Nanoscale capillary freezing of ionic liquids confined between metallic interfaces and the role of electronic screening.

Room-temperature ionic liquids (RTILs) are new materials with fundamental importance for energy storage and active lubrication. They are unusual liquids, which challenge the classical frameworks of electrolytes, whose behaviour at electrified interfaces remains elusive, with exotic responses relevant to their electrochemical activity. Using tuning-fork-based atomic force microscope nanorheological measurements, we explore here the properties of confined RTILs, unveiling a dramatic change of the RTIL towards a solid-like phase below a threshold thickness, pointing to capillary freezing in confinement. This threshold is related to the metallic nature of the confining materials, with more metallic surfaces facilitating freezing. This behaviour is interpreted in terms of the shift of the freezing transition, taking into account the influence of the electronic screening on RTIL wetting of the confining surfaces. Our findings provide fresh views on the properties of confined RTIL with implications for their properties inside nanoporous metallic structures, and suggests applications to tune nanoscale lubrication with phase-changing RTILs, by varying the nature and patterning of the substrate, and application of active polarization.

The confinement of liquids at nanoscales leads to a broad spectrum of new properties which can be harnessed in a variety of applications, from energy storage, friction to catalysis [1, 2, 3, 4, 5, 6]. The nanoscale realm hosts indeed a broad spectrum of molecular forces that compete to make new fluid behavior emerge [7, 8, 9, 10] via the interaction of the liquid with the confining interfaces.

In this work, we explore the mechanical bevavior of Room Temperature Ionic Liquid (RTIL) in nanoscale confinement. Such system is a prototype for a dense electrolyte – composed here of pure ions – and accordingly, electrostatic interactions do control the behavior of these liquids. However, the absence of solvent in RTIL leads to strong electrostatic coupling between ions and to the break-down of standard mean-field response, which constitutes the toolbox of dilute electrolytes. Moreover, the behavior of RTILs at interfaces remains elusive, with rich and peculiar behaviors [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21].

Confinement therefore opens an interesting window on the physics of dense electrolytes and their interaction with the confining interfaces [23, 24, 25]. In particular, due to the dominant role of electrostatic forces, one may anticipate that the metallic nature of the confining surfaces should affect the static and dynamic properties of confined RTIL. Such relationship has not been experimentally explored up to now.

We present in Fig. 1a a sketch of the experimental set-up, see Supplementary Material section 1 for more details. Briefly, we glue an electrochemically etched tungsten tip of end radius from 50 nm to 2.5 μm to a millimetric quartz tuning fork, which serves as our force sensor. The tuning fork is excited via a piezo-dither, and the oscillation amplitude and phase shift of the tuning fork with regards to the excitation voltage are monitored through the piezoelectric current flowing through the tuning fork electrodes. By mean of a piezo-element with sub-nanometric resolution in displacement, the probed liquid is confined between the oscillating tunsten tip and substrates of various nature. Importantly, the entire set-up is placed in a vacuum chamber at a pressure of approximately 10−5 mbar.

Figure 1

Experimental Set-up.

(a) Schematic of the experiment. An etched tungsten tip of end radius of curvature R between 50 nm and 2.5 μm is glued to the tuning fork, and immersed in the RTIL. The tuning fork is excited by a piezo dither at a frequency f0 ≈ 32 kHz, and a lock-in and a phase-locked loop maintain constant both the oscillation amplitude h0 and the phase shift between the tuning fork and the excitator. The distance D between the tip and the substrate is controlled through a piezo-element with sub-nanometric resolution in displacement. The substrate can be biased with respect to the tip by a potential difference ΔV . The experimental set-up is placed in a vacuum chamber at a pressure of ≈ 10−5 mbar. (b) Nanorheological measurement on a silicon oil confined between a tungsten tip and a mica sample, showing the variation of conservative (Z’ - black) and dissipative (Z” - red) mechanical impedance (see Eq. (1)); black dotted line is a fit based on Eq. (2). Inset shows typical resonance curves of the tuning fork with the tip immersed in the liquid and far from the surface (1), close to the surface (2) and in contact with the substrate (3).

