Diameter-dependent wetting of tungsten disulfide nanotubes

Significance

The wetting of solid surfaces by liquids is of great interest in scientific fields ranging from lubrication to the strength of composite materials. These interactions can change dramatically at the nanoscale, impacting on current development of novel devices and materials. We have studied the wetting of individual, size-selected tungsten disulfide nanotubes, both experimentally and theoretically. The results show that wetting forces and free energy can vary by orders of magnitude when capillary action is enhanced in open-ended vs. closed-ended nanotubes, as deduced from the influence of specific nanotube size and geometry in governing the final wetting properties. This work provides a comprehensive view of the molecular-level interactions involved in nanotube wetting.

Abstract

The simple process of a liquid wetting a solid surface is controlled by a plethora of factors—surface texture, liquid droplet size and shape, energetics of both liquid and solid surfaces, as well as their interface. Studying these events at the nanoscale provides insights into the molecular basis of wetting. Nanotube wetting studies are particularly challenging due to their unique shape and small size. Nonetheless, the success of nanotubes, particularly inorganic ones, as fillers in composite materials makes it essential to understand how common liquids wet them. Here, we present a comprehensive wetting study of individual tungsten disulfide nanotubes by water. We reveal the nature of interaction at the inert outer wall and show that remarkably high wetting forces are attained on small, open-ended nanotubes due to capillary aspiration into the hollow core. This study provides a theoretical and experimental paradigm for this intricate problem.

Wetting of solid surfaces is an intricate and subtle phenomenon that is fundamental to many fields ranging from lubrication to composite materials to capillary effects (1, 2). In recent years, unique nanoscale aspects of wetting have been revealed, highlighting the importance of a molecular-level understanding of wetting. Theoretical studies based on molecular dynamics (MD) and Monte Carlo simulations revealed that the macroscale theory of wetting may deviate from the nanoscale behavior for particular surface geometries and droplet sizes (3). A comprehensive review distinguished two size-related effects. Continuum hydrodynamics of simple liquids is valid down to the nanometer length scale, whereas surface effects can influence at larger scales (4). In addition, experiments have detected heterogeneity in the nanowetting properties of ostensibly similar individual nanoparticles. This behavior was attributed to nanoscale surface properties such as chemistry, shape, and topography (5).

Study of nanotube wetting is an exciting endeavor, the first step in their incorporation as fillers into ultrastrength nanocomposites. Wetting interactions of nanotubes with different liquids (6–8), polymers (9), and many other materials have been examined both theoretically and experimentally (10–13). Chemical interactions, geometrical and structural factors come into play in such studies (14). For instance, enhanced wetting of carbon nanotubes (CNTs) (15) with open end has been attributed to capillary suction of water into the hollow stem of the nanotube (16). Inorganic WS₂ and MoS₂ nanotubes (INTs) (17) were shown to disperse very well in a variety of polymers, enabling preparation of nanocomposites with enhanced mechanical properties (18), thermal stability (19), and improved rheological behavior (20). Nonetheless, the nature of the interaction between an individual nanotube and polymer liquid has received little attention and is poorly understood, partly due to the technological challenge posed by such studies.

Here, we report a combined experimental and theoretical study on the microscopic interaction of WS₂ nanotubes (INT-WS₂) with water. We apply a unique experimental approach based on manipulation and pullout of individual nanotubes from water films using both environmental scanning electron microscopy (ESEM) and atomic force microscopy (AFM) techniques. Detailed theoretical calculations based on density functional theory (DFT) and force-field MD simulations together with thermodynamic analysis provide strong support for water capillary effect. Furthermore, MD simulations show that the general behavior seen for water occurs also for carbon tetrachloride. The overall interaction energy exhibited a clear trend with nanotube diameter, due to capillarity within the open-ended tubes and influence of their curvature.

Results and Discussion

Two kinds of INT-WS₂ were investigated: type I nanotubes were <40 nm in diameter and 1–3 μm long, consisted of up to 10 walls, and had a hollow core with an open end. Type II nanotubes were 40–150 nm in diameter, 2–30 μm long, with up to 30 walls. The latter were generally capped and partially filled with an oxide at the core. Typical micrographs of each type are shown in Fig. 1 A and B.

Fig. 1.

TEM micrograph of the two kinds of WS₂ nanotubes used in this series of experiments. (A) A 30-nm-diameter INT with open cap and no oxide filling (type I); (B) A 100-nm INT, with large number of outer walls and a closed cap (type II). (C) SEM image of condensed water droplets on an assortment of cooled (type II) WS₂ nanotubes. In the Inset, zoom-in on two single water droplets and their manually measured contact angles.

The interaction of water with bulk and single-layer (graphene-like) WS₂ and MoS₂ surfaces has been recently studied (21–23). To learn about the interaction of the WS₂ nanotubes with water, the contact angle (θ) of water on the (outer) surface of individual INT-WS₂ was directly measured inside an ESEM by condensing water on the nanotubes at ∼4 °C (Fig. 1C).

The small water droplets that condensed on the cooled nanotubes were subsequently measured—for ∼30 such droplets, the average measured contact angle was θ = 60° ± 8°, compared with a contact angle of 70° found for a clean flat layer of WS₂ (21). Because water is known to bind well to dangling bonds on metal dichalcogenides, this result attests to the defect-free nature of the nanotube walls. Comparable results were obtained for a monolayer of MoS₂, showing that water does not adsorb on the defect-free surfaces of MoS₂ (21, 23). Thus, the interaction between water and the defect-free nanotube wall is weak. To investigate the difference in water–tubule interactions between the nanotube wall and its end, as well as to probe the microscopic mechanism of the solid–liquid interaction, we next measured the pullout forces of individual nanotubes dipped into a fluid bath. For this purpose, the nanotubes were attached to a force-transducer (AFM cantilever) as described in Materials and Methods and S2. WS₂ Nanotube Pullout Measurements.

ESEM Experiments.

A single WS₂ nanotube attached to a cantilever tip was manipulated until it reached the proximity of a water film that was condensed on a cooled stainless-steel stub (further details of the experimental setup in S2. WS₂ Nanotube Pullout Measurements; schematic rendering of the setup in Fig. S1). Then the tip was gently manipulated toward the water film until the INT made contact with the film, allowing the film to spontaneously wet the nanotube (Fig. 2A and Figs. S2 and S3). At this point, the nanotube was pulled backward using the nanomanipulator in steps of ∼10 nm every 5–10 s. While pulling out the INT (type I), a surprisingly large water meniscus, with a cone-like shape, was obtained (Fig. 2B and Movie S1). Such movies reveal that the interaction is with the tip of the nanotube, and there is no visible accumulation of water along the nanotube walls. The INT was pulled continuously outward until it snapped out and separated from the water film (Fig. 2C). The maximum height of the water meniscus was denoted as l (Fig. 2B), and the total distance traversed by the INT tip (from initial to the final point) is X (Fig. 2C). The force required to pull out the nanotube was calculated according to Hooke’s law and expressed as F_max = (X − l)*k, where k is the calibrated spring constant of the cantilever. The work is calculated by integrating the force with distance traveled until separation of water meniscus. This calculation makes the assumption that the water surface “grabs” the NT at a fixed point on its surface and there is no slip during pullout. The assumption is reasonable considering the discussion surrounding the MD simulations below showing that the main attraction of water is at tube apex.

Fig. S1.

Setup of the ESEM pullout experiments. A represents a nanomanipulator with an AFM probe attached at its end. B is an illustration of a cooled stainless-steel stub with water film formed on its left side. The stub was kept at 4 °C and water vapor pressure of 6.5–7 torr. (C) Expanded view of the AFM nanotube tip just before touching the water film. In the lower part, SEM micrographs taken in FIB. (D) WS₂ nanotubes are protruding out of the blade edge, and an AFM tip is shown approaching it. (E) A nanotube was attached using a platinum source, and the AFM tip is ready for use.

Fig. 2.

(A) Initially, the INT-tip touches the surface of the water film. (B) Just before the snapping out of the nanotube-tip from the water “cone” (denoted as the maximum force point, l). (C) Image of the water film and the nanotube right after the separation; the position of the edge of the tube represents the overall distance traveled by the cantilever during pullout (X).

Fig. S2.

An illustration of the pullout experiment with calculation of the pullout force. (A) The nanotube is positioned at its starting point where the end of the nanotube is in contact with the water film surface (dotted line). (B) The maximum water protrusion is presented with height l. (C) The nanotube was pulled out of the water film, and the total distance traveled by the nanomanipulator, from the starting point, is measured and denoted as X. The red dashed line represents the initial point of the water film.

Fig. S3.

An ESEM micrograph during a pullout test. In this micrograph, the nanotube was pushed to penetrate the water film surface. In this early stage, the water film was not yet pierced and the nanotube bent. One can also notice the concave shape of the water surface, implying a strong resistance of the water film to the nanotube penetration.

