# Thermodynamics at Solid–Liquid Interfaces

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## Abstract

**:**

## 1. Introduction

## 2. Theory of Phonons

## 3. Methodology

## 4. Results

## 5. Conclusions

- The thermal conductivity increases with increasing the strength of the solid–liquid interaction. Up to ${\epsilon}_{sl}=0.8$ $\epsilon $, this increase is linear. The slope of the thermal conductivity between ${\epsilon}_{sl}=0.8$ $\epsilon $ and ${\epsilon}_{sl}=1$ $\epsilon $ decreases, suggesting a possible asymptotic state. However, further simulations covering a broader range of solid–liquid interactions are required to confirm the above.
- We attribute the observed increase of the thermal conductivity to a larger number of phonon states available in the system. The thermal conductivity does not, however, follow the trend of the VDOS. We attribute this to the Umklapp scattering, which is known to increase as the number of phonons increases. Scattering events have a negative effect on thermal conductivity; this is probably the reason for the decreasing slope of the thermal conductivity for ${\epsilon}_{sl}>0.8$ $\epsilon $.
- We speculate that as the strength of the solid–liquid interaction further increases and more phonon modes become available, an increase in scattering will cause the thermal conductivity to reach an asymptotic state and even decrease. A similar phenomenon is observed with respect to the temperature effects on the thermal conductivity of CNTs.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The thermal conductivity of the liquid in the x-direction as a function of the channel length in the same direction, ${L}_{x}$, for a channel of height 6.58 $\sigma $, and a strength of solid–liquid interaction ${\epsilon}_{sl}=0.8$ $\epsilon $. The thermal conductivity converges for channel lengths greater than 10 $\sigma $.

**Figure 2.**The Heat Flux Autocorrelation Function for bulk and confined liquid argon, for ${\epsilon}_{sl}=0.8$ $\epsilon $. Reconstructed from Frank and Drikakis [17].

**Figure 3.**The component of the thermal conductivity in the direction parallel to the surface, as a function of the strength of the solid–liquid interaction. The different curves correspond to the thermal conductivity as calculated by directly integrating HFACF (■); the thermal conductivity as calculated by fitting a sum of two exponential functions on the HFACF (◆); and the decomposed short- (●), long-range (◆) components of the thermal conductivity.

**Figure 4.**The relaxation time, and strength of the long-range phonons, as a function of the strength of the solid–liquid interaction.

**Figure 5.**The density profiles of the liquid for different values of the strength of the solid–liquid interaction.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Frank, M.; Drikakis, D.
Thermodynamics at Solid–Liquid Interfaces. *Entropy* **2018**, *20*, 362.
https://doi.org/10.3390/e20050362

**AMA Style**

Frank M, Drikakis D.
Thermodynamics at Solid–Liquid Interfaces. *Entropy*. 2018; 20(5):362.
https://doi.org/10.3390/e20050362

**Chicago/Turabian Style**

Frank, Michael, and Dimitris Drikakis.
2018. "Thermodynamics at Solid–Liquid Interfaces" *Entropy* 20, no. 5: 362.
https://doi.org/10.3390/e20050362