Ionic Liquids Behave As Dilute Electrolyte Solutions

Ionic liquids behave as dilute electrolyte solutions

Matthew A. Gebbiea, Markus Valtinerb, Xavier Banquyc, Eric T. Foxd, Wesley A. Hendersond, and Jacob N. Israelachvilia,c,1

aMaterials Department and cDepartment of Chemical Engineering, University of California, Santa Barbara, CA 93106; bInterface Chemistry and Surface Engineering, Max-Planck-Institut für Eisenforschung GmbH, 40237 Düsseldorf, Germany; and dDepartment of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC 27695

Contributed by Jacob N. Israelachvili, April 25, 2013 (sent for review March 5, 2013) We combine direct surface force measurements with thermody- ion concentrations on the order of 50–80% of the maximum ion namic arguments to demonstrate that pure ionic liquids are ex- density (24, 25). With such high effective free-ion concentrations, − pected to behave as dilute weak electrolyte solutions, with typical the Debye lengths for typical ionic liquids, κ 1, should be on the effective dissociated ion concentrations of less than 0.1% at room order of 0.1 Å (4, 9), which is at least 1–2 orders of magnitude temperature. We performed equilibrium force–distance measure- smaller than the molecular dimensions of even the smallest ionic ments across the common ionic liquid 1-butyl-3-methylimidazolium liquid cations and anions. This discrepancy is typically provided fl bis(tri uoromethanesulfonyl)imide ([C4mim][NTf2]) using a surface as evidence that ionic liquids should completely electrostatically forces apparatus with in situ electrochemical control and quanti- screen charged surfaces within several bound (Stern) ion layers tatively modeled these measurements using the van der Waals (1–2 nm), beyond which charged surfaces no longer impact ion and electrostatic double-layer forces of the Derjaguin–Landau– density or ordering (9, 21–23). This screening behavior has been Verwey–Overbeek theory with an additive repulsive steric (entro- observed in theoretical studies involving simplified model ionic pic) ion–surface binding force. Our results indicate that ionic liquids (9, 21–23). liquids screen charged surfaces through the formation of both In contrast, X-ray reflectivity, atomic force microscopy (AFM), bound (Stern) and diffuse electric double layers, where the diffuse and surface forces apparatus (SFA) measurements have shown double layer is comprised of effectively dissociated ionic liquid that strong ion–surface interactions can induce ion ordering that ions. Additionally, we used the energetics of thermally dissociat- extends up to 10 nm into solution (per surface) (12–20). Notably, ing ions in a dielectric medium to quantitatively predict the equi- the sign and magnitude of the charge density intrinsic to solid librium for the effective dissociation reaction of [C4mim][NTf2] surfaces are crucial determinants for the ranges of the surface- ions, in excellent agreement with the measured Debye length. Our induced ordering and for the templating of the specific structure results clearly demonstrate that, outside of the bound double formed by the bound ion layers (19, 20). For example, a combined layer, most of the ions in [C4mim][NTf2] are not effectively disso- X-ray reflectivity–molecular dynamics study on ionic liquid–solid ciated and thus do not contribute to electrostatic screening. We interfaces demonstrates that replacing a neutral graphene surface also provide a general, molecular-scale framework for designing fi with a negatively charged muscovite mica surface leads to a sub- ionic liquids with signi cantly increased dissociated charge densi- stantial increase in the range of surface-induced ion ordering ties via judiciously balancing ion pair interactions with bulk dielec- and changes the structure of the bound ion layers from a mixed tric properties. Our results clear up several inconsistencies that cation–anion layering motif to an alternating cation–anion layering have hampered scientific progress in this important area and guide structure (20). the rational design of unique, high–free-ion density ionic liquids Furthermore, a study of the differential capacitance of ionic and ionic liquid blends. liquids at electrode surfaces indicates that ionic liquids electrostatically screen charged surfaces through the formation of elec- Boltzmann distribution | electrostatic interaction | interfacial phenomena tric double layers consisting of distinct inner (bound/compact) and outer (diffuse) double layers (26). This screening mechanism is fl onic liquids are uids composed solely of ions (1, 2). Much of consistent with proposed models, analogous to the Gouy–Chapman– fi Ithe recent scienti c interest surrounding ionic liquids derives Stern model for dilute electrolyte solutions (27, 28). Nevertheless, from the fact that ionic liquids have been demonstrated for nu- the prevailing picture is that ionic liquids should behave as highly fi merous applications, such as safe, high-ef ciency electrochemical concentrated, but largely dissociated, electrolyte solutions. storage devices (3, 4), self-assembly media (5), and lubrication (6). Here, we report quantitative equilibrium force–distance mea- A key paradigm within ionic liquids research is that the physical surements of two dissimilarly charged surfaces: single-crystalline properties of ionic liquids can be controlled to an unprecedented muscovite mica and molecularly smooth, polycrystalline gold degree through the judicious design of cation–anion pairs (1–9). — “ ” (0.2 nm rms roughness), interacting across an ionic liquid 1- Thus, ionic liquids are known as designer solvents/materials (1). butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide However, fully realizing this advantage requires the development ([C4mim][NTf2]) (Fig. 1B)—using the electrochemical (EC) SFA of a comprehensive framework that can be used to rationalize the A ’ technique described in Fig. 1 . These results were quantitatively relationship between an ionic liquid s molecular structure and its modeled using the van der Waals and electrostatic double-layer bulk and interfacial behavior and properties, which are governed forces of the Derjaguin–Landau–Verwey–Overbeek (DLVO) by a complex interplay of coulomb, van der Waals, dipole, hy- theory with an additive monotonic repulsive steric (entropic) drogen bonding, and steric interactions (10, 11). ion–surface binding force. Additionally, we propose a general, Recent work has greatly progressed a fundamental understanding of ionic liquids at charged interfaces, but there are currently inconsistencies between experiment and theory (4, 7–9, – Author contributions: M.A.G., M.V., X.B., and J.N.I. designed research; M.A.G., M.V., and 12 23); this is particularly true for the ranges of surface-induced X.B. performed research; M.A.G., M.V., X.B., E.T.F., and W.A.H. contributed new reagents/ ordering and electrostatic screening. For example, a comparison analytic tools; M.A.G., M.V., X.B., and J.N.I. analyzed data; and M.A.G., M.V., X.B., and of the values obtained from ionic conductivity and ion diffusion J.N.I. wrote the paper. coefficient measurements with ionic liquid electrolytes led to the The authors declare no conflict of interest. postulation that ionic liquids behave as highly dissociated elec- 1To whom correspondence should be addressed. E-mail: [email protected]. trolytes with an immense concentration of free ions in solution, This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. where typical ionic liquids are expected to exhibit effective free- 1073/pnas.1307871110/-/DCSupplemental.

