Surface induced smectic order in ionic liquids – an X-ray reflectivity study of [C₂₂C₁im]⁺[NTf₂]⁻

Abstract

Surface induced smectic order was found for the ionic liquid 1-methyl-3-docosylimidazolium bis(trifluoromethlysulfonyl)imide by X-ray reflectivity and grazing incidence scattering experiments. Near the free liquid surface, an ordered structure of alternating layers composed of polar and non-polar moieties is observed. This leads to an oscillatory interfacial profile perpendicular to the liquid surface with a periodicity of 3.7 nm. Small angle X-ray scattering and polarized light microscopy measurements suggest that the observed surface structure is related to fluctuations into a metastable liquid crystalline SmA₂ phase that was found by supercooling the bulk liquid. The observed surface ordering persists up to 157 °C, i.e. more than 88 K above the bulk melting temperature of 68.1 °C. Close to the bulk melting point, we find a thickness of the ordered layer of L = 30 nm. The dependency of L(τ) = Λ ln(τ/τ₁) vs. reduced temperature τ follows a logarithmic growth law. In agreement with theory, the pre-factor Λ is governed by the correlation length of the isotropic bulk phase.

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1 Introduction

Ionic Liquids (ILs) are organic salts with a melting point below 100 °C. They are typically composed of bulky and asymmetric cations, containing a positively charged moiety, polar groups and/or aliphatic side chains. The balance between Coulomb, polar, van der Waals interactions and hydrogen bonding, leads to complex structures in the liquid phase. This results in remarkable solvent properties, that are rarely found in other materials and can be tailored by the selection of a specific anion and cation combination.^1,2 Over the last three decades, synthesis of new ILs that are stable under ambient conditions opened up new fields for applications.³ Thus, ionic liquids hold immense promise as environmentally friendly replacements for conventional solvents and reaction media in chemical, energy and nano applications.^2,4 Most of these applications involve processes at surfaces and interfaces in contact with other media. In the SILP (Supported Ionic Liquids Heterogeneous Phase Catalysis) process the chemical reaction takes place in an IL thin film, wetting a solid support material with high surface area.^5–7 Here, one rate limiting step is the diffusion of reactants and products across the IL/gas interface. Therefore, to better understand the interfacial transport mechanisms and optimize the performance of ILs in SILP catalysis a detailed knowledge of the IL surface structure is highly desirable.⁸

The bulk structure of ILs was extensively studied experimentally by X-ray scattering,^9–19 neutron scattering^10,11,13,20 coherent anti-Stokes Raman scattering²¹ and by computer simulations.^16,22–29 One particular feature, that draws significant attention, is the appearance of a so-called pre-peak in scattering experiments.¹⁶ These pre-peaks were observed for a wide range of ILs with aliphatic side chains longer than a butyl group. Corresponding to a length scale of a few nanometers, this peak was attributed to a high degree of intermediate range mesoscopic order. It is caused by micro phase separation in the polar networks composed of the charged moieties and domains of the non-polar alkyl side chains.²⁴ Beyond this intermediate range mesoscopic order, long range translational order is observed in Ionic Liquid Crystals (ILCs).^9,30–33 Such ILCs with long aliphatic side chains can form smectic mesophases over an extended temperature range.^34,35 From computer simulations, a detailed understanding of their phase behavior depending on electrostatic and vdW interactions has been obtained.^36–40

These bulk heterogeneities affect their molecular scale arrangement at surfaces and interfaces. Simulations of imidazolium based IL surfaces indicate that the aliphatic part of the cation points towards the interface. Nevertheless, due to the low packing of the aliphatic alkyl-chains, the aromatic ring as well as the alkyl-chains were found to be present within the uppermost surface region.^41–43 Experimentally, angle-resolved X-ray photoelectron spectroscopy shows an enrichment of the aliphatic chains at the interface of [C_nC₁im]⁺-based ILs with n > 2.^44–49 Smaller anions tend to give a stronger enrichment. These observations are consistent with sum frequency generation spectroscopy showing that the imidazolium ring is parallel to the surface and the aliphatic chain is pointing toward the gas phase.^50,51 Interfacial profiles with sub-nanometer resolution across free IL surfaces^52–55 and buried interfaces^56,57 were obtained by X-ray reflectivity (XRR) experiments.^58,59 Jeon et al. observed a surface crystalline layer in [C₄C₁im]⁺[PF₆]⁻ using grazing incident X-ray diffraction (GIXD).⁶⁰ Using resonant soft X-ray reflectivity, it was shown that the micro phase separation in ILs with long aliphatic side-chains drives an oscillatory near surface structure with a periodicity on the nanometer length scale.⁵⁵ Towards the bulk, this structure is exponentially decaying with a correlation length matching the corresponding value found in the isotropic bulk liquid. Like in bulk, the oscillatory surface profiles originate from alternating regions enriched with ionic and aliphatic moieties.⁵⁵ Recently, long ranged order has been found for ionic liquid films and in confinement.^61,62

Here, we present a study of the 1-methyl-3-docosylimidazolium bis(trifluoromethlysulfonyl)imide ([C₂₂C₁im]⁺[NTf₂]⁻, Fig. 1) surface. This imidazolium based IL with long C₂₂ side chains exhibits pronounced microphase separation.⁶³ Using X-ray reflectivity and grazing incidence scattering, we obtain information on the temperature dependent surface structure with molecular scale resolution. Complementary information from small angle X-ray scattering, polarized light microscopy and calorimetric measurements suggest that the observed surface structure is related to fluctuations into a metastable liquid crystalline phase that was found by supercooling the bulk liquid.

