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Density Functional Theory Predictions of Derivative Thermodynamic Properties of a Confined Fluid

Gennady Y. Gor, Geordy Jomon, Andrei L. Kolesnikov

Abstract

Fluids in nanopores are of importance for many engineering applications, including energy storage in supercapacitors, hydrocarbons recovery from unconventional sources, or water desalination. Thermodynamic properties of fluids confined in nanopores differ from the properties of the same fluids in bulk. Density functional theory (DFT) has been widely used for modeling thermodynamics of confined fluids. However, it is rarely used for calculations of derivative thermodynamic properties. Here we use a rather simple DFT model for argon based on the Percus-Yevick equation, and showed that with standard parametrization it fails to predict derivative properties. However, slight adjustment in parameters leads to quantitative predictions of isothermal compressibility and thermal expansion coefficient at a selected temperature. Using the adjusted parameterization we performed the calculations of compressibility of argon confined in carbon slit pores of various sizes, and demonstrated that the compressibility of argon in confinement is lower than that in bulk and is pore size dependent. We confirmed the DFT predictions using the Monte Carlo molecular simulations. In addition to isothermal compressibility, we calculated the thermal expansion coefficient of confined argon. Our calculations showed that it behaves similar to compressibility -- it is always lower than the bulk value and gradually increases for smaller pore sizes. For several selected pore sizes we verified the DFT calculations by Monte Carlo simulations. Overall, our results suggest that the classical DFT can be utilized for calculations of derivative thermodynamic properties of confined fluids, which are computationally challenging to predict using molecular simulations.

Density Functional Theory Predictions of Derivative Thermodynamic Properties of a Confined Fluid

Abstract

Fluids in nanopores are of importance for many engineering applications, including energy storage in supercapacitors, hydrocarbons recovery from unconventional sources, or water desalination. Thermodynamic properties of fluids confined in nanopores differ from the properties of the same fluids in bulk. Density functional theory (DFT) has been widely used for modeling thermodynamics of confined fluids. However, it is rarely used for calculations of derivative thermodynamic properties. Here we use a rather simple DFT model for argon based on the Percus-Yevick equation, and showed that with standard parametrization it fails to predict derivative properties. However, slight adjustment in parameters leads to quantitative predictions of isothermal compressibility and thermal expansion coefficient at a selected temperature. Using the adjusted parameterization we performed the calculations of compressibility of argon confined in carbon slit pores of various sizes, and demonstrated that the compressibility of argon in confinement is lower than that in bulk and is pore size dependent. We confirmed the DFT predictions using the Monte Carlo molecular simulations. In addition to isothermal compressibility, we calculated the thermal expansion coefficient of confined argon. Our calculations showed that it behaves similar to compressibility -- it is always lower than the bulk value and gradually increases for smaller pore sizes. For several selected pore sizes we verified the DFT calculations by Monte Carlo simulations. Overall, our results suggest that the classical DFT can be utilized for calculations of derivative thermodynamic properties of confined fluids, which are computationally challenging to predict using molecular simulations.
Paper Structure (12 sections, 25 equations, 4 figures, 1 table)

This paper contains 12 sections, 25 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Classical DFT
  4. Bulk Fluid
  5. Compressibility or Bulk Modulus
  6. Thermal expansion coefficient
  7. Slit Pore Model
  8. Molecular Simulation
  9. Results
  10. Model Parameterization
  11. Discussion
  12. Conclusion

Figures (4)

  • Figure 1: (a) Vapor-liquid binodals for argon, dotted line is based on experimental data from CoolProp bell2014pure, and theoretical binodals predicted using the EOS with two different parameterizations -- from the literature ravikovitch2006density (dashed line) and parameterization proposed here (solid line). (b) Saturation pressure of argon as a function of temperature predicted with PY EOS and from CoolProp bell2014pure.
  • Figure 2: (a) Bulk modulus of bulk liquid argon. (b) Thermal expansion coefficient of bulk liquid argon. Dotted line is based on experimental data from CoolProp bell2014pure, and theoretical binodals predicted using the EOS with two different parameterizations -- from the literature ravikovitch2006density (dashed line) and parameterization proposed here (solid line).
  • Figure 3: Bulk modulus (a) and compressibility (b) of argon in slit pores of various sizes. The shaded region in Fig. \ref{['fig:modulus-slit']}b shows the error for prediction of bulk compressibility. The calculations based on DFT are in excellent agreement with the calculations from GCMC.
  • Figure 4: Thermal expansion coefficient of confined argon in slits of various sizes. Calculations based on DFT (Eq. \ref{['alpha-expt']}) confirmed by the calculations based on molecular simulations (Eq. \ref{['alpha_GCMC']}).