Long-range electrostatic screening in ionic liquids

Significance

Liquid solutions with high concentrations of electrically charged ions are key elements of many energy storage technologies and are prevalent in biology. Nevertheless, they remain poorly understood. We study ionic liquids—liquids composed solely of ions—with the goal of providing a general picture of concentrated ionic solutions. Using molecular-scale experiments, we show that, surprisingly, less than 0.1% of the ions in ionic liquids are “free” to contribute to electrostatic screening, with the remainder “stuck” as neutral aggregates. Our temperature-dependent results provide fundamental guidance for designing high-performance ionic liquids for numerous applications. More broadly, we provide a novel way of envisioning concentrated ionic solutions with wide-ranging implications, such as elucidating the nanoscale properties of underwater bioadhesives and other self-assembled biomolecules.

Abstract

Electrolyte solutions with high concentrations of ions are prevalent in biological systems and energy storage technologies. Nevertheless, the high interaction free energy and long-range nature of electrostatic interactions makes the development of a general conceptual picture of concentrated electrolytes a significant challenge. In this work, we study ionic liquids, single-component liquids composed solely of ions, in an attempt to provide a novel perspective on electrostatic screening in very high concentration (nonideal) electrolytes. We use temperature-dependent surface force measurements to demonstrate that the long-range, exponentially decaying diffuse double-layer forces observed across ionic liquids exhibit a pronounced temperature dependence: Increasing the temperature decreases the measured exponential (Debye) decay length, implying an increase in the thermally driven effective free-ion concentration in the bulk ionic liquids. We use our quantitative results to propose a general model of long-range electrostatic screening in ionic liquids, where thermally activated charge fluctuations, either free ions or correlated domains (quasiparticles), take on the role of ions in traditional dilute electrolyte solutions. This picture represents a crucial step toward resolving several inconsistencies surrounding electrostatic screening and charge transport in ionic liquids that have impeded progress within the interdisciplinary ionic liquids community. More broadly, our work provides a previously unidentified way of envisioning highly concentrated electrolytes, with implications for diverse areas of inquiry, ranging from designing electrochemical devices to rationalizing electrostatic interactions in biological systems.

Electrolyte solutions are multicomponent liquids that are composed of ions (solutes) dissolved in a liquid phase (solvent), a classic example being salt water. Like any ideal mixture, the driving force for the dissolution of ions in electrolyte solutions is entropic. Unlike ideal mixtures, the long-range nature and high interaction free energy of the electrostatic interactions between ions ensures that the physical properties of all but the most dilute electrolyte solutions exhibit pronounced deviations from ideal behavior. These deviations primarily arise from the steric “crowding” of ions and the electrostatic correlation of ions, for example the formation of neutral ion pairs, both of which increase the range of electrostatic interactions, compared with ideal solutions (1). As a result, the development of a general conceptual picture of concentrated electrolyte solutions remains challenging. Nevertheless, electrolytes with high ionic concentrations are prevalent in biological systems (2) and technological applications, such as energy storage devices (3–5), so overcoming this challenge remains an important task.

In this work, we study room-temperature ionic liquids (RTILs), single-component liquids composed solely of ions, in an attempt to provide a starting point for a new conceptual understanding of electrostatic screening in concentrated electrolytes. Although RTILs do not have neutral solvent molecules separating the constituent ions, the high degrees of ion crowding and electrostatic correlations present in RTILs are expected to be fundamentally related to ion crowding and electrostatic correlations in highly concentrated electrolyte solutions (5). To date, thousands of RTILs have been identified with diverse physical properties that can be tuned via careful design of cation–anion pairs (6). Although these properties are largely governed by the same strong coulombic interactions that underlie the 801 °C melting point of crystalline sodium chloride at atmospheric pressure, the large sizes and asymmetric charge distributions of RTIL ions suppress the formation of ordered crystals. Notably, the high thermal and electrochemical stabilities, negligible volatilities, and variable intrinsic ionic conductivities of many RTILs make them promising materials for numerous applications, including electric double-layer capacitors, batteries, and self-assembly media (3–10). Many of these applications depend critically on interfaces between charged surfaces and RTILs. Nevertheless, the fundamental characteristics of RTIL electric double layers remain an active area of research and discussion (5, 11).

A generally accepted picture is that the electric double layers formed by RTILs consist of ordered layers of cations and anions, with these perturbed ionic concentrations quickly approaching bulk distributions on the order of several ionic diameters (5). Much of this understanding was developed through nanoscale computational studies of coarse-grained ionic systems (5, 11–16) that are reminiscent of high-temperature molten salts. These studies predict that the electric double layers formed by RTILs should be short-range and exhibit pronounced charge density oscillations, similar to the screening behavior identified in pioneering work on molten KCl (15). Recent theoretical studies emphasize that complex ion ordering in RTILs can intimately depend on the electrochemical potentials of the charged surfaces (5, 17–19), but these studies have left intact the picture that the electric double layers formed by RTILs should be very short-ranged.

Experimentally, the short-range, surface-induced ordering of ions in RTILs has been confirmed with X-ray scattering experiments, atomic force microscopy (AFM) force measurements, and surface forces apparatus (SFA) measurements (17, 20–23), with these studies highlighting that the ordering of RTIL ions at surfaces exhibits many subtleties. For example, Atkin et al. (22) used AFM to demonstrate that gold electrode surfaces immersed in RTILs can undergo ion-mediated surface reconstructions under externally applied electrochemical potentials. Perkin et al. (23) have shown that RTIL ions self-assemble into ordered (smectic-like) bilayers when the cations contain pronounced nonpolar domains. Recent SFA measurements have added to these pictures by demonstrating the presence of a long-range monotonic, exponentially decaying, equilibrium force that extends to distances of up to 35 ionic diameters per surface (24, 25). Modeling this force as a diffuse double-layer interaction with a decay length corresponding to the Debye length led to the hypothesis that RTILs can be conceptualized as very weakly dissociated electrolyte “solutions,” where the electrostatic screening behavior is dominated by a small population of effectively dissociated ions (24).

