QLL thickness measurements were performed with a commercial atomic force microscope (AFM) by Veeco (currently Bruker), model Multimode, using the NanoScope IIIa controller and the Quadrex module. Force curves were registered at a frequency of 1.744 Hz and a sampling of 8192 data points per curve. Measurements were performed with different commercial AFM tips provided by Bruker (silicon, silicon nitride, and Pt/Ir-coated silicon), whose characteristics are summarized in Table S1 in the Supplement. Additionally, we used a commercial silicon nitride tip functionalized by immersion in 1 M chlorotrimethylsilane in heptane.

Raw data generated by the AFM operating software (NanoScope 5.30r3, Veeco) was exported with NanoScope Analysis 1.40 (Bruker) and post-processed with an in-house-developed software written in Scilab 5.4.0 (Scilab Enterprises, 2012). Our software allows a semiautomatic analysis of force curves and saves individual image files, showing the shape of the curves and the regions analyzed, as well as a spreadsheet with the quantitative information extracted from the curves.

Calibrations required for a proper analysis of the AFM force curves are detailed in the Supplement.

Pt/Ir-coated silicon AFM tips (SCM-PIC, Table S1) were characterized by scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS) (Carl Zeiss NTS SUPRA 40 at the Centro de Microscopías Avanzadas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires). The goal of this characterization is to compare the morphology and composition of the tips before and after usage in AFM indentation experiments.

The temperature of the sample at the AFM was controlled with a set of commercial accessories provided by Veeco: the Thermal Applications Controller, the Sample Heater/Cooler Peltier, and the Heater/Cooler Scanner HC-AS-130V. This allows controlling the sample temperature between -30 and 100 ∘C with a precision of ±0.1 ∘C. The relative humidity (RH) and temperature of air in contact with the sample was measured with a Sensirion humidity–temperature sensor (model SH71).

Two environmental chambers, which will be further described in the following paragraphs, were developed in this work to control the RH of the sample and, in one case, the temperature of the air in contact with the ice.

Ice samples to be measured at a working temperature (Tice) (controlled and measured with the Peltier accessory below the sample) were prepared by controlled vapor deposition using the following procedure.

During calibration, the humidity in the EC or mEC was maintained below 80 % RH (relative to Tice) using dry nitrogen gas, in order to avoid ice or water condensation.

When using the mEC, the copper cooler temperature (Tcooler) was set between 3 and 6 K above Tice. This temperature gradient could not be further reduced, since for Tcooler closer to Tice we observed condensation on the fluid cell and/or on the AFM tip, as we will discuss in the following sections.

After calibration, we first controlled the desired RH, between 90 % and 105 % (relative to Tice), while keeping the mica substrate temperature (Ts) 2 to 5 K above the desired working temperature (Tice) to avoid condensation due to RH fluctuations that may occur during this step. Oversaturation conditions made it more difficult to measure contact images or force curves on the ice–QLL surface (due to condensation on the tip). Hence, in most of the experiments we worked at slight undersaturation conditions.

By using the Peltier accessory, Ts was then lowered 2 to 3 K below Tice, reaching oversaturation (RH between 105 % and 120 %). Ice deposition was then allowed during 4 to 8 min. It must be noted that the inverse procedure (setting Ts first and then increasing RH) is not preferred. In order to obtain reproducible, equilibrium ice layers, one should increase oversaturation slowly and steadily. This can be achieved more easily by lowering Ts with the commercial accessory rather than increasing humidity.

Finally, the temperature was raised from Ts to Tice, and the ice was stabilized for 10 to 20 min prior to measuring the force curves.

The small volume of the mEC allowed observing the RH changes during the ice deposition protocol. Figure 4 shows the RH changes during the sample preparation, where a marked drop of humidity almost immediately after the drop in temperature (due to ice deposition) can be observed. When temperature rises again, humidity increases too, and RH reaches values close to 100 % (relative to Tice).

Even though we did not perform specific experiments to verify the structure and orientation of the prepared ice, we claim that we studied polycrystalline ice. This procedure is rather similar to that of many of the reviewed experiments (Bluhm et al., 2000, 2002; Pittenger et al., 2001). Pittenger et al. (2001) reported that they obtained polycrystalline ice with smooth surface at the scale visible to an optical microscope. In some of the experiments, we obtained AFM contact images that confirmed a smooth ice surface (roughness lower than 5 nm in most cases, images not shown). We did not observe the ice droplets mentioned by Bluhm et al. (2000), probably due to the fact that they prepared samples with thicknesses of few ice bilayers. In our case, ice samples thicknesses were not measured systematically (as it was not the focus of this work), but in most of the experiments ice thickness exceeded the spanned indentation depth (hundreds of nanometers to 5 µm, the maximum vertical distance that can be measured with the AFM scanner used for these experiments). In a few experiments we were able to measure the ice thickness, since the AFM tip reached the infinitely hard mica substrate (Fig. S6, Supplement). Considering these macroscopic thicknesses, we can assure that we studied the ice–vapor interface without the influence of the underlying substrate or nano-confinement effects.

