined by architectural coefficients from the chemical formula. The LCT was successfully applied for the prediction of solid–liquid–liquid equilibria of mixtures made of linear alkanes, branched alkanes, and methanol or ethanol and the corresponding binary subsystems . Additionally, the phase behavior of mixtures containing hyperbranched polymers could be modeled successfully. − Upon introduction of empty lattice sites, also compressible mixtures can be described .…”