The experimental work done by the cantilever during the pullout, computed as described in Materials and Methods, can be compared with the calculated work of formation of the water meniscus, the surface area of which is mathematically approximated as a catenoid of revolution (S3. Phenomenological Estimation of the Surface Energy of the Water Meniscus Beneath the Pulled-Out Nanotube Tip). Two parameters were determined in the experiment, namely, the height of the water “cone,” l, and the radius of its base, D_c/2 (Fig. S4). Using Eq. S4, these two parameters were used to calculate the surface area of the water “cone.” Multiplying this area by the surface tension of water, γ = 72.3 mJ/m², gives the work expended in forming the meniscus. The results are summarized in Table 1. Good correspondence between the measured and calculated quantities was obtained.

Fig. S4.

The cross-sections of the water meniscus calculated using Eqs. S2 and S3 for different stages of the pullout corresponding to catenoid (meniscus) heights I = 0.1, 0.2, 0.3, 0.4, and 0.5 μm (from the Bottom to the Top). The Inset shows an ESEM image of a nanotube with diameter of 25 nm pulled out from the water surface with I indicated.

Table 1.

Comparison of experimental and calculated pullout work

Nanotube diameter, nm	Calculated work, fJ	Cantilever work, fJ
70	50	23 (7)
90	69	47 (14)
100	81	66 (20)

Experimental nanotube diameters were within 1 nm of the values reported here. The calculated work was computed from the calculated area of catenoid of revolution and surface tension of water, based on the ESEM image of meniscus. For the cantilever work the experimental uncertainty is presented in parentheses.

AFM Experiments.

Similar single nanotube pullout experiments were also carried out using an AFM setup (S2. WS₂ Nanotube Pullout Measurements, S2.2. AFM Pullout Measurements). The AFM experiments allow on-line monitoring of the wetting force and can be done under ambient (equilibrium) conditions. In the present experiment, a nanotube was attached to an AFM tip and lowered toward a water reservoir. The AFM was programmed to lower the nanotube tip until sensing a “jump-in” (the initial contact point). This small deflection represents (for the larger diameters, see below) the wetting force of the nanotube wall. This force should correspond to that predicted by the Wilhelmy balance technique (6). Indeed, presuming a wetting angle of 60° for the 90-nm-diameter nanotube, we predict initial wetting force of 20 nN compared with 23 nN actually measured. At this point, the nanotube was pulled back out of the water by retraction of the z-piezo, while recording the AFM cantilever deflection.

According to the Wilhelmy balance formulation, the wetting force on the nanotube should not change throughout the pullout as long as the contact perimeter remains constant. Because the ultimate pullout force is dominated by the meniscus growth that occurs as the water surface is pinned to the nanotube end, we must consider here specifically the geometry of the nanotube tip. To compare the pullout forces, they were normalized by the nanotube cross-sectional area at its end. As shown earlier, the walls of the INT do not seem to interact strongly with water, but the tip apex does. Therefore, the relevant normalization area is calculated as π/4(D_out² − D_in²), where D_out and D_in are the outer and inner diameters of the nanotube, respectively. Note that, for type II nanotubes, D_in = 0. A detailed explanation appears in S2. WS₂ Nanotube Pullout Measurements, S2.1. ESEM Pullout Measurements. The normalized force was plotted against the nanotube diameter, and the results are presented in Fig. 3A, incorporating the results from both the AFM and ESEM setups. Pullout work was computed for the AFM measurements as with ESEM results, with the exception that here the ultimate force was measured in real time by recording the cantilever deflection and the force during pullout was modeled as decaying linearly with distance.

Fig. 3.

(A) Normalized pullout forces of INT measured in ESEM (blue rhombi) and AFM (red squares). (B) Pullout work vs. the nanotube (outer) diameters. Blue rhombi are the results calculated by the DFT calculations. Red squares are results calculated from the AFM pullout experiments (see text).

Although the ESEM and AFM experiments exhibit the same trend for the normalized pullout forces, the pullout forces are significantly lower for the ESEM experiments for the two smallest diameter nanotubes. This difference can be possibly attributed to the different ambient conditions in the ESEM and AFM pullout experiments: the very small radius of the liquid contact leads to enhanced vapor pressure of the water meniscus, which is described by the Kelvin equation (24). Due to the partial vacuum in the ESEM, we can expect even more rapid evaporation and earlier collapse of the water meniscus. As a result, the contact area of this small volume decreases rapidly during the ESEM measurements and the water neck breaks at a lower cantilever force, compared with the ambient AFM experiments. In any event, the graph shows a clear distinction between the type I and type II nanotubes. Wetting forces of the former show almost no dependence on size, albeit some variations for the three largest diameter nanotubes are observed, which can be attributed to defects at the NT cap that resulted in a collapse and possible small crack. This is discussed in S4. Collapse of Large-Diameter Nanotubes, and shown in Fig. S5. Such fluctuations in force, as well as in work (see next section and Fig. 3B), are small relative to the differences seen for small-diameter nanotubes. For the type I nanotubes, there is a dramatic rise in force with lower diameter. These forces, normalized to the cross-sectional area, are on the order of 1–2 GPa, which approaches the strength of the nanotubes, ∼6–20 GPa (25). Indeed, in some cases, we observed breakage of the nanotube after the water pullout. These results lead to a hypothesis of strong capillary forces inside the small, open nanotubes. To investigate this microscopic phenomenon, we made use of atomistic calculations.

Fig. S5.

A and B are SEM micrographs of large-diameter INT-WS₂ collapsed at their ends. The collapsed elliptical structure exists only at the INT end. The rest of the nanotube has a cylindrical shape. TEM micrographs of WS₂ nanotubes. C is a top view of a WS₂ nanotube, one can notice the brighter end of the nanotube indicating a less dense area. (D) A closer examination of the INT reveals that the end of the nanotube has a hollow core and most likely a collapsed edge. Away from the nanotube end, remains of tungsten oxide can be seen in the core of the nanotube.

DFT Calculations.

To better understand the results of these pullout experiments, DFT calculations were undertaken. First, the interaction energies between water surface and the edge of a WS₂ slab with dangling bonds were calculated. Subsequently, the interaction energies for INTs of different diameters were calculated by extrapolation from the previous detailed calculations and are shown in Fig. 3B. Details of the calculations are provided in S5. DFT Calculations, and in Figs. S5–S10. These energies are compared with the work of formation of the meniscus. Formally, a force balance should be performed to equate the force applied by the cantilever with the force required to break the water bridge. Due to changing volume of the liquid throughout the pullout, this cannot be quantified simply in terms of forces. We therefore compare energies rather than forces with the implicit assumption that the energy released by relaxation of the meniscus compensates the energy lost by breaking the nanotube–water interaction. The results show good agreement with type II nanotubes over a wide range of diameters but were almost insensitive to diameter of the nanotubes. There is, however, a large discrepancy for type I INTs and a minor difference for the type II INTs with the largest diameters. For example, the calculation for a WS₂ nanotube with diameter of 25 nm and composed of 10 walls yields a total binding energy around 0.52 fJ (Fig. S7). This value is ∼10³ times smaller than 195 fJ calculated for the surface energy (i.e., work of formation) of the rising water meniscus in the experiment.

Fig. S10.

Evolution of the potential energy with the retracted distance of a WS₂ tip during MD simulations of pullout tests from the surface of water film. WS₂ tips of different morphology were taken into account: open-ended and capped (24,0)@(36,0) nanotubes, double-walled (32,0) nanostripe. Lines indicate the break-off point of the nanotube–water contact distance.

Fig. S7.

The estimated binding energy E_b between water surface and the tip of a multiwalled WS₂ nanotube dependence on the parameters of nanotube—diameter and number of walls k.

It can be therefore concluded from the DFT calculations that the interaction of the nanotube tip outer wall is not sufficiently strong to account for the strong binding with the water, in particular for the small-diameter, open-ended (type I) nanotubes. Even the presence of reactive W atoms at the tip, as considered in these models, cannot alone lead to a binding energy commensurate with the surface energy of the water meniscus that develops during pullout.

MD Simulations.

