# Condensation pressures in small pores: An analytical model based on density functional theory

## Abstract

Integral methods are used to derive an analytical expression describing fluid condensation pressures in slit pores bounded by parallel plane walls. To obtain this result, the governing equations of density functional theory (DFT) are integrated across the pore width assuming that fluid densities within adsorbed layers are spatially uniform. The thickness, density, and free energy of these layers are expressed as composite functions constructed from asymptotic limits applicable to small and large pores. By equating the total free energy of the adsorbed layers to that of a liquid-full pore, we arrive at a closed-form expression for the condensation pressure in terms of the pore size, surface tension, and Lennard-Jones parameters of the adsorbent and adsorbate molecules. The resulting equation reduces to the Kelvin equation in the large-pore limit. It further reproduces the condensation pressures computed by means of the full DFT equations for all pore sizes in which phase transitions are abrupt. Finally, in the limit of extremely small pores, for which phase transitions may be smooth and continuous, this simple analytical expression provides a good approximation to the apparent condensation pressure indicated by the steepest portion of the adsorption isotherm computed via DFT. {copyright} {ital 1999 American Institute ofmore »

- Authors:

- Sandia National Laboratories, Livermore, California 94551-0969 (United States)

- Publication Date:

- OSTI Identifier:
- 362677

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 111; Journal Issue: 9; Other Information: PBD: Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; 40 CHEMISTRY; FREE ENERGY; VAPOR CONDENSATION; ADSORPTION; POROUS MATERIALS; PORE STRUCTURE; SIZE; PHASE TRANSFORMATIONS; DENSITY; SURFACE TENSION

### Citation Formats

```
Nilson, R.H., and Griffiths, S.K.
```*Condensation pressures in small pores: An analytical model based on density functional theory*. United States: N. p., 1999.
Web. doi:10.1063/1.479726.

```
Nilson, R.H., & Griffiths, S.K.
```*Condensation pressures in small pores: An analytical model based on density functional theory*. United States. doi:10.1063/1.479726.

```
Nilson, R.H., and Griffiths, S.K. Wed .
"Condensation pressures in small pores: An analytical model based on density functional theory". United States. doi:10.1063/1.479726.
```

```
@article{osti_362677,
```

title = {Condensation pressures in small pores: An analytical model based on density functional theory},

author = {Nilson, R.H. and Griffiths, S.K.},

abstractNote = {Integral methods are used to derive an analytical expression describing fluid condensation pressures in slit pores bounded by parallel plane walls. To obtain this result, the governing equations of density functional theory (DFT) are integrated across the pore width assuming that fluid densities within adsorbed layers are spatially uniform. The thickness, density, and free energy of these layers are expressed as composite functions constructed from asymptotic limits applicable to small and large pores. By equating the total free energy of the adsorbed layers to that of a liquid-full pore, we arrive at a closed-form expression for the condensation pressure in terms of the pore size, surface tension, and Lennard-Jones parameters of the adsorbent and adsorbate molecules. The resulting equation reduces to the Kelvin equation in the large-pore limit. It further reproduces the condensation pressures computed by means of the full DFT equations for all pore sizes in which phase transitions are abrupt. Finally, in the limit of extremely small pores, for which phase transitions may be smooth and continuous, this simple analytical expression provides a good approximation to the apparent condensation pressure indicated by the steepest portion of the adsorption isotherm computed via DFT. {copyright} {ital 1999 American Institute of Physics.}},

doi = {10.1063/1.479726},

journal = {Journal of Chemical Physics},

number = 9,

volume = 111,

place = {United States},

year = {1999},

month = {9}

}