Fig. 1 Molecular structure of 1-methyl-3-docosylimidazolium bis(trifluoromethlysulfonyl)imide ([C₂₂C₁im]⁺[NTf₂]⁻); color code: fluorine (green), oxygen (red), sulfur (yellow), nitrogen (blue), carbon (grey) and hydrogen (light grey). Arrows indicate typical intramolecular distances. Molar masses of anion and cation are 280 g mol⁻¹ and 392 g mol⁻¹ respectively.

2 Materials and methods

2.1 Synthesis and characterization

[C₂₂C₁im]⁺[NTf₂]⁻ was synthesized from 1-methylimidazol (≥99%, Merck, Darmstadt), 1-bromodocosane (Santa Cruz Biotechnology, Dallas) and [Li]⁺[NTf₂]⁻ (>98%, Tokyo Chemical Industry, Tokyo). Subsequently, the IL was purified by recrystallization from a cold ethanol/water (75 : 25) mixture and zone melted in glass tubes under vacuum.^64–66 Details on material synthesis and purification are described in ref. 67.

The temperature dependent molecular volume V = V_m[1 + α(T − T_m)] of the bulk liquid was determined by pycnometry. Interpolation by linear regression yield a molecular volume of V_m = 1.015 nm³ at the melting point T_m = 68.1 °C and a volumetric thermal expansion coefficient α = 0.745 × 10⁻³ K⁻¹.

Phase transition temperatures and entropies ΔS = ΔH/T of [C₂₂C₁im]⁺[NTf₂]⁻ were determined by differential scanning calorimetry (Mettler Toledo DSC-822) using scan rates between 1 K min⁻¹ and 10 K min⁻¹ (ESI†). Equilibrium phase transition temperatures were obtained by extrapolating to zero heating and cooling rates.

Polarized light microscopy (POM) was carried out using a 10× objective and wave plate between crossed polarizer (Zeiss Photomicroscope III). The IL was contained between two glass cover slips with a sample thickness of approx. 100 μm. Temperature dependent measurements at a rate of approx. 20 K min⁻¹ were performed using a heating microscope stage (Linkam THMS600).

2.2 Bulk X-ray scattering

Bulk X-ray scattering data was measured in transmission geometry using Cu K_α, λ = 0.154 nm radiation (Rigaku MicroMax 007 X-ray generator, Osmic Confocal Max-Flux curved multilayer optics). The IL was contained in an 1 mm thick glass capillary (wall thickness 0.01 mm). Capillaries were placed in a nitrogen stream (Oxford Cryostream 700) and a temperature controlled copper holder inside a vacuum tube for wide and small angle scattering experiments respectively. Scattering data was recorded on an online image plate detector (Mar345, MarResearch) at a sample-detector distance of 352 mm and 2089 mm. Background from high energy radiation, was removed by a Laplace filter based masking algorithm. Scattering patterns I(q) vs. momentum transfer q = 4π/λ sin(θ) were obtained by radial averaging of the 2D-scattering patterns.

2.3 X-ray reflectivity

X-ray reflectivity (XRR) experiments were performed at the liquid interface scattering apparatus (LISA) at P08, PETRA III, DESY Hamburg.⁶⁸ The size of the focussed X-ray beam (18 keV X-ray energy, λ = 0.069 nm) was 500 μm × 8 μm at the sample position. Scattering pattern was collected on a hybride pixel detector (Dectris Eiger 1M, 75 μm × 75 μm pixel size) at 1.2 m sample-detector distance. The liquid was contained in a circular PTFE sample trough (1 mm depth, 9 cm diameter). The trough was placed in a temperature controlled (Julabo FN25-HE) stainless steel (EN 1.4571) chamber (stability ±0.006 K) under helium atmosphere (Fig. 2). To improve the temperature homogeneity at the IL/helium interface, the steel cell was packed in 5 cm thick melamine isolation foam.

Fig. 2 Sample cell for XRR experiments. The IL (1, purple) is contained in a PTFE trough (2, white). The outer steel cell (3, gray) is temperature controlled by a fluid circulating trough flow channels (4) and resistive heating pads (80 W, not shown). The lid (5, grey) contains feedthroughs for PT1000 temperature sensors (6, white) and helium in- and outlet. Windows for the incident and reflected X-ray beam (7, red, size and angles exaggerated) were made of 50 μm thick Kapton foils (8, orange).

The PTFE trough was cleaned in Piranha solution (3 parts H₂SO₄ 98%, 1 part hydrogen peroxide 30%) for at least 20 minutes, thoroughly rinsed with ultrapure water, and dried in a nitrogen stream. [C₂₂C₁im]⁺[NTf₂]⁻ was filled into the heated trough at 90 °C until a convex meniscus was formed.