Another set of experiments was performed in the mEC during deposition of ice at a RH around 120 %. These assays allow comparing the QLL thickness obtained at a RH around 100 % for a stabilized ice sample with those obtained upon oversaturation and a non-stabilized ice sample.

In order to evaluate the hydrophilicity of AFM tips, we prepared thin layers of glycerol on glass slides and silicon wafers. The substrates were treated with a Piranha solution (3:1 mixture of concentrated sulfuric acid and 30 % hydrogen peroxide solution) in order to remove organic impurities and increase the hydrophilicity of the surface. We prepared the glycerol films by spin-coating at different velocities, obtaining metastable layers less than 5 µm in thickness (as measured with AFM force curves).

Force curves on ice obtained with the EC with silicon tips in the temperature range from -7 to -2 ∘C were similar to those previously described (Petrenko, 1997; Butt et al., 2000; Döppenschmidt and Butt, 2000; Pittenger et al., 2001). Their general shape can be seen in the central panel of Fig. 5, as compared with the force curve determined on mica (top panel). As discussed in the introduction and in the Supplement, the usual interpretation of this kind of force curve is that the jump-in distance is related to the interaction with the ice interface prior to contact (possibly a frustrated capillarity due to the presence of the QLL) and that contact with the solid ice surface begins at ztip=0 and extends in the lineal region that follows (positive ztip values). Indentation slopes in ice are in the same order of magnitude to those found in other works in similar conditions, as they depend on temperature, velocity, and tip shape (Pittenger et al., 2001, Fig. 4).

Table 1 reports relevant features of the measured force curves. Force curves measured on the same position over the ice surface show high reproducibility, as previously reported (Petrenko, 1997; Butt et al., 2001; Pittenger et al., 2001). Such reproducibility, also reported by Petrenko (1997), suggests that after indentation the ice surface reconstructs quickly by capillary condensation (Pittenger et al., 2001) or flow from the QLL. Indentation slopes show standard deviations lower than 1 % (it must be noticed that the significant figures reported are consistent with the propagated uncertainty, which is higher, due to the uncertainty of the spring constant). Jump-in distances show higher standard deviations (around 10 %).

Some authors have assigned the observed jump-in distance to the thickness of the QLL (Petrenko, 1997; Döppenschmidt and Butt, 2000) on the basis of two assumptions: (1) the jump-in starts just when the tip makes contact with the QLL and (2) the jump-in ends when the tip reaches the solid layer beneath the QLL. These assumptions have been under discussion in the community (Döppenschmidt and Butt, 2000; Pittenger et al., 2001). Regarding the first assumption, Döppenschmidt and Butt apply a small correction on the jump-in distance (from 1 to 2 nm) considering van der Waals forces. Mate et al. (1989) estimate a larger bias, around 7 nm, if the tip is covered by a liquid film prior to contact when measuring the thickness of a 22 nm liquid film. Computer simulations (Gelman Constantin, 2015; Pickering et al., 2018) have also shown that for hydrophilic AFM tips the QLL deforms to reach the tip (frustrated capillarity), which would produce jump-in distances larger than equilibrium QLL thicknesses. The second assumption has been questioned as well and will be discussed in more detail in this section.

Jump-in distances obtained in our EC are reported in Table 1 and plotted in Fig. 6 together with results from similar studies (Petrenko, 1997; Bluhm et al., 1999, 2000; Döppenschmidt and Butt, 2000; Pittenger et al., 2001; Goertz et al., 2009). Symbols for the same temperature represent measurements on different positions over the ice surface. Error bars correspond to twice the standard deviation of several measurements performed at a fixed position. The set of measurements exhibits a weak dependence with temperature, which would become much weaker if the measurement corresponding to the largest jump-in at Tm-T=2.0 K would be discarded. The dispersion of the measurements at the same temperature may have different explanations. For instance, temperature gradients in the sample could produce differences in QLL thicknesses or a patch of mica with no solid water, and only a liquid layer can exist. The effect of temperature gradients will be quantitatively discussed in Sect. 3.2.

