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Observing liquid flow in nanotubes by 4D electron microscopy

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Science  27 Jun 2014:
Vol. 344, Issue 6191, pp. 1496-1500
DOI: 10.1126/science.1253618

Watching lead flow at the nanoscale

Microfluidic devices have recently become useful in commercial chemical synthesis. But what about fluid dynamics at the nanometer scale? Lorenz and Zewail used an electron microscope with nanosecond time resolution to capture images of molten lead flowing through a nanotube. They flash-melted the metal with a laser pulse to begin their flow measurements at a precise time point. The experiments offered insights into viscous friction as well as heat-transfer dynamics in a channel one-thousandth as wide as a strand of hair.

Science, this issue p. 1496

Abstract

Nanofluidics involves the study of fluid transport in nanometer-scale structures. We report the direct observation of fluid dynamics in a single zinc oxide nanotube with the high spatial and temporal resolution of four-dimensional (4D) electron microscopy. The nanotube is filled with metallic lead, which we melt in situ with a temperature jump induced by a heating laser pulse. We then use a short electron pulse to create an image of the ensuing dynamics of the hot liquid. Single-shot images elucidate the mechanism of irreversible processes, whereas stroboscopic diffraction patterns provide the heating and cooling rates of single nanotubes. The temporal changes of the images enable studies of the viscous friction involved in the flow of liquid within the nanotube, as well as studies of mechanical processes such as those that result in the formation of extrusions.

Advances in nanofabrication have made it possible to reduce the size of microfluidic devices and to study fluid flow at the nanometer scale (1, 2). Nanoscale fluid dynamics and transport properties are dominated by surface effects and may substantially differ from those occurring at larger scales. For water in carbon nanotubes, for example, flow rates have been reported to exceed the predictions of classical continuum theory by several orders of magnitude (35). However, the degree of the enhancement remains a point of discussion (6). The study of a single nanochannel, rather than a large ensemble, should reduce the experimental uncertainty and provide an opportunity to visualize mechanical and fluid dynamics at the nanoscale. Such experiments not only incur the challenge of preparing suitable structures, but also require appropriate tools to initiate and probe liquid flow in situ.

Electron microscopy affords the necessary spatial resolution to study liquids confined in carbon nanotubes and between graphene sheets (7, 8). Static high-resolution transmission electron micrographs have revealed water networks in single nanotubes with diameters of 2 to 5 nm (9). Moreover, the filling of single-walled nanotubes with mercury through electrocapillarity has been demonstrated (10). Slow fluid phenomena have been imaged with a time resolution of seconds, such as the deformation of water droplets encapsulated in tubes with diameters of about 100 nm under electron beam heating (11) or the condensation of water vapor in larger nanotubes, as observed with an environmental scanning electron microscope (12). Recently, in situ nanomanipulation in a scanning electron microscope was used to manufacture nanofluidic devices consisting of a single boron nitride nanotube (diameter 30 to 80 nm) bridging two sides of a thin membrane; large osmotically induced electric currents generated by a salinity gradient across the tube were demonstrated (13). Imaging liquid flow directly and with a time resolution sufficient to capture the fast processes occurring far from equilibrium would provide further insight into fluid dynamics in a single nanotube.

Here, we used 4D electron microscopy to visualize nanofluidic phenomena in real time, combining the spatial resolution of a transmission electron microscope with the (ultra)fast time resolution of optical techniques (14, 15). We initiate the dynamics by melting the lead core of a ZnO nanotube in situ with a temperature jump induced by a single laser pulse. The core reaches a temperature of several hundred degrees above the melting point, then recools on a time scale of 200 ns. The dynamics that ensue when the pressurized liquid expands in the nanochannel are imaged using an electron pulse accelerated to 120 keV, corresponding to a de Broglie wavelength of 3.3 pm. This approach permits us to study a wide range of nanofluidic phenomena in individual nanotubes. Short lead columns appear to move randomly in the nanotubes, splitting into shorter sections and fusing again. Droplets form on the outside of the tube on a time scale of nanoseconds when the pressurized liquid forces its way through microscopic leaks or shoots out of an open end. The laser-induced pressure jump induces the fission of a small lead column, the explosion of a droplet, or even the rupture of the tube wall. Lastly, the nature of the flow itself and the role of viscous friction at the nanoscale were elucidated by recording the expansion dynamics of the lead column. For such length scales, we developed a simplified model that allows for the extraction of the slip length, which is determined here to be on the order of 100 nm.

