^{1}and Volker C. Weiss

^{2,a)}

### Abstract

Inorganic molten salts, such as NaCl, are known to show characteristically lower values of Guggenheim's corresponding-states surface tension γred at a given reduced temperature T/T c than simple or aprotic polar fluids. Recently, the corresponding values of γred for (some) room temperature ionic liquids (RTILs) were found in the same region as those for weakly polar fluids, that is, markedly above the values typical of inorganic molten salts despite the ionic character of RTILs. Here, we present the results of simulations of an ionic model fluid in which the strength of attractive dispersion interactions among the ions is varied relative to the Coulomb interactions. For weak dispersive interactions, the behavior known for real inorganic molten salts is found. If the attractive dispersion energy of two unlike ions at contact exceeds 20% of the Coulombic attraction in such an isolated ion pair, γred increases markedly and approaches the region of values for simple and polar fluids. Rough theoretical estimates of the relative strengths of dispersive and Coulombic attractions in molten inorganic salts and in RTILs support our conclusion that the dispersion interactions in RTILs are strong enough for their corresponding-states surface tension to behave regularly and, thus, to deviate from the values one would expect for strongly ionic systems.

We are indebted to Florian Müller-Plathe who suggested this study and provided helpful comments on the manuscript. We would also like to thank Simon Butler for carefully reading the manuscript.

I. INTRODUCTION

II. MODEL AND SIMULATION DETAILS

A. Definition of the model

B. Simulation details

III. RESULTS

A. Coexistence curves and surface tension

B. Critical parameters

C. Corresponding-states surface tension

IV. DISCUSSION AND CONCLUSION

### Key Topics

- Surface tension
- 30.0
- Mean field theory
- 21.0
- Critical point phenomena
- 18.0
- Molten salts
- 18.0
- Diamond
- 8.0

## Figures

Densities ρ* of the coexisting phases (open symbols) as a function of temperature T* and estimates of the location of the critical point (filled symbols) for λ = 0 (circles), λ = 0.05 (squares), λ = 0.2 (diamonds), and λ = 0.3 (triangles).

Densities ρ* of the coexisting phases (open symbols) as a function of temperature T* and estimates of the location of the critical point (filled symbols) for λ = 0 (circles), λ = 0.05 (squares), λ = 0.2 (diamonds), and λ = 0.3 (triangles).

Densities ρ* of the coexisting phases (open symbols) as a function of temperature T* and estimates of the location of the critical point (filled symbols) for λ = 0.4 (circles), λ = 0.5 (squares), λ = 0.7 (diamonds), and λ = 1.0 (triangles).

Densities ρ* of the coexisting phases (open symbols) as a function of temperature T* and estimates of the location of the critical point (filled symbols) for λ = 0.4 (circles), λ = 0.5 (squares), λ = 0.7 (diamonds), and λ = 1.0 (triangles).

Surface tension γ* (open symbols) as a function of temperature T* for λ = 0 (circles), λ = 0.05 (squares), λ = 0.2 (diamonds), and λ = 0.3 (triangles). The filled symbols mark the respective critical temperature estimated from γ*(T*) by fitting to Eq. (9) ; the fits themselves are represented by continuous lines.

Surface tension γ* (open symbols) as a function of temperature T* for λ = 0 (circles), λ = 0.05 (squares), λ = 0.2 (diamonds), and λ = 0.3 (triangles). The filled symbols mark the respective critical temperature estimated from γ*(T*) by fitting to Eq. (9) ; the fits themselves are represented by continuous lines.

Surface tension γ* (open symbols) as a function of temperature T* for λ = 0.4 (circles), λ = 0.5 (squares), λ = 0.7 (diamonds), and λ = 1.0 (triangles). The filled symbols mark the respective critical temperature estimated from γ*(T*) by fitting to Eq. (9) ; the fits themselves are represented by continuous lines.

Surface tension γ* (open symbols) as a function of temperature T* for λ = 0.4 (circles), λ = 0.5 (squares), λ = 0.7 (diamonds), and λ = 1.0 (triangles). The filled symbols mark the respective critical temperature estimated from γ*(T*) by fitting to Eq. (9) ; the fits themselves are represented by continuous lines.