Molecular resolution is obtained by recording XRR patterns up to a sufficiently high momentum transfers q_z perpendicular to the sample surface. Therefore, the specular reflected X-ray beam was recorded for incident angles α_i ≤ 1.9°. This corresponds to momentum transfers q_z = 4π/λ sin α_i ≤ 6 nm⁻¹. Specular intensities were extracted from the 2D patterns by integration over an area of 40 × 40 detector pixels. The background signal predominantly originates from the diffuse scattering contributions of the bulk liquid. It exhibits an approximately concentric intensity distribution around the primary beam axis. Therefore, background intensities were measured at a horizontal offset of 20 pixels and a vertical offset, adjusted to keep the total scattering angle 2θ for the specular reflection and the background equal. XRR segments measured at different absorber settings were merged and interpolated on an equidistant q_z-grid.

2.4 Grazing incidence scattering

Grazing incident X-ray scattering experiments were performed at the six-circle liquid diffractometer at beamline ID10-EH1 at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France using an energy of 8 keV (λ = 0.155 nm). The IL was contained in a circular stainless steel trough (120 mm diameter, 1 mm depths). To reduce the background signal from air scattering the sample was kept under helium atmosphere during X-ray irradiation. First, the sample was heated to 96 °C followed by gradual cooling to the desired temperature with a rate of 0.25 K min⁻¹. Signals were collected by a gas filled multi-channel detector (Gabriel 150 mm) in vertical orientation. Grazing incident X-ray scattering patterns were recorded at an incident angle α_i = 0.12° i.e. 80% of the measured critical angle of total reflection α_c = 0.15°.

3 Analysis

3.1 X-Ray reflectivity

XRR can provide information on the density profile ρ(z) across liquid surfaces on a molecular length scale. For an ideal sharp surface profile, the so-called Fresnel reflectivity R_F(q_z) is obtained.Here, r_e denotes the classical electron radius. The complex refractive index n for hard X-rays is close to unity i.e. |n − 1| ≪ 1. Values can be obtained from tabulated energy dependent molecular X-ray scattering factors f.^69–71 For large momentum transfers q_z ≫ q_c and a small X-ray absorption cross section of the material i.e. ℑ(f) ≪ ℜ(f), eqn (1a) is well approximated byHence, R_F rapidly decays by the fourth power of q_z.^72,73

Deviations from an ideal surface cause modulations in the Fresnel normalized XRR patterns. Within the Born approximation, the XRR pattern R(q_z) is linked to its corresponding real space electron density profile ρ_e(z) across the liquid surface via Fourier transformation^72,73

where ρ_−∞ and ρ_+∞ is the electron density of the vapor phase and bulk liquid respectively. However, due to the phase problem a direct inversion of eqn (3) to obtain the density profile ρ_e(z) from an experimental reflectivity pattern R(q_z) is in the general case not possible.^74,75 Therefore, in most cases model profiles ρ_e(z) have to be constructed. Subsequently, the free model parameters can be determined from the experimental data by fitting.

3.2 Model profiles and fitting procedure

Electron density profiles ρ_e(z) across IL surfaces were made up of different contributions:To limit the number of free parameters, the temperature dependent bulk electron density ρ^b_e was independently determined by pycnometry. Following Névot and Croce, the cumulative normal distribution functionaccounts for the intrinsic molecular scale surface roughness σ_s.^72,76 Deviations from this ideal surface structure are encoded in the last term of eqn (4). Here, ψ(z) is an oscillatory function, modulated by an envelope ϕ(z).

The oscillatory function with periodicity d is expanded in a series

Without loss of generality, we can set the coefficients a₁ = 1 and ξ₁ → ∞. Taking into account first and second order terms only, perfect fits to the experimental XRR data were found. This oscillatory near surface structure is motivated by the crystal structure of [C₂₂C₁im]⁺[NTf₂]⁻,⁶³ molecular dynamic simulations,^26,29 and liquid structure factor calculations²⁵ of related materials. Maxima in ψ(z) account for the ionic regions composed of the imidazolium rings and [NTf₂]⁻ anions. These molecular moieties exhibit an electron density above the bulk average ρ^b_e. On the other hand, the location of the cations aliphatic side chains correspond to the minima of ψ(z). In previous studies, similar oscillatory near surface structures have been observed for different ILs.^53–55

The oscillatory function ψ(z) in eqn (6) corresponds to the microscopic structure of smectic layers of the IL moieties. The envelope ϕ(z) in eqn (4) plays the role of a locally varying smectic order parameter profile. Within a simple variant of the Landau-de Gennes formalism,⁷⁷ one can determine that smectic order parameter profile ϕ(z) of a smectic surface layer of thickness L in between a vapor phase and the bulk liquid. Here, only the leading terms

with the free parameters for the amplitude S⁻, decay length ξ_s, and surface layer thickness L are considered. The amplitudes S⁰ and B were determined by the continuity and differential continuity condition at z = L. To further reduce the number of free parameters, the bulk correlation length ξ_b was independently determined by X-ray scattering.

