# Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. Hill’s Nanothermodynamics

#### 2.2. Maxwell Relations for a Slit Pore

#### 2.3. The Disjoining Pressure

#### 2.4. A Mechanical Description of the Slit Pore

## 3. Simulation Details

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Visualization of the fluid particles in a slit pore of height ${L}_{x}=4\sigma $, chemical potential ${\mu}^{*}=1$, and temperature ${T}^{*}=2$. The fluid particles are rendered in red, and their diameter is rendered at $\sigma $. The solid is not rendered. The solid lines illustrates the edges of the simulation box. The simulation was rendered with Open Visualization Tool (OVITO) [45].

**Figure 2.**(

**a**) Normal mechanical pressure, (

**b**) tangential mechanical pressure, and (

**c**) fluid number density $\rho $ as a function of th e x-direction for slit pore heights $h=2.04\sigma $, $2.59\sigma $, and $8\sigma $.

**Figure 3.**Fluid number density $\rho =N/V$ as a function of slit pore height h. The bulk fluid number density is shown as a dashed line.

**Figure 4.**Entropy density $s=S/V$ as a function of slit pore height h. See Equation (36). The dashed line shows the entropy density of the bulk ${s}^{\mathrm{b}}$.

**Figure 5.**Internal energy density $u=U/V$ as a function of slit pore height h. See Equation (35). The dashed line shows the internal energy density of the bulk ${u}^{\mathrm{b}}$.

**Figure 8.**Surface tension $\gamma $ as a function of slit pore height h, see Equation (33). The dashed line shows the surface tension at infinite separation ${\gamma}^{\infty}$.

**Figure 10.**The scaling of normal pressure minus integral pressure as a function of the inverse slit pore height h.

**Table 1.**The reduced units are denoted with an asterisk in superscript, for example ${T}^{*}$. The variables are reduced using the molecular diameter $\sigma $, potential well depth $\u03f5$, fluid particle mass m and Boltzmann constant ${k}_{\mathrm{B}}$.

Description | Definition |
---|---|

Energy | ${E}^{*}=E/\u03f5$ |

Entropy | ${S}^{*}=S/{k}_{\mathrm{B}}$ |

Temperature | ${T}^{*}=T{k}_{\mathrm{B}}/\u03f5$ |

Distance | ${x}^{*}=x/\sigma $ |

Pressure | ${p}^{*}=p{\sigma}^{3}/\u03f5$ |

Chemical potential | ${\mu}^{*}=\mu /\u03f5$ |

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**MDPI and ACS Style**

Galteland, O.; Bedeaux, D.; Kjelstrup, S.
Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore. *Nanomaterials* **2021**, *11*, 165.
https://doi.org/10.3390/nano11010165

**AMA Style**

Galteland O, Bedeaux D, Kjelstrup S.
Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore. *Nanomaterials*. 2021; 11(1):165.
https://doi.org/10.3390/nano11010165

**Chicago/Turabian Style**

Galteland, Olav, Dick Bedeaux, and Signe Kjelstrup.
2021. "Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore" *Nanomaterials* 11, no. 1: 165.
https://doi.org/10.3390/nano11010165