Three-dimensional electric double layer at the solvent-free liquid/liquid interface between two immiscible ionic liquids

Abstract

The structure of the electric double layer (EDL) at the liquid/liquid interface between hydrophobic and hydrophilic ionic liquids (ILs), trioctylmethylammonium bis(nonafluorobutanesulfonyl)amide (TOMAC4C4N) and ethylammonium nitrate (EAN), was explored using molecular dynamics (MD) simulations. Analyses of the charge density distribution and radial distribution function at this solvent-free IL/IL interface revealed that the smaller ions constituting the hydrophilic EAN phase are inserted into the interfacial “pockets” formed by the capillary wave, whose minimum wavelength is determined by the sizes of the larger ions constituting the hydrophobic TOMAC4C4N phase. The larger ions at the interface were coordinated by the smaller ions across the interface, forming overscreening ionic layers because of the absence of solvents. This specific interfacial ion coordination led to a three-dimensional EDL, in which the smaller counterions in the interfacial “pockets” interact closely with the larger ions. This contrasts with the case of the conventional oil/water interface, where ions in the water phase are hydrated and cannot be inserted into the “pockets”, forming a two-dimensional EDL that is insensitive to the interfacial roughness. Simulations of various types of liquid/liquid interfaces revealed that this unique EDL structure is not specific to the IL/IL interface: the amphiphilicity of smaller ions and the interfacial structure of the larger ions play a key role. Moreover, when a smaller ion in the hydrophilic IL phase is transferred to the hydrophobic IL phase, the ion is often accompanied by other smaller ions, forming an “ionic liquid finger”.

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1. Introduction

The interface between two immiscible electrolyte solutions (ITIES), the so-called electrochemical liquid/liquid interface, can be electrochemically polarized within the potential window. The edges of the window are defined by the transfer of supporting electrolyte ions dissolved in one liquid phase to the other. Since 1902, when Nernst and Riesenfeld¹ reported that ion transfers could be controlled by applying potential at the phenol/water interface, electrochemical oil (O)/water (W) interfaces have been intensively studied.^2–15 Furthermore, new ITIES systems other than the O/W interfaces have been discovered, such as O/O,^16–18 fluorous solvent (F)/W,^19–23 ionic liquid (IL)/W,^24–32 and IL/O interfaces.^33–36

ILs are salts in the liquid state around room temperature. They are solvent-free and have specific properties, such as flame resistance, high ionic conductivity, and high structural designability.³⁷ Particularly, the high structural designability of cations and anions endows ILs with a wide variety of physicochemical properties. Electrochemistry at the IL/W interface has been enabled by designing IL ions to possess high hydrophobicity,^26,38,39 and conversely, at the IL/O interface with IL ions of high hydrophilicity.^33–36 ILs are known to form specific structures in the bulk and at the interface. In the IL bulk, it has been reported using molecular dynamics (MD) simulations that alternating ionic shells are formed around a central ion of interest.⁴⁰ At the interface, ILs also form alternating ionic layers, which is known as overscreening.^31,41–48 This feature is unique to ILs, which are solvent-free, and is not observed in conventional electrolytes.

In this study, according to the designability and unique local structures, we focused on the IL–IL two-phase system composed of trioctylmethylammonium bis(nonafluorobutanesulfonyl)amide (TOMAC4C4N) and ethylammonium nitrate (EAN), which were used as the hydrophobic and hydrophilic ILs for electrochemical IL/W^49,50 and IL/O^33,36 interfaces, respectively. The two-phase system of two immiscible ILs has already been reported;^51–65 however, the interfacial structure has not yet been explored either with or without potential control. The IL–IL two-phase system has promising applications in hydrocarbon separation,⁵³ metal ion extraction,^55,57,59,61 and metal nanoparticle synthesis.⁶⁰ In the latter two applications, ion and electron transfer occurs across the IL/IL interface, making the understanding of the electric double layer (EDL) structure essential. This system is expected to be a new class of ITIES, electrochemical IL/IL interface, and furthermore, an IL-specific EDL—unlike that at conventional liquid/liquid interfaces—is expected at the IL/IL interface.

The present study aims to elucidate the microscopic structure and potential dependence of an electrochemical IL/IL interface using molecular dynamics (MD) simulations, to uncover the physicochemical properties of solvent-free liquid/liquid interfaces. MD simulations are powerful tools to support experimental results and to reveal microscopic structures that are difficult to elucidate experimentally. Three electrochemical liquid/liquid interfaces have been previously investigated using MD simulations, namely the O/W,⁶⁶ IL/W,⁶⁷ and F/W²⁰ interfaces. The EDL structure at the O/W interface⁶⁶ was reported to be of the discrete Helmholtz-type, where cations in one liquid phase and anions in the other liquid phase interact closely across the interface. At the IL/W⁶⁷ and F/W²⁰ interfaces, hydrophobic ions in IL or F (IL was added as the supporting electrolyte) formed the interfacial ionic layers without a diffuse layer, whereas ions in W formed a Gouy–Chapman-type EDL. At a solvent-free IL/IL interface, ions are in contact with each other not only within each liquid phase but also across the interface, which would lead to an interfacial structure that differs from the conventional EDL. In this study, we introduce the solvent-free IL/IL interface as a new class of electrochemical liquid/liquid interfaces. Notably, the IL/IL interface forms a specific EDL in which small hydrophilic IL ions are inserted into the interfacial “pockets” created by the interfacial roughness, forming a three-dimensional EDL.