However, the molecular mechanism of this apparent ion dissociation in RTILs remained to be explored. Unlike conventional, fully dissociated dilute electrolyte solutions, where the free-ion concentration is independent of temperature and the Debye length only modestly increases with temperature, one would expect the concentration of effectively dissociated ions and Debye length of RTILs, and other highly concentrated electrolytes where ionic aggregation is prominent, to strongly depend on the temperature. For these weakly dissociated electrolytes, increasing the temperature will dissociate ionic aggregates, significantly decreasing the Debye length.

Using the SFA technique, we studied two common aprotic ionic liquids with the bis(trifluorosulfonyl)imide ([NTf₂]⁻) anion and two different 1-alkyl-3-methylimidazolium cations: [C₂mim]⁺ and [C₃mim]⁺ (Fig. 1). Our results suggest that a long-range, monotonic force may be a general feature of the electric double layers formed by RTILs in contact with macroscopic charged surfaces, whenever surface-bound ion layers are unable to fully compensate surface charges. For mica surfaces, we find this long-range force to be in series with a short-range, nonmonotonic “oscillatory” structural force that is in agreement with the nanoscale surface-induced ion ordering identified in previous work on RTILs (17, 20–25). Further, we show that the long-range screening behavior of RTILs can be rationalized via a thermally activated population of either free ions or correlated charge domains, reminiscent of the free electron/hole approximation used in semiconductor physics.

Fig. 1.

Chemical structures and approximate dimensions of the RTIL ions. Molecular dimensions in angstroms were calculated from the van der Waals radii of the constituent atoms.

Results and Analysis

Equilibrium Force–Distance Measurements.

Force–distance, F(D), measurements were performed using a standard SFA 2000 (26), with resistive heating coils incorporated into the steel SFA housing (Fig. 2). A detailed description of the force and distance measuring methods can be found in ref. 26. Briefly, the top surface was actuated at constant angstroms-per-second displacement rates via a piezoelectric crystal, and the distance between the surfaces, D, was monitored with angstrom-scale resolution through interferometry. The two surfaces move at constant rates when the surfaces are not interacting, and colloidal interaction forces cause the surfaces to accelerate or decelerate. The deflection of a double-cantilever spring was used to determine the interaction force between the two surfaces at each distance to nanonewton resolution. This procedure enabled us to determine the distances between, and forces across, the surfaces with experimental errors of F/R = ±0.02 mN/m and D = ±0.2 nm.

Fig. 2.

Schematic of the SFA (26). The temperature was controlled via resistive heaters, and the distance between the two surfaces, D, was defined with respect to the contact of the two mica surfaces in the absence of RTIL, where D = 0.

Each SFA experiment was set up with two freshly prepared single-crystalline mica surfaces. [C₂mim][NTf₂] and [C₃mim][NTf₂] were synthesized, purified, dried, and characterized using a previously established procedure for the preparation of electrochemical-grade RTILs (27). The sizes of these [C_Rmim]⁺ cations and [NTf₂]⁻ anions (Fig. 1) both exceed the size of the 4-Å radius of K⁺ sites on mica surfaces, and mica surfaces develop negative surface potentials (17, 23–25) when exposed to bulk [C_Rmim][NTf₂] RTILs. This negative potential likely develops through a combination of the dissociation of surface-bound K⁺ ions present at cleaved mica surfaces, which are then replaced by larger [C_Rmim]⁺ cations—“crowding” (13)—and/or the overadsorption of [NTf₂]⁻ anions in the first surface-bound RTIL layer—“overscreening” (13). Our experiments cannot distinguish between these two possibilities, and the actual negative potential of mica surfaces may result from a complex combination of these two mechanisms. The resulting K⁺ concentration in the RTILs would be negligible, even if every K⁺ ion were to be replaced by [C_Rmim]⁺ cations.

Forces were measured on approach rates below which dynamic forces are negligible, as ascertained by forces that are independent of approach rates. Representative force–distance profiles, F(D), measured while bringing together two mica surfaces across [C₂mim][NTf₂] and [C₃mim][NTf₂] are shown by the data points in Fig. 3. Attractive forces arising from separating the surfaces more quickly than the extremely long times required for the viscous RTILs to flow back into the interface were measured during retraction of the mica surfaces, even for separation rates as slow as 2 Å/s (Fig. S1). Equilibrium force–distance measurements are the focus of this study.

Fig. 3.

Representative force–distance profiles measured across (A) [C₂mim][NTf₂] at T = 22 °C (blue data points) and 50 °C (green data points) and (B) [C₃mim][NTf₂] at T = 22 °C (black data points) and 45 °C (red data points). The open circles represent distances where the forces were measured without surface deformations, and the filled circles indicate progressive flattening of the surfaces under increasing loads, where the pressure applied to the bound ion layers stays approximately constant. The solid lines are fitted using the diffuse double-layer interaction potential, Eq. 1. The interaction potential is plotted for all D, but fits were numerically optimized for D > 1.5 (κ*)⁻¹, as discussed in the text. The parameter values presented on the plot correspond to the fitted parameters of the representative data. The average fitted parameters and SEs are presented in Tables 1 and 2.

Fig. S1.

