^{1,a)}, Alexei R. Khokhlov

^{1}and Igor I. Potemkin

^{1}

### Abstract

A Flory-Huggins type lattice approach is used to describe theoretically a heterogeneous mixture composed of an ionic liquid (IL) and a nonionic liquid (nIL). It is analyzed, how the behavior of the system depends on the difference in the affinities of the cations and the anions to the neutral molecules (i.e., on the “amphiphilicity” of the IL with respect to the nIL). It is proved that if the difference in the affinities is not large, two macrophases coexist in the mixture; if the difference exceeds a certain threshold value, the mixture becomes microheterogeneous: depending on its composition, it can turn either into ion clusters dispersed over the phase having low concentration of ions, or into clusters of neutral molecules dispersed over the phase having high concentration of ions. If the system is not close to the critical point, the ion clusters can be only small: the maximal ratio of their diameter to an ion diameter is of the order of ten; however, the clusters of nonionic molecules can be large, if the difference in the affinities has a certain value. It is predicted also that cavities can nucleate inside an IL, and clusters of ions can appear in a saturated vapor of an IL.

This work was supported by the Ministry of Science and Education of the Russian Federation (State Contract No. ∏1365, signed on 2 September 2009) in the framework of the realization of the federal task program “Scientific and scientific-educational personnel of innovational Russia” in the years 2009–2013.

I. INTRODUCTION

II. THE METHOD

III. RESULTS AND DISCUSSION

IV. CONCLUSIONS

### Key Topics

- Free energy
- 40.0
- Electrostatics
- 24.0
- Surface tension
- 12.0
- Ionic liquids
- 9.0
- Critical point phenomena
- 7.0

## Figures

Schematic diagram representing the values of the Flory-Huggins parameters characterizing the dispersion interactions between the components of the considered system.

Schematic diagram representing the values of the Flory-Huggins parameters characterizing the dispersion interactions between the components of the considered system.

Volume fractions of: (a) cations, ϕ _{+}, (b) anions, ϕ _{−}, and (c) normalized potential of electrostatic field, , as functions of the coordinate *z* perpendicular to the interface between two macro phases of a IL/nIL mixture (I) and as a function of the distance *r* to the center of a cluster formed in a IL/nIL mixture (II–V) at , Δχ = 6, χ_{+−} = 0, *u* = 1.

Volume fractions of: (a) cations, ϕ _{+}, (b) anions, ϕ _{−}, and (c) normalized potential of electrostatic field, , as functions of the coordinate *z* perpendicular to the interface between two macro phases of a IL/nIL mixture (I) and as a function of the distance *r* to the center of a cluster formed in a IL/nIL mixture (II–V) at , Δχ = 6, χ_{+−} = 0, *u* = 1.

Volume fractions of: (a) cations, ϕ _{+}, (b) anions, ϕ _{−}, and (c) normalized potential of electrostatic field, , as functions of the coordinate *z* perpendicular to the interface between two macrophases of a IL/nIL mixture (I) and as a function of the distance *r* to the center of a cluster formed in a IL/nIL mixture (II–V) at , Δχ = 7.3, χ_{+−} = 0, *u* = 1.

Volume fractions of: (a) cations, ϕ _{+}, (b) anions, ϕ _{−}, and (c) normalized potential of electrostatic field, , as functions of the coordinate *z* perpendicular to the interface between two macrophases of a IL/nIL mixture (I) and as a function of the distance *r* to the center of a cluster formed in a IL/nIL mixture (II–V) at , Δχ = 7.3, χ_{+−} = 0, *u* = 1.

Dependencies of surface tension σ_{ s } of the phase boundary between the IL and the nIL phases on the amphiphilicityΔχ of the IL at χ_{+−} = 0, *u* = 1, and different affinities of the IL to the nIL: (a), (b), (c), (d).

Dependencies of surface tension σ_{ s } of the phase boundary between the IL and the nIL phases on the amphiphilicityΔχ of the IL at χ_{+−} = 0, *u* = 1, and different affinities of the IL to the nIL: (a), (b), (c), (d).

Phase diagram of the IL/nIL mixture in coordinates (, Δχ) (i.e., affinity of the IL to the nIL, and amphiphilicity of the IL) at the average volume fraction of IL in the mixture equal to 0.5, andχ_{+−} = 0, *u* = 1. (a) The upper boundary of the domain corresponding to the stability of a mixture consisting of two macrophases. The domain over this boundary corresponds also to stability of separate nIL clusters. (b) The upper boundary of the domain corresponding to a homogeneous IL/nIL mixture, in which stable fluctuations of the components concentrations are not possible. (c) The lower boundary of the domain corresponding to the stability of separate IL clusters. (d) The lower boundary of the domain corresponding to the stability of separate nIL clusters having radius smaller than 10 *a*.

Phase diagram of the IL/nIL mixture in coordinates (, Δχ) (i.e., affinity of the IL to the nIL, and amphiphilicity of the IL) at the average volume fraction of IL in the mixture equal to 0.5, andχ_{+−} = 0, *u* = 1. (a) The upper boundary of the domain corresponding to the stability of a mixture consisting of two macrophases. The domain over this boundary corresponds also to stability of separate nIL clusters. (b) The upper boundary of the domain corresponding to a homogeneous IL/nIL mixture, in which stable fluctuations of the components concentrations are not possible. (c) The lower boundary of the domain corresponding to the stability of separate IL clusters. (d) The lower boundary of the domain corresponding to the stability of separate nIL clusters having radius smaller than 10 *a*.

Schematic drawings of: (I), a cluster of ions surrounded by the nIL phase; (II), a cluster of neutral molecules surrounded by the IL phase; (III), the phase boundary between the IL phase and the nIL phase. The cations and the anions are shown as circles. The neutral molecules are not shown, they are represented by the striped background.