2. MD simulation

2.1. System

An IL-IL two-phase system was prepared using EAN ([EA⁺]NO₃⁻, Fig. 1a) as the hydrophilic IL phase and TOMAC4C4N ([TOMA⁺][C4C4N⁻], Fig. 1b) as the hydrophobic IL phase. Two graphene layers (GRs) sandwiching the IL–IL two-phase system were used as electrodes to polarize the IL/IL interface (Fig. 2). The force field employed was on the framework of OPLS-AA.⁶⁸ The force field parameters were taken from the literature as follows: Jorgensen et al. in 2024⁶⁹ for EA⁺ and the alkyl chains of TOMA⁺; CL&P⁷⁰ for NO₃⁻,⁷¹ C4C4N⁻,⁷² and around the N atom in TOMA^+ 73,74 (see Fig. S1 and Table S1–S4). For the force field for sp² carbons of GR, the bond, angle, and dihedral potentials were adopted from the OPLS-AA parameters with bond lengths of 1.42 Å and angles of 120°. Since non-polarizable force fields overestimate the electrostatic interactions in ILs, the ionic charges were scaled by a factor of 0.8 to account for the effect of electronic polarization.^71,75 The compositions in the system are shown in Table S5.

Fig. 1 Ionic structures for the (a) hydrophilic and (b) hydrophobic ILs.

Fig. 2 Simulation box for the IL-IL two-phase system sandwiched between two GR sheets.

2.2. Simulation details

The equations of motion were calculated by using the leap-frog algorithm. For non-bonded interactions, the Lenard-Jones and the coulombic potentials had a cutoff of 12 Å. Electrostatic calculations were carried out by using the PME method with an accuracy of 1.0 × 10⁻⁵. To constrain the C–H and N–H bond lengths, the LINCS algorithm was used. The simulation time step was 2 fs. The energy minimization of the initial configuration in the system was carried out with the target maximum force of 100 kJ mol⁻¹ nm⁻¹. A v-rescale thermostat⁷⁶ (coupling constant: 2.0 ps) and a c-rescale barostat⁷⁷ (coupling constant: 4.0 ps) were used to equilibrate the system at 400 K and 1 bar. The bulk simulation for each IL phase was performed under 3-dimensional periodic boundary conditions using the NPT ensemble for 10 ns. The equilibrated bulk structures of the two IL phases were used in the initial configuration for interfacial simulations. A rectangular simulation box (4.673 nm × 4.686 nm × 80.00 nm) was prepared, in which the two IL phases were aligned and sandwiched between two GR sheets along the z-axis to form a GR|TOMAC4C4N|EAN|GR configuration, as shown in Fig. 2. The liquid length in the z-direction for both IL phases was longer than 10 nm, which is sufficient to prevent overlap of the two electric double layer (EDL) structures within each IL phase (see Section 3.1 for the results). In the xy-directions, the cell width (∼4.6 nm) was made long enough compared with the minimum wavelength of the capillary waves at the IL/IL interface, which is determined by the size of the large ions, TOMA⁺ and C4C4N⁻, ∼10 Å.

While fixing the x and y coordinates of the C atoms of the two GR sheets and applying 1 bar to the sheets from the vacuum sides, the system was equilibrated under the NVT ensemble for 10 ns. After equilibration, the z positions of the GR sheets were fixed so that their distance matched the average one (26.88 nm) during the equilibration run. The system was then equilibrated again under the NVT ensemble for 20 ns. This final structure was used as the initial configuration for the uncharged interfacial system. For the charged system, the C atoms of the two GR sheets were charged evenly with the same magnitude but with the opposite sign; The surface charge of the GR sheet on the EAN side q_GR,EAN was 0.00, ±3.68, ±7.32 µC cm⁻², with that on the TOMAC4C4N side q_GR,TOMAC4C4N being −q_GR,EAN. The system was equilibrated under the NVT ensemble for 20 ns. Both the uncharged and charged systems were analyzed with a 100 ns production run with the Yeh–Berkowitz correction.⁷⁸ Five independent simulations with different initial structures were averaged. Trajectories were recorded every 10 ps for atomic coordinates. All simulations were performed using GROMACS 2021.2.⁷⁹

