^{1,2,a)}and Pavel Izák

^{1}

### Abstract

Molecular dynamics simulations of n-hexane adsorbed onto the interface of 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide ([bmim][Tf2N]) are performed at three n-hexane surface densities, ranged from 0.7 to 2.3 μmol/m2 at 300 K. For [bmim][Tf2N] room-temperature ionic liquid, we use a non-polarizable all-atom force field with the partial atomic charges based on ab initio calculations for the isolated ion pair. The net charges of the ions are ±0.89e, which mimics the anion to cation charge transfer and polarization effects. The OPLS-AA force field is employed for modeling of n-hexane. The surface tension is computed using the mechanical route and its value decreases with increase of the n-hexane surface density. The [bmim][Tf2N]/n-hexane interface is analyzed using the intrinsic method, and the structural and dynamic properties of the interfacial, sub-interfacial, and central layers are computed. We determine the surface roughness, global and intrinsic density profiles, and orientation ordering of the molecules to describe the structure of the interface. We further compute the survival probability, normal and lateral self-diffusion coefficients, and re-orientation correlation functions to elucidate the effects of n-hexane on dynamics of the cations and anions in the layers.

This research was supported by the Grant Programme of the Ministry of Education, Youth and Sports (Project No. LH12020) and by the Czech Science Foundation (Grant No. P106/12/0569).

I. INTRODUCTION

II. SIMULATION METHODOLOGY

A. Molecular models

B. Simulation details

C. Intrinsic interface analysis

III. RESULTS AND DISCUSSION

A. Surface tension

B. Structure

1. Center-of-mass and charge density profiles

2. Surface roughness

3. Atomic density profiles

4. Orientation ordering

C. Dynamics

1. Mobility

2. Diffusion

3. Re-orientation

IV. CONCLUSIONS

### Key Topics

- Gas liquid interfaces
- 44.0
- Interface diffusion
- 29.0
- Interface structure
- 24.0
- Chemical interdiffusion
- 21.0
- Diffusion
- 16.0

## Figures

Chemical structures of (a) bmim+, (b) Tf2N−, and (c) n-hexane along with atom types.

Chemical structures of (a) bmim+, (b) Tf2N−, and (c) n-hexane along with atom types.

The surface tension, γ, for the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K as a function of the n-hexane surface density, ρ s . Open circles represent our simulation results while the filled circle corresponds the experimental result for the neat interface. 35 The simulation result for the neat interface is taken from our previous work. 15 Dotted lines serve as a guide to the eye.

The surface tension, γ, for the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K as a function of the n-hexane surface density, ρ s . Open circles represent our simulation results while the filled circle corresponds the experimental result for the neat interface. 35 The simulation result for the neat interface is taken from our previous work. 15 Dotted lines serve as a guide to the eye.

Number (left column) and charge (right column) density profiles of cations, anions, ion pairs (total) and n-hexane for the [bmim][Tf2N]/n-hexane systems, evaluated for the overall system and for the interfacial, sub-interfacial, and central layers at a temperature of 300 K; (a) the neat interface (taken from our previous work 15 ), (b) the interface with the n-hexane surface density ρ s = 0.743 μmol/m2, and (c) the interface with ρ s = 2.228 μmol/m2. The scale on the z axis shows distances where the total density is half the bulk density.

Number (left column) and charge (right column) density profiles of cations, anions, ion pairs (total) and n-hexane for the [bmim][Tf2N]/n-hexane systems, evaluated for the overall system and for the interfacial, sub-interfacial, and central layers at a temperature of 300 K; (a) the neat interface (taken from our previous work 15 ), (b) the interface with the n-hexane surface density ρ s = 0.743 μmol/m2, and (c) the interface with ρ s = 2.228 μmol/m2. The scale on the z axis shows distances where the total density is half the bulk density.