This set-up allows us to measure the mechanical impedance Z* = F*/h0 = Z′ + i · Z″ of the confined liquid, defined as the ratio of the complex amplitude of the dynamic force F* acting on the tip, to the amplitude h0 of the tip oscillation. The inset of Fig. 1b shows a typical resonance curve of the tuning fork for a fixed excitation voltage of the piezoelectric element, with the tip immersed in a newtonian silicon oil (1) far from the surface, (2) close to the surface and (3) in contact with the substrate. As the interaction of the tip with its environment is modified, one observes a change in both the resonance frequency and the amplitude at resonance. The shift in resonance frequency δf is related to the conservative force response Z’, whereas the broadening of the resonance (change of quality factor Q0 → Q1) is related to dissipation Z” [26]. During a typical experiment, two feedback loops allow us to work at the resonance and maintain constant the oscillation amplitude h0 of the tuning fork. Monitoring the frequency shift δf and the excitation voltage V thus provides a direct measurement of real (Z′ = Re(Z*)) and imaginary (Z″ = Im(Z*)) part of the mechanical impedance:

The experimental set-up has been fully benchmarked using a newtonian silicon oil, as shown in Fig. 1b. Experimentally Z* is extracted from the frequency shift δf and the change in the quality factor at the resonance (Q0 → Q1): where f0 is the bare resonance frequency and K0 [N/m] is the tuning force spring constant. The advantages of the tuning fork are twofold: first, an ultrahigh stiffness of K0 ≈ 40 kN/m which prevents any mechanical instability during the approach and second, very low oscillation amplitude (0.1 - 2 nm) together with very low intrinsic dissipation characterized by high quality factors of up to tens of thousands in vacuum and in the range of few thousands even when the tip is immersed in high viscosity liquid. These characteristics made the tuning fork AFM the ideal instrument to study, for example, tribology in individual nanostructures such as nanowires and nanotubes [26].

The ionic liquid under investigation is [Bmim][BF4] (Sigma Aldrich, 98.5% purity), which is further filtered through a 100 nm hole teflon membrane before use. A drop is deposited on the substrate and the AFM tungsten tip is immerged in the liquid. The liquid is left at rest in the vacuum chamber at least for 12h to remove water impurities. The substrate can be biased with respect to the tip by a potential difference ΔV . To verify the high purity of the ionic liquid, we systematically check the absence of long-term electrochemical current when applying a potential drop between -1.8 V and 1.8 V, which is smaller than the electrochemical window for this liquid [27].

We have explored various substrates, namely Mica, HOPG, doped silicon, and platinum, whose characteristics are described in the Supplementary Materials section 2. Note also that platinum and doped silicon may be coated by natural oxide layers of up to 1 nm in thickness [28, 29], but we anticipate from our results below that this value is much smaller than the typical length at which the phenomena under investigation occur, in the range of tens of nanometers.

Confinement induced freezing

We plot in Fig. 2a the typical variation of the elastic Z′ = Re(Z*) (black curve) and dissipative Z″ = Im(Z*) (red curve) parts of the mechanical impedance, as the tungsten tip approaches a HOPG surface in the ionic liquid. Far from the substrate - zone (i) - the elastic response Z′ ≈ 0 within the experimental precision; one can observe a minute attractive component reminiscent of what is observed in [30, 31]. The dissipative component Z″ increases gently as the confinement thickness decreases; quantitatively, the increase of Z″ with decreasing confinement D can be described by the Reynolds dissipative response of a viscous newtonian fluid sheared under an oscillating sphere [32]: where R ≈ 1 − 2.5 μm is the radius of curvature of the tip, η ≈ 0.15 Pa.s the liquid bulk viscosity, f0 ≈ 32 kHz the oscillation frequency and D [nm] the distance between the tip and the substrate. This expression assumes no slip at the liquid/substrate interfaces, which is expected for such strongly interacting systems [7]. To avoid errors induced by the real geometry of the tungsten tip, see Fig S1 in Supplementary Materials, we calibrated the technique on a silicon oil with viscosity η ≈ 0.1 Pa.s, comparable to η ≈ 0.15 Pa.s for ionic liquid; As shown in Figs. 1c and 2a, this prediction reproduces very well the experimental data and allows determining the “hydrodynamic zero”, which defines the absolute distance D between the tip and the substrate, see Supplementary Material Section 1.