Representative short-range interaction forces measured across [C₂mim][NTf₂] at 22 °C with R = 1 cm surfaces on approach (blue) and separation (red). The y axis is presented in units of force, F (without R normalization), because the Derjaguin approximation fails within the “oscillatory” regime due to a combination of surface deformation and curvature effects. On separation, we still observe evidence of solvation and double-layer forces; however, these equilibrium forces are superimposed on an additional weakly attractive dynamic force. This dynamic attractive force results from separating of the surfaces at rates that exceed the extremely long times required for the viscous RTILs to flow back into the interface under equilibrium conditions. Thus, the red points should not be interpreted as true equilibrium forces. In the absence of dynamic effects and/or energy dissipation, the forces measured when separating the two surfaces should exactly overlay the forces measured when bringing the two surfaces together.

To increase the sensitivity of our measurements in the long-range regime of the force–distance profiles (10 < D < 100 nm), we used surfaces with larger radii (lower curvatures) than the typical 1- to 2-cm-radius surfaces used previously by us and other researchers (23–25). This strategy is similar to using colloid probes in AFM to increase sensitivity of AFM measurements to weak, long-range colloidal forces. The 4- to 5-cm-radius surfaces we used in the majority of these experiments enabled us to increase our sensitivity to colloidal forces by a factor of approximately five relative to our previous measurements, where we used surfaces with R ≈ 1-cm radii (24). This is the case because the force resolution is set by the absolute value of the measured forces, whereas the magnitudes of the long-range double-layer forces scale as F/R, via the Derjaguin approximation (26, 28). The inherent tradeoff to this strategy is that extensive surface deformations (flattening) begin to occur at surface separations D < 5 nm with the larger-radius surfaces, limiting the final pressures that we can apply to the strongly surface-bound ion layers. As a result, we cannot fully “force out” all of the ion layers to access the entire range of “oscillatory” forces that were the focus of previous studies (21–23).

To ensure consistency with previous studies and to rule out large surface radii as the origin of the monotonic forces we report, we also prepared 1-cm-radius surfaces for a subset of experiments. These experiments exhibited quantitative agreement with the larger radius surfaces in the intermediate ranges of the force–distance profiles (D > 5 nm) and enabled us to measure pronounced nonmonotonic forces at surface separations of D < 5 nm. Representative results highlighting the short range nonmonotonic forces are presented in Figs. S2 and S3.

Fig. S2.

Representative short-range interaction forces measured across [C₂mim][NTf₂] with R = 1 cm surfaces at room temperature (blue) and 50 °C (green). The y axis is presented in units of force, F (without R normalization), because the Derjaguin approximation fails within the “oscillatory” regime due to a combination of surface deformation and curvature effects. For the room-temperature force profile (blue), (κ*)⁻¹ = 6.7 nm and ψ = 80 mV. For the 50 °C force profile (green), (κ*)⁻¹ = 4.2 nm and ψ = 100 mV.

Fig. S3.

Representative short-range interaction forces measured across [C₃mim][NTf₂] with R = 5 cm surfaces at room temperature (black) and 74 °C (red). The y axis is presented in units of force, F (without R normalization), because the Derjaguin approximation fails within the “oscillatory” regime due to a combination of surface deformation and curvature effects. For the room-temperature force profile (black), (κ*)⁻¹ = 7.5 nm and ψ = 67 mV. For the 74 °C force profile (red), (κ*)⁻¹ = 3.3 nm and ψ = 40 mV.

Analysis of Force–Distance Profiles.

The lines plotted in Fig. 3 correspond to fits of a constant potential solution to the linearized Poisson–Boltzmann equation, Eq. 1, to the asymptotic long-range distance regime of each force profile, D > 1.5 (κ*)⁻¹, where the equation is well approximated by a simple exponential decay (28, 29):

$$\frac{F}{R}=2\pi E=\frac{8\pi e^2{n}^{\ast }}{{\mathrm{k}}_{\mathrm{B}}T{\kappa }^{\ast }}\frac{{\psi }^2(1-\exp (-{\kappa }^{\ast }D))}{\exp \left({\kappa }^{\ast }D\right)-\exp (-{\kappa }^{\ast }D)}\approx \frac{8\pi e^2{n}^{\ast }}{{\mathrm{k}}_{\mathrm{B}}T{\kappa }^{\ast }}{\psi }^2\exp (-{\kappa }^{\ast }D)$$ [1]

$${\left({\kappa }^{\ast }\right)}^{-1}\equiv \sqrt{\frac{\epsilon {\epsilon }_0{\mathrm{k}}_{\mathrm{B}}T}{2n^{\ast }{\left(q^{\ast }\right)}^2}},$$ [2]

where (κ*)⁻¹ (meters) is the effective Debye length, n* (meters⁻³) is the number density of effective charge carriers (free ions or coordinated aggregates of ions that behave as electrostatic monopoles, that is, “quasiparticles”), q* = ze (coulombs) is the effective carrier charge, z = 1 is the carrier valence, ψ (volts) is the diffuse double-layer potential of the mica surfaces, ε = 12.3 for [C₂mim][NTf₂] and ε = 11.6 for [C₃mim][NTf₂] is the (measured) low-frequency bulk dielectric permittivity (30), ε₀ (farads per meter) is the vacuum permittivity, T (kelvin) is the temperature, and k_B (joules per kelvin) is the Boltzmann constant. At distances of D ≤ (κ*)⁻¹, the F(D) profiles deviate from the predictions of mean-field theory and exhibit nonmonotonic “oscillatory” features. The ranges and magnitudes of these repulsive forces are consistent with previous work that attributed these oscillatory forces to the ordering of the RTIL ions next to charged mica surfaces, with the instabilities corresponding to the abrupt ejection of mixed layers of ions into the reservoir (21–25). Additional discussion of these short-range “oscillatory” forces is presented in Supporting Information.