Experiments were performed using the UEM-1 instrument (16). Lead-filled ZnO nanotubes (17) were placed on a graphite film (1 to 6 monolayers on 2000 mesh copper) and studied at 363 K, well below the melting point of lead (Tm = 600.64 K) (18). Figure 1A shows a micrograph of a typical nanotube under irradiation with a train of picosecond laser pulses (532 nm; repetition rate 0.5 Hz, fluence 33 mJ/cm2). The tube has an irregular shape with a wall thickness between 10 and 15 nm and an inner diameter that varies between 30 and 50 nm. At the bottom of the image, a lead particle 150 nm in diameter is visible, which formed when molten lead leaked through an imperfection in the wall, draining the tube in its vicinity. At the top, voids have formed in the remaining lead core. Movie S1 shows how the column repeatedly splits into shorter sections that appear to perform random jumps and merge again later, their movement being the result of both their initial rapid expansion and their slower contraction upon cooling. As it resolidifies, the lead column is trapped in non-equilibrium configurations, such as the one containing voids; changes in diffraction contrast indicate that ordered domains are formed with random orientations.

Fig. 1 Imaging of a single nanotube and temporal evolution of an extrusion.

(A) Micrograph of a lead-filled ZnO nanotube under irradiation with the picosecond laser. At the bottom, molten lead has leaked out of the tube, and voids have formed in the remaining lead core at the top. Scale bar, 100 nm. (B to F) Fate of an extrusion formed by a single laser pulse. When the filled nanotube in (B) is laser-heated, part of the molten core is forced out of the tube through a leak, as visible in (C), which was recorded after 96 ns. After the tube has cooled, the extrusion is slowly reabsorbed on a time scale of several minutes [(D) to (F)]. Scale bar, 200 nm.

The laser pulse directly heats the solid lead core and transforms it into a hot, pressurized liquid, thus triggering its rapid expansion and initiating the dynamics we observe; at the wavelength used, ZnO absorbs only weakly. Metal nanoparticles are known to melt in less than 100 ps (19, 20), which is fast on the time scale of the nanofluidic processes studied here (nanoseconds). Melting is therefore complete before flow dynamics occur. We performed time-resolved diffraction experiments to study the temperature jump and cooling rates (16). Figure 2A displays the selected-area diffraction pattern of the nanotube shown in Fig. 2B. Besides the reflections of the graphite substrate, groups of spots are visible, which arise from domains of the lead core fulfilling the Bragg condition (circles). Their intensity as a function of time after laser excitation was measured by recording stroboscopic diffraction patterns with the electron pulses of the microscope (Fig. 2C). For these studies of the temperature jump and cooling dynamics, the laser fluence was reduced to one-tenth of the initial value to avoid melting of the sample and altering the lead core irreversibly with every laser shot.

Fig. 2 Diffraction pattern of a nanotube, temporal evolution of the diffraction intensity, and temperature dependence.

(A) Selected-area diffraction pattern of the nanotube shown in (B). Scale bars, 2 nm−1 and 500 nm, respectively. The lead core gives rise to the circled groups of (200) reflections. (C) The integrated diffraction intensity is shown as a function of time after laser excitation. From a fit with an exponential function, broadened to account for temporal jitter and the finite width of the electron probe pulse, a cooling time τc = 226 ± 9 ns is obtained. (D) Plot of the diffraction intensity as a function of the sample temperature without pump laser. Error bars indicate SEM of 20 measurements for every data point.