Diameter of the coexistence curve (open symbols) as a function of temperature T* for λ = 0 (circles), λ = 0.05 (squares), λ = 0.2 (diamonds), and λ = 0.3 (triangles). The continuous lines represent the correlations for given in Table I . The estimated locations of the respective critical point are marked by filled symbols.

Diameter of the coexistence curve (open symbols) as a function of temperature T* for λ = 0 (circles), λ = 0.05 (squares), λ = 0.2 (diamonds), and λ = 0.3 (triangles). The continuous lines represent the correlations for given in Table I . The estimated locations of the respective critical point are marked by filled symbols.

Diameter of the coexistence curve (open symbols) as a function of temperature T* for λ = 0.4 (circles), λ = 0.5 (squares), λ = 0.7 (diamonds), and λ = 1.0 (triangles). The continuous lines represent the correlations for given in Table I . The estimated locations of the respective critical point are marked by filled symbols.

Diameter of the coexistence curve (open symbols) as a function of temperature T* for λ = 0.4 (circles), λ = 0.5 (squares), λ = 0.7 (diamonds), and λ = 1.0 (triangles). The continuous lines represent the correlations for given in Table I . The estimated locations of the respective critical point are marked by filled symbols.

Variation of the critical temperature (circles connected by continuous lines) and of the critical density (squares connected by dashed lines) with λ; shown are the simulation results (open symbols) and the predictions of a simple MSA-based theory (filled symbols) as defined by Eq. (11) .

Variation of the critical temperature (circles connected by continuous lines) and of the critical density (squares connected by dashed lines) with λ; shown are the simulation results (open symbols) and the predictions of a simple MSA-based theory (filled symbols) as defined by Eq. (11) .

Reduced surface tension γred as a function of the reduced temperature T/T c for 0 ⩽ λ ⩽ 1.0. Shown are the data for λ = 0 (black open circles), λ = 0.05 (blue open squares), λ = 0.2 (green open diamonds), λ = 0.3 (red open triangles), λ = 0.4 (black filled circles), λ = 0.5 (blue filled squares), λ = 0.7 (green filled diamonds), and λ = 1.0 (red filled triangles). The dashed line represents our data for the conventional Lennard-Jones fluid.

Reduced surface tension γred as a function of the reduced temperature T/T c for 0 ⩽ λ ⩽ 1.0. Shown are the data for λ = 0 (black open circles), λ = 0.05 (blue open squares), λ = 0.2 (green open diamonds), λ = 0.3 (red open triangles), λ = 0.4 (black filled circles), λ = 0.5 (blue filled squares), λ = 0.7 (green filled diamonds), and λ = 1.0 (red filled triangles). The dashed line represents our data for the conventional Lennard-Jones fluid.

Comparison of the reduced surface tension γred as a function of the reduced temperature T/T c for real fluids (filled symbols) and for the model fluids with selected values of λ (open symbols). Shown are data for the simple fluid argon (black filled circles), the polar fluid CHClF2 (blue filled diamonds), and the molten salts NaCl (red filled triangles up and down) and KCl (green filled triangles left and right), for which two sets of critical parameters have been employed (see main text). Generic results for room temperature ionic liquids are exemplified by data for [bmim][BF4] (orange filled circles) and for [bmim][NTf2] (gray filled squares). For comparison, the simulation results for λ = 0 (black open circles), λ = 0.05 (blue open squares), λ = 0.2 (green open diamonds), and λ = 1.0 (red open triangles) are indicated.

Comparison of the reduced surface tension γred as a function of the reduced temperature T/T c for real fluids (filled symbols) and for the model fluids with selected values of λ (open symbols). Shown are data for the simple fluid argon (black filled circles), the polar fluid CHClF2 (blue filled diamonds), and the molten salts NaCl (red filled triangles up and down) and KCl (green filled triangles left and right), for which two sets of critical parameters have been employed (see main text). Generic results for room temperature ionic liquids are exemplified by data for [bmim][BF4] (orange filled circles) and for [bmim][NTf2] (gray filled squares). For comparison, the simulation results for λ = 0 (black open circles), λ = 0.05 (blue open squares), λ = 0.2 (green open diamonds), and λ = 1.0 (red open triangles) are indicated.

## Tables

Critical temperature and critical density for different values of λ; correlation between the diameter of the coexistence curve, , and the temperature T*.

Critical temperature and critical density for different values of λ; correlation between the diameter of the coexistence curve, , and the temperature T*.

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