The average values of the fitting parameters obtained from analyzing force–distance profiles measured over multiple independent experiments are presented in Tables 1 and 2. The quoted uncertainties are based on statistical analysis of at least 15 different force profiles for each temperature, with a 95% confidence interval. Forces were also measured at intermediate and higher temperatures than those shown in Fig. 3. The average surface potentials, ψ, and interaction decay lengths, (κ*)⁻¹, for all of the experiments are listed Tables 1 and 2, and the raw data used to calculate averages can be found in Table S1 and S2.

Table 1.

[C₂mim][NTf₂] average electrostatic parameters (Eqs. 1 and 2) and calculated activation energies (Eq. 4)

Temperature, K	Effective Debye length (κ*)−1, nm	Diffuse double-layer potential Ψ, mV	Activation energy Ea, kBT
22	6.7 ± 0.1	90 ± 25	9.4
40	5.7 ± 0.1	100 ± 20	9.6
50	4.3 ± 0.5	90 ± 25	9.3
60	3.4 ± 0.2	100 ± 25	9.1

Table 2.

[C₃mim][NTf₂] average electrostatic parameters (Eqs. 1 and 2) and calculated activation energies (Eq. 4)

Temperature, K	Effective Debye length (κ*)−1, nm	Diffuse double-layer potential Ψ, mV	Activation energy Ea, kBT
22	7.4 ± 0.1	72 ± 9	9.6
32	6.6 ± 0.2	75 ± 7	9.7
45	5.5 ± 0.5	66 ± 4	9.8
74	3.5 ± 0.2	50 ± 11	9.5

Table S1.

[C₂mim][NTf₂] interaction parameters fitted with Eq. 1

Temperature, °C	Experiment	Run	Effective Debye length (κ*)−1, nm	Mica potential ψ, mV
22	1	1	6.83	99
22	1	2	6.60	84
22	1	3	6.87	97
22	1	4	6.56	96
22	1	5	6.70	72
22	1	6	6.52	100
22	1	7	6.57	102
22	1	8	6.88	80
22	1	9	6.71	80
22	1	10	6.81	70
22	2	1	6.85	102
22	2	2	6.59	104
22	2	3	6.76	117
22	2	4	6.86	129
22	2	5	6.77	94
22	2	6	6.45	85
22	3	1	6.81	134
22	3	2	6.75	142
22	3	3	6.66	143
22	3	4	6.60	114
22	4	1	6.71	82
22	4	2	6.83	71
22	4	3	7.08	74
22	4	4	6.95	69
22	4	5	6.81	80
22	4	6	6.42	81
22	4	7	6.73	100
22	4	8	6.50	103
22	5	1	6.62	65
22	5	2	6.56	56
22	5	4	6.92	59
22	5	5	6.89	57
22	5	6	6.98	64
40	1	11	5.75	94
40	1	12	5.60	77
40	1	13	5.45	77
40	1	14	5.71	85
40	1	15	5.87	103
40	1	16	5.74	102
40	1	17	5.83	97
40	1	18	5.73	88
40	1	19	5.62	89
40	1	20	5.87	101
40	1	21	5.84	95
40	1	22	5.95	103
40	1	23	5.53	91
40	3	5	5.67	90
40	3	6	5.37	107
40	3	7	5.58	123
40	3	8	5.46	137
40	3	9	5.81	79
40	3	10	5.73	151
40	3	11	5.74	110
40	3	12	5.59	102
50	3	13	4.16	106
50	3	14	4.03	82
50	3	15	4.57	93
50	3	16	4.76	110
50	3	17	4.62	110
50	3	18	4.56	158
50	3	19	3.55	123
50	3	20	4.60	111
50	5	7	4.62	63
50	5	8	4.73	55
50	5	9	4.56	62
50	5	10	4.43	71
50	5	11	3.51	50
50	5	12	3.60	56
50	5	13	4.67	68
60	1	24	3.63	117
60	1	25	2.97	72
60	1	26	3.56	131
60	1	27	3.55	120
60	1	28	3.54	127
60	1	29	3.71	81
60	1	30	3.53	113
60	1	31	3.75	115
60	1	32	3.32	65
60	1	33	3.83	128
60	1	34	3.39	75
60	4	9	3.43	125
60	4	10	3.36	95
60	4	11	3.03	101
60	4	12	3.23	104
60	4	13	3.60	117
60	4	14	3.70	100
60	4	15	3.61	120
60	4	16	3.05	142
60	4	17	3.23	122
60	4	18	3.29	91
60	4	19	3.38	100
60	4	20	3.38	122
60	4	21	3.37	166

Table S2.

