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Abstract
This work details the implementation of classical density functional theory (DFT) for the study of inhomogeneous fluids. Classical DFT is coupled with the perturbedchain statistical association fluid theory (PCSAFT) equation of state to describe the behavior and structure of fluids close to interfaces and fluids confined in pores.
The first part of this thesis is aimed to introduce some details, characteristics and relevance of inhomogeneous fluids. Chapter 2 gives a succinct description of statistical mechanics concepts that lay the foundation on which molecular simulations, classical DFT and thermodynamic models are based upon. The classical DFT formalism is introduced in Chapter 3, where it will be shown that the key concepts that define an inhomogeneous system under the classical DFT framework are the grand potential functional, the Helmholtz free energy functional, and the external potential. Out of these, the attention is focused on the Helmholtz free energy functional, which contains the whole information of the particles that conform the inhomogeneous fluid. The real form of the Helmholtz free energy functional is not known, however, it can be approximated with the Helmholtz free energy of a thermodynamic model, which in this work it is done with the PCSAFT equation of state. PCSAFT uses thermodynamic perturbation theory to describe the properties of fluids, which defines the hard chain fluid as the reference state, followed by perturbations due to dispersive interactions and association between particles. Each of the functionals corresponding to the reference state and perturbations used in this work are also described. In particular, the hard sphere term is treated with fundamental measure theory, which is the most used functional used for repulsive interactions. Dispersive interactions are described with the weighted density approximation and the dispersion term of PCSAFT used for bulk fluids. Moreover, for associating interactions a thorough analysis is carried out for three functionals all based on Wertheim’s thermodynamic perturbation theory, one of which is developed in this work. Finally, chain formation contributions to Helmholtz free energy functional uses a special case of the association functional in the limit of complete association. In this work the chain formation functional from interfacial statistical association fluid theory (iSAFT) is implemented.
Chapter 4 is dedicated to the determination of interfacial tension of the vaporliquid interface with classical DFT and the PCSAFT equation of state. In the first part of this chapter different forms of the dispersion functional based on PCSAFT are used for the determination of the interfacial tension of nonassociating fluids, such as hydrocarbons and other inorganic and organic substances. Additionally, classical DFT is used to predict the interfacial tension of mixtures of several compounds finding excellent agreement with experimental data. In the second part of this chapter, associating contributions are taken into account for the calculation of the interfacial tension of substances that are able to form hydrogen bonds, such as alkanols, acetic acid and water. Three functionals are used to describe the properties of the vaporliquid interface of associating fluids, where it is found that classical DFT with PCSAFT show deviations in the calculation of the interfacial tension of alkanols and other associating compounds. Therefore, new pure molecular parameters for PCSAFT are proposed by including the interfacial tension during the fitting procedure. The new parameters are assessed by comparing their performance in the correlation of vapor pressure, liquid density and interfacial tension for each of the association functionals. It is found that while deviations of the interfacial tension can be considerably decreased for the lighter alkanols, heavier alkanols show a large increase in the deviation of vapor pressures. The results obtained with the three association functionals are fairly similar, and it is still inconclusive if the large deviations found for the heavier alkanols are due to the formulation of the association term, or the other terms.
The study of fluids confined in porous media is done in Chapter 5. The calculation of gas adsorption with classical DFT is carried out for systems at supercritical conditions, which means that the fluids do not show capillary condensation or evaporation. In these calculations, a model of a single slitlike pore is used, where the shape of a single pore is formed by two planar walls separated with a distance characteristic of the pore size. Additionally, a solidfluid potential is used to take into account the interactions between the particles in the solid and the fluid particles. Therefore, to fully characterize a confined system, the slitlike pore model requires three parameters: the specific area of the solid, the value of the energy interaction parameters between solid and fluid and the average size of the single pore. These parameters are fitted to experimental data of excess adsorption, finding excellent greement. The parameters are then used to predict adsorption of mixtures, where slight deviations are found when compared to experimental data.
The main challenge in the study of adsorption is that the description of the solid is a difficult task as both the chemistry and geometry must be determined simultaneously. This means that the modelling procedure requires a recursive methodology as one of those properties is usually infer from the other. Even though good agreement is found with the singe slitlike pore model, porous media cannot be fully characterized with a single pore size. Therefore, a pore size distribution (PSD) model is followed to improve the characterization of porous materials. The PSD can be obtained experimeniv tally, however, to use this information in the prediction of the adsorption of different fluids the solidfluid interactions must be known. In this work, the PSD of activated carbons is determined with methane adsorption at supercritical conditions. For this system, it is assumed that the solidfluid interaction can be approximated with the geometric mean of the energy parameters of the methane molecule and the carbon atom. The determination of the PSD is carried out successfully using regularized regression methods, where the resulting PSD is in agreement with published data and the adsorption isotherms have an excellent agreement with experimental results. Additionally, a more complex description of the chemistry of solids is taken into account by inserting association sites on the wall surface. In this way, classical DFT can be used to study adsorption of associating fluids on activated surfaces, which have a great impact on the behavior of confined fluids.
Finally, in Chapter 6 some of the conclusions found in this thesis are presented, together with a clear road of how this implementation of classical DFT with PCSAFT could be extended to improve our understanding of inhomogeneous fluids.