As a result of the temperature jump, the diffraction intensity initially drops sharply and then recovers exponentially with a time constant of 226 ns (solid line in Fig. 2C). We find this to be a typical cooling time, which leaves only a short time window during which the liquid behavior can be observed. From a calibration measurement of the diffraction intensity as a function of the sample temperature (Fig. 2D), we determined the initial temperature jump of the tube to be 106 K. By extrapolating to high laser fluence and taking the different tube dimensions into account (16), we estimate that the nanotube in Fig. 1A reaches an initial temperature greater than 1000 K, well above the melting point of lead.

Although it is certain that in situ melting of the lead core and fluid motion have taken place (movie S1), the elucidation of the nature of these processes obviously requires a time resolution that matches their inherent time scale. This is achieved here by recording micrographs with a single electron burst, fired at a short delay after the laser pulse, analogous to the method used for flash photography of fast-moving objects. Figure 1B depicts the image of a nanotube (outer diameter 130 nm) with a continuous lead column. The pressure jump induced by a single laser pulse forces part of the molten core to leak through the tube wall. At a delay time of 96 ns, a nearly spherical lead droplet (diameter 150 nm) has erupted on the outside of the tube (Fig. 1C). Such extrusions (see also Fig. 3) probably form when the liquid forces its way through microscopic channels in the amorphous ZnO walls of the tube. The diameter of these channels must be considerably smaller than the size of the extrusions, on the order of several nanometers.

Fig. 3 Dynamics of different phenomena observed in single-shot experiments.

Micrographs of the nanotubes were recorded before and after exposure to a single laser pulse. (A to D) Lead shooting out of the open end of a nanotube. The difference image (D) is obtained by subtracting (B) from (C); red and blue denote positive and negative intensity, respectively. (E to H) A short lead column fissioning. In (H), the movements of the fragments are indicated by arrows. (I to L) A nanotube rupturing at high laser fluence. Shown in (K) [and in (L) at higher magnification] is a fragment of the shattered tube wall with a lump of lead attached to it. Scale bars, 200 nm.

The extrusion has shrunk to a diameter of 110 nm after 10 s (Fig. 1D) and is slowly being reabsorbed by the tube, long after the heat provided by the laser pulse has been dissipated (Fig. 1, E and F, and movie S2). On a time scale of 3 min, it contracts further to a diameter of 50 nm before it finally disappears from view; its volume decreases linearly with time (fig. S4). The extrusion fills a void in the tube formed upon cooling of the lead column, which is energetically favorable because it reduces the total surface area of the column and extrusion. This process is likely attributable to the suppression of the melting point of the material confined in the small channel connecting the extrusion to the interior of the tube (21). Moreover, surface melting of lead nanoparticles occurs well below the bulk melting point (21), so that a continuous path exists along which lead atoms can migrate back into the tube.

In Fig. 3, we display images of various irreversible flow phenomena. Figure 3A shows the open tip of a nanotube with an inner diameter of 60 nm. After the laser pulse (Fig. 3C), a lead particle 110 nm in diameter is seen to adhere to the tip; a single-shot image (Fig. 3B) reveals that at 29 ns, the droplet has already formed. The difference of these two images is displayed in Fig. 3D, where red and blue encode positive and negative intensity, respectively. The image reveals that the droplet shrinks as the lead column cools and contracts. When we exposed the tube to further laser pulses, the lead sphere successively grew and expanded strongly at short delays, before it shrank again upon cooling (fig. S5).

Figure 3E depicts a nanotube with an inner diameter of 55 nm that has been almost completely drained in situ, except for a lead column 250 nm in length. When heated with the laser pulse, the column splits into two segments (Fig. 3F, recorded at 34 ns). For this to happen, the energy deposited by the laser must be sufficient to overcome the barrier for fission. In Fig. 3G, taken at a long delay time after the laser pulse, only the larger of the two segments is still visible, while the shorter one has been accelerated out of the frame. A small spherical extrusion 40 nm in diameter is visible on top of the tube, which can already be discerned in Fig. 3F. Its formation must have preceded the separation of the segments, which have already moved away from the site of the leak. Figure 3H summarizes the sequence of events. After the laser pulse, the extrusion rapidly erupts on the side of the tube and the column fissions. The smaller and larger segments move apart with speeds of about 1.5 and 2 m/s, respectively, as estimated from the distance they have traveled in Fig. 3F. The smaller segment leaves the image frame, whereas the larger segment flows back upon cooling and settles near the extrusion.