9674–9679 | PNAS | June 11, 2013 | vol. 110 | no. 24 www.pnas.org/cgi/doi/10.1073/pnas.1307871110 Downloaded by guest on October 1, 2021 potential was sensed) and applied potentials of ΔU = −500, 0, and +500mVareshowninFig.2.For the measurements that were performed at constant ΔU, the system was allowed to equilibrate for at least 5 min at each potential before beginning the equilibrium F(D) measurements. Immediately, after applying each potential, the magnitudes of the current densities measured at the gold electrode were found to decay to a negligible baseline current density within several seconds (on the order of ∼10–50 nA/cm2), consistent with the charging of an electric double layer (i.e., no faradaic currents were observed). Static (equilibrium) F(D) measurements were taken by using a piezoelectric crystal to move the gold surface in constant voltage steps of ∼1.5–3.0 V, which corresponds to constant distance, D, steps of between 3 and 5 nm. The surfaces were allowed to equilibrate at each point for 45 s before moving to the next D. The voltage–distance calibration for the piezoelectric crystal was determined at surface separation distances, D, where no interaction forces were measured. This procedure allowed us to determine the equilibrium interaction forces across the surfaces at each measured D, and the experimental error of the measured data points are F =±0.01 mN/m and D =±0.2 nm. All equilibrium F(D) measurements were seen to be reversible, as long as the applied forces did not result in signiﬁcant deforma- tions of the surfaces (Fig. S1).

Force Curve Analysis. The measured force–distance profiles exhibit a long-range interaction regime (D out to 35 nm) that is solely Fig. 1. (A) Schematic of the electrochemical surface forces apparatus (EC attributable to electrostatic forces. The forces measured in this SFA). The electrochemical potential of the top gold electrode surface was regime asymptotically decay with an exponential decay length of controlled through a custom-built electrochemical SFA attachment based on 11 ± 2 nm and are well-fitted by equations describing over- a three-electrode setup (32, 43). When immersed in [C4mim][NTf2], musco- lapping diffuse electric double layers. For surface separations vite mica is known to acquire a negative surface charge through the disso- D < + + 3 nm, short-range forces, arising from a nontrivial interplay ciation of surface-bound K ions; the resultant K concentration within the of van der Waals forces, ion–surface binding forces, and forces Ψ bulk ionic liquid is negligible (17, 20). The mica surface potential, M, was induced by ion structuring begin to dominate the force profiles. assumed to be independent of applied potentials, ΔU. The distance between the two surfaces, D, was defined with respect to the contact of the gold The solid lines overlaying the experimental points in Fig. 2 were fitted using Eq. 1: and mica surfaces in the absence of [C4mim][NTf2], where D = 0. Equilibrium (static) force measurements were performed at constant applied potentials, À Á À Á Δ F A πnkT y s − : y2 − s2 −κ D U, and the open circuit potential (OCP), where the potential was sensed to H 8 M Au 0 5 M Au exp − = − + be 140 mV. Degradation peaks in postexperimental cyclic voltammetry R 6 D2 κ expðκ DÞ + expð−κ DÞ measurements were used to account for small shifts in potential referencing D across experiments (Fig. S2). All results described here were measured at + πW − ; [1] applied potentials, ΔU, that did not induce faradaic reactions at the gold 2 0 exp λ0 electrode surface. (B) Molecular structure and dimensions of the 1-butyl-3- fl methylimidazolium bis(tri uoromethanesulfonyl)imide ([C4mim][NTF2]) cat- where ion and anion. Conformations and dimensions were calculated through the conjugate gradient energy minimization of the chemical structures using the ne2 eΨ eσ universal force field (44). 2 2 M Au κ ≡ ; yM = ; sAu = ; ««0kT kT κ««0kT