Intrinsic number density profiles for the individual atoms that belong to the ions and n-hexane in the interfacial layer of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K. (a) The neat interface, (b) the interface with the n-hexane surface density ρ s = 0.743 μmol/m2, and (c) the interface with ρ s = 2.228 μmol/m2. The scale on the z axis shows distances from the true positions of the interface.

Intrinsic number density profiles for the individual atoms that belong to the ions and n-hexane in the interfacial layer of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K. (a) The neat interface, (b) the interface with the n-hexane surface density ρ s = 0.743 μmol/m2, and (c) the interface with ρ s = 2.228 μmol/m2. The scale on the z axis shows distances from the true positions of the interface.

(a) Diagram showing the coordinate axes used for the orientation analysis of bmim+. (b) Diagram displaying the three main orientations of the bmim+.

(a) Diagram showing the coordinate axes used for the orientation analysis of bmim+. (b) Diagram displaying the three main orientations of the bmim+.

Orientation of bmim+ and Tf2N− in the interfacial layer of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K (red = high probability, blue = low probability). The first column: probability distribution (cos θ, Φ) for the imidazolium ring of bmim+; θ and Φ are the angles depicted in Fig. 5(a) ; the second column: two-dimensional plot (cos θ, z) for the alkyl chain of bmim+; θ is the tilt angle of the vector N1-C22 with respect to the interface normal z; the third column: probability distribution (cos θ, cos Φ) for Tf2N−; θ is the tilt angle of the vectors S-C with respect to z and Φ is the tilt angle of the vector S-S with respect to z; the fourth column: probability distribution (cos θ, cos Φ) for Tf2N−; θ is the tilt angle of the vectors S-O with respect to z and Φ is the tilt angle of the vector S-S with respect to z. (a) the neat interface, (b) the interface with the n-hexane surface density ρ s = 0.743 μmol/m2, and (c) the interface with ρ s = 2.228 μmol/m2.

Orientation of bmim+ and Tf2N− in the interfacial layer of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K (red = high probability, blue = low probability). The first column: probability distribution (cos θ, Φ) for the imidazolium ring of bmim+; θ and Φ are the angles depicted in Fig. 5(a) ; the second column: two-dimensional plot (cos θ, z) for the alkyl chain of bmim+; θ is the tilt angle of the vector N1-C22 with respect to the interface normal z; the third column: probability distribution (cos θ, cos Φ) for Tf2N−; θ is the tilt angle of the vectors S-C with respect to z and Φ is the tilt angle of the vector S-S with respect to z; the fourth column: probability distribution (cos θ, cos Φ) for Tf2N−; θ is the tilt angle of the vectors S-O with respect to z and Φ is the tilt angle of the vector S-S with respect to z. (a) the neat interface, (b) the interface with the n-hexane surface density ρ s = 0.743 μmol/m2, and (c) the interface with ρ s = 2.228 μmol/m2.

Two-dimensional plot (cos θ, z) of n-hexane molecules in the adsorbed layer onto the [bmim][Tf2N] interface at a temperature of 300 K; θ is the tilt angle of the vector C1-C17 with respect to the interface normal z. (a) The interface with the n-hexane surface density ρ s = 0.743 μmol/m2, (b) the interface with ρ s = 0.1.418 μmol/m2, and (c) the interface with ρ s = 2.228 μmol/m2.

Two-dimensional plot (cos θ, z) of n-hexane molecules in the adsorbed layer onto the [bmim][Tf2N] interface at a temperature of 300 K; θ is the tilt angle of the vector C1-C17 with respect to the interface normal z. (a) The interface with the n-hexane surface density ρ s = 0.743 μmol/m2, (b) the interface with ρ s = 0.1.418 μmol/m2, and (c) the interface with ρ s = 2.228 μmol/m2.

Survival probability, L(t), for the cation, anion and n-hexane in the interfacial and sub-interfacial layers of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K; t is time. (a) the neat interface (taken from our previous work 15 ), (b) the interface with the n-hexane surface density ρ s = 0.743 μmol/m2, (c) the interface with ρ s = 0.1.418 μmol/m2, and (d) the interface with ρ s = 2.228 μmol/m2.