At higher fluences and with multiple pulses, the laser-induced pressure jump can easily rupture the tube wall at defect sites. Figure 3I shows a tube that has already been exposed to several laser pulses. Two segments of the previously continuous lead column remain, one featuring an extrusion on either side and the other located at a breach of the tube wall, where lead has accumulated into an oblong mass. Upon irradiation with a further laser pulse, in this case doubling the pulse energy, the tube visibly deforms and the extrusions explode into an array of smaller particles (Fig. 3K). Most notably, as can be seen at higher magnification (Fig. 3L), part of the wall ruptures under the laser-induced pressure jump and detaches with a lead particle clinging to it. The resolution of Fig. 3J, taken at 18 ns, is somewhat reduced at this high laser fluence. Nonetheless, we clearly observe the lead particle in flight, appearing between the two lead column segments. By comparing the single-shot image with the images taken before and after, we can infer that it detached from the left segment and was propelled to the right while adhering to the wall fragment, which remained attached on its right side and moved as if on a hinge.

In the absence of the above irreversible phenomena, it is possible to study viscous friction at the nanoscale. To this end, we focused on nanotubes that are robust enough to withstand laser pulses of high fluence. When the tube in Fig. 4A (inner diameter 55 nm; fig. S6) is heated with a single laser pulse, its lead core rapidly expands (140 nm at a delay of 54 ns). Figure 4B displays the entire dynamics obtained from more than 100 single-shot experiments. During the first 30 ns, the meniscus advances with a nearly constant speed of 3.9 m/s. The column subsequently contracts more slowly, shrinking to its initial length in 300 ns. The scatter of the data points reflects changes in the initial conditions of every experiment, leading to slightly different dynamics. Apart from variations of the shape of the meniscus, we also observe that the column recedes after every laser pulse by several nanometers, likely because lead leaks out of the other end of the tube, which results in negative expansion at delays longer than 300 ns.

Fig. 4 Expansion dynamics of the liquid in a single nanotube.

(A) Single-shot images showing the partially filled tube with inner diameter of 55 nm (see also fig. S3); scale bar, 100 nm. When heated with a single laser pulse, the lead column expands (140 nm at 54 ns, dark contrast) before returning to its original length at long times. (B) The complete dynamics obtained from a series of such experiments. The gray lines have been inserted to guide the eye. The friction coefficient f is estimated from a fit of the initial expansion (blue line and dots), where the fit function has been convoluted with a Gaussian of 10 ns full width at half maximum to account for the finite duration of the probe electron pulse. Error bars indicate SE of the fit used to extract the displacement of the meniscus. (C) Numerical simulations for two different column lengths l, where the parameters of the simulation have been adjusted to match the experiment (16). In particular, we obtained good agreement with a cooling time of 100 ns. Here, a friction coefficient f = 0.5 ∙ f0 = 0.5 · 8πη was used, where η is the viscosity of lead at 1700 K (33).

To model the expansion dynamics, we developed an analog of Washburn’s law (22), which successfully describes the dynamics of capillary filling for incompressible liquids. However, we assume that the expansion of the liquid column, not the capillary force, drives the fluid motion (16). Assuming laminar flow and neglecting the energy cost of displacing and deforming the meniscus, we treat the liquid as a cylinder whose longitudinal expansion is slowed by viscous friction. By solving the resulting differential equation numerically, we obtain the displacement of the meniscus as a function of time, as shown in Fig. 4C for typical column lengths of l = 15 μm and 10 μm (black and blue curves, respectively); the free parameters have been adjusted to match the experiment (16). The qualitative agreement with the observed dynamics suggests that the model captures the underlying physics.