molecular-scale framework that can be used to predict the and where AH (in joules) is the Hamaker constant, D (in meters) temperature-dependent effective free-ion density for ionic liquids, is the surface separation, « (11.6) is the relative permittivity of −1 provided that the ion dissociation energy (interaction potential) [C4mim][NTf2] (4), κ (in meters) is the Debye screening length, E « in vacuum, d, and the low-frequency relative permittivity, ,of ΨM (in volts) is the outer Helmholtz plane (OHP) mica potential, an ionic liquid can be independently determined. σAu (in coulombs per square meter) is the OHP gold charge den- Our results further show that the relative charges and poten- sity, λ0 (in meters) is a steric decay length, W0 (in joules per square tials of confining surfaces, as well as the chemical nature of each meter) is a fitted steric prefactor, T (295 K) is the temperature, e (in − of the two ion species in single-component ionic liquids, can impact coulombs) is the elementary charge, n (in meters 3) is the number the qualitative nature of surface–surface interactions across nano- density of dissociated ions, k (in joules per kelvin) is Boltzmann’s fi « con ned ionic liquids by resulting in the presence (or absence) of constant, and 0 (in farads per meter) is the permittivity of free space. PHYSICS long-range electrostatic interactions. These results provide insights The parameter values can be found in Table 1 and Table S1 with a into current inconsistencies regarding the ranges of electrostatic detailed discussion of the fitting procedure provided in SI Text. screening and surface-induced ordering in ionic liquids, and thus Eq. 1 represents a “DLVO-type” interaction potential—a have important implications for the utilization of ionic liquids in well-established equation for colloidal interactions—where the numerous applications, including as electrolytes in electrochemical first term is the mica–gold van der Waals interaction, the second storage devices, self-assembly media, and lubricants. is a linearized Poisson–Boltzmann equation for overlapping electric double layers (29, 30), and the third is an empirical steric Results and Analysis repulsion potential arising from surface-bound ions. For dissimilar Equilibrium Force–Distance Measurements. Representative force– surfaces, the electric double-layer interactions can be attractive distance profiles, F(D), for the open circuit potential (OCP) (the for all separations, repulsive for all separations, or change sign from

Gebbie et al. PNAS | June 11, 2013 | vol. 110 | no. 24 | 9675 Downloaded by guest on October 1, 2021 Fig. 2. Points correspond to experimental data and solid lines correspond to forces calculated using Eq. 1.(A) Representative equilibrium force–distance, F (D), proﬁles measured between mica and gold on approach. Measurements were taken while monitoring the open circuit potential (OCP) (red) and at three

different applied potentials, ΔU, across the ionic liquid [C4mim][NTf2]. Inset shows the same data for distances of D < 10 nm. Equilibrium F(D)proﬁles measured on retraction are reversible and are shown in Fig. S1.(B and C) Distance dependence of the individual and total calculated interaction potentials for (B) ΔU = OCP and (C) ΔU =+500 mV. Calculations for ΔU = −500 and 0 mV can be found in Fig. S3.

attractive to repulsive (or vice versa) at finite distances. Fig. 2 B and ultimately determines the OHP charge density of the isolated C shows the relative magnitude and distance dependence of each gold surface, σAu, there is no equation that directly relates the of the three calculated force contributions, as well as the total two values; the value of σAu must be determined by fitting the calculated force–distance potential (the contributions are addi- measured force–distance profiles. tive) for ΔU =+500 mV and OCP. Importantly, although the The long-range interaction forces are well fitted by a Debye − electrochemical potential that is applied to the gold surface, ΔU, screening length of κ 1 = 11 ± 2 nm for all applied potentials,

Table 1. Measured, calculated, and ﬁtted parameters using Eq. 1 Applied potential, Sensed potential, Applied potential, Applied potential, Eq. 1 parameters ΔU; −500 mV OCP; −140 mV ΔU;0mV ΔU; +500 mV