2.3. Analysis of trajectory

The MD trajectories were analyzed to obtain the number density distribution along the z-axis direction ρ_i(z). The representative points were their N atoms for all the four ions (TOMA⁺, C4C4N⁻, EA⁺, and NO₃⁻; see Fig. 1). The charge density distribution ρ_c,_total(z) was calculated by multiplying ρ_i(z) by the charge of each atom in the force field q^FF_i (eqn (1)).The potential distribution ϕ(z) was obtained by numerically integrating the Poisson equation in the z-axis twice (eqn (2)).where ε₀ is the dielectric constant of the vacuum, and the relative permittivity ε_r is set to 1. The potential was referenced to the vacuum phase on the TOMAC4C4N side. The bulk potentials of TOMAC4C4N phase ϕ_TOMAC4C4N and EAN phase ϕ_EAN were evaluated by averaging the potentials in their bulk z region of 10–15 nm and 20–25 nm, respectively. The interfacial potential difference Δϕ was defined as their difference (ϕ_EAN − ϕ_TOMAC4C4N).

Two-dimensional mapping of the orientation angle distribution vs. z-axis was obtained by mapping the orientation angle distribution d(z,θ) of an interatomic vector in the z region z ∼ z + dz (dz = 0.1 nm). The orientation angular distribution was normalized to satisfy eqn (3).

where θ is the angle of the interatomic vector with respect to the z-axis (Fig. 3a). The orientation of the following interatomic vectors were analyzed; for TOMA⁺, two vectors from the N atom to the terminal C atoms of the methyl and octyl groups; for C4C4N⁻, vectors from the N atom to the terminal C atoms of the perfluorobutyl groups; for EA⁺, a vector from the N atom to the terminal C atom of the ethyl group; for NO₃⁻, a vector normal to the plane formed by three O atoms (Fig. 3b).

Fig. 3 Definition of (a) the orientation angle θ of an interatomic vector with respect to the z-axis and (b) interatomic vectors in ions; for NO₃⁻, a vector normal to the plane formed by three O atoms.

The three-dimensional radial distribution function g(r) was obtained using eqn (4).

where r is the distance of the target atom from the central atom, and n(r) is the number of target atoms between r and r + dr (dr = 0.01 nm). g(r) was normalized to converge to 1 in the bulk.

3. Results and discussion

3.1. Interfacial potential difference

Charging the two GR electrodes with an equal magnitude and opposite sign imposed a potential difference across the IL–IL two-phase system. Fig. 4 shows the potential profiles along the z-axis. In each bulk region (TOMAC4C4N phase; 3 nm < z < 11 nm, EAN phase; 15 nm < z < 22 nm), the potentials were flat, and the potential shifts were observed only at the GR/TOMAC4C4N, TOMAC4C4N/EAN, and EAN/GR interfaces. These shifts indicated that the interfacial charges were sufficiently screened, resulting in the formation of EDLs at these three interfaces. The EDLs at the two IL/GR interfaces showed alternately charged ionic multilayers, like those observed in our previous MD studies.^{20,31,67,80,81} The potential profiles in the vicinity of the TOMAC4C4N/EAN interface (z = ∼12.5 nm), which is the new electrochemical liquid/liquid interface investigated in the present study, are shown in Fig. 4b. The interfacial potential difference at the TOMAC4C4N/EAN interface was 0.00 V at q_GR,EAN = 0.00 µC cm⁻² and increased to +0.08 and −0.13 V upon charging up the GRs with q_GR,EAN = +7.32 and −7.32 µC cm⁻², respectively, demonstrating that the IL/IL interface is polarizable. At q_GR,EAN = ±7.32 µC cm⁻², we observed a rare event where an ion in the EAN phase transferred to the TOMAC4C4N phase, indicating that the potential is at the potential window edge at these charging conditions and that the potential window width is 0.2 V. This potential window coincides with the experimental one (Fig. S2 and S3) obtained with electrochemical measurements at liquid/liquid interfaces formed at a micropipette-tip.^26,27,36 Assuming a linear relationship between the surface charge density q_LL,EAN on the EAN side of the IL/IL interface and the interfacial potential difference Δϕ, the capacitance (q_LL,EAN/Δϕ) was estimated to be 64 µF cm⁻² (Fig. S4). This value is significantly larger than those reported for other electrochemical liquid/liquid interfaces, 10 times higher than that of the O/W interface⁶⁶ and three times higher than that of the IL/W interface.⁶⁷

Fig. 4 Potential profiles along the z-axis at various q_GR,EAN values; +7.32 (dark red), +3.68 (red), 0.00 (black), −3.68 (light blue), and −7.32 (blue) µC cm⁻² (a) for overall in the system, referenced to the potential of GR on the TOMAC4C4N side, and (b) in the vicinity of the TOMAC4C4N/EAN interface, referenced to the bulk potential of the TOMAC4C4N.

