The separation of isomers out of close boiling mixtures is a challenging task in chemical industry and can be required when it comes to production of fuel additives to manipulate the fuel’s octane number. A possible unit operation capable of separating isomers is given by adsorption. Eligible reduction of the effort for obtaining the needed adsorption isotherms can be provided by using a convenient theoretical approach to predict thermodynamic properties, based on less information as possible. For this purpose, we suggest the application of the Density-Functional-Theory (DFT) [1,2] together with the modified Lattice-Cluster-Theory (m-LCT), which is an extension of the originally version (LCT), developed by Freed and coworkers [3]. The combination of DFT with m-LCT allows the prediction of adsorption isotherms of isomers and their mixtures.
Regarding isomers, the LCT is capable to predict thermodynamic properties of isomers having the same carbon atom number, when it is adjusted just to experimental data, i.e. vapor pressures and liquid densities of one isomer. The LCT can formally be interpreted as double series expansion in lattice coordination number z and interaction energy ε, that has been carried out up to the order of z-2ε2 in the past [3], delivering satisfying predictions of physical properties of large molecules. Regarding the treatment of small molecules, the LCT had to be modified in a physical consistent and systematical way by extending the double series expansion to the order of z-3ε2 using statistical thermodynamics resulting in m-LCT. The impact of this improvement related to the predicted vapor-pressure of branched alkanes [4] as well as to the predicted adsorption isotherms [5] will be discussed.
Given a few points of an adsorption isotherm of a pure linear substance, we are able to predict adsorption isotherms of isomers and even isomer mixtures. We can furthermore study the impact of temperature change or porosity on adsorption isotherms. Therefore, we adjust external potential parameters to one experimental n-hexane adsorption isotherm from literature [6], calculate adsorption isotherms of its isomers using the same parameter set and compare predictions regarding temperature change and different isomers to further data from the same study [6]. While Bárcia et al. [6] adjusted 24 Langmuir parameters to describe the adsorption of four isomers at three different temperatures, the DFT+m-LCT framework only requires six parameters. However, three of those parameters are just related to bulk properties and can be obtained separately. We are also able to predict binary mixture adsorption and compare separation efficiencies of adsorption and distillation by plotting bulk phase compositions against confined phase composition in analogy to McCabe-Thiele diagrams.
Literature:
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[2] C. Lastoskie, K.E. Gubbins, N. Quuirke, J. Phys. Chem. 97 (1993) 4786.
[3] J. Dudowicz, K.F. Freed, W.G. Madden, Macromolecules 23 (1990) 4803.
[4] K. Langenbach, S. Enders, Fluid Phase Equilibria 331 (2012) 58.
[5] P. Zimmermann, T. Goetsch, T. Zeiner, S. Enders, Mol. Physics available online http://www.tandfonline.com/doi/full/10.1080/00268976.2017.1298861. [6] P.S. Bárcia, J.A.C. Silva, A.E. Rodrigues, Microporous Mesoporous Mat. 79 (2005) 145.