2 Gold surface charge density, σAu; mC/m 0 ± 0.1 0 ± 0.1 0.4 ± 0.1 3.6 ± 0.1

Mica surface potential, ΨM;mV −198 ± 8 −191 ± 8 −196 ± 8 −193 ± 5 Debye length, κ−1;nm 13± 212± 212± 210± 2 −4 −4 −4 −4 Total dissociated ion concentration, Ci;M 0.8± 0.3 × 10 0.9 ± 0.3 × 10 0.9 ± 0.3 × 10 1.4 ± 0.3 × 10

9676 | www.pnas.org/cgi/doi/10.1073/pnas.1307871110 Gebbie et al. Downloaded by guest on October 1, 2021 a thicker layer of bound ions is required to screen the increasingly negative gold surface charge density, brings the range and magnitude of this electrostatic attraction into quantitative agreement with the ΔU = OCP (Fig. 2): both force–distance −1 profiles exhibit κ = 12 ± 2 nm, ΨM of approximately −195 mV, 2 and σAu = 0 ± 0.1 C/m . Thus, the bound ion layer at the gold surface fully screens the electrode for ΔU = OCP and −500 mV, whereas the bound ion layer at the mica, again, does not fully screen the surface. From these results, we discern that bound ion layers enriched + in [C4mim] cations electrostatically screen polycrystalline gold surfaces more effectively than bound ion layers enriched in − [NTf2] anions. This contrast in screening efficiency likely arises from the substantial differences between the molecular struc- + − + tures of the [C4mim] and [NTf2] ions: [C4mim] cations are largely planar, contain well-defined polar and nonpolar regions, and exhibit a lower degree of conformational flexibility com- − pared with the bulkier [NTf2] anions (Fig. 1B). These observations are consistent with studies of ionic liquids at the free vacuum interface, where the size, polarity, and shape asymmetry of ionic liquid cations and anions are shown to differently impact their structuring at the free vacuum interface, with ionic liquids forming increasingly charge-separated electric double layers at Fig. 3. Diagram of the diffuse electric double layers formed by [C4mim] the ionic liquid–vacuum interface as the degree of cation–anion Δ =+ [NTf2] ions for U 500 mV. Analogous electric double layers are formed asymmetry is increased (33, 34). for all other potentials. Effectively dissociated pairs of ions are generated via The short-range portions (D < 3 nm) of the force–distance the equilibrium dissociation reaction above. Light gray shading in the in- profiles are fitted by the superposition of a mica–gold van der terface outside the outer Helmholtz plane (OHP) represents a dielectric fluid – Waals attraction and a monotonic steric “hydration-type” repulsion consisting of an effectively neutral cation anion network. The lines overlaying ± the diagram indicate the relative concentration gradient of dissociated ions: (decay length, 0.6 0.15 nm) corresponding to a characteristic B blue represents cations; red, anions; and green, Ccation = Canion = 1/2 Ci,bulk.The length of the adsorbed ions (Fig. 1 ). The superposition of these bound and diffuse electric double layers are enriched in cations (blue) at the two short-range force contributions qualitatively captures the negative mica surface and anions (red) at the positive gold surface. transition from the force regimes where the long-range diffuse double-layer forces are the sole contributor to the measured – fi fi 1 e−κD force distance pro les, to the regimes where the force pro les which agrees with the asymptotic form of Eq. that decays as , are dominated by short-range, specific ion–ion and ion–surface κ−1 where is the Debye length. This long-range effect indicates interactions. This empirical monotonic repulsion is, however, that the surface-bound ions (i.e., the ions within the inner unable to fully describe the complex, nonmonotonic features of Helmholtz plane or Stern layer) are not able to fully screen the the short-range portions of the measured force–distance profiles. 1 charged surface. The level of agreement between Eq. and the In particular, the force–distance profiles measured at the OCP – fi “ measured force distance pro les (Fig. 2) indicates that the re- (Fig. 2) exhibit nonmonotonic behavior that is indicative of ” sidual potential propagating past the bound ion layers (two complex ion ordering. As a result, the agreement between the charged surfaces) is screened by an exponentially decaying dif- measured and theoretically modeled forces progressively diverges – fuse electric double-layer type mechanism (Fig. 3). Because ionic as the surface–surface separation distance, D, decreases from liquids are solvent-free, the diffuse double layer must consist of D = 1toD = 0 nm. The physical origins of the forces measured – an effectively neutral, coordinated cation anion network (i.e., in the short-range portions of the profiles are extremely complex “ ” like solvent molecules ) that exists in equilibrium with a small because continuum theories of colloidal interactions no longer — fraction of effectively dissociated ions (Fig. 3) analogous to the apply, and the trends exhibited at D < 3 nm will be addressed – double-layer electrode screening found for dilute solvent salt in a future publication. mixtures (31, 32), where the plane of origin for this electrostatic interaction is the OHP. For [C4mim][NTf2], the OHP is shifted Thermodynamic Model for the Effective Free-Ion Concentration in out from the surfaces by between 0 ± 0.1 nm (OCP, ΔU = 0 and Ionic Liquids. Our results indicate that the general electrostatic + ± ΔU = − 500 mV) and 1.5 0.1 nm ( 500 mV) per surface, screening behavior of [C4mim][NTf2] (long-range) is consistent depending on the relative surface potentials. with a diffuse electric double-layer mechanism when the Stern Strikingly, the long-range portions of the measured equilib- layers, “solvent molecules,” and dissociated ions (Fig. 3) are − rium force–distance profiles for applied potentials, ΔU, that are properly defined. Remarkably, the 11 ± 2-nm Debye length, κ 1, more positive than the OCP are fundamentally different from for this system indicates that the concentration of freely disso- − the profiles measured for applied potentials that are more neg- ciated ions in [C mim][NTf ] at 295 K is C = 1.1 ± 0.5 × 10 4 M