Reflectivity curves were numerically calculated using the Parratt formalism after dividing the profile into 0.05 nm slabs of constant density.^72,78 Dispersion effects were included using X-ray form factors from Henke et al.⁶⁹ Density profiles were extracted from the experimental XRR data by parameter refinement using a simulated annealing algorithm.⁷⁹ Damping of the specular reflectivity due to capillary wave roughness of the liquid surface^80,81 was taken into account by

assuming a surface tension γ = 30 mN m⁻¹,⁸² a molecular cutoff q_m = π nm⁻¹ and a resolution of Δq = 1.3 × 10⁻³q_z. However, changes in surface tension and molecular cutoff give comparable quality fits with similar density profiles. This is explained by parameter coupling between the intrinsic surface roughness σ_s, and the capillary wave damping factor Γ_cw(q).

3.3 Surface thermodynamics

Within a generic approach, interface induced phase transitions such as wetting, interfacial premelting, or surface induced ordering can be described by a continuum model.^83–85 In this model, a thin surface layer of thickness L is wetting the bulk. In the case of surface induced ordering, the bulk consists of an isotropic liquid (l). The surface layer (s), forming at the liquid/vapor (v) interface, exhibits a higher degree of order. This leads to a negative surface excess entropy.⁸⁶ In the standard continuum model, the interfacial free energy of the system is expressed by an effective thickness-dependent γ(L).

γ(L) = γ_lv + φ(L)Δγ (9a)

Δγ = γ_ls + γ_sv − γ_lv (9b)

Here, Δγ is the deviation from Antonow's rule, coupling the interfacial free energies between the vapor with the bulk liquid (γ_lv) and the surface phase (γ_sv), and between the bulk liquid and the surface phase (γ_ls), respectively. For large layer thicknesses L → ∞, one obtains φ = 1. This implies, that the total surface energy γ(L) is given by the sum of two non-interacting (ls) and (sv) interfaces. Above the onset temperature T₁ where no ordered surface layer exists, we find φ = 0 and γ = γ_lv. For intermediate thicknesses, the transition between these two cases is mediated by an exponential function with decay length Λ.

By minimization of the total free energy of the system, a logarithmic growth law of the ordered surface layer thickness L vs. reduced temperature is obtained.

Above the onset temperature τ₁ the ordered surface layer vanishes. This transition temperature is determined by the molar latent heat of fusion ΔH_m between the isotropic bulk and ordered surface phase per molar volume V_m. Approaching the bulk transition temperature T₀, the ordered surface layer thickness diverges.

4 Results and discussion

4.1 Bulk structure

Upon heating, [C₂₂C₁im]⁺[NTf₂]⁻ shows a phase transition from the crystalline phase to an isotropic liquid at T_m = 68.1 (Fig. 3 and Fig. S1, ESI†). However, three phase transitions were observed by DSC during cooling. For the peak at T_LC = 67.1 °C a transition entropy of ΔS_LC = 2.5 J mol⁻¹ K⁻¹ was found (Fig. 3 and Fig. S2, ESI†). This resembles typical values for the formation of liquid crystalline mesophases.⁸⁷ Similarly, a tendency to form liquid crystalline-like structures has been proposed for long aliphatic side chains by MS-CG simulations.^36,37 The transition temperature is only about 1 K below the melting point. No corresponding transition was observed during heating. Therefore, we conclude that the transition is related to a metastable phase. For other imidazolium based ILs with long aliphatic C₁₆ to C₁₈ side chains and smaller [Cl]⁻, [BF₄]⁻ and [PF₆]⁻ anions thermodynamically stable SmA₂-phases have been found.^9,30–33

Fig. 3 DSC of [C₂₂C₁im]⁺[NTf₂]⁻ measured during heating (red) and cooling (blue) with a temperature rate of 1 K min⁻¹ (solid lines) and 10 K min⁻¹ (dashed lines). Arrows indicate the formation of a liquid crystalline smectic mesophase. Curves for 1 K min⁻¹ are shifted vertically by ±0.5 J K⁻¹ g⁻¹ for clarity.

Indeed, a focal conic texture, indicating a smectic A liquid crystalline mesophase, was observed in POM (Fig. 4c).⁶³ Together with the SAXS data (Fig. 4) and the dimensions of the molecular moieties (Fig. 1) this mesophase is identified as a SmA₂ liquid crystalline phase. While the absence of bâtonnets typically is linked to nematic to smectic phase transitions⁸⁸ no signs for a nematic phase was found by DSC, POM and X-ray scattering. At 58.4 °C and 57.7 °C a double peak was observed in DSC. The higher temperature peak was attributed to the smectic to crystal transition. Its transition temperature strongly varied for different DSC measurements. The second peak is likely related to a solid–solid transition between two different crystal structures.

Fig. 4 Liquid crystalline smectic [C₂₂C₁im]⁺[NTf₂]⁻ mesophase. (a) Comparison of X-ray scattering patterns in the bulk liquid phase (green, T = 96 °C) and the mesophase obtained by rapid cooling (blue). (b) SAXS pattern of the FSDP at 69.8 °C (liquid, green line) and 59.8 °C (SmA₂, blue circles). The black line indicates a fit to a pseudo-Voigt profile. (c) Polarized light microscopy image at 60.4 °C, showing a focal conical texture.