[C₃mim][NTf₂] interaction parameters fitted with Eq. 1

Temperature, °C	Experiment	Run	Effective Debye length (κ*)−1, nm	Mica potential ψ, mV
22	1	1	7.44	62
22	1	2	7.43	69
22	1	3	7.48	69
22	1	4	7.46	65
22	1	5	7.45	66
22	1	6	7.52	71
22	1	7	7.42	50
22	2	1	7.51	72
22	2	2	7.57	73
22	2	3	7.40	74
22	2	4	7.59	75
22	2	5	7.42	68
22	2	6	7.44	71
22	2	7	7.53	70
22	2	8	7.46	70
22	2	9	7.58	75
22	2	10	7.41	74
22	2	11	7.58	80
22	2	12	7.47	79
22	3	1	7.39	82
22	3	2	7.30	87
22	3	3	7.45	80
22	3	4	7.47	76
22	4	1	7.35	82
22	4	2	7.33	82
22	4	3	7.24	75
30	2	8	6.65	75
30	2	9	6.88	81
30	2	10	6.60	81
30	2	11	6.69	83
30	2	12	6.81	85
30	2	13	6.54	75
30	2	14	6.87	77
33	1	8	6.30	59
33	1	9	6.66	63
33	1	10	6.45	66
33	1	11	6.33	71
33	1	12	6.37	72
33	1	13	6.58	74
33	1	14	6.37	73
33	1	15	6.58	74
33	1	16	6.37	75
33	1	17	6.58	74
33	1	18	6.37	73
33	1	19	6.58	74
33	1	20	6.37	75
33	1	21	6.54	79
33	1	22	6.45	78
33	1	23	6.81	83
33	1	24	6.82	85
45	1	25	5.41	69
45	1	26	5.25	66
45	1	27	5.87	61
45	1	28	5.94	63
45	1	29	5.84	73
45	1	30	6.20	70
45	1	31	5.57	70
45	1	32	5.45	64
45	1	33	6.03	68
45	2	15	5.17	66
45	2	16	5.44	68
45	2	17	5.58	67
45	2	18	5.06	57
45	2	19	4.20	61
45	2	20	5.96	70
74	1	40	3.75	51
74	1	41	3.22	37
74	1	42	3.38	44
74	1	43	3.75	45
74	1	44	3.57	38
74	1	45	3.44	57
74	1	46	3.30	45
74	1	47	3.49	58
74	1	48	3.72	67
74	1	49	3.56	65
74	1	50	3.77	68
74	1	51	3.23	50

Based on the current literature, a mean-field theory describing the distributions of point charges would seem to be incapable of capturing the asymptotic decay behavior of the electric double layers formed by RTILs. Indeed, if every ion is assumed to independently contribute to electrostatic screening (i.e., full “dissociation”) then the room-temperature Debye lengths of the [C₂mim][NTf₂] and [C₃mim][NTf₂] RTILs used in this study should be on the order of 0.1 Å (calculated with ε = 1–10), which is orders of magnitude smaller than the ionic sizes. However, we propose that the much larger interaction decay lengths that we measure across [C₂mim][NTf₂] and [C₃mim][NTf₂], (κ*)⁻¹ = 6.6 nm and 7.5 nm (room temperature), respectively, are effective Debye lengths, where the effective ionic strength (activity) of the RTILs, n* (meters⁻³), substantially differs from the total ionic concentration determined from the RTIL density and molar mass.

The effective Debye lengths that we report always exceed the accepted theoretical Bjerrum length, l_B (5), for [C₂mim][NTf₂] and [C₃mim][NTf₂] (4.6 and 4.9 nm at room temperature), Eq. 3,

$$l_{\text{B}}=\frac{e^2}{4\pi \epsilon {\epsilon }_0{\mathrm{k}}_{\mathrm{B}}T},$$ [3]

where e (coulombs) is the elementary charge, ε₀ is the vacuum permittivity, ε is the relative permittivity of each RTIL, k_B (joules per kelvin) is the Boltzmann constant, and T (kelvin) is the temperature. l_B is the distance beyond which electrostatic interactions between the free ions or quasiparticle domains are disrupted by thermal energy. Thus, our rescaled mean-field approach fulfills the fundamental requirement that (κ*)⁻¹ > l_B. For particles and/or length scales that are smaller than l_B, RTILs cannot be modeled using this approach.

As an extension of our recent “dilute electrolyte” analogy (24), we rationalize these measured effective ionic strengths by considering RTILs to behave as thermally dissociable dielectric fluids that are in equilibrium with a Boltzmann-distributed population of either free ions or quasiparticle “ions” (electrostatic monopoles) that exceed an RTIL specific activation energy, E_a. We are not suggesting that the RTIL ions form exclusive ion pairs where each ion coordinates with only one specific counterion; rather, we propose that the strong coulombic interactions between RTIL ions that drive local charge neutrality by causing each cation to be preferentially surrounded by anions (and vice versa) result in the bulk fluid behaving, for large ensembles, as a dipolar network. This picture is consistent with X-ray and neutron reflectivity measurements that independently establish that the strong electrostatic interactions between RTIL ions drive the ions to order into nanoscale bicontinuous cation–anion networks (31, 32). In our model, we use the measured bulk low-frequency dielectric permittivities of the RTILs, ε (30), to account for the dielectric behavior of this network. Thermally activated charge fluctuations, either free ions or correlated charge domains, then behave as (mathematical) point charges (Fig. 4), taking on the role of ions in the traditional Poisson–Boltzmann model for dilute electrolyte solutions.

Fig. 4.

Electric double layers formed by the RTILs between two surfaces with D >> (κ*)⁻¹. In the “Bound ions (‘Stern layers’)” region, a portion of the negative surface charge is screened via surface-bound cation-rich ion layers. For [C₂mim][NTf₂] and [C₃mim][NTf₂] at mica surfaces, this region extends approximately two to three ion layers per surface. In the “Diffuse layer” the residual negative potential—the diffuse layer potential, ψ—is screened via a monotonic, steeply decaying concentration of excess positive charge. The blue (cation) and red (anion) lines and blue (positive)-to-purple (neutral) shading approximate the smeared-out excess effective ionic concentrations throughout the diffuse double layer, n*/n*_bulk. The temperature dependence of the measured decay (Debye) length demonstrates that the charge carriers can be viewed as a Boltzmann-distributed population of effective ions with thermal energy exceeding an RTIL specific activation energy, E_a. The purple circle in the region labeled “Bulk” has a diameter that is approximately the Bjerrum length, l_B (Eq. 3). RTILs behave as nanoscale, highly charge-ordered (correlated) liquids over distances shorter than l_B.