4 2 i PHYSICS ative than the OCP (Fig. 2). For ΔU > OCP, the force profiles (mol/L), corresponding to 0.003% dissociation. Therefore, the −10 exhibit a long-range attraction that is consistent with a positive dissociation constant is Kd = 7.3 ± 0.7 × 10 (pKd = 9.14). OHP charge at the gold surface and a negative OHP potential at The value for Kd appears to be explicable in terms of the en- the mica surface. Therefore, the bound ion layers formed at both ergetics of thermally dissociable ions interacting in a dielectric the mica and gold surfaces do not fully electrostatically screen medium, providing further evidence for electric double-layer the surfaces. formation by ion dissociation: as a first approximation, the equi- For ΔU ≤ OCP, the force profiles exhibit a weaker long-range librium mole fraction (solubility) of dissociated (uncoordinated) attraction, whereas an electrostatic repulsion would be expected pairs of ions (for electroneutrality) in a dielectric medium of as- for the case of negative gold charging. Shifting the OHP out by sociated (electrically neutral) [C4mim][NTf2] ions, Xd,canbe 3 nm for ΔU = −500 mV, hence accounting for the fact that calculated from the Boltzmann distribution as follows:

Gebbie et al. PNAS | June 11, 2013 | vol. 110 | no. 24 | 9677 Downloaded by guest on October 1, 2021 Δμi E with the electric double-layer forces measured in the current d – Xd = exp − ≅ exp − ; [2] study (13 17). kT «kT In our system, we expect the isolated single-crystalline mica surfaces to induce alternating cation–anion layering motifs that where Δμi (in joules) is the chemical potential change for ions extend into the [C4mim][NTf2], as has been observed previously going from the associated to dissociated state in a dielectric me- (17, 20). However, the ion structures templated by the poly- E dium, d (in joules) is the ion dissociation energy (interaction crystalline gold surfaces will necessarily be more disordered than k ’ potential) in vacuum, (in joules per kelvin) is Boltzmann s the structures induced by single-crystalline mica surfaces. Because T « constant, (295 K) is the temperature, and (11.6) is the rela- the presence of even a subnanometer scale surface roughness can 2 tive permittivity of [C4mim][NTf2] (4). Although Eq. only be sufficient to smear out the discrete oscillatory character of accounts for low-frequency dielectric screening of the interaction force–distance profiles (36, 39), we infer that the polycrystalline potential, coulombic interactions typically account for greater nature of the gold surfaces used in our experiments is responsible than 90% of the total interaction energy between ionic liquid E = for the suppression of pronounced discrete oscillatory insta- ions (7, 35). Electronic structure calculations show that d bilities. Nevertheless, the trends in the short-range repulsions 315.26 kJ/mol (128.50 kT per pair of ions) for [C4mim][NTf2] that arise from the overlap of the strongly bound ion layers is (35), and this value yields a dissociated ion concentration of Ci = × −4 consistent with previous work on ionic liquids and dilute elec- 1.2 10 M (mol/L), agreeing with the experimental results to trolyte solutions (13–17, 31, 32, 36). within 10%. We do, however, note that the room temperature effective Discussion and Conclusions dissociated ion concentration on the order of 50–80% of the fi total ionic density that has been postulated by comparing ionic Although our results may, at rst glance, appear to stand in conductivity to diffusivity measurements for ionic liquids (i.e., contradiction to previous SFA and AFM studies on ionic liquids “ ” – the ionicity approach) (24, 25) stands in stark contrast to the that found only short-range structural forces (13 19), we discuss freely dissociated ion concentration of 0.003% calculated from why our higher-resolution results not only are consistent with fi our equilibrium force measurements. However, conductivity and the existing scienti c literature but also provide insights into diffusivity measurements inherently include kinetic (dynamic the apparent discrepancies that exist regarding the ranges of transport) effects, and thus are not directly related to the equi- electrostatic screening and surface-induced molecular ordering librium (static) association and dissociation (i.e., the Kd value) in ionic liquids. of pairs of ions (40). Furthermore, the ionicity approach to Notably, results from AFM measurements with in situ elec- predicting the effective concentration of dissociated ions in ionic trochemical control of the substrate surface indicate that the liquids (24, 25) never explicitly considers the energetics of disso- near-surface structuring of the ionic liquid ions depends on the ciating ionic liquid ions. Therefore, although the ionicity approach magnitude and sign of the applied electrochemical potentials has great utility