Above the melting point, the X-ray scattering patterns of [C₂₂C₁im]⁺[NTf₂]⁻ exhibit three diffuse peaks at q₀ = 1.7 nm⁻¹, 7.9 nm⁻¹ and 12.9 nm⁻¹ (Fig. 4a). The two peaks II and III at large momentum transfer q were associated with charge alternation and adjacency correlations.^15,29 From the peak position, a periodicity 2π/q₀ ≈ 3.6 nm is estimated at T = 96 °C. Having a periodicity similar to the molecular length scale (Fig. 1), the origin of the first sharp diffraction peak (FSDP) can be identified with the polarity alternation i.e. microphase separation of the ionic and aliphatic moieties.^12,25,26,29

Quantitative analysis by fitting a generalized Teubner–Strey model to the scattering patterns yield a periodicity d_b(T) = 3.74 nm − 0.348 × 10⁻² nm K⁻¹ (T − T_m) and a correlation length ξ_b(T) = 4.79 nm − 0.0298 nm K⁻¹ (T − T_m). A detailed X-ray scattering study of the [C₂₂C₁im]⁺[NTf₂]⁻ bulk structure in comparison to [C₁₈C₁im]⁺[FAP]⁻, [C₁₈C₁im]⁺[NTf₂]⁻, [C₁₈C₁im]⁺[NNf₂]⁻ and [C₂₂C₁im]⁺[NNf₂]⁻ is found in ref. 67.

Upon rapid cooling below the SmA₂ transition temperature T_LC, the FSDP becomes much sharper. The periodicity d_LC = 2π/q₀ = 3.68 nm was found to be only 1.6% shorter then the value in the isotropic liquid. Albeit much weaker in intensity, a 2nd order reflection is observed at 2q₀ = 3.4 nm⁻¹. Analysis of high-resolution SAXS data by fitting a pseudo-Voigt function to the FSDP reveals a total FWHM of 0.0185 nm⁻¹ (Fig. 4a). This value is close to the resolution limit of the instrument. From the Scherrer formula we estimate domain sizes ≥0.7 μm i.e. long ranged translational order. In contrast, the intensity, position and shape of the high-q peaks II and III remain almost unchanged. Together with the small change in the position of the FSDP, this indicates a strong structural similarity of the liquid crystalline phase and the mesoscopic structure found in the liquid phase.¹⁹

4.2 Surface structure

Density profile ρ_e(z) across the liquid surface with molecular scale resolution were extracted from the XRR patterns. Fig. 5a shows XRR curves R(q_z) versus momentum transfer of the [C₂₂C₁im]⁺[NTf₂]⁻ surface for different temperatures above the bulk melting point. To highlight features originating from density modulations adjacent to the liquid surface, data was normalized to the Fresnel reflectivity R_F(q_z) of an structure-less surface (eqn (1)). For [C₂₂C₁im]⁺[NTf₂]⁻ we calculate a critical momentum transfer of total reflection ℜ(q_c) = 0.23 nm⁻¹.⁶⁹ This corresponds to a critical incidence angle α_c = 0.070° at 18 keV. From the experimental data we extract a critical momentum transfer q_c = 0.21 nm⁻¹. This agrees well with the value calculated from eqn (1b). As expected, below q_c we obtain a reflectivity close to unity. Spikes in the region around q_z ≈ q_c are caused by the R_F normalization with minute uncertainties in the calculated critical momentum transfer q_c.

Fig. 5 (a) Temperature dependent XRR curves of the [C₂₂C₁im]⁺[NTf₂]⁻ surface normalized to the Fresnel reflectivity R_F(q_z) (symbols) and calculated patterns (solid lines). Vertically dashed lines at 2π/d_s = 1.69 nm⁻¹ and 3.37 nm⁻¹ indicate the positions of the 1st and 2nd order quasi-Bragg peaks. (b) Electron density profile ρ_e(z) obtained by fitting eqn (4) to the experimental XRR data. Horizontal tics indicate the layer thickness L of the ordered structure near the IL surface. Curves measured at 115 °C (red), 87 °C (purple), 73 °C (yellow), 70 °C (green), and 68 °C (blue) are vertically shifted for clarity.

Deviations from an ideal surface cause modulations in the Fresnel normalized XRR patterns (Fig. 5). For the highest temperature of 115 °C (red symbols), a step-like reflectivity curve is obtained. At lower temperatures, this step gradually transforms into a dip (purple curve, 87 °C). These modulations are directly linked to changes in the density profiles across the IL surface by Fourier transformation (eqn (3)). Therefore, the observed dip, resembling an inverted Lorentzian peak, correspond to an exponentially damped oscillatory density profile across the IL surface.^57,89 Qualitatively similar XRR curves were obtained for [C₁₈C₁im]⁺[FAP]⁻.⁵⁵ Using resonant scattering techniques, the oscillatory surface profile was attributed to alternating layers. They are composed of aliphatic side chains and ionic moieties i.e. the anions and positively charged imidazolium rings. The periodicity d_s = 2π/q₀ ≈ 3 nm of the oscillatory surface profiles estimated from the peak position q₀ = 2 nm⁻¹ is similar to the bulk value d_b.