Survival probability, L(t), for the cation, anion and n-hexane in the interfacial and sub-interfacial layers of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K; t is time. (a) the neat interface (taken from our previous work 15 ), (b) the interface with the n-hexane surface density ρ s = 0.743 μmol/m2, (c) the interface with ρ s = 0.1.418 μmol/m2, and (d) the interface with ρ s = 2.228 μmol/m2.

## Tables

The surface density of the molecules ρ t , cation, anion, and n-hexane mole fractions, x c , x a , and x s = 1 − x c − x a , respectively, and the amplitude of the surface roughness, a, and frequency-like parameters of the surface roughness, ξ and b, in the interfacial and sub-interfacial layers of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K; ρ s is the n-hexane surface density. Results for the neat [bmim][Tf2N] interface is taken from our previous work. 15

The surface density of the molecules ρ t , cation, anion, and n-hexane mole fractions, x c , x a , and x s = 1 − x c − x a , respectively, and the amplitude of the surface roughness, a, and frequency-like parameters of the surface roughness, ξ and b, in the interfacial and sub-interfacial layers of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K; ρ s is the n-hexane surface density. Results for the neat [bmim][Tf2N] interface is taken from our previous work. 15

The stretched exponent β, characteristic residence time τ, and average residence time τ C of the stretched exponential decay (4) for bmim+, Tf2N−, and n-hexane in the interfacial and sub-interfacial layers of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K; ρ s is the n-hexane surface density. Results for the neat [bmim][Tf2N] interface is taken from our previous work. 15

The stretched exponent β, characteristic residence time τ, and average residence time τ C of the stretched exponential decay (4) for bmim+, Tf2N−, and n-hexane in the interfacial and sub-interfacial layers of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K; ρ s is the n-hexane surface density. Results for the neat [bmim][Tf2N] interface is taken from our previous work. 15

The normal and lateral self-diffusion coefficients, D z and D xy , respectively, of bmim+, Tf2N−, and n-hexane in the interfacial, sub-interfacial, and central layers of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K; ρ s is the n-hexane surface density. Results for the neat [bmim][Tf2N] interface is taken from our previous work. 15 Also listed are the values of the self-diffusion coefficients in the bulk [bmim][Tf2N] predicted from the MD simulations of Logotheti et al. 22 and obtained experimentally by Tokuda et al. 46

The normal and lateral self-diffusion coefficients, D z and D xy , respectively, of bmim+, Tf2N−, and n-hexane in the interfacial, sub-interfacial, and central layers of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K; ρ s is the n-hexane surface density. Results for the neat [bmim][Tf2N] interface is taken from our previous work. 15 Also listed are the values of the self-diffusion coefficients in the bulk [bmim][Tf2N] predicted from the MD simulations of Logotheti et al. 22 and obtained experimentally by Tokuda et al. 46

The stretched exponent β, characteristic re-orientation time τ, and average re-orientation time τ C of the stretched exponential decay, f(t) = exp [−(t/τ)β], for the vectors C8-C22 and C5-H12 on bmim+, vectors S-S and S-C on Tf2N−, and vector C1-C17 on n-hexane molecule in the interfacial, sub-interfacial, and central layers of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K; ρ s is the n-hexane surface density. Results for the neat [bmim][Tf2N] interface is taken from our previous work. 15

The stretched exponent β, characteristic re-orientation time τ, and average re-orientation time τ C of the stretched exponential decay, f(t) = exp [−(t/τ)β], for the vectors C8-C22 and C5-H12 on bmim+, vectors S-S and S-C on Tf2N−, and vector C1-C17 on n-hexane molecule in the interfacial, sub-interfacial, and central layers of the [bmim][Tf2N]/n-hexane systems at a temperature of 300 K; ρ s is the n-hexane surface density. Results for the neat [bmim][Tf2N] interface is taken from our previous work. 15

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