A first-order comparison with the literature shows that our QLL thickness results lie in the lower range of all reported values. QLL thicknesses reported by Pittenger et al. (2001) are in the same range as ours, whereas Döppenschmidt and Butt (2000) reported higher values, with a larger temperature dependence. Pittenger et al. (2001) state that the jump-in distances determined in their experiments are not representative of the QLL thickness, since they are almost constant (around 3 nm) over a wide temperature range (1–17 K below the melting temperature). They also doubt on the reliability of the large QLL thicknesses measured by Döppenschmidt and Butt (2000) assuming that the tip penetrates the ice during the jump-in. Hence, the above-mentioned assumption that the jump-in ends when the tip reaches the solid layer beneath the QLL will not be valid. In fact, they show that ice indentation distance at zero force has a strong dependence on temperature (as we found for experiments in the mEC and as we will discuss next).

Computer simulations (Gelman Constantin et al., 2015; Gelman Constantin, 2015) suggest that hydrophilic tips indent ice more easily (with lower free-energy barriers, due to the attractive interaction) than their hydrophobic analogues. In addition, it was found that the ice layers below the QLL deform prior to contact with the tip. These results also reinforce the hypothesis by Pittenger et al. (2001) that QLL thicknesses obtained from AFM jump-in distances with hydrophilic tips are overestimated due to ice indentation. It should be stressed that the same artifact could affect Petrenko's results, although the author uses stiffer cantilevers (which reduce the ice indentation distance, since it compensates for capillary forces at smaller deflections). In addition, Petrenko obtained the deflection sensitivity from the retract portion of force curves on ice at low temperatures, instead of using a more rigid substrate like mica or glass, as we did here. Therefore, the procedure adopted by Petrenko could lead to an underestimation of the deflection sensitivity (Attard, 2007), which would imply an overestimation of the jump-in distances.

Results by Bluhm and Salmeron (1999) and Bluhm et al. (2000) present an opposite trend to most of the literature values, that is, lower QLL thicknesses at higher temperatures. However, it should be noted that they measure QLL thickness over much thinner samples (0.3 to 3 nm), which corresponds to a few bilayers of ice-like water molecules on the substrate. It should be stressed that these experiments do not give information on the QLL of bulk ice, even if the structure of water on the substrate could be related to that of crystalline ice. Nano-film properties might show a large dependence on the thickness and the influence of the substrate.

Goertz et al. (2009) obtained a QLL thickness much higher than the AFM results previously discussed, by using interfacial force microscopy. The IFM experiment is very similar to AFM force curves, but the setup avoids mechanical instabilities (jump-in and pull-off) and generally uses larger tips. The difference between IFM and AFM results could be due to the difference in the size of the tip (150 µm spherical tip radius), to the poor control of the sample temperature (temperature is only controlled below the sample, while the large glass tip was not cooled), or to a fail in the suppositions required for the analysis of the force curves, as described previously.

AFM force curve measurements with the mEC using silicon tips (SNL, as in the experiments in the EC) or silicon nitride tips (DNP) over the same temperature range, whose results are summarized in Table 2, exhibit some differences with those obtained with the EC.

Firstly, with both kinds of tips, many experiments (7 out of 12) ended with a complete loss of the signal in the laser detector. We found two possible explanations for these observations. This new configuration (mEC), with lower temperature gradients in the chamber, surely leads to lower temperature on the tip. This may allow some condensation on the reflecting back coating of the cantilever, which prevents the laser beam from reaching the detector. Moreover, the reduction of the temperature gradients could also have an effect on the attractive interactions between the tip and the ice surface due to condensation on the tip, or changes on the ice surface. An increase in the attractive interactions could lead to a large bending of the cantilever, with a consequent large deflection of the laser spot out of the area of the detector.

Secondly, some other experiments (four of them) produced force curves with no jump-in (like in the lower panel in Fig. 5). The absence of jump-in led us to suggest that in those experiments the QLL, if present, should have a thickness lower than 1 nm (the minimum jump-in distance that could be detected in these experiments, due to noise in the deflection signal). The force curves indicate that the tip goes abruptly from the vapor phase (horizontal region, no net forces on the tip) to indenting the solid ice phase (diagonal linear region). Indentation slopes are reported in Table 2; a comparison with those reported in Table 1 is out of the scope of this article and needs to take into the account the tip shape and the uncertainty of the spring constant and that of deflection sensitivity. Thus, how can we explain the difference with the results using the EC? Temperature gradients along the sample in the EC could be the key.