To identify the origin of this unusually high capacitance, the total charge density distribution, ρ_c,total(z), at the IL/IL interface was examined (Fig. 5a). In the bulk of each phase (z < 11 nm, z > 15 nm), the charge density was zero; however, at the interface, slight deviations from zero in the form of small peak pairs were observed. These peak magnitudes are significantly smaller than those reported previously for the O/W⁶⁶ and IL/W⁶⁷ interfaces, where distinct positive and negative peaks were spatially separated along the z-axis, consistent with a Helmholtz-type or Gouy–Chapman-type EDL. To investigate this unusual polarizability behavior, the total charge density distribution was decomposed into the two contributions from the TOMAC4C4N (TOMA⁺, C4C4N⁻) and EAN (EA⁺, NO₃⁻) phases (Fig. 5b). When the GR on the EAN side was negatively (positively) charged, positive (negative) peaks appeared on the TOMAC4C4N side of the interface, while negative (positive) peaks appeared on the EAN side. This switching was caused by ion accumulation at the interface such as a cation (anion)-rich on the TOMAC4C4N side and an anion (cation)-rich on the EAN side (Fig. S5), which has already been reported for the electrochemical liquid/liquid interfaces.^20,66,67 Notably, the charged EDL regions of the two phases overlapped in the z-axis. This overlap led to the cancellation of positive and negative charge peaks within the xy plane, resulting in a reduction in the total charge density. The surface charge density of the accumulated ions on the TOMAC4C4N and EAN sides of the interface is equal in magnitude to q_GR (Fig. S6); therefore, this apparent enhancement of the capacitance arises from an underestimation of the interfacial potential difference. This behavior is different from the EDL structures of conventional electrochemical liquid/liquid interfaces,^20,66,67 where the overlap of the positive and negative peaks was marginal. This peak overlap can be attributed to either an interfacial mixed layer^82,83 of ILs or the interdigitation of two immiscible ILs at the interfacial region.

Fig. 5 Charge density distributions along the z-axis for (a) all ions in the system (black solid) at various q_GR,EAN values; +7.32 (dark red), +3.68 (red), 0.00 (black), −3.68 (light blue), and −7.32 (blue) µC cm⁻² and (b) all ions, and ions in the TOMAC4C4N (red dashed) and EAN (blue dashed) phases at various q_GR,EAN values.

3.2. Interfacial “pockets” and insertion of ions

To examine the ionic behavior at the IL/IL interface, the in-plane distribution of ions at the interface was analyzed using MD snapshots. Fig. 6a shows how to view the IL/IL interface from the EAN phase side. On the TOMAC4C4N side (Fig. 6b–d), all atoms consisting the IL are displayed, while on the EAN side (Fig. 6e–g), only EAN atoms with z < (Z_min + Z_max)/2 are shown, where Z_min and Z_max are the minimum z-coordinate of the atoms in the EAN phase and maximum z-coordinate of the atoms in the TOMAC4C4N phase, respectively (see Fig. 6a). In Fig. 6c, on the TOMAC4C4N side at electrical neutrality (q_GR,EAN = 0.00 µC cm⁻²), the N atoms of TOMA⁺ (green) and C4C4N⁻ (purple) were evenly distributed at the interface. With the charge applied to the interface (q_GR,EAN = ±7.32 µC cm⁻², Fig. 6b and d), the EDL switched to either a cation-rich or an anion-rich state, consistent with the density profiles in Fig. 5b and S5b. In Fig. 6f, on the EAN side at q_GR,EAN = 0.00 µC cm⁻², multiple EA⁺ (red) and NO₃⁻ (blue) were unevenly distributed in the area occupied by hydrophobic ions. At q_GR,EAN = ±7.32 µC cm⁻² (Fig. 6e and g), similar aggregates were observed. Considering the difference in ionic radius between the two phases (Fig. S7), these hydrophilic ion aggregates suggested the formation of interfacial “pockets” due to the interfacial roughness rather than a mixed IL layer. Here, the size of the “pockets” was comparable to the minimum wavelength of the capillary waves at the IL/IL interface, which was determined by the size of large ions, TOMA⁺ and C4C4N⁻, ∼10 Å.

Fig. 6 (a) Two viewing ways of the interfacial structure at the TOMAC4C4N/EAN interface, where Z_min and Z_max are the minimum z-coordinate of the EAN atoms and maximum z-coordinate of the TOMAC4C4N atoms, respectively. (b)–(g) Snapshots of the interface at three q_GR,EAN values for the (b)–(d) TOMAC4C4N and (e)–(g) EAN sides. The color for each atom: the N atom in TOMA⁺ (green), the other atoms in TOMA⁺ (yellow), the N atom in C4C4N⁻ (purple), the other atoms in C4C4N⁻ (light blue), EA⁺ (red), and NO₃⁻ (blue). The scale is the same for all the snapshots (b)–(g) with the scale bar of 2 nm in (b).