As an example of the underlying physics, even a simple ion, such as K⁺, is, in reality, composed of highly correlated charged particles (protons and electrons), with the formal positive charge coming from one missing electron. Nevertheless, K⁺ ions can be modeled as point charges for length scales (Gaussian surfaces) that are much larger than the angstrom-scale size of K⁺ ions. For RTILs, the length scales (Gaussian surfaces) over which electrostatic screening in RTILs can be envisioned in terms of point charges need to exceed l_B (Fig. 4). This picture shares conceptual similarities with the “dressed ion” theory of electrolyte solutions (29), an exact statistical mechanical theory that uses charged quasiparticles to model the electrostatic interaction forces between surfaces that are immersed in (nonideal) primitive model electrolyte solutions. However, RTILs have yet to be fully analyzed within this framework.

The physical relevance of viewing bulk RTILs as thermally dissociable dielectric fluids is substantially strengthened by our observation that the measured effective Debye lengths, (κ*)⁻¹, decrease as the temperature increases. In the absence of thermally driven ion dissociation, double-layer interactions would increase in range at higher temperatures. Furthermore, several recent theoretical studies proposing that RTILs already behave as highly dissociated (uncorrelated) “electrolytes” at room temperature also appear to predict that the electric double layers formed by RTILs should increase in range with increasing temperature (5, 11). In contrast, our weakly dissociated “dilute electrolyte” model (24) predicts that the double layers formed by RTILs should decrease in range with increasing temperature, as we observe in the current study. Thus, these temperature-dependent measurements provide an unambiguous way to distinguish between the various models.

Calculation of Charge Carrier Activation Energies.

Charge carrier activation energies of E_a = 9.4 ± 0.3 k_BT for [C₂mim][NTf₂] and E_a = 9.7 ± 0.2 k_BT for [C₃mim][NTf₂] were calculated from the Boltzmann distribution, Eq. 4:

$$n^{\ast }=n_{\text{tot}}\exp \left(\frac{-E_{\text{a}}}{{\mathrm{k}}_{\mathrm{B}}T}\right),$$ [4]

where n* (meters⁻³) is the (measured) number density of effective charge carriers, n_tot (meters⁻³) is the total ionic concentration, as determined from the RTIL density and molar mass, and E_a is the charge carrier activation energy. E_a values are reported in units of k_BT with T = 295 K. The calculated values of E_a were found to be constant over the 22–75 °C temperature range studied, consistent with an electrostatic screening mechanism that is dominated by thermally excited charge carriers. This temperature independence is not expected to hold for substantially elevated temperatures. For extremely high temperatures (T ≥ 1,500 K), the Bjerrum length would become smaller than the size of the RTIL ions, and n* will approach the actual molar density of the RTILs. If this temperature limit could be reached without decomposing the RTIL ions, then RTILs should behave as fully “dissociated” ionic melts, as has been observed for high-temperature molten salts (5, 15).

These activation energies of E_a = 9.4 ± 0.3 k_BT for [C₂mim][NTf₂] and E_a = 9.7 ± 0.2 k_BT for [C₃mim][NTf₂] compare well with the activation energy of E_a = 11 k_BT that we determined for [C₄mim][NTf₂] (24) and follow the same trend as the dielectric permittivity for this [C₂mim][NTf₂], [C₃mim][NTf₂], [C₄mim][NTf₂] series of RTILs. Using our previous approach of estimating the charge carrier activation energy as the energy required to separate a reference RTIL ion pair within a bulk dielectric fluid also works well for these two RTILs (Eq. 5):

$$E_{\text{a}}=\mathrm{\Delta }{\mu }^{\text{i}}\approx \frac{\mathrm{\Delta }{E}_{\text{d}}}{\epsilon },$$ [5]

where μⁱ (joules) is the chemical potential of a reference ion pair, ΔE_d (joules) is the calculated vacuum interaction energy between a [C_Rmim]⁺ cation and [NTf₂]⁻ anion averaged over all configurations, and ε corresponds to the measured low-frequency bulk permittivity for each RTIL. For example, the ΔE_d of 132 k_BT (33) and ε of 12.3 (30) for [C₂mim][NTf₂] yields an estimated E_a of 10.7 k_BT, which agrees with the measured E_a of 9.4 k_BT to within 15%. The success of such a simple electrostatic model highlights that electrostatic interactions are the primary determinant of the measured E_a. Further, the simplicity of this molecular-scale model may enable one to quickly estimate, and ultimately tune, the electrostatic screening of properties of RTILs by judiciously balancing bulk dielectric properties with molecular ion pair interaction energies.

Notably, if effectively free “dissociated” ions are taken to be the charge carrier that dominates diffuse layer screening, then these [C_Rmim][NTf₂] RTILs, and by extension other similar aprotic RTILs, would exhibit bulk dissociated ion concentrations of less than 0.1% at room temperature. A similar framework was recently proposed to model the bulk autoionization of pure water (34).

Discussion and Conclusions

The electrostatic screening properties of [C₂mim][NTf₂] and [C₃mim][NTf₂] that we report in the current study are in excellent agreement with our previous study of [C₄mim][NTf₂] in electrochemically active interfaces (24). In both studies, we find that the electric double layers formed by RTILs exhibit a near-surface regime composed of multiple strongly bound layers of ions, where the degree of ordering of the bound ion layers depends on the crystallinity of the confining surfaces. This ubiquitous near-surface regime is in series with a longer-range exponentially decaying diffuse double layer, when the bound ion layers cannot fully screen charged surfaces (Fig. 4). In essence, we propose a Gouy–Chapman–Stern (1) picture of electric double layers in RTILs, where the bound “Stern layer” is several ion layers thick, and the diffuse layer “ions” are either free cations and anions or charged quasiparticles.

