Surface Phases and Surface Freezing in an Ionic
Liquid
Supplementary Information
Diego Pontoni,
†,#Julia Haddad,
‡,#Bridget M. Murphy,
¶,§Sven Festersen,
¶Oleg Konovalov,
kBenjamin M. Ocko,
⊥and Moshe Deutsch
∗,‡†ESRF - The European Synchrotron & Partnership for Soft Condensed Matter (PSCM), 71 Avenue des Martyrs, 38000 Grenoble, France
‡Physics Dept. & Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan, Israel
¶Institute for Experimental and Applied Physics, Christian-Albrechts-Universit¨at, Kiel, Germany
§Ruprecht Haensel Laboratory, Christian-Albrechts-Universit¨at, Kiel, Germany kESRF - The European Synchrotron, 71 Avenue des Martyrs, 38000 Grenoble, France
⊥NSLS-II, Brookhaven National Laboratory, Upton, NY 11973, USA #Contributed equally to this work
Materials, Cell, and Procedures
The RTILs used here, 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imides, ( de-noted [Cnmim]+[NTf2]−) were purchased as powders at room temperature from Iolitec,
Ger-many, with manufacturer-stated purities > 98% (n = 18) and > 95% (n = 20).
Figure S1: 1H-NMR spectra of the [C20mim][NTf2] sample. Bottom: measured spectrum.
Top: magnified ×128. Red arrows mark impurities.
The relevant part of the 1H-NMR spectrum of the DMSO-dissolved [C
20mim][NTf2]
sam-ple is shown in Fig. S1. Peak shifts are (in ppm): 0.85(t, 3H), 1.23(m, 34H), 1.77(quintet, 2H), 3.85(s, 3H), 3.92(s, 3H), 4.14(t, 2H), 7.69(s,1H), 7.75(s, 1H), 9.09(s, 1H). As for all
responding to traces of the alkylating agent, a Br-terminated alkyl chain, here H(CH2)20Br,
used in the synthesis. This peak is observed in Fig. S1 as a triplet at 3.51 ppm. Its inte-gral corresponds to a bulk concentration of ∼ 2 mol%, far exceeding the amount needed for forming, and surface-freezing, the Langmuir-Gibbs surface monolayer, as discussed in the main text. A similar-magnitude increase (above the 34 of an ideally-pure material) in the integral of the cation’s chain peak at 1.23 ppm, also supports the presence, and the ∼ 2 mol% concentration, of guest chain molecule in our sample. Finally, several other impurities also appear at lower concentrations in the figure, marked by red arrows.
Samples were placed in a machined PCTFE tray 45 mm long and ∼ 1 mm deep, kept inside a hermetically sealed sample cell having thin Kapton x-ray windows, and temperature controlled to ≤ 0.05 ◦C.
Comparing repeated scans at the same spot with those at a fresh spot helped detecting and avoiding beam damage. Water adsorption, intrinsically very low for these hydrophobic long-chain RTILs, was further minimized by the hermetic cell sealing and the relatively high measurement temperatures. Indeed, no evidence for water adsorption was found upon comparing measurements done under sealed air-filled cell and under slow dry helium flow. Repeated measurements over a long time-scale also did not show changes attributable to adsorbed water layer buildup at the surface.
X-ray measurements
Detailed descriptions of the measurement methods used here, liquid surface x-ray reflectivity (XRR), grazing incidence diffraction (GID), and Bragg-rod (BR) measurements, are available in the literature.1–3 We briefly discuss below only the parts needed for understanding the
discussion in the main text.
The XRR measurements were done using the liquid-surface diffractometers4–6 HEMD at ID15A, EH1 at ID10 (both at ESRF, France) and LISA (P08, PETRA III, DESY, Germany),
with wavelengths λ = 0.1771 ˚A, 0.5586 ˚A, and 0.4958 ˚A, respectively. The GID and BR measurements were done at ID10 (ESRF, France) with λ = 0.5586 ˚A, under dry helium flow, to reduce background scattering.
X-ray reflectivity
XRR measures the surface-reflected fraction, R(qz), of the intensity of an x-ray beam
im-pinging on the liquid surface at a grazing angle α and reflected at an angle β = α. The corresponding scattering vector, qz = (4π/λ) sin(α), is surface-normal, and thus XRR probes
the laterally-averaged surface-normal electron density profile, ρ(z). Theory
There are several ways for deriving ρ(z) from the measured R(qz), the most popular, and
sim-plest, among which is the use of the Born approximation.1,2 This, however, requires
Fourier-transforming analytically the derivative of a mathematical model constructed to represent ρ(z), which is not always possible. Thus, we have employed here the Parratt method,1,2,7 where the model ρ(z) is approximated by a stack of thin layers, having each a constant electron density, and the reflected and transmitted waves are calculated at each interface consecutively moving up from the bulk. The model-defining parameters best reproducing the measured R(qz) are calculated iteratively using least-squares fit methods.