To investigate the hypothesis of capillary suction of water into the hollow core of the open-ended nanotubes, detailed MD simulations were carried out. The MD simulations of the water–WS₂ nanotube interactions were performed in two main modes. In mode 1 simulation, imbibition of an isolated water drop into an open-ended (24,0)@(36,0) 2H–WS₂ double-wall nanotube tip with inner and outer diameters of 24.2 and 36.2 Å (measured for the W atomic cylinders), was studied. Both the case of S-terminated inner and W-terminated outer wall (I) and the opposite situation were considered (II) (Fig. S8). The MD simulations showed, for case (I), instantaneous (weak) water adsorption with H atoms pointing to the tip. For case (II), the exposed inner W atoms were decorated by H₂O molecules with the O atom of the water between two W atoms and the formation of a labile circular water chain (the average W–O distance in this case is about 2.5 Å) along the tip circumference. Labile chain-like water fragments could be observed on the outer surface of nanotubes, although they mostly remained confined to the tube apex region and did not coalesce into a stable outer coating on the basal sulfur surface of the nanotube (Fig. S8). In general, fast kinetics of water imbibition into the hollow core of the WS₂ nanotube, following the (t)^1/2 rule (26), was observed for both cases (water imbibition in case I was 1.5 times faster compared with case II; see further details in S6. MD Simulations). The analysis of the radial distribution functions for O and H atoms within a nanotube shows that the water remains as a liquid and did not crystallize in the confined space of the hollow core. To summarize these simulations, MD has convincingly shown rapid capillary penetration of water into the hollow stem of narrow and open-ended (type I) WS₂ nanotubes irrespective of the exposed atom at the edge of the tube. Therefore, the capillary kinetics is irrelevant to the steady-state pullout situation studied here.

Fig. S8.

Side views on the imbibition of H₂O drop during 1 ns into the fragments of double-walled (24,0)@(36,0) 2H–WS₂ nanotubes with frontal tip consisting of S- and W-terminated inner and outer walls (1), or W- and S-terminated inner and outer walls (2), with frontal tip consisting of S- and W-terminated inner and outer walls of WS_1.9 stoichiometry (3). Pullout using open end of a (28,28) nanotube from a CCl₄ film deposited on graphite (4). For clarity, only the CCl₄ molecules are depicted, not the nanotube walls. Corresponding radial distributions of O and H atoms within the nanotube cavities are depicted on the right panels.

In mode 2, the retraction of a nanotube tip from the water film has been considered, for different model structures. The starting models in the present study were again double-walled (24,0)@(36,0) nanotubes with 2H–WS₂ polytypic arrangement (Fig. S9). To emphasize the edge effect of the nanotubes with respect to capillarity, three cases were considered—open-ended and capped nanotubes and a nanostripe of similar size. Due to inadequate computer resources, the MD simulations were limited to small systems compared with experiment and have been launched with the nanotube tip and water film already in contact. These MD calculations capture the salient features of the water–nanotube interaction during pullout, shedding insight on the interaction between the water surface and a pulled-out nanotube (Fig. 4).

Fig. S9.

Side and head-on views of the model tips used in MD simulations of the pullout of small WS₂ nanotubes from the vicinity of thin water film (mode 2): double-walled (24,0)@(36,0) 2H–WS₂ nanotube with capped rear end (A), (24,0)@(36,0) 2H–WS₂ nanotube with capped frontal end (B), and double-walled (32,0) 2H–WS₂ nanostripe (C).

Fig. 4.

Side-view screenshots of the MD simulations of pullout tests from the surface of water film using WS₂ nanotips of different morphology: open-ended (24,0)@(36,0) nanotube (A), capped (24,0)@(36,0) nanotube (B), and double-walled (32,0) nanostripe (C). The MD time and the distance of the tip withdrawn from the film are shown below.

The direct visualization of the tip pullout reveals the multistage character of this process (Fig. S10 and Movie S2). First, water molecules did not climb up the outer surface of the receding nanotube in any of the cases studied here. On the other hand, the strong capillary interaction between the open-ended INT tip and the water is clearly visible in Fig. 4A. Significantly, the water continues the ascent during the entire pullout process, even after the nanotube has disengaged from the water surface. The water catenoid formed near the open-ended nanotube tip exhibits mechanical instability (asymmetric shape) at a distance of 25 Å and is fully separated from the tip at a distance of 50 Å.

When using capped nanotubes, quite different behavior is observed (Fig. 4B and Movie S3). First, the retraction of the tip is not accompanied by strong attraction of water molecules. Only a small meniscus is formed during the pullout, which is attributed to the weak water cap interaction. The instability of the small meniscus occurs around 12 Å, in this case. The water meniscus narrows very quickly upon pullout and disappears at a small separation of the tip from the water surface. It is important to note that the present model of the capped nanotubes does not take into account the imperfections in the cap and residual WO_x solid that are more common in the core of the very large-diameter nanotubes, both of which would increase the adhesion energy of the tip with water. The pullout of a nanostripe tip shows some similarities to the features of an open-ended WS₂ nanotube (Fig. 4C; S6. MD Simulations, S6.2. Comments on the MD Simulations; Movie S4) without the capillary action. The water molecules do not ascend along the wall and a complete breakup of the water–tip contact is observed only at 36 Å.

To minimize computer resources, the models were restricted in size, and hence the water meniscus was much smaller than in the experiments. Thus, the absolute values of the forces should be smaller than the measured ones. However, the MD simulation predicts the same tendency for the affinity of the receding WS₂ tips with respect to water with maximum forces of 2.11, 0.34, and 1.76 nN for the open and capped nanotubes and the nanostripe, respectively.

Because water is an atypical liquid, with relatively high surface tension and influence of hydrogen bonding, we have also carried out MD simulations for a nonpolar, centrosymmetric molecule, CCl₄. The same overall features as observed for water occur (meniscus formation upon pullout as well as capillary imbibition into the hollow nanotube core). However, the CCl₄ has a much higher affinity to the outer walls of the nanotube, so that partitioning of energy contributions for the inner and outer liquid bridges is of approximately equal weight. Pullout videos for open and closed nanotubes pulled out from a thin film of carbon tetrachloride are shown in Movies S5 and S6.

Thermodynamic Analysis.

The difference in free energy ΔG between n moles of liquid within the cavity and the same n moles of liquid on a flat surface can be expressed as follows:

$$\mathrm{\Delta }G=n\left(\mu \left(r\right)-\mu \left(\infty \right)\right)=nRT\cdot \text{ln}\left[\frac{p_r}{p_{\infty }}\right],$$ [1]

where μ and p are the chemical potentials and vapor pressures for the liquid within a cavity and for the flat surface (indices r and ∞, respectively). Using the Young–Laplace equation (see S7. Thermodynamics Model, for full details of the analysis), the capillary work of the water within the nanotube can be expressed as follows:

$$\mathrm{\Delta }G=\frac{\pi \rho }{4M_r}RT{D}_{in}^{2}h\cdot \ln \left(1-\frac{4\gamma }{p_{\infty }{D}_{in}}\cos \theta \right)=0.107\cdot {\left(D_{out}-1.23k\right)}^{2}h\cdot \ln \left(1-\frac{\mathrm{2,854.577}}{\left[D_{out}-1.23k\right]}\cos \theta \right),$$ [2]

where, D_in and D_out are inner and outer diameters, k is the number of WS₂ layers composing the wall of nanotube. h is the height of ascending capillary column; γ, ρ, and M_r are surface tension, density, and molecular weight (at temperature T = 296 K) for water. γ = 72.31·10⁻³ N/m², ρ = 0.99754·10³ kg/m³, and T and p_∞ correspond to temperature and external pressure. Because the argument of the logarithm is limited to positive values, the wetting angle θ must be less than 90°. The use of macroscopic values of γ is justified because the surface tension of water grows significantly only for curvature radii below ∼2 nm (27). Second, for the diameters of nanotubes used in the present experiments, water penetrates along the full length of the nanotube cavity, h (28), which is taken here to be 250 nm. The work of capillary action of water inside the nanotube is plotted vs. diameter for different numbers of walls in Fig. 5.

Fig. 5.

Plot of the capillary energy ΔG estimated for water imbibition into WS₂ nanotubes with length h = 250 nm, vs. inner diameter (determined by the outer diameter of nanotube D and the number of layers comprising the wall, k. The wetting angle between H₂O and the inner core of the WS₂ nanotube is assumed to be 89.80°. Experimental values of the pullout work W obtained after AFM measurements are plotted for comparison as the black dots with the black curve serving only as a guide for the eye.

A suitable fit of thermodynamic model to the experimental data is possible only if the contact angle is at the hydrophobic/hydrophilic limit, that is, close to 90°, higher than the value 60–70° observed from direct ESEM observations or measured on planar WS₂. This discrepancy reflects the decrease of cosθ for high curvature of a liquid surface, here the water meniscus in the WS₂ nanotube. This trend was suggested in earlier theoretical models and recent MD simulations (29, 30).

Because only the small-diameter tubes have open ends, the analysis of capillary action presented in Fig. 5 is mostly relevant for them. The fact that, for the 20-nm diameter nanotube, the experimental pullout work was 500 fJ, and in some cases such small nanotubes were found to be broken after the experiment, suggests that the capillary force exceeded their strength (∼6–20 GPa). These results conform well with the extrapolation of the thermodynamic analysis, which provides independent support for the idea that a major contribution for the pullout work of small-diameter (type I) tubes comes from the capillary imbibition of water into the hollow core of the nanotubes.