Below 73 °C (yellow symbols) two Bragg-like peaks emerge in the XRR curves. They correspond to 1st and 2nd order reflections at q₀ = 1.68 nm⁻¹ and 2q₀ = 3.35 nm⁻¹, respectively. As temperature decreases towards the transition temperature T_LC where long ranged translational order was observed in bulk, these peaks get sharper and their intensities increase (green and blue symbols). Like the dip, these peaks originate from an oscillatory surface profile. However, the appearance of two distinct Bragg-like 1st and 2nd order peaks indicate an increasing surface order. In analogy, in the SAXS bulk measurements the 2nd order FSDP was only observed in the liquid crystalline smectic phase. This suggests the formation of surface induced smectic order with a smectic layer of thickness L wetting the isotropic liquid bulk phase.

Fig. 6a shows the grazing incidence scattering patterns recorded from the [C₂₂C₁im]⁺[NTf₂]⁻ surface at 70.2 °C. At the grazing angle α_i = 0.12°, corresponding to 80% of the critical angle of total reflection, the X-ray beam does not penetrate into the bulk liquid. Instead, an evanescent wave with a decay length of approx. 10 nm ≈ 3d_s is formed. Therefore, in the grazing incidence experiments the bulk signal is strongly suppressed. This allows to detect the relatively weak scattering from the near surface region where oscillatory density profiles were observed. Long-range lateral order at the surface, e.g. a 2D crystalline structure, gives rise to sharp streaks along q_⊥ at distinct q_‖ values.⁹⁰

Fig. 6 (a) Grazing incident X-ray scattering patterns of [C₂₂C₁im]⁺[NTf₂]⁻ at (a) 70.2 °C and (b) 92.0 °C. (c) I_s(q_‖) at 92.0 °C (red), 76.2 °C (yellow), 72.2 °C (green) and 70.2 °C (blue). (d) Bulk scattering I_b(q) at 69.8 °C (blue circles) and 95.8 °C (red diamonds). Vertical lines indicate the position of the 2nd and 3rd maxima in the bulk scattering at 7.9 nm⁻¹ and 12.9 nm⁻¹, respectively.

However, in contrast to the experiments by Jeon et al. on [C₄C₁im]⁺[PF₆]^− 60 at all temperatures no indications for long-ranged in-plane order have been found in our experiments. Instead, two broad diffuse peaks are observed (Fig. 6c). Their positions and widths are similar to the peaks II and III observed in bulk (Fig. 6d). However, unlike in bulk the relative peak intensity is strongly changing with temperature. Upon cooling, the intensity of peak III at 13 nm⁻¹ is significantly increasing. In contrast, the corresponding bulk peak intensity remains almost unchanged.¹⁸ At low temperatures, the long axis of the smectic fluctuations adjacent to the surface are preferably aligned parallel to the surface normal. Thus, the in-plane scattering signals in the q_‖-direction originating from charge alternation (peak II) and adjacency correlations (peak III) are enhanced. When the thickness of the smectic layer L reaches the decay length of the evanescent X-ray wave the peak intensities saturate. This texture effect affects only the peak intensities, leaving their position and shape unchanged with respect to the isotropic bulk liquid. This observation confirms our interpretation that the structure of the [C₂₂C₁im]⁺[NTf₂]⁻ surface above its melting point is governed by fluctuations of the metastable smectic mesophase rather than by formation of a 2D surface crystal.

4.3 Growth law

To obtain quantitative density profiles across the IL surface, the experimental XRR data was analyzed using eqn (4). For all temperatures, the experimental XRR pattern is perfectly reproduced by the curves calculated from the model profiles (Fig. 5). Model parameters of the best fits are summarized in Table 1. Detailed analysis showed that the values extracted for the smectic layer thickness L are robust parameters (ESI†).

Table 1 Model parameters of the XRR best fits (Fig. 5b) using eqn (4)

T (°C)	L (nm)	ξ b (nm)	d (nm)	z 0 (nm)	σ s (nm)	S ^0	S ^−	B	a 2	ξ 2 (nm)
a Parameters were fixed to the interpolated bulk values extracted from SAXS.^67 b Parameters were determined by continuity and differential continuity conditions. ξs was fixed at 2000 nm.
68	30.0 ± 2.0	4.78	3.73	2.28	0.18	1.71	−98	126	0.15	26
70	16.8 ± 2.2	4.73	3.73	2.29	0.17	1.64	−152	12.6	0.15	18
73	12.5 ± 1.2	4.64	3.73	2.24	0.10	1.62	−189	6.50	0.12	19
87	6.5 ± 0.6	4.21	3.70	2.14	0.18	1.58	−294	2.90	0.15	9
115	2.8 ± 2.5	3.38	3.56	1.89	0.25	1.55	−503	0.19	0.05	20

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Horizontal tics in Fig. 5b indicate the layer thickness L of the ordered structure near the IL surface. For z ≤ L, the envelope ϕ(z) of the density profile is given by eqn (7), whereas for z > L the envelope is exponentially decaying with the bulk correlation length ξ_b determined by X-ray scattering.⁶⁷

Fig. 7 shows the layer thickness L/d of the normalized surface structure divided by its periodicity d vs. reduced temperature τ (red circles). The blue line is a fit to the theoretically predicted growth law assuming exponentially decaying short range interactions (eqn (10a)). Approaching the bulk transition temperature T₀, the surface layer thickness L is diverging. From the fit we obtain T₀ = 68.2 °C.