We hypothesized that the ionic aggregation in the “pockets” is due to the absence of solvent molecules, since solvation would inherently prevent the aggregation. To confirm the validity of this hypothesis, we investigated the TOMAC4C4N/W(EAN) interface, diluting the EAN phase with water. Fig. 7 shows the snapshots of the interface at q_GR,EAN = +7.32 µC cm⁻², where cations were accumulated on the EAN side and anions on the TOMAC4C4N side, viewed in the same way as Fig. 6e. At the IL/IL interface (Fig. 7a), one can see the aggregates of smaller ions, EA⁺ (red) and NO₃⁻ (blue), partly inserted into the interfacial “pockets”. In contrast, at the TOMAC4C4N/W(EAN) interface (Fig. 7b), the ion aggregates were not observed, and the number of the inserted ions drastically decreased. To further confirm this hydration effect, we replaced EA⁺ with Li⁺, a hard ion with a strong hydration shell. In Fig. 7c for the TOMAC4C4N/W(LiNO₃) interface, the ion insertion into the interfacial “pockets” was strongly suppressed. The snapshots for the three liquid/liquid interfaces shown in Fig. 7 illustrate that significant ion insertion occurred only at the solvent-free IL/IL interface. Notably, for the two IL/W interfaces, the total charge density distribution, ρ_c,total(z), exhibited clear positive and negative peaks (Fig. S8), consistent with the previous studies^20,66,67 although they were partly overlapped along the z-axis. We note here that the interfacial roughness, the total amplitude of the capillary waves, at the IL/IL interface was 2.5 Å, comparable to that of the IL/W interfaces (Fig. S9). The interfacial roughness did not significantly change regardless of the applied potential. We also note that these are smaller than experimentally obtained values at O/W interfaces,⁸ because of the underestimation in MD caused by cell size limitations. Considering the minimum wavelength of the capillary wave is determined by the size of the larger ions, the size (depth and width) of the interfacial “pockets” at these three interfaces is also comparable. In other words, the differences in the EDL structures between the IL/IL and IL/W interface are induced by water, which plays a crucial role in determining the EDL structure at liquid/liquid interfaces.

Fig. 7 Snapshots on the EAN side of the interface at +7.32 µC cm⁻² as in Fig. 6e at the (a) TOMAC4C4N/EAN, (b) TOMAC4C4N/W(EAN), and (c) TOMAC4C4N/W(LiNO₃) interfaces. The color definition is the same as in Fig. 6, with the addition of water (black) in Fig. 7b, c and Li⁺ (red) in Fig. 7c. The scale is the same for all the snapshots (a)–(c) with the scale bar of 2 nm in (a).

To further illuminate how water molecules disrupt ion aggregation at the interface, the distribution of ion aggregations between TOMA⁺ and NO₃⁻ was investigated. Fig. 8 shows the number density distribution, at q_GR,EAN = 0.00 µC cm⁻², of the N atom of TOMA⁺ classified by the coordination number of NO₃⁻ within a cutoff distance of 0.67 nm which corresponds to the first coordination shell of the N atom of NO₃⁻ around the N atom of TOMA⁺ (Fig. S10). Fig. 8a shows that, in the TOMAC4C4N bulk (z < 10 nm), the number densities of N atoms not coordinated by NO₃⁻ are equal to the total number of N atoms because no NO₃⁻ exists in this phase. At the IL/IL interface (10 nm < z < 14 nm, Fig. 8b), TOMA⁺ was coordinated by NO₃⁻ in the EAN phase across the interface, and the coordination number increased up to 5 as the TOMA⁺ position is closer to the interface. On the other hand, at the IL/W interfaces, TOMA⁺ was coordinated with no more than two NO₃⁻ (Fig. 8c and e) and remained predominantly surrounded by more than 5 water molecules across the interface (Fig. 8d and f). Because of the capillary wave on the IL/IL interface, TOMA⁺ at the IL/IL interface protrude to or recede from the EAN side. The receded TOMA⁺ at the IL/IL interface could be coordinated by only a few NO₃⁻, whereas for the protruded TOMA⁺ the coordination number of NO₃⁻ increased. These interfacial structures allowed ions in the TOMAC4C4N phase to be coordinated with the hydrophilic ions in the EAN phase across the interface, similarly to interfacial ion pairing at the interface previously discussed.^84–87 In contrast, hydrated NO₃⁻ at IL/W interfaces, whose roughness was comparable to the IL/IL interface, were excluded from the interfacial “pockets”. Thus, ion insertion is governed by two factors: the size difference between the hydrophobic and hydrophilic ions and the presence of solvents. For the former, the larger the large ions are compared with the small ions, the more room the interfacial “pockets” provides for the small ions. For the latter, solvation makes it difficult for the solvated and enlarged small ions to enter the “pockets”. In the solvent-free system studied here, these two requirements are satisfied, leading to the formation of the specific EDL structure, whereas in the conventional liquid/liquid interfaces,^20,66,67 the EDL structure has been reported under conditions where a solvent (water) is present and hard ions are employed as supporting electrolytes in the hydrophilic phase. As shown in Fig. 9a, the EDL structure at the conventional liquid/liquid interfaces^20,66,67 is more two-dimensional, in which cations and anions indirectly interact face-to-face across the interface due to the solvent presence. On the other hand, at the IL/IL interface (Fig. 9b), cations and anions interact with ion coordination across the interface, where the EDL is formed along the capillary wave-roughened interface and is more three-dimensional.