This work presents a systematic study of the interactions between individual WS₂ nanotubes and water or any other liquid. Two different experimental setups (ESEM and AFM) were used showing the marked difference between slender and open-ended tubes (type I) and large-diameter and capped nanotubes (type II). Different theoretical approaches, namely, DFT, MD, and thermodynamic considerations were used to analyze the experimental data. Semiquantitative agreement was obtained between the DFT analysis and the experimental data for large-diameter (type II) tubes. However, the small-diameter nanotubes with open end (type I) deviated considerably from the interaction energy predicted by DFT. MD analysis, although limited to small-diameter tubes and overall small model size compared with the experiment, showed unequivocally that capillary action between the water and the open-ended nanotubes stimulates penetration of the water molecules into the hollow core and their fast ascent, leading to substantially larger energy for the pullout work. Obviously, the present framework is applicable to various types of nanoparticles and liquids and not constrained to INT and water. Preliminary results presented here using CCl₄ show a similar capillary imbibition and meniscus formation, although the affinity of the CCl₄ for the nanotube wall leads to near-equal energy partition between inner and outer liquid interactions. These results form a comprehensive framework for studying the interaction between single nanoparticle and liquefied matrices that could provide a deeper understanding of nanocomposite behavior. Furthermore, open-ended WS₂ nanotubes can be used as nanopipettes and nanosensors. For example, a single nanotube could aspirate about 10⁶ water molecules. By incorporating such a nanotube in a field effect transistor device (31), we estimate that detection of <10 contaminant molecules can be achieved.

Materials and Methods

The WS₂ nanotubes were of two types: type I nanotubes were produced by fluidized-bed reactor, resulting in nanotubes with diameter <40 nm and containing up to 10 walls (32). Type II nanotubes ranged between 40- and 150-nm diameter with up to 30 walls and were produced in a one-pot process (33).

Single Nanotube AFM Tip Fabrication.

All of the pullout experiments (ESEM and AFM) were performed using calibrated AFM probes with single INT-WS₂ nanotubes attached to the tip. For the attachment of the nanotube, INT-WS₂ powder was dispersed on the edge of a platinum-coated razor blade (Fig. S1). Using a nanomanipulator, the calibrated AFM tip is manipulated to the edge of the blade where the INTs hang out from the edge. Using the manipulator, the nanotube was adjusted to an angle of ∼15° with the cantilever normal to compensate for the angle of the cantilever holder, and ensure vertical immersion of nanotube into the liquid. The edge of the AFM tip is attached to the distal end of a single INT-WS₂ using a 200-nm-thick layer of evaporated platinum, binding the nanotube firmly to the tip (Fig. S1). The platinum “glue” is deposited in a focused ion beam (FIB) set-up (FEI; Helios 600). The fabricated tip is then analyzed (nanotube diameter and length) using a high-resolution scanning electron microscope (Zeiss; Ultra 55).

AFM Measurements.

AFM measurements were made using an NTEGRA system and Smena head (NT-MDT). For the water pullout experiments, a special add-on, water reservoir, was used under ambient conditions (∼23 °C). In the experiments, a nanotube affixed to a precalibrated AFM cantilever was used. The AFM was directed downward to land on the water surface until a cantilever deflection threshold was detected (which indicates that the water surface is being pierced by the nanotube tip). Immediately upon reaching the contact point, the nanotube was pulled out to fully remove the INT from the water by retraction of the z-piezo. The force acting on the nanotube during immersion and retraction was monitored through the cantilever deflection signal. During retraction, the cantilever was bent toward the water surface until it reached a peak attractive force (maximum bending of the cantilever), at which point the nanotube snapped away from the water. This critical force was equated with the pullout force. The water pullouts were repeated 10–20 times for each kind of nanotube experiment.

ESEM Pullout Experiments.

The ESEM water pullouts were performed using an FEI XL-30 ESEM. The ESEM was equipped with a water-cooled thermoelectric stage (temperature controlled). A water film was created by condensation of water on a cooled (4.5–5 °C) stainless-steel stub and using a water vapor pressure ranging between 6.5 and 7 torr. A tip consisting of precalibrated AFM cantilever with a nanotube attached to it was then mounted on a nanomanipulator (Kliendiek; model MM3A-EM) inside an ESEM. This setup enabled a precise control of the tip movement with a precision of less than 10 nm. The tip was approached using a nanomanipulator (Fig. S1). The end of the nanotube was carefully brought into contact with the water film. Subsequently, the INT was slowly retracted, which led to development of a water meniscus. The meniscus gradually increased in size until the retraction distance where the nanotube tip separated from the water. The pullout force was calculated by Hooke’s law, using the difference between the water protrusion maximal height and the tip height at the final location of the NT apex.

MD Simulations.

MD simulations of all nanosystems have been performed using in-house code as for NVT ensembles (T = 300 K). Temperature was controlled in all simulations with the velocity scaling. Newton’s equations of motion were integrated with the time step of 2 fs via the Verlet leapfrog algorithm for 250,000 steps. The water film was initially annealed and equilibrated under the same conditions for 500,000 steps. The apex of the nanotube tip was initially positioned ∼3 Å from the equilibrated water surface, which corresponded to the distance 25 Å from the substrate. Two velocities of the tip withdrawal have been tested for selected nanosystems as 0.025 and 0.25 Å/ps (2.5 and 25 m/s). No essential difference was established between these cases. Thus, the results presented in this work are given for the speed 0.25 Å/ps, which allowed testing of a more diverse set of nanotubes for the same computational time consumption.

The force-field level of theory was applied for these nanosecond simulations. Interactions within the H₂O film were treated in the framework of a flexible simple point charge (SPC) model in the parameterization (34). A WS₂ tip was considered as a body generating electrostatic and van der Waals fields in the framework of a universal force field (UFF) (35). The coupling between parameterization sets for H₂O and WS₂ parts was fulfilled using Coulomb and Lennard–Jones 12-6 potentials, where the missing heteronuclear parameters of 12-6 potentials were obtained after Lorentz–Berthelot mixing rules. Truncation at 12 Å for all short-range nonbonded interactions was applied. The long-range electrostatics interactions were computed without any restriction and approximation.

For the CCl₄, similar methodology was used, with some differences noted here: the molecule was modeled as a “spherical neutral superatom,” where the intermolecular interaction between structureless CCl₄ molecules is modeled using a Lennard–Jones 12-6 potential (36). Truncation was at 20 Å. To account for the larger molecular size, larger nanotubes were used here [single-walled (21,21) and (28,28) or double-walled (21,21)@(28,28)]. Full description of all model setups can be found in the Supporting Information.

S1. AFM-WS₂ Tip Fabrication

AFM probes with a spring constant of 0.1–0.6 N/m and ∼1 N/m (Appnano and Olympus, respectively), were first calibrated using an AFM (Multimode; Bruker) by the built-in thermal tuning software. The calibrated tips were mounted on a nanomanipulator (Kleindiek) inside a focused ion beam (FIB) microscope (FEI; Helios 600). The electron beam-assisted platinum deposition modality of the FIB was then used to attach a WS₂ nanotube to the apex of the AFM tip. The fabricated tip was further imaged using an ultrahigh-resolution SEM (Zeiss; Ultra 55) to estimate the nanotube diameter and length.

S2. WS₂ Nanotube Pullout Measurements

The pullout measurements were done with both ESEM and AFM systems. In each setup, a different AFM probe was used. The fabrication and calibration processes were similar for both types of AFM probes.

S2.1. ESEM Pullout Measurements.

The ESEM water pullouts were performed using a FEI XL-30 ESEM equipped with a gaseous secondary electron detector (GSED) with a 500-μm aperture. The ESEM was also equipped with a water-cooled thermoelectric stage (temperature controlled).

Due to the constraints of the ESEM lenses and detectors (which are fixed and cannot be moved), the experiments were designed as follows and presented graphically in Fig. S1. A stainless-steel stub (with a thin upper gutter-like structure) was fabricated and adjusted to fit the thermoelectric stage dimensions. Water drops and films were obtained by a careful condensation of water vapor on the cooled stainless-steel stub. Condensation of the water was achieved by either varying the cooling stage temperature or by varying the water vapor pressure in the chamber. The temperature was 4 ± 0.2 °C and the water vapor pressure ranged between 6.5 and 7 torr. The nanotube was pulled out from a continuous and large water film, which formed on the stub and was not distorted by the pullout, other than in the close vicinity of the nanotube. The water film thickness (∼0.5 mm) was allowed to stabilize, and then the AFM-WS₂ tip was approached using a nanomanipulator (Fig. S1). Only the tip of the nanotube was contacted to the water film before retraction (Fig. S2A).