A key implication of this study, and of our previous work (24), is that long-range electrostatic interactions should be observed when [C_Rmim][NTf₂] RTILs are confined between (mica) surfaces. In agreement with this prediction, Espinosa-Marzal et al. (25) measured similar long-range electrostatic interactions between two mica surfaces across [C₂mim]⁺- and [C₆mim]⁺-based RTILs. In contrast, Perkin et al. (23) studied [C₄mim][NTf₂] and [C₆mim][NTf₂] between symmetric mica surfaces using an SFA but did not report any long-range electrostatic interactions. Perhaps the origin of this discrepancy is that Perkin et al. (23) focused on short-range ion structuring interactions, which would naturally make the simultaneous identification of weaker long-range interactions highly challenging. From our point of view, there may be a monotonic repulsion in the D > 8 nm portion of the force–distance profiles presented by Perkin et al. for [C₄mim][NTf₂] in figure 2 of ref. 23.

As noted previously (5), the groundbreaking SFA measurements by Horn and colleagues (21) on an RTIL confined between mica surfaces also reported solely short-range ion structuring interactions. Horn et al. (21) studied the protic RTIL ethylammonium nitrate (EAN), and recent AFM work (35) demonstrates that RTILs with small primary ammonium cations such as EAN bind to mica surfaces with an epitaxial cation spacing that matches the charge-site spacing of the underlying mica substrates. In contrast, the sizes of [C_Rmim]⁺ cations significantly exceed the 4-Å radius of charge sites on mica surfaces. Thus, we hypothesize that the lack of long-range interactions across EAN arises from an epitaxial compensation of mica surface charges by bound ion layers, an effect that is reminiscent of our observation that [C₄mim][NTf₂] can fully screen negative gold electrodes via bound ion layers (24).

RTILs are typically imagined as strongly dissociated, highly concentrated “electrolytes” when viewed from the perspective of nanoscale simulations (5). In contrast, our experiments portray RTILs as extremely weakly dissociated “electrolytes.” We reconcile this apparent contradiction by proposing that the degree of ionic correlations and resultant apparent dissociation of RTIL ions very likely depends on the observed length and time scales of the experiment or computation. An analogous approach was utilized to explain why RTILs seem to simultaneously behave as highly polar liquids (ε > 50) over short distance and time scales but as moderate-polarity liquids (ε = 10–15) over larger distances and longer times (30, 36).

Perhaps the apparently independent diffusion of neighboring ions identified in molecular dynamics simulations (5) only looks independent for the very short length and time scales, and the small number of ions, available to current simulations. Our results reveal that much larger ensembles of ions exhibit complex collective phenomena featuring qualitative differences—in both distance and time—from the behavior identified in nanoscale simulations of ions. Thus, our results should prove useful for the design of energy storage devices, such as electrochemical capacitors (3), where RITLs form double layers at extended surfaces and ionic association strongly affects the stored energy density and conductivity properties of electrochemical devices.

As a practical example, the double-layer capacitance of several RTILs significantly increases with increasing temperature (5), an effect that Lockett et al. (37) explained via the thermal dissociation of neutral ionic aggregates. Our current work supports this explanation and provides a quantitative framework for estimating the activation energy of ion dissociation in aprotic RTILs, yielding additional insight into the electrochemical performance of RTIL-based capacitors. More broadly, we provide a molecular-scale framework that can be used to design RTILs with carefully tuned degrees of ionic association by judiciously balancing ion pair interaction energies with bulk dielectric properties.

Beyond RTILs, the general physical insight we offer is that the simple picture of dissociation equilibria between neutral ion pairs and dissociated ions that is often invoked to explain moderately concentrated electrolytes (1) needs to be refined for very highly concentrated electrolytes, where distinguishing between specific pairs of ions loses meaning. We instead propose that local excess charge densities fundamentally determine the length scales of electrostatic screening and show that a “dissociation reaction” between effectively neutral ionic networks and either free ions or higher-order correlated charge domains can provide a useful framework for understanding such systems. For example, recent SFA measurements across concentrated aqueous electrolyte solutions (38, 39) establish that the range of electric double-layer interactions increases as the aqueous electrolyte concentrations are increased from 1 to 3 M, but only as long as the electrolyte cation differs from the K⁺ ion that is native to mica surfaces. Our results suggest that this trend may be due to the progressive formation of effectively neutral ionic networks involving large numbers of strongly interacting ions. Over the longer term, our results may also prove useful for deciphering how electrostatic interactions maintain such a dominant role near the active sites of proteins, ion channels, and similar self-assembling biological systems (2), where local effective salt concentrations can exceed 10 M.

Materials and Methods

The [C₂mim][NTf₂] and [C₃mim][NTf₂] samples were clear and colorless, and NMR, UV-visible spectroscopy, and electrochemical analysis were used to establish that the RTILs were of electrochemical-grade purity. After synthesis and drying, Karl Fischer titration was used to ensure that the (trace) water content of the [C₂mim][NTf₂] and [C₃mim][NTf₂] RTILs was under 15 ppm, and the samples were stored under vacuum at all times.

Before each SFA experiment, the [C₂mim][NTf₂] and [C₃mim][NTf₂] samples were dried under vacuum at 373 K for at least 72 h. After drying, a droplet of RTIL (50–100 μL) was immediately injected between mica surfaces in a gas-tight SFA under dry nitrogen purge conditions, and the SFA was resealed. All experiments were performed in the presence of a reservoir of the desiccant phosphorous pentoxide (P₂O₅). Each experiment lasted between 24 and 72 h, and the P₂O₅ reservoirs were found to be unsaturated at the conclusion of each experiment.

The temperature was monitored during each experiment via a thermistor with a 0.2 °C tolerance. The thermal expansion of mica was accounted for by calibrating the mica thermal expansion in the absence of RTIL samples. The mica thermal expansion coefficient was found to be $1.5\times {10}^{-5}$ C⁻¹, in agreement with literature values.