with regards to studying the dynamic properties (19). The authors of this study concluded that electrode surface of ionic liquids, we reason that these ratios do not appear to be potentials are entirely screened by adsorbed ion layers, and ruled directly proportional to the equilibrium effective ionic concen- out screening by a diffuse electric double layer (19). However, tration that contributes to electrostatic screening in ionic liquids. the forces arising from the overlap of two diffuse electric double- In conclusion, our results show that the ionic liquid [C mim] R ∼ −9 4 layers scales as the radius of the AFM tip ( of 10 m) for the [NTf2] screens charged surfaces through the formation of both sphere-on-flat geometry used in AFM studies. The crossed-cylinder bound (Stern) and diffuse electric double layers, where the dif- fl + geometry used in the SFA leads to the same local sphere-on at fuse double layer is composed of effectively dissociated [C4mim] − scaling for the measured forces, where the radius of the sphere, and [NTf2] ions. Additionally, we used the energetics of ther- R, is equal to the geometric mean of the curvature of the cyl- − mally dissociating ions in a dielectric medium to quantitatively inders (R of ∼10 2 m). As a result, the magnitude of the diffuse predict the equilibrium for the effective dissociation reaction of double-layer forces that we measured in this series of experi- [C mim][NTf ] ions, in excellent agreement with the measured − 4 2 ments, which are on the order of 10 5 N after accounting for the value (Debye length). The theories that we have used during our radius normalization (well within the experimental accuracy of analysis (the theory of electric double-layer forces, the Boltz- − the SFA technique), would correspond to a force of 10 12 N for mann distribution for thermally dissociating ions in a dielectric a nanoscale AFM tip, which is 3 orders of magnitude lower than medium) are general, thermodynamically rigorous theories; thus, − the 10 9 N sensitivity reported for current AFM studies on ionic we expect these observations to be widely applicable to other liquids (18, 19). ionic liquids. We therefore deduce that each combination of ionic Additionally, previous SFA studies on ionic liquids used liquid ions should have a unique (temperature-dependent) dis- symmetric ceramic surfaces to explore the electric double layers sociation constant, Kd, that can be used as a design parameter to formed by ionic liquids (13–17). The force profiles that have been help rationalize and tune both the bulk and interfacial inter- consistently measured across ionic liquids between symmetric actions of the liquid. We also suggest that Kd can be calculated interfaces are repulsive and oscillatory in nature (13–17). The with reasonable accuracy by independently knowing « and Ed for measurement of oscillatory force–distance profiles across fluids each pair of ions, which makes comparing the effective dissoci- arises from the presence of layered, phase-separated regions ated ion concentration and electrostatic screening lengths (and within confined fluid films (36–38). However, short-range oscil- resultant double-layer forces) for a wide range of ionic liquid ion latory forces, when present, are typically only one contribution to pairs a straightforward task. fi fi the forces that are measured across con ned liquid lms (36, 37). Materials and Methods For example, in SFA measurements of two symmetric mica −3 fi surfaces interacting across a 1.0 × 10 M aqueous KCl solution, The ionic liquid [C4mim][NTf2] was synthesized, puri ed, dried, and charac- oscillatory forces were shown to be superimposed on a steep, terized using a previously established procedure for the preparation of short-range monotonic double layer and/or hydration repulsion electrochemical-grade ionic liquids (41). The [C4mim][NTf2] was clear and colorless, and NMR and UV-Vis spectroscopy were used to establish that the at surface–surface separation distances, D, of less than 2 nm (36). fi [C4mim][NTf2] was of electrochemical-grade purity. Raman spectroscopy The oscillatory force pro les measured across ionic liquids found that the ionic liquid has a negligible fluorescence background, further also appear to be superimposed on monotonically increasing confirming its purity, as ionic liquid impurities are often strongly fluorescent. repulsions that are consistent, in both range and magnitude, After synthesis and drying, Karl Fischer titration was used to determine that

9678 | www.pnas.org/cgi/doi/10.1073/pnas.1307871110 Gebbie et al. Downloaded by guest on October 1, 2021 the (trace) water content of the [C4mim][NTf2] was 7 ppm. The [C4mim] shown that the electrochemical window of [C4mim][NTf2] is 4.3 V when

[NTf2] was stored under vacuum until use in the EC SFA experiments. dried, but only 2.9 V when saturated with water (42).