Fig. 8 Number density distribution of the N atom of TOMA⁺ classified by the coordination number of the N atom of NO₃⁻ at the (a) and (b) TOMAC4C4N/EAN, (c) TOMAC4C4N/W(EAN), and (e) TOMAC4C4N/W(LiNO₃) interfaces and the O atom of water at the (d) TOMAC4C4N/W(EAN) and (f) TOMAC4C4N/W(LiNO₃) interfaces.

Fig. 9 Schematics of the structures of the (a) two-dimensional and (b) three-dimensional EDL at the liquid/liquid interfaces.

3.3. Ionic structure at the interface

3.3.1. Interaction between hydrophilic IL and hydrophobic IL. To elucidate the microscopic interfacial structure and local ionic environments at the IL/IL interface, radial distribution functions (RDFs) and coordination numbers were analyzed. Fig. 10 shows the atom–atom RDFs around the N atom of TOMA⁺ at q_GR,EAN = 0.00 µC cm⁻² in the interfacial region (see S11, Fig. S11, and Table S6 in Supporting Information for the definition). Fig. 10a shows that at the TOMAC4C4N/EAN interface, the N atom of TOMA⁺ exhibited a first coordination peak with the N atom of NO₃⁻, reflecting the ion coordination across the interface, while TOMA⁺–EA⁺ correlations appeared from the second coordination shell. These RDFs exhibited an oscillatory distribution of the cation and anion in an out-of-phase manner, which eventually converged in the bulk region. This oscillatory distribution was typically shown in the bulk of ILs⁴⁰ and even at the interface of ILs as overscreening.^31,41–43 The same analysis at the IL/W interfaces (Fig. 10b and c) shows that the TOMA⁺–NO₃⁻ coordination in the first shell persisted, while the second cationic peaks (EA⁺ or Li⁺) were markedly suppressed, indicating that water destroyed the overscreening structure. At the TOMAC4C4N/W(EAN) interface (Fig. 10b), the EA⁺ distribution exhibited a weak coordination peak at 0.7 nm, whereas at the TOMAC4C4N/W(LiNO₃) interface (Fig. 10c), no Li⁺ peak appeared. This difference between EA⁺ and Li⁺ could be attributed to the amphiphilicity of EA⁺, which, owing to its non-polar ethyl group, could approach the hydrophobic IL phase more closely than hydrated Li⁺.

Fig. 10 Atom-atom RDF around the N atom of TOMA⁺ at the (a) TOMAC4C4N/EAN, (b) TOMAC4C4N/W(EAN), and (c) TOMAC4C4N/W(LiNO₃) interfaces at q_GR,EAN = 0.00 µC cm⁻² for the N atoms of the (red) EA⁺ or Li⁺ and (blue) NO₃⁻, and the O atom of (black) water.

Fig. 11 shows the potential dependence of the RDFs and coordination numbers of EA⁺ and NO₃⁻ around the N atom of TOMA⁺ in the first coordination shell of NO₃⁻ at the TOMAC4C4N/EAN interface. Fig. 11a shows the structure in which cations and anions in the EAN phase are alternately coordinated with TOMA⁺, as described above (Fig. 10a). At q_GR,EAN < 0 µC cm⁻², where TOMA⁺ and NO₃⁻ were enriched at the interface, the first peak in the RDF between TOMA⁺ and NO₃⁻ increased in intensity, but the position remained unchanged. The first coordination peak of EA⁺ similarly increased in intensity and slightly shifted closer to TOMA⁺. The increased intensity of the first peaks in the two RDFs suggests an increased number of both cations and anions in the first coordination shell, as observed in the EDL overscreening behavior in ILs at flat electrodes. For the coordination number (Fig. 11b), at q_GR,EAN = 0.00 µC cm⁻², TOMA⁺ was coordinated by three NO₃⁻ and two EA⁺, resulting in local charge neutrality at the interface. When TOMA⁺ and NO₃⁻ were enriched at the interface (q_GR,EAN < 0 µC cm⁻²), the coordination number increased for not only NO₃⁻ but also EA⁺, which again follows the overscreening behavior. Specifically, NO₃⁻ accumulated in the first coordination shell of TOMA⁺ to compensate for its charge; however, in the absence of solvent, small ions such as EA⁺ contributed to the excess charge compensation of NO₃⁻, leading to the formation of local overscreening, analogous to that observed in the bulk³⁸ and at the interface^31,41–43 of ILs. Accordingly, the shift of the first peak in the RDF of EA⁺ shown in Fig. 11a results from the increased population of overscreening NO₃⁻ at q_GR,EAN < 0 µC cm⁻², which enhanced the attraction of EA⁺ in the second coordination shell. Consequently, at the solvent-free IL/IL interface, locally alternating layers of cations and anions are formed, which leads to a three-dimensional EDL (Fig. 9b). On the other hand, at the IL/W interface, the hydration of ions in the W phase suppresses ion coordination across the interface, rather, interfacial ionic interactions are predominantly water-mediated, which suggests a two-dimensional EDL (Fig. 9a).