In several experiments, the nanotube was pushed into the water, which momentarily indented the water surface (Fig. S3), that is, the nanotube was surrounded by a concave water surface. Also, due to the resistance of the water surface tension, the nanotube was initially bent. Upon further pushing of the nanotube, it pierced the concave water surface, leading to a relaxation of both the nanotube and the water surface. At this point, the nanotube straightened and the water surface became flat. Once the nanotube was immersed (one-third of its length) in the water, it was slowly retracted back. So long as the withdrawing nanotube was partially immersed in the water, the water surface remained mostly flat. Once the receding nanotube end was brought above the water surface, a protrusion (meniscus) appeared beneath the nanotube tip and the water surface. Upon further retraction, the water meniscus gradually increased in size until eventually the cantilever restoring force caused a detachment of the nanotube from the water. This was the prevailing scenario for all of the experiments when using WS₂ nanotube and water films. Therefore, in the experiments used for the quantitative analysis reported in this work (Fig. 2 and Fig. S2), the nanotube was carefully brought into contact with the water surface and withdrawn without attempting to push it into the body of the water film.

The pullout force was calculated by the difference between the water meniscus maximal height (l) and the tip height after the water detached from the tip (X) times the spring constant of the AFM cantilever (k) as in Eq. S1:

$$\mathit{F}=\mathit{k}\left(\mathit{X}-\mathit{l}\right).$$ [S1]

This calculation assumes that the water surface “grabs” the NT at a fixed point on its surface and there is no slip during pullout. For the normalization to tip area in Fig. 3A, the relevant normalization area is calculated as π/4(D_out² − D_in²), where D_out and D_in are the outer and inner diameters of the nanotube, respectively for the type I nanotubes, and π/4D_out² for the closed type II nanotubes. The pullout process was recorded, image by image, using Epiphan capture card and proper software. The images were analyzed using ImageJ software.

S2.2. AFM Pullout Measurements.

Pullout AFM measurements were performed using an NTEGRA system and Smena head (NT-MDT). Transient deflection and z-position data were captured on an MI.3110 PCI board using Sbench 5.3 software (Spectrum GmbH). For the water pullout experiments, a custom-made water reservoir was used under ambient conditions (∼23 °C).

In these experiments, the AFM was programmed to lower the probe until it snaps into the water (the initial contact point). Immediately upon reaching the contact point, the nanotube was pulled out of the water by retraction of the z-piezo, while recording the AFM cantilever deflection. The cantilever bowed until it reached a peak force (maximum bending of the cantilever). At this critical force, the nanotube was pulled out of the water. Then, a large drop in the force was observed corresponding to the complete withdrawal of the nanotube from the water film. The force was calculated from the bending of the cantilever (deflection signal) times the calibrated spring constant (from the starting point; Fig. S2).

Cantilever deflection corresponding to the mass of the nanotube or water meniscus are insignificant in the overall force balance relative to the wetting forces, as is true in general at mesoscales, and certainly at submicron scale. For instance, the volume of a typical meniscus here is ∼1 × 10⁻¹⁸ m³, with corresponding mass of 1 × 10⁻¹⁵ kg. The resulting gravitational force is 10 fN. Measured forces in this work are in the range of tens of nanonewtons, that is, six orders of magnitude higher. For a typical cantilever spring constant of about 1 N/m, 10 fN corresponds to 0.0001 Å of cantilever deflection. This value is well below our detection limit and approximately three orders of magnitude below the mean thermal noise of this cantilever at room temperature. A second insignificant force is the buoyancy. This can be calculated by the formula $F=V\ast \mathrm{\Delta }\rho \ast g$, where V is the submersed volume (depth of immersion h × nanotube cross-sectional area), ∆ρ is density difference between water and air, and g is acceleration of gravity. For a 60-nm-diameter nanotube immersed by 200 nm, the force is several attonewtons.

S3. Phenomenological Estimation of the Surface Energy of the Water Meniscus Beneath the Pulled-Out Nanotube Tip

The conical water meniscus formed by the contact with the tip of a nanotube would tend to minimize the surface area. Because the wettability of the inert walls of the INT-WS₂ is low, one may assume that the water adheres exclusively to the tip of the nanotube, as seen in the MD calculations. In the absence of long-range interaction between water and the substrate, the shape of the surface can be represented using the solid of revolution related with a catenoid. The cross-section profile of this solid could be described using a classical case of hyperbolic cosine function (Fig. S4). Let us choose the axis of the nanotube as the main axis and denote the distance from the axis as r, then the corresponding height of the water surface h at r may be expressed as follows:

$$h=a\left(ch\left(-\frac{2r-D_c}{2a}\right)-1\right),$$ [S2]

where a is a constant dependent on the nature of the liquid and substrate, and D_c is the diameter of the meniscus bottom. The latter can be expressed using the height of the meniscus H (H equals l in Fig. S2 in the experimental part) and nanotube diameter D_out as follows:

$$D_c=D_{out}+2a\mathrm{\cdot }arch\left(\frac{H}{\hspace{0.17em}a}+1\right).$$ [S3]

Then, the lateral and basal surface area S of such meniscus can be expressed as follows:

$$S_{lateral}=\pi a\left(2H+D_{OUT}\sqrt{{\left(\frac{H}{a}+1\right)}^2-1}\right),$$

$$S_{basal}=\frac{\pi }{4}{D}_c^2=\frac{\pi }{4}{\left(D_{out}+2a\mathrm{\cdot }arch\left(\frac{H}{a}+1\right)\right)}^2.$$ [S4]

The constant a plays a key role in the estimation of the surface energy. Regrettably, it cannot be predicted and the experimental data on the evolution of the meniscus should be used. The value of a = 1.4 μm can be calculated using Eq. S2 and the electron microscopy images. For a nanotube of 25 nm in diameter and just before break-off, the values D_c = 1.8 μm and H = 0.3 μm were obtained (Fig. S4).

The specific surface energy γ is independent of the size of the water meniscus beneath the pulled nanotube tip at this scale. Deviations from the “bulk” surface tension of liquids occur only at characteristic curvature radii below ∼10 nm, which is in the lower range of the radii of the nanotubes used in this study. Thus, we calculate E_γ using the tabulated value of the surface tension of water at 23 °C, γ = 72.3·10⁻³ J/m²:

$$E_{\gamma }=\gamma \left(S_{lateral}-S_{basal}\right).$$ [S5]

Thus, the surface energy of the water meniscus and the nanotube with the above-mentioned parameters is E_γ = 195 fJ. The force F applied to the nanotube may be estimated as F = 2E_γ/H = 390 fJ/0.3 μm = 1.3 μN. This value is higher than the maximum force reported for a nanotube with 70 nm in diameter, that is, 116 nN. As follows from Eq. S5, there should be almost linear dependence between the height of the conical meniscus H and the surface energy E_γ in the case of D_out/2 << H.

Eqs. S2–S4 allow describing the shape of the water meniscus during pullout. Assuming that the increase in the surface energy calculated from Eq. S5 is the dominating factor in the energy costs of the pullout, one may compare it with the interaction between the tip of the nanotube and the surface energy of the water meniscus as derived from the cantilever work (Fig. S4).

S4. Collapse of Large-Diameter Nanotubes

Examination of the normalized force results obtained by both AFM and the ESEM revealed that the normalized force shows a sudden drop beyond a nanotube diameter of 115 nm (Fig. 3A). Careful examination of such large-diameter nanotubes in high-resolution SEM showed that their tip had collapsed forming an elliptical-shaped edge (Fig. S5). The core of the large-diameter tubes usually contains residual tungsten oxide but is empty at the very end. This hollow core at the end of the large-diameter tubes is mechanically less stable than the oxide-filled cylindrical core and collapses to an elliptical shape (Fig. S5 C and D) (37). This collapse occurs spontaneously and is not related to immersion in water during the experiment.

S5. DFT Calculations

S5.1. DFT Setup.

The calculations of the WS₂|H₂O interface energies were performed using the SIESTA 2.0 code (38, 39) within the framework of the DFT (40, 41); exchange–correlation potential within the generalized gradient approximation with Perdew–Burke–Ernzerhof parametrization (42). The core electrons were treated within the frozen core approximation, applying norm-conserving Troullier–Martins pseudopotentials (43). The valence electrons were taken as 1s¹ for H, 2s²2p⁴ for O, 3s²3p⁴ for S, and 6s²5d⁴ for W. The pseudopotential core radii were chosen to be equal to 0.16, 1.15, and 1.70 a_B for all states of H, O, and S, respectively. For W atoms, the values of the core radii were 2.46, 2.46, and 2.65 a_B for s, d, and p states, respectively. Periodic boundary conditions have been applied for all of the directions, and a cutoff of 10 Å was used for k-point sampling (44). The k-point mesh was generated by the method of Monkhorst and Pack (44). The real-space grid used for the numeric integrations was set to correspond to an energy cutoff of 300 Ry. All of the calculations were performed using variable-cell and atomic position relaxation, with convergence criteria set to correspond to a maximum residual stress of 0.1 GPa for each component of the stress tensor, and maximum residual force component of 0.01 eV/Å. In all of the calculations, a double-ζ basis set was used for all of the atoms as suggested for the simulations of liquid water in SIESTA approach (45).