Figure 2

Confinement induced freezing transition

a) Typical approach curve on a HOPG substrate. Real (Z′, black) and complex (Z″, red) part of the mechanical impedance characterizing conservative and dissipative response of the liquid, versus tip-substrate position D, performed on a HOPG sample. The origin of the tip-substrate position is defined as the hydrodynamic zero obtained by fitting Z″ with equation (2). Upon a critical confinement distance λS, Z changes from a liquid-like response to a solid-like response, characterised by the onset of an elastic contribution (Z′, black dots) and a sharp increase of the dissipation (Z″, red dots), as Z′ and Z″ diverge to values up to 10 N/m. b) Distribution of λS on HOPG; ≈ 12,000 cycles were performed, over 18 distinct locations. Green vertical line is the mean of the distribution. c) Sketch of the freezing induced by confinement: upon a critical confinement the RTIL changes from liquid (i) to solid-like (ii).

As shown in Fig. 2a, in ionic liquids, before reaching the hydrodynamic “zero” D → 0, both the elastic Z′ and dissipative part Z″ of the response suddenly diverge at a critical confinement D = λS. This occurs for a confinement D in the range of a few tens of nanometers, depending on the substrate. We have changed the tip oscillation amplitude h0 over one decade, between 0.1 nm and 1 nm, verifying that λS does not depend on oscillation amplitude and shear rates.

This strong repulsive elastic reponse (with Z′ ≈ 10 N/m) shows that the ionic liquid can now sustain a yield stress of order τ ≈ Z′h0/πR2 ≈ 1 kPa, providing a clear signature of the solid-like response of the confined RTIL for D < λS. This behavior was found repeatedly when performing approach and retract cycles of the tip, either at the same or at distinct locations; typically ≈ 10, 000 cycles were performed for each material, over ≈ 20 distinct locations. We measured accordingly the distribution of threshold confinement thickness, as reported in the inset of Fig. 2 b for HOPG, allowing to extract the mean transition thickness, found to be λS ≃ 60 nm for HOPG.

Going further, the same phenomenon was observed for the various substrates under investigation, Mica, HOPG, doped Silicon and Platinum, with a mean transition thickness λS increasing in the order: Mica (15 nm) < HOPG (60 nm) < doped Silicon (110 nm) < Platinum (160 nm). Interestingly this order corresponds to substrates with increasing metallic character, as for example characterized by the conductivity, from the insulating Mica to the highly conductive Platinum.

Prewetting, capillary freezing and electronic screening

As a first interpretation of these results, one may infer the presence of solid layers pre-existing on the surface of the substrates. To explore this assumption, we have performed AFM images of the surfaces using a sharp tip with a 10 - 50 nm of radius of curvature. While in vacuum, the substrates surface appear atomically smooth on micrometric scales – with a typical rms roughness between 0.3 nm and 1 nm depending on the substrate, see Supplementary Materials Fig. S2 – one indeed observes solid-like terrace structures on the surfaces when immersed in RTIL. This thickness is measured below 1 nm for HOPG and typically in the range of ~ 20 − 30 nm for doped silicon and platinum; no such terrace is evident on Mica, see Supplementary Materials Fig. S3. Such structures are reminiscent of observations using STM and AFM imaging [16, 21, 33, 34].

That such thick structures are present on the substrate surfaces is unexpected per se and raises the question of the prewetting of the surfaces by the RTIL, and the role of the metallic nature of the substrates on this prewetting. We note however that the characteristic height of these solid “prewetting” films is much smaller than the critical thickness at which the transition occurs for each substrates, see Fig. 3, blue dots. Accordingly an alternative thermodynamic explanation should be sought.