Fig. 11 (a) Atom-atom RDF around the N atom of TOMA⁺ at the TOMAC4C4N/EAN interface coordinated with the N atom of (upper) EA⁺ and (bottom) NO₃⁻ at various q_GR,EAN values; +7.32 (dark red), +3.68 (red), 0.00 (black), −3.68 (light blue), and −7.32 (blue) µC cm⁻². (b) Coordination number at various q_GR,EAN around the N atom of TOMA⁺ at the TOMAC4C4N/EAN interface for the N atoms of (red) EA⁺ and (blue) NO₃⁻.

Based on the discussion so far, the following considerations can be made regarding the EDL structure at the liquid/liquid interface between water and a hydrophobic liquid. When the W phase contains ions that are easily hydrated (e.g. Li⁺, EA⁺, Cl⁻, and NO₃⁻) as the supporting electrolyte, a two-dimensional EDL is formed because of the solvation of the ions. However, as shown in Fig. S12a, when the W phase contains amphiphilic ions that are not easily hydrated but are smaller than the size of the interfacial “pockets”, such as tetramethylammonium (TMA⁺) in Fig. S12a, the ions are inserted into the “pockets”. For this case, whether the EDL is two-dimensional or three-dimensional depends on the interfacial structure on the hydrophobic side. If large ions whose polar groups are surrounded by bulky nonpolar groups (e.g. bis(triphenylphosphoranylidene)ammonium,⁶⁶ tetrakispentafluorophenylborate,⁶⁶ and tetrakis[3,5-bis(trifluoromethyl)phenyl]borate²⁶) are chosen as the supporting electrolyte in the hydrophobic phase or constitute the phase itself as an IL, the polar groups of the large ions cannot be protruded toward the hydrophilic side of the interface, making it difficult to form a three-dimensional EDL. In contrast, for asymmetric ions with exposed polar and charged groups like TOMA⁺ and C4C4N⁻ (Fig. 1) in the present study, or ions with flexible side chains like trihexyltetradecylphosphonium (THTDP⁺),^20,21,23 the charge protrusion at the interface facilitates the formation of a three-dimensional EDL (Fig. S12b and c). In other words, the formation of a three-dimensional EDL is determined by (i) how readily ions from both phases can expose their polar groups toward the opposite side of the interface and (ii) how smaller ions can be inserted into the interfacial “pockets”, whose size is determined by the capillary wave.

3.3.2. Orientational correlation dependence on the z direction. Fig. 12 shows the two-dimensional mapping of the orientational angle distribution along the z-axis at q_GR,EAN = 0.00 µC cm⁻². In the color scale of d(z,θ), light blue, d(z,θ) = 1, represents isotropic orientation, whereas red, higher d(z,θ) at 3, indicates a polar orientation at a given z-region. The orientation of interatomic vectors was defined as shown in Fig. 3. In the EAN phase in the bulk (z > 13 nm), both the normal vector of three O atoms plane in NO₃⁻ (Fig. 12a) and the N–C vector of EA⁺ (Fig. 12b) exhibited isotropic distributions. In contrast, within the interfacial region (z < 13 nm), for NO₃⁻, at z =12.5 nm, a distribution of the surface normal vector appears around 0 and 180 degrees, indicating that NO₃⁻ plane was oriented along the interface. This orientation implies in-plane electrostatic interactions between the negatively charged O atoms of NO₃⁻ and the NH₃⁺ moiety of the polar-oriented EA⁺. The ethyl chain of EA⁺ at the interface was preferentially oriented toward the TOMAC4C4N phase. This orientation was energetically favorable because the hydrophobic ethyl group favors the hydrophobic phase over the hydrophilic NH₃⁺ moiety. In the TOMAC4C4N phase, the distribution of the octyl chains of TOMA⁺ varied with the z-position. At z = ∼12 nm, a distribution appears around 120 degrees, whereas at z = ∼13 nm, the distribution becomes concentrated near 135 degrees, loosely pointing to the TOMAC4C4N bulk, similar to the orientation of C4C4N⁻, vectors from the N atom to the terminal C atoms of the perfluorobutyl groups (Fig. S13). These tendencies were also observed at the IL/W⁶⁷ and F/W²⁰ interfaces. In Fig. 12d, the methyl groups of TOMA⁺ preferentially oriented toward the EAN phase at z = ∼13 nm (Fig. 12c), again the same as in the previous studies.^20,67 The z-region of preferential orientation of TOMA⁺ corresponds to that in which EA⁺ and NO₃⁻ in the EAN phase showed polar ordering (Fig. 12a). This polar ordering of the moiety in TOMA⁺ indicated that at z = ∼13 nm, the protrusion of TOMA⁺ toward the EAN phase resulted in the bulky octyl chains preferentially oppositely orienting toward the hydrophobic bulk and the methyl chain orienting toward the hydrophilic phase. Moreover, this z-region corresponds to the interfacial region in the charge density distribution (Fig. 5b), suggesting that the specific EDL structure is governed by interactions between polar-oriented ions.