The preliminary calculations on 2H–WS₂ were in good agreement with the experimental results in the description of lattice parameters (a = 3.20 Å, c = 12.39 Å). The mass density of water was calculated using a supercell of 27 H₂O molecules and was found to be 944 kg/m³.

Several atomistic models of WS₂|H₂O interfaces have been designed and considered. The strength of the covalent-like coordination bonding has been calculated using supercells assembled from a WS₂ nanostripe and H₂O slab with slightly different positions of the molecules (Fig. S6). As a guess for initial coordinates of the water molecules in these supercells, the structure of TIP3P water has been used (46). The periodic supercell consisted of two WS₂ nanostripes including 8 W and 16 S atoms, corresponding to 2 × 1 × 1 unit cells of 2H–WS₂ lattice in rectangular a√3×a representation. The nanostripes were in contact with the water slab represented by 16 H₂O molecules. Such a model based on the 2H–WS₂ structure means that the dangling bonds at each tip of the multiwalled WS₂ nanotubes of zigzag chirality consist of alternating terminations of two walls: either S atoms with twofold coordination or W atoms with two vacant coordination sites. The adhesion of physisorbed water on the (0001) surface of WS₂ has been considered using periodic hexagonal supercells assembled from a WS₂ monolayer and monomolecular H₂O layers with different packing density.

Fig. S6.

Several examples of optimized models for different WS₂|H₂O interfaces with zigzag configuration of the edges were considered in the DFT calculations. (1) W-terminated edges of 2H–WS₂ are saturated with water molecules (blue colored circle); (2) one of the W-terminated edges of 2H–WS₂ is saturated with hydroxyl groups (purple colored circle), whereas positive counterions occur in the bulk of the H₂O slab (Zundel H₅O₂⁺ cation is represented by cyan full circle). Water molecule (blue circle) is attached to the other W-terminated plan; the (0001) WS₂ surface is covered with monomolecular water layer with dense (3) and open-work packing (4). Red full circles represent oxygen; blue, Mo; yellow, S; and H atoms in white.

The total binding energy E_b between water surface and the surface of the tip of a multiwall (open-ended) WS₂ nanotube composed of k walls can be estimated as the sum of the binding energies with each wall:

$$E_b=2\pi {\epsilon }_b{\displaystyle {\sum }_{i=1}^k\left(\frac{D_{out}}{2}-\left(i-1\right)\mathrm{\cdot }w\right)},$$ [S6]

where D_out is the outer diameter of the nanotube and w is the distance between the walls or the interlayer distance in 2H–WS₂ (w = 6.2 Å).

S5.2. Comments on the DFT Calculations.

The dangling bonds at the tip of the nanotube should exhibit a high reactivity toward water molecules, for example, between the W atom at the tip and oxygen of the H₂O molecule. The average cohesion energy between zigzag-like edges of 2H–WS₂ with the water surface was calculated by DFT for several idealized cases. Furthermore, several configurations for the initial position of water molecules at the interface with WS₂ edges were considered (Fig. S6). In case 1, water molecules initially are attached via oxygen to the W edge atoms, that is, saturating the tungsten dangling bonds (blue full circle); in case 2, water molecules are partially dissociated and W atoms are saturated with hydroxyl groups (purple full circle), whereas the counter charge occurs as Zundel H₅O₂⁺ cation far from the edge (cyan full circle in Fig. S6). The binding energies per length of WS₂ edge ε_b were calculated as the difference in the total energies between a combined supercell (with water) and the corresponding free slabs of WS₂ nanostripes and water. All of the models considered have demonstrated very similar binding energies between the WS₂ edges and water surface after the geometry optimization within the range 0.49…0.59 eV/Å.

Although the basal (0001) surface of WS₂ is commonly considered as hydrophobic, the specific influence of its atomistic structure on cooperative effects of the adsorbed H₂O molecules may not be fully ignored. It might be anticipated that ordering of the water molecules via hydrogen bonding or formation of an icy phase could be facilitated by the regular surface patterns of (0001)WS₂. The stability of a few possible H₂O surface structures placed on the WS₂ layer has been tested and compared with the conventional hexagonal H₂O bulk ice as the reference (cases 3 and 4 in Fig. S6). Irrespective of the structure, the estimated adhesion energies of H₂O layers to the (0001)WS₂ surface vary and are comparable to typical values of van der Waals bonding with 0.02–0.03 eV/Ų, which confirms the hydrophobic character of the WS₂ surface. Furthermore, the calculation of the energies of hydrogen bonding between H₂O molecules within different ordered H₂O phases placed near (0001) WS₂ surfaces does not reveal any favorable surface ordering. The energy of OH···O bond in bulk ice; in the dense (case 3 in Fig. S6) and open-work packed H₂O layers (case 4 in Fig. S6) are estimated as −0.34, −0.21, and −0.13 eV/Ų, respectively.

The total binding energy for a nanotube with diameter of 25 nm and 10 walls (using ε_b = −0.53 eV/Å), E_b, is around 0.52 fJ (Fig. S7). This value is ∼10³ times smaller than 195 fJ estimated for the surface energy of rising water meniscus with the geometry as obtained in experiment (S3. Phenomenological Estimation of the Surface Energy of the Water Meniscus Beneath the Pulled-Out Nanotube Tip). Thus, the number of dangling bonds at the tip of a WS₂ nanotube is too small to lead to a strong binding between the nanotube and water surface. Even the presence of reactive W atoms at the tip as considered in these models cannot alone lead to a binding energy exceeding the surface energy of water meniscus developing during pullout.

As noted before, the large-diameter nanotubes (type II) are usually capped. Nonetheless, the cap is not free of defects, and the interaction with the dangling bonds at the imperfections of the cap can lead to increased pullout work from the water surface. Therefore, these DFT calculations can be considered as an upper limit for the interaction energy of the water with the nanotube tip. Thus, strong anchoring of H₂O molecules to the lateral WS₂ surface cannot be responsible for the affinity of the tips of WS₂ nanotubes to the water film (Fig. 3B). MD simulations can shed light on the key role of capillary forces within the nanotubular cavity for a strong tip–water interaction.

S6. MD Simulations

S6.1.1. MD Setup for Study of H₂O–WS₂NT Interaction.

MD simulations of pullout experiments from water with WS₂ nanotubes of small diameters have been performed in two different regimes: the regime of nanotube retraction from a thin water film deposited on a substrate as well as in the regime of fixed nanotube and mobile water drop. Both open and capped model nanotubes have been considered. They were based on double-walled zigzag (24,0)@(36,0) nanotube with 2H–WS₂ polytypic arrangement (diameters of 24.2 and 36.2 Å measured for coaxial W atomic cylinders). The capped WS₂ nanotubes were designed as closed at one end by triangular faces of (WS₂)₂₅₆ and (WS₂)₅₇₆ octahedral fullerenes. In addition, a model of a double-layered (32,0) 2H–WS₂ flat nanostripe with almost the same length of circumference as the nanotubes was considered to look at the influence of curvature on the capillary properties of the water in the nanotubes core. The clusters of the two-walled WS₂ nanotubes and nanostripe had length of ∼60 Å and amounted to ∼1,300 WS₂ units. The atomistic model of the water reservoir was designed as a film of 4,800 H₂O molecules at the bottom of a bath or as a free drop consisting of 1,024 H₂O molecules.

MD simulations of all of the systems studied here have been performed using our own code under conditions of NVT ensemble at temperature T = 300 K. The temperature was controlled in all of the simulations with velocity scaling. Newton’s equations of motion were integrated with a time step of 2 fs via the Verlet leapfrog algorithm for 250,000 steps. The water film was preliminarily annealed and equilibrated under the same conditions during 500,000 steps. The lowest part of the nanotube tip was positioned initially ∼3 Å from the equilibrated water surface, which corresponded to a distance of 25 Å from the substrate. Two lift-up velocities of the tip have been used, namely, 0.025 and 0.25 Å/ps (2.5 and 25 m/s). No essential differences were observed between these two cases. Thus, the results presented in this work are for the lift-up speed of 0.25 Å/ps, which allowed testing a more diverse set of nanotubes for the same consumed computational time.