Figure 3

Effect of substrate electronic properties on the freezing transition.

a) Red dots: Variation of the mean solidification length (red dots) λS on Mica and three conductive substrates: HOPG, Doped Silicon and Platinum versus the normalized Thomas-Fermi wavevector, a · kTF, wih 2a the typical ionic crystal lattice constant. Error bars indicate standard deviation for Mica and standard error for the three conductive substrates, with N ≈ 20 the number of positions investigated in each substrate. Blue open dots represent the typical size of the preexisting solid layers measured with a sharp tip. Error bar represents standard deviation of estimated height. Dotted line is the prediction from Eq. (7). b-c) Schematic representation of the ionic crystal close to an insulator (a · kTF ≪ 1, (b)) and a perfect metal (a · kTF ≫ 1, (c)) for which image charges induced in the substrate decrease the energy of the system.

Looking at Fig. 2a, the drastic change in both elastic response and dissipation from D > λS to D < λS would actually rather suggest a complete confinement induced phase change, with a freezing of the confined RTIL inside the gap. Such confinement induced phase transition is expected when surface energies stabilize the unfavored (solid) phase by compensating for the bulk free energy of freezing. This results in a shift for the phase transition, as observed for capillary condensation (the shifted liquid-gas phase transition) or capillary freezing (shifted crystallization) [35]. The balance of free energy leads to the so-called Gibbs-Thomson equation, which characterizes the critical confinement λS at which the free energies of the liquid and solid phase become equal [35]: where ΔT = TC − TB is the shift in transition temperature, in confinement TC as compared to the bulk transition occuring at TB. For the specific ionic liquid used here, TB = −71° C; γwl and γws are the surface energy of the liquid and solid phase with respect to the wall/substrate, ρ = 1.21 g/mL the density of the liquid phase and L = 47 kJ/kg the latent heat of melting [36] (see supplementary Table S1). Eq. (3) shows that if wetting of the solid-phase on the substrate is favored compared to that of the liquid (γws < γwl) the freezing temperature of the confined phase TC is larger than the bulk freezing temperature TB (TC > TB in Eq. (3)). Putting numbers, one gets TC ~ 25° C for a RTIL confined in a gap of ~ 20 nm with Δγ ~ 0.3 J/m2 (anticipating on the values below). In other words, the RTIL may freeze in nanoconfinement at room temperature. In this scenario, the distribution of confinement length measured experimentally, see inset if Fig. 3, can be understood as a signature of activation due to the first order character of the freezing transition (potentially facilitated by the prewetting phase on the substrate). To get a first hint on the behavior of such systems, we have validated this scenario and the Gibbs-Thomson relationship on the basis of molecular dynamics simulations of a model ionic systems in confinement, see Supplementary Materials, section 6.

A delicate question though is to understand the variations with the metallic nature of the substrate. Following the argument above in terms of the shifted liquid-solid transition, this raises the question of the crystal-substrate surface energy and how it is influenced by the metallic character of the substrate. Physically, one may propose a simple explanation in terms of image charges. To highlight the argument, let us consider a semi-infinite ionic crystal at the interface with a perfect metal, as sketch in Fig. 3b. The network of image charges builds a crystal structure with a (nearly) perfect symmetry with respect to the real half-lattice (right hand side). Accordingly one expects the electrostatic contribution to the surface free energy to (nearly) vanish, as the system behaves as a single bulk lattice: This requires of course a perfectly symmetric crystalline structure and this cancellation is not expected to occur for insulating substrates, or for disordered liquid phases. In other words, the (semi-infinite) ionic crystal has a lower surface energy at the interface with a metal wall as compared to an insulating substrate: This shows that the crystal phase is favored on metallic surface as compared to an insulating one and the Gibbs-Thomson equation (Eq. 3) accordingly implies that the threshold confinement for the freezing transition should be larger with metal as compared to insulating confining surfaces. Going beyond requires to get further predictions for the surface effects at metallic walls which enter the Gibbs-Thomson equation, Eq. (3).