Before each EC SFA experiment, the [C4mim][NTf2] was dried a second time by heating in a vacuum oven under vacuum at 373 K for at least 48 h. ACKNOWLEDGMENTS. We thank C. R. Iacovella for calculating the molec- Following drying, the ionic liquid was immediately injected into a gas-tight ular dimensions and graphically modeling the ionic liquid used in this work (Fig. 1B). We also acknowledge D. Y. C. Chan for discussions and assistance in SFA through an injection port under dry nitrogen purge conditions—the selecting the appropriate theory for calculating the long-range electrostatic fl nitrogen pressure owing through the SFA was higher than ambient pres- portions of the force–distance profiles. This research was supported by the sures. After injection, the SFA was resealed, and all experiments were per- Department of Energy, Office of Basic Energy Sciences, Division of Materials formed in the presence of a reservoir of the desiccant phosphorus pentoxide Sciences and Engineering, under Award DE-FG02-87ER-45331 (development (P O ) that was placed in the SFA chamber. Each experiment lasted between of instrumentation and surface forces measurements) and by the Depart- 2 5 fi 12 and 36 h, and the P O that was removed from the box was unsaturated ment of Energy, Of ce of Basic Energy Sciences, Division of Materials Scien- 2 5 ces and Engineering, under Award 100133311-NCSU (ionic liquid synthesis at the conclusion of each experiment. Additionally, postexperimental cyclic and characterization). M.V. acknowledges financial support through a Marie voltammetry measurements showed that the [C4mim][NTf2] exhibited an Curie International Outgoing Fellowship within the European Community electrochemical window in excess of 4 V (Fig. S2), and previous work has Seventh Framework Program under Award IOF-253079.