Fig. 12 Two-dimensional mapping of the orientational angle distribution along the z-axis for the (a) normal vector of three O atoms plane in NO₃⁻, (b) N–C vector of EA⁺, and (c) N–C_octyl and (d) N–C_methyl vectors of TOMA⁺. The color scale of d(z,θ) represents the orientation distribution; d(z,θ) = 1 is isotropic orientation, and d(z,θ) = 3 is a polar orientation.

4. The formation of “IL finger”

At q_GR,EAN = +7.32 µC cm⁻², we observed a phenomenon where an EA⁺ ion is transferred from the EAN into TOMAC4C4N phase, although it happened infrequently. This indicates that the interfacial potential at this charged state is at the edge of the potential window. This is also the case with NO₃⁻ transfer to the TOMAC4C4N phase at q_GR,EAN = −7.32 µC cm⁻². When ions in the EAN phase are about to transfer to the TOMAC4C4N phase, a structure was formed where the transferring ion is accompanied by other ions in the EAN phase. We call this structure “ionic liquid finger”, shown in Fig. 13. This term comes from the “water finger” at the O/W interfaces, which is formed during the transfer of a hydrophilic ion from W to O,⁷ thereby lowering the intermediate Gibbs energy during the transfer.^88,89 As Marcus previously proposed,⁸⁸ during the ion transfer across a liquid/liquid interface between liquids A and B, the protrusion of liquid A into liquid B and vice versa play important roles in the desolvation/solvation processes for the transferring ions. In the case of the IL/IL interface, when EAN ions transfer into the TOMAC4C4N phase, it is unnecessary for TOMAC4C4N to protrude into the EAN phase because the EAN ions at the IL/IL interface have already completed the first stage of the transfer process, partly desolvated from EAN and partly solvated by TOMAC4C4N. Under these circumstances, two possible transfer mechanisms for a hydrophilic ion are considered: (i) transfer accompanied by the finger structure and (ii) transfer of a sole ion without the finger formation. In mechanism (i), coulombic interactions between unlike ions in the finger reduce the intermediate Gibbs energy, thereby facilitating ion transfer. In mechanism (ii), the large ions in the hydrophobic phase, TOMA⁺ and C4C4N⁻, act as a “catalyst”,⁹⁰ which interact with the transferring small ions across the interface, leading to the ion transfer to the TOMAC4C4N phase without the finger formation.

Fig. 13 Snapshots of ionic liquid fingers when (a) NO₃⁻ and (b) EA⁺ are transferred from the EAN phase (lower) to the TOMAC4C4N phase (upper) across the IL/IL interface.

5. Conclusions

We investigated the EDL structure at the solvent-free IL/IL interface using MD simulation. Amphiphilic ions in the EAN phase were inserted into the “pockets” formed by the interfacial roughness. The large ions in the TOMAC4C4N phase at the interface were coordinated with small ions across the interface, resulting in a three-dimensional EDL. This three-dimensional nature in EDL is not from an increase in the interfacial roughness, but from a solvent-free environment. This was confirmed by the comparison with the IL/W interfaces where the hydrophilic IL is diluted with water, the small ions were hydrated and enlarged, which hindered ionic insertion and interfacial ion coordination, promoting the formation of a two-dimensional EDL. The three-dimensional EDL showed anomalous capacitance enhancement in MD due to charge peak cancellation. However, as predicted in a previous theoretical study on the capacitance at liquid/liquid interfaces,⁷ the three-dimensional EDL may, in reality, exhibit a higher capacitance than its two-dimensional counterpart. This will be verified by electrochemical measurements at the IL/IL interface in the future. By analyzing the EDL structure at the various liquid/liquid interfaces, the EDL structure is determined by two factors: (i) larger ions exposing their polar groups and (ii) small ions inserted into the interfacial “pockets”. Moreover, ions in the EAN phase transfer to the TOMAC4C4N phase with an “IL finger” composed of EAN ions.

Author contributions

K. Y.: investigation, formal analysis, writing – original draft, K. K.: writing – review & editing, K. I.: writing – review & editing, Y. Z.: investigation, Y. Y.: writing – review & editing, T. S.: writing – review & editing, N. N.: project administration, conceptualization, writing – review & editing.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d6cp01551d.

Acknowledgements

We acknowledge Yohei Kuroyama (Kyoto University) for his experimental discovery of an electrochemically polarizable IL/IL interface. This work was partly supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grants (23H03829 and 25K01875).

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