In order to account for the non-ideal metallic nature of the confining walls, one should model the electronic screening inside the substrates. To this end, we use the simple Thomas-Fermi framework, based on a local density approximation for the free electrons gas [37]. This description provides a simple screening equation for the electric potential V (V) in the metal, where the screening length λTF = 1/kTF [m] characterizes the typical length over which a defect charge is screened in the metal and is defined in terms of the density of states at the Fermi level, according to n the state occupation and ϵ the Fermi level. The limit of large kTF (small λTF) corresponds to the perfect metallic case for which V is uniformly zero. The electronic screening therefore modifies the interactions of charge close to the liquid-wall interface and the Green function Ψ for the electrostatic interaction, replacing the Coulomb interaction, obeys equations: where ϵ [F.m−1] is the ionic crystal dielectric constant.

This allows us to calculate the energy of a semi-infinite ionic system in the presence of the metal wall, as with ρc of the charge density. For the crystal phase ρcr(r) = Q ∑(−1)δ(r − R), with R the lattice sites, while for the liquid phase, the charge density ρliq(r) vanishes beyond a few molecular layer close to the wall. The calculation of this energy is a very challenging task, because both the one-body interaction of ions with their image charges, and the two-body interactions between ions are strongly modified by the presence of the confining metallic (TF) wall. In the present work, we develop a simplifying description which captures the main effects of wall metallicity on the surface electrostatic energies, with the objective to rationalize the experimental data. This framework is described in the Supplementary Materials, Section 5. Overall, we predict that the surface tension excess, of the ionic liquid-metal versus the ionic crystal-metal interfaces, is a function of the the TF screening parameter kTF, taking the form where is the difference in surface energies at insulating walls, Δρ = ρ − ρ [m−3] is the density difference between the ionic crystal and ionic liquid phases (Δρ > 0), a [m] is an ionic molecular size (typically given by the ionic crystal lattice constant), Q = e [C] is the elementary ionic charge. The dimensionless function ℱ, whose expression is given in the Supplementary Materials, SM-Eq.(10), is an increasing function of TF screening kTF; it interpolates between 0 and 1 with a cross-over occuring for kTFa ~ 1. As a guideline, it can be well approximated as ℱ(x) ≈ x/(ν + x) with ν ≃ 1.7, see Supplementary Materials. The steps leading to this expression are discussed in details in the Supplementary Materials, Section 5. Overall, the physical picture underlying Eq. (5) is that the electrostatic contribution to the surface energy – in excess to the insulating wall situation – originates merely from the direct interaction of ions close to the surface with their image charge, the latter being modified by the TF screening. Interestingly this approximated approach emerges from exact calculations for the 1D crystal-wall interface, which capture the main ingredients at stake and allows us to calculate analytically the surface energy for any TF screening parameter kTF. These calculations validate the simplified estimate of the excess surface energy in terms of image charge interactions for a dense ionic system at the interface with a metallic wall, which is then extended to the liquid-wall interface. As a complementary check of the framework, molecular simulations of a model ionic system at finite temperature confirm the lower energy of the crystal-wall interface as compared to the liquid-wall interface in the case of insulating confining substrate, as well as the order of magnitude of the various contributions to the surface energies (see Supplementary Materials, section 6). Altogether we obtain Δγ = Δγ0 (1 + δ · ℱ(kTFa)), where Δγ0 [J/m2] is the surface tension difference between of the liquid-wall versus crystal-wall interfaces for an insulating substrate and including also the non-electrostatic contributions to the surface energy (van der Waals, …) and the possible (constant) contribution from the tungsten tip. The dimensionless parameter δ = e2(ρ − ρ)/(16πϵΔγ0) quantifies the contribution of metallicity to the surface energies.

Now using the Gibbs-Thomson result, Eq. 3, one predicts that the increase in surface energy difference for better metals, i.e. for larger Thomas-Fermi wavevector kTF (Eq. 5) will lead to a shift in the critical confinement distance for the freezing transition according to with the value for the perfectly insulating material defined in terms of Δγ0 (here Mica).