Fig. 7 Smectic wetting layer thickness L from fits (red circles) and fit to eqn (10a) (blue line) vs. reduced temperature τ = (T − T₀)/T₀.

This value agrees well with the transition temperature T_LC = 67.1 °C of the metastable smectic bulk phase determined from DSC measurements. On the other hand, surface induced ordering is found only below τ = 0.26. This corresponds to an onset temperature T₁ = 157 °C. Above this temperature, the oscillatory structure near interfaces decays exponentially with a decay length given by the corresponding bulk correlation length ξ_b.⁹¹

For the structurally similar imidazolium based IL [C₁₈C₁im]⁺[FAP]⁻ no such surface ordered structures were found in a previous XRR study.⁵⁵ In contrast, over the entire accessible temperature range the decay length at the surface was found to be equal to the bulk correlation length. However, unlike for [C₂₂C₁im]⁺[NTf₂]⁻ no indications for metastable liquid crystalline mesophases have been found in this system.

In literature, at least three distinct types of interface induced smectic order are discussed: discrete, continuous, and continuous with a prewetting layer. Discrete interface induced smectic order has been found for several liquid crystals at the free surface,^92–94 in pores,⁹⁵ and by simulation.⁹⁶ In these systems, surface freezing via a quantitized layer by layer growth of a smectic liquid crystal was found above the mesophase transition temperature. In contrast, continuous smectic order is characterized by a gradually decaying oscillating density profile. Notably, here the correlation length at the interface is larger than in the isotropic bulk. Several XRR studies,^94,97–100 atomic-force microscopy¹⁰¹ and simulations¹⁰² show evidence for this phenomena. Surface induced continuous smectic order with prewetting is a mixture of the two cases discussed above. Here, a single smectic monolayer is wetting the surface. Below this first layer, similar to the continuous case an oscillating decaying profile is observed.⁹⁴

However, these different varieties of interface induced smectic order phenomena can be described within microscopic wetting theory^103,104 based on smectic order parameter profiles. There, the film growth of undersaturated phases upon approaching two phase coexistence is studied, and phenomena like layering transitions or prewetting can occur. Depending on the intermolecular interaction potentials, phase transition entropies, and temperature one or the other of structures discussed above is realized.

The first category are liquid crystals that exhibit continuous or quasi-continuous bulk phase transitions, e.g., the commonly used 8-CB and 8-OCB with nematic-smectic transition.¹⁰⁰ These transitions are characterized by a vanishing or negligible transition entropy ΔS.⁸⁷ Most of the previously studied LC systems fall in this category. In these systems, wetting theory predicts pinning of the smectic fluctuations at the surface of the nematic bulk. For continuous phase transitions, Ginzburg–Landau theory predicts that the correlation length ξ_s of the smectic fluctuations vs. reduced temperature τ scale with a power law

ξ_s(τ) = ξ₀τ^−ν (11)

with the universal critical exponent ν, which for the Ising model equals 1/2 within mean field approximation and ≈0.63 beyond.⁹⁷ As a result, the extension of the ordered surface structure close to the nematic-smectic transition diverges algebraically for τ → 0.

By contrast, at the isotropic-smectic transition of [C₂₂C₁im]⁺[NTf₂]⁻ we find ΔS_LC = 2.5 mol⁻¹ K⁻¹, which signals a first-order bulk phase transition. From the observed logarithmic growth law for the layer thickness L(τ) one infers complete wetting and effectively short-ranged interactions. Hence, in [C₂₂C₁im]⁺[NTf₂]⁻ the surface-induced smectic layer thickness L reaches values that are substantially larger than its bulk correlation length ξ_b.

Ultimately, the fundamental parameter connecting the system temperature with the surface structure is the pre-factor Λ in the growth law given by eqn (9c). According to theory, this parameter is linked to the bulk correlation length ξ_b in the isotropic phase.^83,103,104 Indeed, we find a very good agreement of Λ/d = 1.2 with the bulk value ξ_b/d = 1.3 determined by SAXS.⁶⁷

A similar behavior is expected for other ILs, exhibiting smectic mesophases. However, in equilibrium surface induced smectic order will only be found for systems where T₁ > T_m. For example, by extrapolation a transition temperature T_LC = −160 °C is predicted for the IL [C₁₄C₁im]⁺[NTf₂]⁻ with shorter C₁₄ cation side chains.³⁴ Assuming τ₁ < 0.3, surface induced smectic order is only expected to be found below −130 °C. This temperature is about 170 Kelvin below its bulk melting point at 41 °C.