The first part of this thesis is aimed to introduce some details, characteristics and relevance of inhomogeneous fluids. Chapter 2 gives a succinct description of statistical mechanics concepts that lay the foundation on which molecular simulations, classical DFT and thermodynamic models are based upon. The classical DFT formalism is introduced in Chapter 3, where it will be shown that the key concepts that define an inhomogeneous system under the classical DFT framework are the grand potential functional, the Helmholtz free energy functional, and the external potential. Out of these, the attention is focused on the Helmholtz free energy functional, which contains the whole information of the particles that conform the inhomogeneous fluid. The real form of the Helmholtz free energy functional is not known, however, it can be approximated with the Helmholtz free energy of a thermodynamic model, which in this work it is done with the PCSAFT equation of state. PCSAFT uses thermodynamic perturbation theory to describe the properties of fluids, which defines the hard chain fluid as the reference state, followed by perturbations due to dispersive interactions and association between particles. Each of the functionals corresponding to the reference state and perturbations used in this work are also described. In particular, the hard sphere term is treated with fundamental measure theory, which is the most used functional used for repulsive interactions. Dispersive interactions are described with the weighted density approximation and the dispersion term of PCSAFT used for bulk fluids. Moreover, for associating interactions a thorough analysis is carried out for three functionals all based on Wertheim’s thermodynamic perturbation theory, one of which is developed in this work. Finally, chain formation contributions to Helmholtz free energy functional uses a special case of the association functional in the limit of complete association. In this work the chain formation functional from interfacial statistical association fluid theory (iSAFT) is implemented.
Chapter 4 is dedicated to the determination of interfacial tension of the vaporliquid interface with classical DFT and the PCSAFT equation of state. In the first part of this chapter different forms of the dispersion functional based on PCSAFT are used for the determination of the interfacial tension of nonassociating fluids, such as hydrocarbons and other inorganic and organic substances. Additionally, classical DFT is used to predict the interfacial tension of mixtures of several compounds finding excellent agreement with experimental data. In the second part of this chapter, associating contributions are taken into account for the calculation of the interfacial tension of substances that are able to form hydrogen bonds, such as alkanols, acetic acid and water. Three functionals are used to describe the properties of the vaporliquid interface of associating fluids, where it is found that classical DFT with PCSAFT show deviations in the calculation of the interfacial tension of alkanols and other associating compounds. Therefore, new pure molecular parameters for PCSAFT are proposed by including the interfacial tension during the fitting procedure. The new parameters are assessed by comparing their performance in the correlation of vapor pressure, liquid density and interfacial tension for each of the association functionals. It is found that while deviations of the interfacial tension can be considerably decreased for the lighter alkanols, heavier alkanols show a large increase in the deviation of vapor pressures. The results obtained with the three association functionals are fairly similar, and it is still inconclusive if the large deviations found for the heavier alkanols are due to the formulation of the association term, or the other terms.
The study of fluids confined in porous media is done in Chapter 5. The calculation of gas adsorption with classical DFT is carried out for systems at supercritical conditions, which means that the fluids do not show capillary condensation or evaporation. In these calculations, a model of a single slitlike pore is used, where the shape of a single pore is formed by two planar walls separated with a distance characteristic of the pore size. Additionally, a solidfluid potential is used to take into account the interactions between the particles in the solid and the fluid particles. Therefore, to fully characterize a confined system, the slitlike pore model requires three parameters: the specific area of the solid, the value of the energy interaction parameters between solid and fluid and the average size of the single pore. These parameters are fitted to experimental data of excess adsorption, finding excellent greement. The parameters are then used to predict adsorption of mixtures, where slight deviations are found when compared to experimental data.
The main challenge in the study of adsorption is that the description of the solid is a difficult task as both the chemistry and geometry must be determined simultaneously. This means that the modelling procedure requires a recursive methodology as one of those properties is usually infer from the other. Even though good agreement is found with the singe slitlike pore model, porous media cannot be fully characterized with a single pore size. Therefore, a pore size distribution (PSD) model is followed to improve the characterization of porous materials. The PSD can be obtained experimeniv tally, however, to use this information in the prediction of the adsorption of different fluids the solidfluid interactions must be known. In this work, the PSD of activated carbons is determined with methane adsorption at supercritical conditions. For this system, it is assumed that the solidfluid interaction can be approximated with the geometric mean of the energy parameters of the methane molecule and the carbon atom. The determination of the PSD is carried out successfully using regularized regression methods, where the resulting PSD is in agreement with published data and the adsorption isotherms have an excellent agreement with experimental results. Additionally, a more complex description of the chemistry of solids is taken into account by inserting association sites on the wall surface. In this way, classical DFT can be used to study adsorption of associating fluids on activated surfaces, which have a great impact on the behavior of confined fluids.
Finally, in Chapter 6 some of the conclusions found in this thesis are presented, together with a clear road of how this implementation of classical DFT with PCSAFT could be extended to improve our understanding of inhomogeneous fluids.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  193 
Publication status  Published  2020 
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 1 Finished

Phase Behavior of Inhomogeneous Fluids
Camacho Vergara, E. L., Gross, J., Solbraa, E., Shapiro, A., Liang, X. & Kontogeorgis, G.
Technical University of Denmark
01/11/2016 → 17/08/2020
Project: PhD