Force field level of theory was applied for these nanosecond-scale MD simulations. Intramolecular and intermolecular interactions within the H₂O film were treated within the framework of SPC model for the parametrization (34). A WS₂ tip was considered as a body with constrained geometry during all MD simulations, yet generating electrostatic and van der Waals fields in the framework of the UFF (35). The coupling between two parametrization sets for H₂O and WS₂ was fulfilled using Coulomb and Lennard–Jones 12-6 potentials, where the missing heteronuclear ε_ij and σ_ij parameters of the 12-6 potential depths were given by using Lorentz–Berthelot rules from the corresponding homonuclear interactions. Truncation at 12 Å for all short-range nonbonded interactions was applied. The long-range electrostatic interactions were computed without any restriction and approximation. The substrate was modeled as a semiinfinite van der Waals solid body using Lennard–Jones 9-3 potential with UFF parametrization (35) and the atom density corresponding to that of diamond. To prevent complete spilling of the water film along the substrate surface, the water film was placed inside a rectangular bath with the base edge lengths of 100 Å and semiinfinite side walls. The walls of the bath were modeled explicitly using repulsive potential of parabolic shape with the slope 25 eV/Ų.

The water was considered as either an isolated compact drop or as a thin film deposited on a substrate. Two different modes were studied. In mode 1, the nanotube was static and a water drop was adsorbed to its tip and allowed to move on its inner as well and the outer surfaces. In mode 2, the nanotube tip was placed near the water film surface, initially. At the onset of the experiment, the water–WS₂ interaction was turned on; the nanotube was withdrawn from the water surface while water was allowed to move on the nanotube surface freely.

S6.1.2. MD Setup for Study of CCl₄–WS₂NT Interaction.

To reveal the influence of hydrogen bonding within a liquid on the capillary effect, similar MD simulations in two modes were performed for the case of carbon tetrachloride, CCl₄. The latter is a molecular liquid with a relatively weak dispersion interaction between molecules and with a lower surface tension relative to that of the water (26·10⁻³ vs. 72·10⁻³ N/m at room temperature).

The same molecular-mechanics tools have been used as for the aforementioned MD simulation of H₂O–WS₂ system. The only specific difference was in description of intermolecular CCl₄–CCl₄ interactions. The high symmetry and absence of dipole moment of a CCl₄ molecule allow approximating it as a “spherical neutral superatom,” where the intermolecular interaction between structureless CCl₄ molecules is modeled using the Lennard–Jones 12-6 potential (36). Truncation at 20 Å for all these interactions was applied. The neglect of long-range electrostatic interactions in this approach shortens drastically the computational time and allows considering a larger set of atomistic models. The drop and the film of CCl₄ were modeled as ensembles of 4,000 and 11,800 molecules, respectively. Three types of substrate beneath the liquid film were considered as semiinfinite van der Waals bodies with the atom densities and parameters corresponding to that of diamond, graphite, and carbon tetrachloride itself. The CCl₄ film was placed inside a rectangular bath with base edge lengths of 250 Å.

Because the size of CCl₄ molecules is larger than for H₂O, larger models of the nanotube tips have been constructed accordingly. The open and capped tips of the single-walled (21,21), (28,28), and double-walled (21,21)@(28,28) WS₂ nanotubes were used (diameters of 36.6 and 48.8 Å measured for coaxial W atomic cylinders). The clusters of open-ended nanotubes for simulations of possible capillary imbibition had lengths of ∼156 Å (50 unit cells, or 2,100, 2,800, and 4,900 WS₂ units). The clusters of open-ended and both-ends-capped nanotubes for simulations of the pullout from CCl₄ surface had lengths of ∼78 Å and amounted up to ∼3,800 atoms.

MD simulations of all of the CCl₄–WS₂ systems studied here have been performed using the same code and under the same conditions as for H₂O–WS₂, yet at temperature T = 270 K to prevent exceeding fugacity of CCl₄ at the nanoscale. Newton’s equations of motion were integrated with a time step of 5 fs up to 500,000 steps. Thus, the lift-up speed during simulations of the pullout process was equal to 0.1 Å/ps (10 m/s).

S6.2. Comments on the MD Simulations.

We first discuss the major results, those using water. The first mode (mode 1) was used to visualize and analyze the kinetics of imbibition by open-ended WS₂ nanotubes. This calculation gave the first glance at the high capillary adhesion of water to small-diameter WS₂ nanotubes, despite their commonly recognized hydrophobic surface (Fig. S8). Indeed, after placing the nanotube in the vicinity of the water drop, the H₂O molecules rapidly adsorb along the circumference of tube end until the edges of the wall became fully occupied. The first step of the water imbibition is characterized by diffusion of H₂O molecules forming labile chain-like water fragments on the inner surface of the hollow core. The internal water pillar climbs with most of the molecules adhering to a monomolecular film on the inner surface until some H₂O molecules escape the hollow core to the edge of the rear part of the nanotube. Subsequently, the water molecules penetrated into the nanotube cavity by a slow diffusion of H₂O molecules forming labile chain-like fragments, which coalesced along the inner surface. The internal water pillar continued climbing, forming an irregular concave meniscus of monomolecular thickness until it reached the rear tip of the nanotube model. Similar labile chain-like water fragments could be observed on the outer surface of the nanotubes, yet they did not advance significantly. Instead, the water molecules concentrated near the frontal tip and did not form any stable outer coating. Additional simulations of the water–nanotube interaction in the same mode was performed with the walls having randomly distributed S vacancies. These studies have established only a slight influence of the wall structure on the water imbibition kinetics at the nanosecond level, but not on the general scenario of the imbibition process and on the strength of the water–wall interaction.

The internal structure of the liquid pillar in steady state can be characterized by means of radial and axial distribution of the atoms within the hollow core of the nanotube (Fig. S8). The analysis of the radial distribution functions for O and H atoms within a nanotube shows that the water remains as a liquid and did not crystallize in the confined space of the hollow core. No essential difference in the shape and intensity profiles is observed for the water distribution in steady state (1 ns) for the two cases, even when 5 at% of sulfur vacancies were introduced into the nanotube structure. A higher molecular density can be found only at a distance of ∼3.1 Å from the inner sulfur plane of the wall corresponding to van der Waals' bound water layer.

The second mode of the MD simulations (mode 2) has been aimed at reproducing directly the pullout of small WS₂ nanotubes from the vicinity of a thin water film and to study the effect of different types of nanotube tips. In addition to a few models of open-ended nanotubes, a capped nanotube and a nanostripe have been considered (Fig. S9). The model of a nanostripe may be ascribed to a nanotube with minimal possible curvature (large-diameter nanotube) and also excludes the capillary effect.

Despite its simplicity and the size limitation of the atomistic model accessible for MD simulations, the present study correctly reproduces the expected shape evolution of the water film and qualitatively reproduces the potential energy profile during pullout of the open-ended nanotube (Fig. S10). The direct visualization of the dynamics during tip retraction (Fig. 4) revealed the multistage character of the pullout process. Withdrawal of the tip of the open-ended nanotube in the vicinity of the water film is accompanied by a pronounced decrease in the energy (Fig. S10). Water molecules leap from the film and rapidly adsorb at the walls’ edges along the entire circumference. Furthermore, the initial stage of pullout is characterized by the formation of a water meniscus coaxial with the nanotube. The tapered water meniscus has a symmetric axis of revolution at this stage. Simultaneously, during the tip withdrawal, the water pillar continues to grow within the nanotube cavity. Both processes are accompanied by the gain in energy observed up to the tip height of ∼6.5 Å and maximal energy gain of ∼0.16 eV per nanotube. This energy gain is attributed to the strong interaction between the receding nanotube and the imbibed water adsorbed to the tube wall. At this point, the pullout force surpasses considerably the force of the surface tension of the meniscus. The reorganization of the water molecules at the vicinity of the tip may play a certain role in the energy gain as well, yet this process is too labile and no formation of specific ice-like solid phase was detected.

Further tip withdrawal results in necking of the water meniscus. Simultaneously, the energy of the system increases as the surface energy gets more and more dominant. At a distance of ∼25 Å, the meniscus loses its shape stability and transforms into a column. In contrast to the earlier stages, here the water column is rotating and does not have a stable axis of revolution (Fig. 4 and Movie S2). From this point on, the potential energy curve has a complicated unpredictable character, yet with general tendency of increasing energy. The water molecules that assemble in this column migrate in opposite directions in the direction of the tip and the water drop surface until a monomolecular water chain is formed. The complete disappearance of a continuous water column between the water film and the nanotube tip can be observed at a tip–water distance of ∼50 Å. Beyond this point, the water drop remaining at the tip relaxes into a hemisphere, whereas the water film adapts again a quasiflat surface. It is important to note that the water that penetrated into the cavity of the WS₂ nanotube does not leave and continues to climb during all stages of the pullout process.