However, for smaller anions such as [BF₄] and [PF₆] ILC transition temperatures T_LC strongly increase. For example, in [C₁₄C₁im]⁺[PF₆]⁻ a value of T_LC − T_m = 5 K is found.³⁴ Thus, surface induced smectic order might be also relevant for ILs composed of commonly used cations.

5 Conclusions

At the free [C₂₂C₁im]⁺[NTf₂]⁻ surface, pronounced ordering was observed. Oscillatory surface profiles give rise to strong quasi-Bragg peaks in the XRR patterns. Quantitative analysis by fitting of model profiles shows that close to the melting point a smectic surface layer of thickness L is wetting the isotropic bulk liquid. These findings are in conclusively agreement with MS-GS and MD simulations, showing smectic-like layering for some IL interfaces.^43,105

Fig. 8 shows a schematic representation of the surface structures at 68 °C and 115 °C. Notably, close to the melting point we find smectic layer thicknesses up to 30 nm. This corresponds to an ordered surface structure, extending 8 times the smectic periodicity d below the liquid surface. Therefore, unlike for other ILs such as [C₁₈C₁im]⁺[FAP]⁻, the oscillatory near surface structure persists far beyond the bulk correlation length of ξ_b/d = 1.3.

Fig. 8 Electron density profiles and schematic representation of the near surface structure at (a) 68 °C and (b) 115 °C. The size of anions (blue), imidazolium rings (red) and aliphatic side chains (yellow) are not to scale. Profiles are identical to Fig. 5b. The in-plane order (not shown) remains liquid-like for all temperatures.

The ordered surface layer thickness L vs. temperature is quantitatively described by a logarithmic growth law. This dependency follows the prediction from a generic thermodynamic model for interface induced phase transitions. In agreement with theory, the pre-factor Λ in the logarithmic growth law agrees with the bulk correlation length ξ_b of the isotropic liquid phase. Upon cooling, the smectic layer thickness L/d in [C₂₂C₁im]⁺[NTf₂]⁻ diverges at a temperature T₀. Interestingly, T₀ agrees well with the transition temperature T_LC of a metastable liquid crystalline smectic SmA₂-mesophase formed from the supercooled isotropic liquid. This indicates that the observed layered surface structure in [C₂₂C₁im]⁺[NTf₂]⁻ is governed by surface induced smectic order, i.e. fluctuations into the metastable SmA₂-phase. On the other hand, we find an upper transition temperature of T₁ = 157 °C for the ordered surface layer. Note that this behavior is very different from the power law scaling found for LCs with quasi-continuous nematic-smectic phase transitions.^97,100 In contrast to other soft matter systems such as liquid crystals or alkanes, surface induced smectic ordering in the ionic liquid [C₂₂C₁im]⁺[NTf₂]⁻ is relevant over a much larger temperatures range.

In bulk, smectic mesophases were found for a wide class of neat and mixed ILs.¹⁹ Based on our results, we therefore presume that similar surface structures are also formed in other ILs. From our previous bulk⁶⁷ and surface studies,⁵⁵ we anticipate that the tendency for surface induced smectic order is larger for smaller anions and longer aliphatic side chains. This tendency is supported by clear trends observed in a new volume based approach to predict the thermodynamical behavior of ILs and ILCs.³⁴

The well ordered surface structures observed for [C₂₂C₁im]⁺[NTf₂]⁻ over a surprisingly large temperature range might significantly reduce the diffusion of guest molecules across an IL/gas interface. Indeed, for [C₁₆C₁im][NO₃] MD simulations show 5-fold smaller diffusion constants perpendicular to the layers of the smectic phase.¹⁰⁶ Formation of such diffusion barriers for reactants and products, might adversely affect the performance of ILs in SILP processes.⁸ Further experiments on different ILs will be required to shed light on the complex interplay between the molecular structure of the anions and cations and the tendency for surface induced smectic order.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Grazing incidence surface scattering and preliminary XRR data were obtained at ID10-EH1, ESRF The European Synchrotron, Grenoble, France. XRR experiments were conducted at the LISA instrument at beamline P08, Petra III, DESY, Hamburg, Germany funded by BMBF (project 05K10FK2 and 05K130FK2). We thank Gunnar Kircher (MPI-P) for [C₂₂C₁im]⁺[NTf₂]⁻ synthesis, Xilin Wu (MPI-P) and Guoming Liu (Chin. Acad. Sci.) for assistance during the synchrotron experiments and Peter Reichert (MPI-P), Julia Haddad (Bar-Illan Univ.), and Hans-Jürgen Butt (MPI-P) for helpful discussions. J. M. and M. M. acknowledge the MAINZ Graduate School of Excellence, funded through the Excellence Initiative (DFG/GSC 266) and the German Israeli Foundation for scientific research and development (2306-2310.14/2011) for financial support. B. H. received a scholarship funded by the ESRF The European Synchrotron, Grenoble, France. H. L. was supported by the China Scholarship Council. Open Access funding provided by the Max Planck Society.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp04852a

‡ Present address: Department of Chemistry and Physical Science, School of Natural and Social Sciences, Mount Vernon Nazarene University, 800 Martinsburg Road, Mount Vernon, Ohio 43050, USA.

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