If the temperature of the air layer in contact with the ice surface is higher than Tm, a liquid layer can cover the sample. A simple heat transfer calculation (chapter 11, Bird et al., 2007) can provide the thickness of the stationary state liquid layer: S(t→∞)=L1-TLκlT0κs-1, where S is the thickness of the liquid layer, L is the total thickness of the system (ice + liquid water), TL and T0 are the temperature of the system surface (in contact with air) and the ice bottom (in contact with the Peltier element), respectively, and κl and κs are the thermal conductivities of the liquid and solid phases. It is evident, from the results displayed in Fig. 7, that if the air in contact with the sample is only slightly above 0 ∘C, thick liquid layers appear over the ice surface. Clearly, this will lead to an overestimation of the QLL thickness. Smaller temperature gradients (where ice surface presents a temperature larger than reported, but below 0 ∘C) could also affect QLL thickness measurements. It must be noted that, among the experimental techniques reviewed in this article, the smaller QLL thickness measurements were achieved in experiments in which ice was only in contact with water vapor, such as Brewster reflectometry (Elbaum et al., 1993), XPS (Bluhm et al., 2002), X-ray scattering (Lied et al., 1994; Dosch et al., 1995, 1996), and IR spectroscopy techniques (Sadtchenko and Ewing, 2002, 2003). For these measurements below 0 ∘C, the low thermal conductivity in the gas phase implies lower heat transfer between the gases and the QLL, which can be easily compensated for by the cooling system, resulting in small temperature gradients through the sample, and yielding to smaller QLL thicknesses. On the contrary, ellipsometry (Beaglehole and Nason, 1980; Furukawa et al., 1987) and AFM determinations (Petrenko, 1997; Bluhm and Salmeron, 1999; Döppenschmidt and Butt, 2000; Bluhm et al., 2000; Pittenger et al., 2001) give thicker QLL values. Even though in the ellipsometry experiments the samples were only in contact with water vapor, Beaglehole and Nason (1980) and Furukawa et al. (1987) experiments use thick ice samples (several millimeters to centimeters) that are only cooled from below, which might produce relevant temperature gradients in the samples. For instance, in one of the experiments (Beaglehole and Nason, 1980) the authors report temperature gradients around 0.5 ∘C in the ice sample.

For one of the experiments with silicon nitride tips (DNP1) using the mEC, we performed force curves at the same Tice but adjusting Tcooler at several temperatures. Table 2 shows the results for two of such Tcooler temperatures and Tice=-5 ∘C. Jump-in distances do not show a significant difference for both temperatures, although it seems that for higher Tcooler the distances tend to be slightly higher and with a higher dispersion. However, there is a clear difference in the indentation slope: the lower Tcooler, the steeper the indentation slope. In other words, when the temperature gradient is higher, it is easier for the tip to indent the first layers of ice. Even though we could not extend the measurements with the mEC to the range of temperature gradients that exist in the experiments with the EC (where Tcooler could be considered close to ambient temperature), one may suppose that the effect on the slope should be even higher. This observation is consistent with that by Pittenger et al. (2001) on the temperature dependence of the indentation distance at zero force and supports his claim that QLL thicknesses obtained from AFM jump-in distances (Petrenko, 1997; Döppenschmidt and Butt, 2000) are overestimated, as discussed above.

Figures S3 and S4 in the Supplement show that the force curves determined in the mEC with silicon nitride tips, as it was previously mentioned for the EC, are very reproducible. The reproducibility of all the force curves can be captured by considering the averages and standard deviations of ice indentation slopes and jump-in distances on Table 2.

It can be stressed that experiments with more hydrophobic tips could be more appropriate for these studies. Petrenko (1997) noticed that silicon tips were less appropriate than more hydrophobic tips to study the ice–QLL interface, due to high adhesion forces. With lower adhesion forces, the biases that affect the jump-in distances due to capillary forces would be smaller. Firstly, because the use of hydrophobic tips reduces the deformation of the QLL and the tendency to form a neck between the tip and the sample. Secondly, because it reduces the net attractive forces acting on the tip, which produces a lower indentation of the solid ice during the jump-in. Hence, we performed further experiments with four platinum-covered tips and a silicon nitride tip functionalized with trimethylchlorosilane. In all cases, we obtained curves with no jump-in (type c curves in Fig. 5). Figure S5 of the Supplement shows as mode of example some force curves determined with Pt/Ir-coated tips for the approach and retract branches of the curves, where it can be observed that no adhesion forces are present in the retract portions of the curves.