Schematic drawings of: (I), a cluster of ions surrounded by the nIL phase; (II), a cluster of neutral molecules surrounded by the IL phase; (III), the phase boundary between the IL phase and the nIL phase. The cations and the anions are shown as circles. The neutral molecules are not shown, they are represented by the striped background.

Dependence of the free energy of the IL/nIL mixture consisting of the nIL phase and IL clusters dispersed over it, as a function of the clusters radius *R* at , χ_{+−} = 0, *u* = 1 and (a) Δχ = 5.37, (b) Δχ = 5.38, (c) Δχ = 5.4. The horizontal line represents the free energy the system would have, if it consisted of two macrophases. A cluster is stable if it corresponds to the minimum of a curve, and the minimum is lower than the horizontal line.

Dependence of the free energy of the IL/nIL mixture consisting of the nIL phase and IL clusters dispersed over it, as a function of the clusters radius *R* at , χ_{+−} = 0, *u* = 1 and (a) Δχ = 5.37, (b) Δχ = 5.38, (c) Δχ = 5.4. The horizontal line represents the free energy the system would have, if it consisted of two macrophases. A cluster is stable if it corresponds to the minimum of a curve, and the minimum is lower than the horizontal line.

Dependencies of the radius *R* of a stable cluster formed by ions in the nIL phase on the difference Δχ − Δχ^{*} between the amphiphilicity of the IL and the critical value of the amphiphilicity at which the surface tension of the phase boundary of a macroheterogeneous IL/nIL mixture vanishes. χ_{+−} = 0, *u* = 1, and (a), (b) , (c) , (d) . The left end of each dependence corresponds to the minimal value Δχ − Δχ^{*}, at which a stable cluster is possible.

Dependencies of the radius *R* of a stable cluster formed by ions in the nIL phase on the difference Δχ − Δχ^{*} between the amphiphilicity of the IL and the critical value of the amphiphilicity at which the surface tension of the phase boundary of a macroheterogeneous IL/nIL mixture vanishes. χ_{+−} = 0, *u* = 1, and (a), (b) , (c) , (d) . The left end of each dependence corresponds to the minimal value Δχ − Δχ^{*}, at which a stable cluster is possible.

Dependence of the free energy of the IL/nIL mixture consisting of the IL phase and nIL clusters dispersed over it, as a function of the clusters radius *R* at , χ_{+−} = 0, *u* = 1 and (a) Δχ = 5.4, (b) Δχ = 5.42, (c) Δχ = 5.43, (d) Δχ = 5.44, (e) Δχ = 5.45, (f) Δχ = 5.46. The horizontal line represents the free energy the system would have, if it consisted of two macrophases. A cluster is stable if it corresponds to the minimum of a curve, and the minimum is lower than the horizontal line.

Dependence of the free energy of the IL/nIL mixture consisting of the IL phase and nIL clusters dispersed over it, as a function of the clusters radius *R* at , χ_{+−} = 0, *u* = 1 and (a) Δχ = 5.4, (b) Δχ = 5.42, (c) Δχ = 5.43, (d) Δχ = 5.44, (e) Δχ = 5.45, (f) Δχ = 5.46. The horizontal line represents the free energy the system would have, if it consisted of two macrophases. A cluster is stable if it corresponds to the minimum of a curve, and the minimum is lower than the horizontal line.

Dependencies of the radius *R* of a stable cluster formed by neutral molecules in the IL phase on the reciprocal 1/(Δχ − Δχ^{*}) of the difference between the amphiphilicity of the IL and the critical value of the amphiphilicity at which the surface tension of the phase boundary of a macroheterogeneous IL/nIL mixture vanishes. χ_{+−} = 0, *u* = 1, and (a) , (b) , (c) .

Dependencies of the radius *R* of a stable cluster formed by neutral molecules in the IL phase on the reciprocal 1/(Δχ − Δχ^{*}) of the difference between the amphiphilicity of the IL and the critical value of the amphiphilicity at which the surface tension of the phase boundary of a macroheterogeneous IL/nIL mixture vanishes. χ_{+−} = 0, *u* = 1, and (a) , (b) , (c) .

Phase diagram of the IL/nIL mixture in coordinates (*T*, *kT*Δχ) at the average volume fraction of IL in the mixture equal to 0.5, andχ_{+−} = 0, , . (a) The upper boundary of the domain corresponding to the stability of a mixture consisting of two macrophases. The domain over this boundary corresponds also to stability of separate nIL clusters. (b) The lower boundary of the domain corresponding to the stability of separate IL clusters. c) The lower boundary of the domain corresponding to the stability of separate nIL clusters having radius smaller than 20 *a*.

Phase diagram of the IL/nIL mixture in coordinates (*T*, *kT*Δχ) at the average volume fraction of IL in the mixture equal to 0.5, andχ_{+−} = 0, , . (a) The upper boundary of the domain corresponding to the stability of a mixture consisting of two macrophases. The domain over this boundary corresponds also to stability of separate nIL clusters. (b) The lower boundary of the domain corresponding to the stability of separate IL clusters. c) The lower boundary of the domain corresponding to the stability of separate nIL clusters having radius smaller than 20 *a*.

Dependencies of the surface tension σ_{ s } of the phase boundary between the IL and the nIL phases on the absolute temperature *T* at χ_{+−} = 0, and different amphiphilicities of the IL: (a) , (b) , (c) .

Dependencies of the surface tension σ_{ s } of the phase boundary between the IL and the nIL phases on the absolute temperature *T* at χ_{+−} = 0, and different amphiphilicities of the IL: (a) , (b) , (c) .

Article metrics loading...

Full text loading...

Commenting has been disabled for this content