Model and fits
We use the model in Ref. 8 of a liquid crystal (LC) phase of thickness L overlying a ”normal” RTIL layered phase, with the layering decaying with depth into the bulk.9 The two phases have a common period d, but different order-decay functions and characteristic lengths, ξs
and ξb. Following Ref. 10, the total ρ(z) is partitioned into two contributions: a constant
hydrocarbon contribution, starting at z = 0, the surface plane, and an oscillatory layering contribution, starting slightly below the surface plane, at z = z , to allow for the layer of
air-protruding alkyl chains of the top cation-anion sheet.9 ρ(z) is thus given by:
ρ(z) = ρbΦ(z/σs)[1 + (1 − ZHC/ZRT IL)φ(z)ψ(z)], (1)
where Φ(z/σs) = [1 + erf(z/
√
2σs)]/2 represents the constant hydrocarbon contribution,
gradually rising over a width σs, the laterally-averaged surface roughness, from ρ(z = 0)/ρb =
0 to a constant value of unity. ZRT ILand ZHC are the total number of electrons in a molecule
and in its hydrocarbon equivalent.8,10 ψ is the oscillatory contribution to ρ(z), which can be
expanded in a series: ψ(z) = ∞ X j=1 ajexp(−z/ξj) cos[2πj(z − z0)/d], (2)
Mars et al.8 find perfect fits for their [C22mim][NTf2] measurements truncating the series
after the second term and using a1 = 1 and ξ1 → ∞. This is found to be the case also for
our [C20mim][NTf2] data fits.
Finally, φ(z) is the envelope function of the oscillatory contribution to the density profile, determining its decay with depth. It is given by:
S0+ S1sinh(z/ξs) if z ≤ L
φ(z) = (3)
S2exp(−z/ξb) if z > L.
To ensure smooth continuity at z = L, the two functions in Eq. 3 and their first derivatives are equated at z = L, thus eliminating two of the Si’s:
S0 = − S1[(ξb/ξs) cosh(L/ξs) + sinh(L/ξs)] (4)
Following Ref. 8 we used 0.5˚A-thick slices of this ρ in the Parratt algorithm. Similarly, the number of fit parameters was reduced by adopting the ξb values from our
temperature-dependent bulk measurements, and fixing ξs= 15000 ˚A and σ0 = 1.2 ˚A. The fits were found
to be insensitive to the exact values of these parameters. For further details of the model see Refs. 8,10.
Bragg rod
The Bragg Rod (BR), the surface-normal intensity distribution along qz at the in-plane
qx-position of a GID peak, is given by:2,3
IBR(qz) ∝ " sin(Qz`/2) Qz`/2 2 exp[−(Qzσ0)2] # exp[−(qzσz)2]|T (α)|2|T (β)|2, (5)
where Qz = qzcos(η) − qxsin(η) is the scattering vector component along the molecule’s
long axis, ` and η are its length and its tilt angle from the surface normal, and σ0 and σz
are the crystalline monolayer’s intrinsic and capillary roughness parameters. The surface enhancement factors T (x), |T (x)|2 = 2 sin x/ sin x +pcos2α c− cos2x 2 (6) reach ∼ 4 at x ≈ αc, the critical angle for total external x-ray reflection, and fast approach
T (x) ≈ 1 for x > αc. This yields the strong Vineyard peak11 at qz = qc in the main text
Fig. 5(a).
References
(1) Pershan, P. S.; Schlossman, M. L. Liquid Surfaces and Interfaces: Synchrotron X-ray Methods; Cambridge University Press: Cambridge, UK, 2012.
(2) Als-Nielsen, J.; McMorrow, D. Elements of Modern X-ray Physics; Wiely: New York, USA, 2001.
(3) Ocko, B. M.; Wu, X. Z.; Sirota, E. B.; Sinha, S. K.; Gang, O.; Deutsch, M. Surface Freezing in Chain Molecules: Normal Nlkanes. Phys. Rev. E 1997, 55, 3164–3182. (4) Honkim¨aki, V.; Reichert, H.; Okasinski, J. S.; Dosch, H. X-Ray Optics for Liquid
Surface/Interface Spectrometers. J. Synch. Rad. 2006, 13, 426–431.
(5) Murphy, B. M.; Greve, M.; Runge, B.; Koops, C. T.; Elsen, A.; Stettner, J.; Seeck, O. H.; Magnussen, O. M. A Novel X-Ray Diffractometer for Studies of Liquid-Liquid Interfaces. J. Synch. Rad. 2014, 21, 45–56.
(6) Smilgies, D.-M.; Boudet, N.; Struth, B.; Konovalov, O. Troika II: A Versatile Beamline for the Study of Liquid and Solid Interfaces. J. Synch. Rad. 2005, 12, 329–339.
(7) Parratt, L. G. Surface Studies of Solids by Total Reflection of X-Rays. Phys. Rev. 1954, 95, 359–369.
(8) Mars, J.; Hou, B.; Weiss, H.; Li, H.; Konovalov, O.; Festersen, S.; Murphy, B. M.; Rutt, U.; Bier, M.; Mezger, M. Surface Induced Smectic Order in Ionic Liquids - An X-Ray Reflectivity Study of [C22C1im]+[NTf2]−. Phys. Chem. Chem. Phys. 2017, 19,
26651–26661, See also Correction note, DOI: 10.1039/c8cp91851a.
(9) Haddad, J.; Pontoni, D.; Murphy, B. M.; Festersen, S.; Runge, B.; Magnussen, O. M.; Steinr¨uck, H.-G.; Reichert, H.; Ocko, B. M.; Deutsch, M. Surface Structure Evolution in a Homologous Series of Ionic Liquids. Proc. Natl. Acad. Sci. U. S. A. 2018, 115, E1100–E1107.
(10) Mezger, M.; Ocko, B. M.; Reichert, H.; Deutsch, M. Surface Layering and Melting in an Ionic Liquid Studied by Resonant Soft X-ray Reflectivity. Proc. Natl. Acad. Sci. U. S. A. 2013, 110, 3733–3737.
(11) Vineyard, G. H. Grazing-Incidence Diffraction and the Distorted-Wave Approximation for the Study of Surfaces. Phys. Rev. B 1982, 26, 4146–4159.