In Fig. 3, we compare the prediction for λS with the experimental data for the various substrates investigated. Note that in doing this comparison, we estimated the values of Thomas-Fermi length based on the substrate conductivity and carrier density, see Supplementary Material Sec. 2. We also fixed the molecular length to the crystal lattice constant as 2a = 0.67 nm (as estimated from the molar volume of the IL). As shown in Fig. 3, a good agreement between the theoretical predictions and the experimental results is obtained, yielding and δ = 10.1. From the value for λ0 and Eq. 3, one gets Δγ0 ≈ 0.2 J/m2. Using Eq. 6, and assuming ρ/ρ ~ 0.8 as typical from such systems [38], this would predict a value of δ ≈ 100, in fair agreement with the one obtained from the fit of the experimental data, δ ≈ 10.

Finally, we might also expect the bias voltage ΔV applied between the two confining substrates to affect surface energies and tune the freezing transition. While measuring the critical confinement distance λS for each applied voltage ΔV , we could indeed observe hysteresis cycles in the critical confinement length, with a peak to peak amplitude of approximately 20 nm. Following Eq. (3), we can interpret the dependence of critical confinement length λS on bias voltage ΔV by considering the additional contributions to surface energies due to the charged capacitance at the substrate/ionic liquid interface as: where the last term is the area energy density stored in the capacitor, with C the interfacial capacitance per surface area, and Δ̃γ takes into account all of the other electronic and non-electronic contributions to surface energies. Considering a typical capacitance of the order of 0.1 F.m−2 [39], we obtain an additional surface energy of 0.2 J.m−2, leading to a predicted cycle amplitude of 15 nm, in very good agreement with our experimental results. Those results suggest voltage induced controls of ionic liquid materials, as experienced in previous experiments [40, 41] and theoretical work [42, 43].

Discussion

The agreement between the experimental data (Fig. 3 and 4) and the predictions support the proposed picture of a shifted freezing transition, with wetting properties tuned by the electronic screening inside the confining substrates and the bias voltage between the confining substrates. There is room for improvement of the theory, with a more complete description of the effect of the electronic screening on the RTIL wetting. This theoretical framework, which has not been developed up to now, will be the object of future work.

Figure 4

Voltage induced freezing.

Hysteresis cycle in the solidification length λS versus tip-sample bias ΔU (V) for HOPG (red), Doped Silicon (blue) and Platinum (black). Arrow indicates cycle direction. The absolute cycle position is shifted for clarity. Mean absolute cycle position is <λS> = 45 nm for HOPG, <λS> = 85 nm for Silicon and <λS> = 150 nm for Platinum.

Our results also have implications for the question of dynamics of charging in dense electrolytes confined between metal surfaces, which is relevant to supercapacitors dynamics [12]. Despite the importance of these phenomena for further developement of supercapacitors, there is so far a lack of experimental studies at the nanoscale, while unexpected phenomena were predicted at these scale [44]. Our work underlines that the nanoscale is a peculiar lengthscale for ionic liquids, and leads to strongly different behavior from what is observed in the bulk. Our measurements unveil an overlooked phenomenon, suggesting that further improvements of the performances can be sought at the scales dominated by the atomic nature of matter. Other exotic behaviors might emerge for confinements of the order of the ion size [44, 45, 46], while the presence of disordered and rough surfaces, as typically present in supercapacitors might prevent the freezing transition reported here [12]. Further experimental and theoretical investigation of these regimes seems now to be necessary in light of our study.

In the context of lubrication, our results also suggest to take benefit of the dramatic and abrupt RTIL phase-change to tune nanoscale friction via modifications of the substrate, from insulating to metallic, and possibly with dedicated patterning of the metallic coating. The relatively weak solid phase indeed allows to avoid (undesired) direct substrate-substrate contact by generating strong normal forces. The solid phase can also be regenerated in situ, as it takes its origin in the RTIL confinement. Furthermore the modifications of the confinement induced transition under voltage drop allows to modify finely the lubricating state by active polarization. While such perspectives require further exploration, they open new and exciting perspectives for phase-changing lubricants.