The removal of the tip of a capped nanotube from the water drop surface shows an entirely different behavior (Fig. 4 and Movie S3). First, the initial withdrawal of the tip is not accompanied by any significant accumulation of water molecules at the tip end nor with an energy gain. The maximal gain in energy due to adsorption of the water does not exceed ∼0.02 eV per nanotube. A small meniscus can be observed during pullout, obviously due to the weak physisorption of water on the hydrophobic surface of the cap and due to the capillary force still acting far behind the cap. However, in this model, the water cannot penetrate the empty core of the nanotube and the propagation of capillary action is not possible during lifting of the tip. At a distance of ∼12 Å, the meniscus narrows to the point that it completely disappears, leaving a few water molecules at the tip. This model case demonstrates explicitly the role of capillary force in the high affinity of the open-ended WS₂ nanotubes to the water despite their general hydrophobic character.

A weaker capillary activity should be expected for open-ended nanotubes of large diameters. The model of a WS₂ nanostripe may be considered as an extreme case of nanotube with negligibly small curvature. The main driving force for the attraction between the WS₂ wall and the water film in this model should be related explicitly to the interaction between nonsaturated rim atoms at the WS₂ strip edge and H₂O molecules. Furthermore, the system could gain energy from reorganization of the water structure in the vicinity of the WS₂ edges, which is saturated with adsorbed H₂O molecules. MD simulations have demonstrated that retracting of nanostripe-like tip exhibits some similarities to open-ended WS₂ nanotubes (Fig. 4 and Movie S4). Rapid adsorption of water molecules can be observed along all of the circumference of the nanostripe with a maximal energy gain ∼0.09 eV per nanostripe. A characteristic catenoid-like profile of the pulled-out water can be observed along the planes of the nanostripe. Such wedge-like structure is assembled from a much larger number of water molecules, than the water assembled near the capped nanotube end. On the other hand, in analogy to the outer face of the nanotube, wetting of the basal (0001) face of the nanostripe is minimal. Nonetheless, as expected, further lifting of the nanostripe from the water film further diminishes the structural stability of the water wedge with the complete break of contact already at 36 Å, which is much earlier than for the model of open-ended nanotube (contact break at 50 Å).

These MD simulations in both modes for the case of liquid CCl₄ have only proven that the capillary imbibition and consequential pullout effect are not unique for water possessing an extended network of relatively strong hydrogen bonding. Molecular van der Waals liquids may demonstrate a similar behavior, yet with some peculiarities.

Particularly, MD simulations of CCl₄ and WS₂ nanotubes in mode 1 present a strong capillary effect, because they ultimately achieve complete filling of nanotubular cavities with CCl₄ molecules (Fig. S8, frame 4, and Movie S5). However, in contrast to the water, carbon tetrachloride possesses a stronger affinity to the hydrophobic WS₂ wall. Molecular layers of CCl₄ also form on the outer surfaces of the nanotubes. This phenomenon does not depend on the diameter of nanotubes or on the number of WS₂ layers composing the wall in these MD simulations. In all models considered, the development of CCl₄ imbibition begins with the rapid migration and spreading of molecules along inner WS₂ surface. The first molecular layer adheres to inner surface immediately upon exposure, whereas the first molecular layer at outer WS₂ surface occurs with a delay. Ultimately, the entire outer surface is covered by a stable CCl₄ monolayer, and then bilayer coating.

Both the internal and external CCl₄ layers can be characterized by means of radial distribution of the molecules. As for water, the analysis shows that CCl₄ remains as a liquid and does not crystallize in the confined space of the hollow nanotube core. Both inner and outer CCl₄ have the characteristic patterns of polymolecular adsorption and multishell ordering of liquid at inner and outer cylindrical surfaces.

Thus, the capillary activity of inorganic WS₂ nanotubes is pronounced for both liquids—H₂O and CCl₄—and may play a crucial role in the mechanism of pullout. Obviously, it is the only significant force for the pullout from the water film using an open-ended nanotube. The pullout from the film of tetrachloromethane includes also significant contribution from adhesion to the outer surface of the nanotube.

During the second mode of the MD simulations, the pullout of small WS₂ nanotubes from a film of carbon tetrachloride was directly simulated. The (undesired) influence of the substrate beneath the film depends here on the strength of interaction between nanotube tip and CCl₄ molecules. The molecules were attracted more to a diamond substrate than the nanotube. Therefore, tests with this substrate did not show penetration of molecules into the open-ended tips. Using the less dense graphite substrate, attraction to the substrate is significantly reduced regardless of the thickness of CCl₄. The withdrawal of a tip from CCl₄ film on these substrates is accompanied with formation of the conical meniscus as for the water pullout (Movie S6). The largest meniscus can be observed for the model of a thick CCl₄ film, when the influence of substrate is minimal. In all considered cases, the outer surface of the tips was densely covered by CCl₄ molecules.

Comparison of the applied forces and basic geometrical characteristics allow estimation of the relative contributions from the capillary effect and the adsorption on the nanotube outer surface. Such an estimate is only qualitative, because the size of our models is still far from the size of experimental nanostructures, and the ratio between the outer surface area and the volume of the hollow nanotube core is overestimated.

The forces achieved during pullout using an open-ended and capped (21,21) nanotube from the CCl₄ film deposited on graphite are 1.61 and 1.08 nN, respectively. This agrees well with the tendency observed in the MD experiments of the pullout from water film. However, the corresponding values of critical withdrawal height required to break the contact between the tip and the CCl₄ film are 23.5 and 52.5 Å, that is, larger detachment meniscus for capped than open nanotube. The origin of this result may be explained due to lower evaporation of CCl₄ molecules from the neck of the meniscus in the vicinity of the capped nanotube tip. In the latter case, a cloud of CCl₄ molecules can be observed at the tip after detachment, where two to three molecular layers are adsorbed on the surface of the cap.

S7. Thermodynamics Model

The chemical potential of a liquid with the relative vapor pressure has the following form:

$${\mu }_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}={\mu }_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}^0+RT\mathrm{\cdot }\ln \hspace{0.17em}p.$$ [S7]

Thus, the difference in the free energy ΔG of n moles of liquid within the cavity and the same n moles of liquid with flat surface is equal to the following:

$$\mathrm{\Delta }G=n\left({\mu }_{H_{2}O}\left(r\right)-{\mu }_{H_{2}O}\left(\infty \right)\right)=nRT\mathrm{\cdot }\ln \left(\frac{p_r}{p_{\infty }}\right),$$ [S8]

where p_r and p_∞ are the vapor pressures for the lower, convex surface of the liquid in a cavity with diameter D_in (inner diameter of a nanotube) and for the liquid with flat surface, respectively. The liquid pressure in the concave meniscus (equal but opposite sign of vapor pressure for the liquid in a nanotubular cavity) can be calculated using Young–Laplace equation as follows:

$$-p_r=p_{\infty }+\mathrm{\Delta }p=p_{\infty }-\frac{4\gamma }{D_{in}}\cos \theta ,$$ [S9]

where γ is the surface tension of liquid and θ is wetting angle. The number of moles embedded into the nanotubular cavity is equal to the following:

$$n=\frac{V}{V_m}=\frac{\pi }{4}{D}_{in}^{2}h\frac{\rho }{M},$$ [S10]

where V_m, ρ, and M_r are molar volume, density, and molecular weight of liquid, and h is the height of capillary column. Finally, the combination of Eqs. S7–S9 gives the following:

$$\begin{array}{r}\mathrm{\Delta }G=\frac{\pi \rho }{4M_r}RT{D}_{in}^{2}h\mathrm{\cdot }\ln \left(1-\frac{4\gamma }{p_{\infty }{D}_{in}}\cos \theta \right)=\\ =0.107\mathrm{\cdot }{\left(D_{out}-1.23k\right)}^{2}h\mathrm{\cdot }\ln \left(1-\frac{2854.577}{\left(D_{out}-1.23k\right)}\cos \theta \right).\end{array}$$ [S11]

Because the experimental measurements use the outer diameter of nanotubes D_out, the inner diameter of nanotube D_in can be substituted for D_out and the number of walls of a multiwalled nanotube as follows:

$$D_{in}=D_{out}-1.23\mathrm{\cdot }k,$$

where the units of D are nanometers and 1.23 is the doubled interlayer distance in WS₂ (lattice parameter c for the bulk 2H–WS₂). The values of the physical properties of water and the environmental conditions are as follows: T = 296 K, p_∞ = 1 atm, γ = 72.31·10⁻³ N/m, ρ = 0.998·10³ kg/m³ as well as the more convenient expression of the energy in femtojoules, D in nanometers, h in micrometers gives the final form of Eq. S11 for the energy gain due to capillary rise of water into nanotube.