The displacement x of the advancing meniscus at early times t after the laser pulse was derived asEmbedded Image (1)where f is the friction coefficient, xe is the equilibrium displacement of the meniscus after the temperature jump, v0 is its initial velocity, and m is the mass per unit length of the lead column. Here, t0 is included to allow for a delayed onset of the expansion. Equation 1 expresses the intuitive result that in the absence of friction (f = 0), the meniscus moves freely with constant velocity v0; when f is small, Eq. 1 reduces toEmbedded Image (2)Thus, friction manifests itself in the deviation of the expansion curve from linearity. In Washburn’s law, the friction coefficient is assumed to be the same as for Poiseuille flow, f0 = 8πη, where η is the dynamic viscosity of bulk liquid lead (22).

In contrast to the simulation in Fig. 4C, where we have chosen f = 0.5 · f0, the experimental expansion curve was found not to deviate strongly from a straight line, indicating that f must be relatively small. Using Eq. 1, f was determined from a fit of the blue dots in Fig. 4B; the mass per unit length m = 2.69 × 10−11 kg/m is known, the velocity v0 = 3.9 m/s is obtained from a linear fit of the early expansion curve, and xe = 150 nm is estimated from the maximum displacement of the meniscus in the image. The friction coefficient f was obtained to be 0.06 · f0 (i.e., 6% of the value of macroscopic continuum dynamics). Within the experimental errors, we conclude that f is reduced by at least one order of magnitude relative to the bulk value (23).

Whereas Poiseuille’s law, from which f0 is derived, assumes that the liquid is stationary at the interface, the substantial reduction of the friction coefficient indicates a finite slip velocity of the lead column at the tube wall. Slippage is described in terms of the slip length δ, the distance from the interface at which the velocity profile of the flowing liquid extrapolates to zero (2, 24, 25). A modified Poiseuille law incorporating slip (4) givesEmbedded Image (3)where R = 27.5 nm is the radius of the tube. From the dynamics in Fig. 4B, we obtained a slip length of 112 nm, implying that the velocity profile of the moving column is almost flat. Such a large slip length is supported by the strength of the interaction between liquid lead and the ZnO tube as well as by the nature of the experiment, which is carried out under far-from-equilibrium conditions.

The contact angles of liquid metals on metal oxide surfaces are usually larger than 90° (26, 27); that is, the surface repels the liquid. For rough surfaces, such as the irregular inner walls of the ZnO tubes, this effect is even more pronounced. Under such nonwetting conditions, large slip lengths have been measured, up to tens of micrometers in the extreme case of superhydrophobic surfaces (25). We also note that the lead column may have an oxide skin (28), which increases the apparent viscosity of liquid metals at low shear rates (27). However, it is difficult to predict how this would affect the nanofluidic behavior at the high shear rates in our experiment (~107 s−1, as estimated from the flow velocity and the tube dimensions). Under such conditions, the slip length may also increase with shear rate. Simulations for smooth surfaces have found the slip length to diverge at shear rates of ~108 s−1 (25, 29). Moreover, on rough surfaces, large shear rate–dependent slip lengths have been demonstrated experimentally (30); however, nano-sized vapor bubbles on the surface may play a role in such experiments (30).

We believe that the approach presented here should find applications in the study of nanoscale phenomena that have previously been inaccessible, including the investigation of nanofluidic structures or biological channels (31) with high spatial and temporal resolutions. The study of phase transitions in nanoconfined environments constitutes another area that will benefit from the capability to manipulate and visualize single nanotubes in situ.

Supplementary Materials

www.sciencemag.org/content/344/6191/1496/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S6

Movies S1 and S2

References (3440)

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: Supported by NSF grant DMR-0964886 and Air Force Office of Scientific Research grant FA9550-11-1-0055 in the Physical Biology Center for Ultrafast Science and Technology at Caltech, which is supported by the Gordon and Betty Moore Foundation. U.J.L. was partly supported by a postdoctoral fellowship from the Swiss National Science Foundation.
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