Dynamic Forces

When bringing the mica surfaces together, we found dynamic forces to be unmeasurably small, within error, for the approach rates we report in this manuscript (5–10 Å/s). In contrast, we always measure dynamic attractive forces when separating the two surfaces, even for separation rates as slow as 2 Å/s (Fig. S1). These attractive dynamic forces are much stronger than those that would be predicted via traditional hydrodynamic drag models that assume continuum fluids of bulk viscosity.

From a molecular point of view, the magnitudes of these dynamic forces should be significantly larger on separation than on approach, in agreement with our experimental results, due to differences in the fluid flow mechanisms when the RTIL ions flow out of, rather than into, nanoconfined gaps. The expulsion of ions out of confined spaces should only involve molecular motions on the order of a single ion-pair diameter for single-layer instabilities.

In contrast, the fluid must be moved out of the bulk reservoir and into the entire micrometer-scale area of the nanoconfined interface as two surfaces are pulled apart, involving the motion of many RTIL ions over distances that are extremely large compared with the size of the individual ions. This is likely a much slower and more complex process than the expulsion of ions. Separation rates on the order of angstroms per minute or even angstroms per hour would likely be required to avoid overloading the spring and inducing additional nonequilibrium dynamic attractions as the surfaces are separated. Unfortunately, such slow separation rates are impractical for our experiments, as we need to collect dozens of force runs at different temperatures.

Short-Range Nonmonotonic Forces and Colloidal Stability

The nonmonotonic features (∼0.5-nm plateaus) in the force–distance profiles correspond to “oscillatory” transitions, where ordered layers of ions are forced out from between the mica surfaces and into the bulk reservoir (Figs. S2 and S3). Given the highly correlated nature of strongly interacting RTIL ions, we expect that these ion layers consist of both cations and anions but are enriched in cations, due to the negative mica surface potential. The surface separation distance at which we detect the first oscillation is D $\approx$ 5 nm (∼2.5 nm per surface) for both [C₂mim][NTf₂] and [C₃mim][NTf₂], in agreement with previous measurements across other RTILs (21–25). Assuming that the plateau distance of ∼0.5 nm for each RTIL corresponds to a characteristic effective molecular “diameter” for each ion pair, this would mean that the RTILs form solvation layers of about five molecular “diameters” in thickness per surface.

As the temperature is raised, the number and location of observed ion layers remains unchanged, and the layers are forced out of the interface under similar compressions, with an observed likelihood of being removed under slightly decreased pressures at increased temperatures. This observation suggests that the ions pack into similar surface-induced structures for the entire temperature range of 22–75 °C. Perhaps the strong coulombic interactions between RTIL ions enables them to maintain surface-induced structures at these elevated temperatures. However, the solvation layers formed by cyclohexane confined between mica surfaces was also observed to remain unchanged between 22–41 °C (40).

At all temperatures, the surfaces begin to progressively flatten under very large applied loads (F > 10 mN). Once the surfaces enter this regime of flattening, the surface area increases in proportion to the load, so the pressure applied to the strongly bound ion layers stays approximately constant. As a result, no additional ions are forced out of the interface. For [C₂mim][NTf₂], the final film thickness was measured to be ∼2.5 nm under high loads. Thus, we conclude that the measured final film thickness of ∼2.5 nm corresponds to a confined structure consisting of between four and six total layers of ions between the surfaces (two or three ion layers per surface). The final film thickness increases to ∼3 nm for [C₃mim][NTf₂]. Since the [C₃mim]⁺ cation is larger than the [C₂mim]⁺ cation by only one –CH₂− group, the final number of confined ion layers most likely corresponds to the same number of ion layers or, at most, one additional ion layer at high compressions (two to four per surface) for [C₃mim][NTf₂].

In comparison, seminal experiments on the formation of (room-temperature) solvation layers by traditional liquids demonstrate that the range of surface-induced layering can be as short as 1 nm per (mica) surface for small, highly mobile molecules such as water (41), and as long as 4.5 nm per (mica) surface for octamethylcyclotetrasiloxane (42), a large oblate spheroid molecule. For a wide variety of polar and nonpolar liquids confined between mica surfaces, liquids typically form solvation layers that extend to distances of about five molecular diameters (of the liquid) per surface at room temperature (40–42). These layers result in alternating repulsive and attractive “oscillatory” contributions to the force–distance profiles measured across confined liquids, analogous to those measured across RTILs. For traditional liquids, these “oscillatory” forces are always superimposed with the van der Waals and electric double-layer forces of standard Derjaguin–Landau–Verwey–Overbeek theory (40–42).

For [C₂mim][NTf₂] and [C₃mim][NTf₂] confined between mica surfaces, these “oscillatory” solvation forces are clearly superimposed with a strongly repulsive electrostatic force, as shown in Fig. 3 of the main text. Surface–surface van der Waals interactions also occur across RTILs, and the dielectric/optical properties of RTILs should be used to account for the screening of van der Waals attractions. In the current study, the combination of strongly repulsive double-layer and solvation forces overwhelms the van der Waals attraction down to the final measured separation distances of D ∼ 2.5–3 nm.

Although the formation of solvation layers by RTILs in contact with solid surfaces is one of the most widely discussed aspects of RTIL interfacial behavior, we conclude that RTILs show a propensity for forming solvation layers that is very similar to that exhibited by many other polar and nonpolar liquids.

The practical implication of this conclusion is that the solvation layers formed by RTILs should be viewed as fundamentally similar to the solvation layers formed by other liquids. Namely, these solvation layers will indeed contribute to colloidal stability, but the ultimate dispersion (aggregation) state of colloidal particles immersed in RTILs will also critically depend on van der Waals and electrostatic interactions. After all, a knowledge of solvation interactions alone is not sufficient to predict the colloidal stability of particles immersed in other liquids that form solvation structures of comparable ranges and magnitudes.