In two cases (PIC1 and DNP-S1, Table 2), after repeated use of the tips,we started to obtain different force curves, similar to type b in Fig. 5. We believe that adhesion between the tip and the sample lead to detachment of the covering layer in those tips, increasing the overall hydrophilicity of the tip and causing the artifices described above for silicon and silicon nitride tips. Figure 8 shows the SEM micrographs of the AFM Pt/Ir-coated silicon AFM tips, before and after indentation experiments, where it can be observed that, after usage, the roughness of the AFM tip increases markedly. Table 3 shows the EDS results obtained for the AFM tips before and after usage. Results show that after usage the relative amount of Pt in the sample decreases, probably due to a loss of the Pt cover in the tip zone that indents the ice. It should be stressed that Pt content does not reduce to zero. This is probably due to the fact that the EDS experiments collect X-ray radiation that originates in a volume of approximately 1 µm3 around the AFM tip apex, which is larger than the indentation volume. Hence, results in Table 3 are probably affected by a region of the tip not in contact with the sample, which may keep its Pt coating. It can also be observed that S, Cl, and Zn appear after indentation experiments, probably due to contamination of the tip with residues of these elements in the mica sheet.

Another set of experiments was performed using platinum-covered AFM tips during deposition of ice at -5 ∘C and 110 % RH (with tip PIC6) and at -2.5 ∘C and 113 % RH (with tip PIC4). Both experiments show force curves with jump-in (similar to those in the central panel of Fig. 5). QLL thickness values obtained for these experiments are (i) 11.8±3.3 nm for Tice=-5.0 ∘C, Tcooler=-4 to -6 ∘C, and RH 110 % and (ii) 23.8±4.1 nm for Tice=-2.5 ∘C, Tcooler=5 to 6 ∘C, and RH 113 %. These results are similar to those obtained with the more hydrophilic tips, probably because they were obtained upon repeated indentations of ice samples. Thus, the platinum coverage on the tip apex was probably lost during the measurements, as mentioned for some of the experiments previously described. Additionally, it should be stressed that in the later experiments force curves were determined during deposition of ice under oversaturation conditions, whereas all our previous results correspond to slight undersaturation conditions where ice was allowed to stabilize 10–20 min prior to measurements. Thus, the later experimental conditions could lead to thicker (non-equilibrium) QLL values. Pickering et al. (2018) performed grand-canonical MD simulations under condensation conditions (oversaturation) and found non-equilibrium QLL thicknesses larger than the equilibrium values. They suggest that “the pressure should be controlled in experiments with a precision of at least 10 % or that it should be kept slightly below the saturation point, where the QLL depth would not be significantly affected”, as we found in our experiments.

Summarizing, the absence of a jump-in on some of the force curves measured in this work (more systematically with hydrophobic tips in the mEC) enforces the hypothesis that the QLL thickness is below 1 nm in the temperature range of the experiments (-7 to -2 ∘C). However, a doubt arises: could it be the case that the later tips are not hydrophilic enough and hence the capillary force with the QLL (if present) is not strong enough to cause a jump-in? To discard this possible artifact of our experiments, we studied the hydrophilicity of the more hydrophobic tips used. We generated thin layers of glycerol over glass and silicon slides with a spin coater. We used glycerol instead of water due to the low vapor pressure of glycerol, which allows generating thin liquid films of approximately constant thickness. Additionally, glycerol is more viscous than water and hence is a better probe of the QLL (which is expected to be more viscous than bulk liquid water) (Goertz et al., 2009). Figure 9 represents a force curve obtained with one of the platinum-covered tips over a thin glycerol film. The approach portion of the curve clearly shows two features of interest: a vertical contact region, where the tip reaches the rigid substrate, at ztip=0; and a jump-in approximately 3 µm away from the substrate. This force curve proves the presence of a 3 µm glycerol film on the substrate and, more importantly, shows that the capillary (or frustrated capillary) force between the tip and the film is strong enough to cause a jump-in. Thus, this experiment shows that the tip is sufficiently hydrophilic to show a jump-in due to the capillary force between a liquid (or quasi-liquid) film and the tip. This means that the apparent absence of the jump-in in most of the experiments over ice with hydrophobic tips is due to a QLL thickness below the limit of detection of this experimental technique. Considering the inherent noise in the deflection signal in these experiments, we can conclude that the QLL thickness is below 1 nm. These results are comparable or even lower than the smallest experimental QLL thicknesses previously reported (Elbaum et al., 1993; Lied et al., 1994; Dosch et al., 1995, 1996; Bluhm et al., 2002; Sadtchenko and Ewing, 2002, 2003) and are in the same range of computer simulation results (Furukawa and Nada, 1997; Limmer and Chandler, 2002; Conde et al., 2008; Pickering et al., 2018). Subtle differences between QLL thicknesses of different crystal faces in these studies remain to be confirmed and are out of the scope of this work.