1. Freemantle M (1998) Designer solvents–ionic liquids may boost clean technology 24. Tokuda H, Tsuzuki S, Susan MA, Hayamizu K, Watanabe M (2006) How ionic are development. Chem Eng News 76(13):32–37. room-temperature ionic liquids? An indicator of the physicochemical properties. 2. Rogers RD, Seddon KR (2003) Chemistry. Ionic liquids—solvents of the future? Science J Phys Chem B 110(39):19593–19600. 302(5646):792–793. 25. MacFarlane DR, et al. (2009) On the concept of ionicity in ionic liquids. Phys Chem 3. Galinski M, Lewandowski A, Stepniak I (2006) Ionic liquids as electrolytes. Electrochim Chem Phys 11(25):4962–4967. Acta 51:5567–5580. 26. Lockett V, Horne M, Sedev R, Rodopoulos T, Ralston J (2010) Differential capacitance 4. Weingärtner H (2008) Understanding ionic liquids at the molecular level: Facts, of the double layer at the electrode/ionic liquids interface. Phys Chem Chem Phys problems, and controversies. Angew Chem Int Ed 47:654–670. 12(39):12499–12512. 5. Antonietti M, Kuang D, Smarsly B, Zhou Y (2004) Ionic liquids for the convenient 27. Fedorov MV, Kornyshev AA (2008) Ionic liquid near a charged wall: Structure and synthesis of functional nanoparticles and other inorganic nanostructures. Angew capacitance of electrical double layer. J Phys Chem B 112(38):11868–11872. Chem Int Ed 43:4988–4992. 28. Feng G, Zhang JS, Qiao R (2009) Microstructure and capacitance of the electrical 6. Ye C, Liu W, Chen Y, Yu L (2001) Room-temperature ionic liquids: A novel versatile double layers at the interface of ionic liquids and planar electrodes. J Phys Chem C – lubricant. Chem Commun (Camb) 2001(21):2244–2245. 113(11):4549 4559. 7. Tsuzuki S, Tokuda H, Hayamizu K, Watanabe M (2005) Magnitude and directionality 29. Parsegian VA, Gingell D (1972) On the electrostatic interaction across a salt solution – of interaction in ion pairs of ionic liquids: Relationship with ionic conductivity. J Phys between two bodies bearing unequal charges. Biophys J 12(9):1192 1204. Chem B 109(34):16474–16481. 30. McCormack D, Carnie SL, Chan DY (1995) Calculations of electric double-layer force – 8. Armand M, Endres F, MacFarlane DR, Ohno H, Scrosati B (2009) Ionic-liquid materials and interaction free energy between dissimilar surfaces. J Coll Int Sci 169(1):177 196. for the electrochemical challenges of the future. Nat Mater 8(8):621–629. 31. Hillier AC, Sunghyun K, Bard AJ (1996) Measurement of double-layer forces at the 9. Kornyshev AA (2007) Double-layer in ionic liquids: Paradigm change? J Phys Chem B electrode/electrolyte interface using the atomic force microscope: Potential and anion dependent interactions. J Phys Chem 100(48):18808–18817. 111(20):5545–5557. 32. Fréchette J, Vanderlick TK (2001) Double layer forces over large potential ranges as 10. Crowhurst L, Lancaster NL, Pérez-Arlandis JM, Welton T (2004) Manipulating measured in an electrochemical surface forces apparatus. Langmuir 17(24):7620–7627. solute nucleophilicity with room temperature ionic liquids. J Am Chem Soc 33. Lockett V, Sedev R, Bassell C, Ralston J (2008) Angle-resolved X-ray photoelectron 126(37):11549–11555. spectroscopy of the surface of imidazolium ionic liquids. Phys Chem Chem Phys 10(9): 11. Castner EW, Jr., Wishart JF, Shirota H (2007) Intermolecular dynamics, interactions, 1330–1335. and solvation in ionic liquids. Acc Chem Res 40(11):1217–1227. 34. Lockett V, et al. (2010) Orientation and mutual location of ions at the surface of ionic 12. Mezger M, et al. (2008) Molecular layering of fluorinated ionic liquids at a charged liquids. Phys Chem Chem Phys 12(41):13816–13827. sapphire (0001) surface. Science 322(5900):424–428. 35. Hunt PA, Gould IR, Barbara K (2007) The structure of imidazolium-based ionic liquids: 13. Horn RG, Evans DF, Ninham BW (1988) Double-layer and solvation forces measured in Insights from ion-pair interactions. Aust J Chem 60(1):9–14. a molten salt and its mixtures with water. J Phys Chem 92(12):3531–3537. 36. Israelachvili JN, Pashley RM (1983) Molecular layering of water at surfaces and or- 14. Bou-Malham I, Bureau L (2010) Nanoconfined ionic liquids: Effect of surface charges dering of repulsive hydration forces. Nature 306(5940):249–250. fl – on ow and molecular layering. Soft Matter 6(17):4062 4065. 37. Christenson HK, Gruen DWR, Horn RG, Israelachvili JN (1987) Structuring in liquid 15. Ueno K, Kasuya M, Watanabe M, Mizukami M, Kurihara K (2010) Resonance shear alkanes between solid surfaces: Force measurements and mean-field theory. J Chem fi – measurement of nanocon ned ionic liquids. Phys Chem Chem Phys 12(16):4066 4071. Phys 87(3):1834–1841. 16. Perkin S, Albrecht T, Klein J (2010) Layering and shear properties of an ionic liquid, 38. Cummings PT, Docherty H, Iacovella CR, Singh JK (2010) Phase transitions in nano- fi fi 1-ethyl-3-methylimidazolium ethylsulfate, con ned to nano- lms between mica confined fluids: The evidence from simulation and theory. AIChE J 56(4):842–848. – surfaces. Phys Chem Chem Phys 12(6):1243 1247. 39. Frink LJD, van Swol F (1998) Solvation forces between rough surfaces. J Chem Phys 17. Perkin S, et al. (2011) Self-assembly in the electrical double layer of ionic liquids. Chem 108(13):5588–5598. – Commun (Camb) 47(23):6572 6574. 40. Atkins P, dePaula J (2009) Physical Chemistry (Oxford Univ Press, Oxford, UK), 7th Ed, 18. Hayes R, Warr GG, Atkin R (2010) At the interface: Solvation and designing ionic pp 832–854. liquids. Phys Chem Chem Phys 12(8):1709–1723. 41. Zhou Q, Fitzgerald K, Boyle PD, Henderson WA (2010) Phase behavior and crystalline 19. Hayes R, et al. (2011) Double layer structure of ionic liquids at the Au(111) electrode phases of ionic liquid-lithium salt mixtures with 1-alkyl-3-methylimidazolium salts. interface: An atomic force microscopy investigation. JPhysChemC115(14):6855–6863. Chem Mater 22(3):1203–1208. 20. Zhou H, et al. (2012) Nanoscale perturbations of room temperature ionic liquid 42. O’Mahony AM, et al. (2008) Effect of water on the electrochemical window and structure at charged and uncharged interfaces. ACS Nano 6(11):9818–9827. potential limits of room-temperature ionic liquids. JChemEngData53(12):2884–2891. 21. Guang F, Cummings PT (2011) Supercapacitor capacitance exhibits oscillatory be- 43. Valtiner M, Banquy X, Kristiansen K, Greene GW, Israelachvili JN (2012) The electro- havior as a function of nanopore size. J Phys Chem Lett 2(22):2859–2864. chemical surface forces apparatus: The effect of surface roughness, electrostatic 22. Bazant MZ, Storey BD, Kornyshev AA (2011) Double layer in ionic liquids: Over- surface potentials, and anodic oxide growth on interaction forces, and friction be- screening versus crowding. Phys Rev Lett 106(4):046102. tween dissimilar surfaces in aqueous solutions. Langmuir 28(36):13080–13093. 23. Lynden-Bell RM, Frolov AI, Fedorov MV (2012) Electrode screening by ionic liquids. 44. Rappé AK, et al. (1992) UFF, a full periodic table force field for molecular mechanics Phys Chem Chem Phys 14(8):2693–2701. and molecular dynamics simulations. J Am Chem Soc 114(25):10024–10035. PHYSICS

Gebbie et al. PNAS | June 11, 2013 | vol. 110 | no. 24 | 9679 Downloaded by guest on October 1, 2021