Abstract
We report light-driven levitation of macroscopic polymer films with nanostructured surface as candidates for long-duration near-space flight. We levitated centimeter-scale disks made of commercial 0.5-micron-thick mylar film coated with carbon nanotubes on one side. When illuminated with light intensity comparable to natural sunlight, the polymer disk heats up and interacts with incident gas molecules differently on the top and bottom sides, producing a net recoil force. We observed the levitation of 6-mm-diameter disks in a vacuum chamber at pressures between 10 and 30 Pa. Moreover, we controlled the flight of the disks using a shaped light field that optically trapped the levitating disks. Our experimentally validated theoretical model predicts that the lift forces can be many times the weight of the films, allowing payloads of up to 10 milligrams for sunlight-powered low-cost microflyers at altitudes of 50 to 100 km.
INTRODUCTION
Currently used flight mechanism cannot be used to achieve sustained flight in Earth’s mesosphere—the upper layer of the atmosphere located at altitudes between ~50 and ~80 km (1). Modern aircraft are not able to fly for an extended period of time above ~30 to 50 km because the air density at these altitudes is too low to generate lift for airplanes and balloons (2–4). On the other hand, space satellites rarely dip below ~150 km because the air at such altitudes becomes thick enough to cause excessive drag and heating (5, 6). The only vehicles capable of flying in the mesosphere are rockets, but for only minutes at a time (1). We argue below that photophoresis or light-driven motion (7–9) can potentially provide a no-moving-part mechanism for sustained flight in near space (1, 10).
Recent photophoresis studies have primarily focused on microscopic particles in atmospheric aerosols (11–15) and the optical trapping of microscopic particles, for example, to create three-dimensional displays (16). In the free molecular regime, where the mean free path λ is much larger than the characteristic size a of the object, the photophoretic force results from the difference in the velocity of the incident and departing gas molecules from a hot surface (17–19). In the continuum regime (λ ≪ a), the force is generated through the thermal creep of the gas over the edges of the sample from the cold side to the hot side (20–23). The photophoretic force has been shown to reach a maximum in the transition regime, where the Knudsen number
However, it is also possible to generate a photophoretic force in ultrathin structures that have a negligible temperature difference but instead have different surface properties on the top and bottom surfaces, as previously demonstrated for micron-sized particles (28–30). In the free-molecular regime, gas molecules colliding with a heated structure absorb energy from the surface and leave with a higher average speed. The measure for such energy transfer through gas-surface collisions is called the thermal accommodation coefficient,
(A) Schematic diagram of the main mechanism behind the photophoretic force due to a difference in the thermal accommodation coefficient (in the free molecular regime). (B) Photograph of a 6-mm-diameter mylar disk covered by a layer of CNTs. (C) The porous surface of the CNT layer that traps incoming air molecules, allowing for the gas molecules to absorb more heat and approach unity thermal accommodation coefficient partially covering the smooth surface. The inset shows a closeup of the trap created by the nanotubes (D) Sequential screenshots of two levitating 6-mm-diameter disks under incident light intensity of
RESULTS AND DISCUSSION
To demonstrate that this levitation approach can be used not only on the microscopic but also on the macroscopic scale, we fabricated centimeter-scale samples with submicron thickness and different surfaces on the top and bottom. By coating the thinnest commercially available mylar film with carbon nanotubes (CNTs) on only one side (Fig. 1B), we increased the thermal accommodation coefficient on the bottom and generated a photophoretic force that levitated flat disks with centimeter-scale diameters. Notably, these levitating samples can be made using simple fabrication methods from low-cost materials and achieve stable mid-air hovering at pressures corresponding to altitudes of ~80 km in the atmosphere.
Specifically, we used 500-nm-thick mylar film (also known as OS film in the model airplane community) and deposited a 300-nm-thick layer of CNTs on its bottom side (see Materials and Methods for detail). This layer served three critical functions: (i) to act as a lightweight light absorber with measured visible-range absorptivity of ~90%, (ii) to improve the mylar film’s structural rigidity, and (iii) to provide enhanced surface-gas interactions that increase the accommodation coefficient. The areal density of the resulting CNT-coated film was thermal ~1 g/m2 with an overall thickness of ~0.8 μm. When illuminated by light-emitting diode (LED) arrays with intensity of ~0.5 W/cm2 (five Suns), the structure became up to ~100 K hotter than the environment (see fig. S2).
The CNT layer has a nanostructured surface shown in Fig. 1C, which tends to trap incoming gas molecules as illustrated in Fig. 1A. These traps make the air molecules collide with the surface multiple times on average before leaving, resulting in a higher thermal accommodation coefficient for the CNT-air side compared to the mylar-air side. This difference between the surface properties results in a higher departing velocity for the air molecules on the CNT (bottom) side compared to the mylar (top) side. The net momentum transfer from these gas-surface interactions results in an upward recoil force that levitates the sample, as shown for the free molecular regime in Fig. 1D (see the Supplementary Materials for the discussion of the force in continuum and transition regimes).
We note that this lift force is not due to the temperature difference between the top and bottom, as in our previous experiments (10). Using the thermal conductivity of mylar
To study the force generated by a difference in the thermal accommodation coefficient (Δα-force), we developed a theoretical model and calculated the areal density of an object that can be levitated under a certain flux and a known Δα. Briefly, in the free molecular regime, Δα-force increases proportionally with pressure and reaches a maximum at Knudsen numbers of order unity. Further increases in pressure reduce Δα-force as P−2, which is faster than the P−1 scaling that is typical for the temperature difference forces (20) (see the Supplementary Materials for full formulation). Our model follows the well-established semi-empirical approach (8, 13, 19, 24) to predict the total lift force but not its different components such as area force, edge force, and shear force, which were previously calculated for radiometers (38). While the separation of force components can provide additional theoretical insights, such detailed analysis requires Monte Carlo simulations or numerical solution of the Boltzmann equation, which are computationally demanding and beyond the scope of this study.
Figure 2A shows the predicted areal density of an object that can be levitated using Δα-force with Δα = 0.15 ± 0.05 and flux of ~0.5
(A) Areal density of a disk with a given radius and micron thickness that can be levitated under
(A) (i) Side and (ii) top-view schematic diagram of the test setup consisting of eight LED arrays below an acrylic vacuum chamber, a 74% transparent metallic mesh placed several centimeters above the bottom surface of the acrylic chamber and a levitating disk sample. (B) Experimental measurements of the intensity of the trapping light beam from eight LED arrays at 7-cm (i and ii) and 10-cm (iii and vi) heights above the LEDs. Note that the high-intensity ring surrounding the microflyer confines its in-plane movement and that the intensity at the center drops as the height increases, which stabilizes the flight height.
To levitate samples for extended periods of time, we designed a light field that can optically trap the sample. This light trap consisted of a central area with intensity high enough to levitate the disk, surrounded by a ring of even higher intensity, which creates a restoring force by tilting the disk and pushing back toward the center (Fig. 3). The uneven light field also creates a ΔT-shear force (35) that points in the same direction. Determining which restoring mechanism is dominant in our experiments is complicated and is beyond the scope of this study.
Considering the dimensions and thermal properties of the sample material, the thermalization time constant can be estimated as
Several tests using side and oblique video recording revealed that the light trap was effective, and the samples levitated at a height comparable to their diameter above the mesh (see movies S1 to S3). This equilibrium height is determined by the intensity of light the samples receive as a function of the distance from the LEDs. The samples stay levitated at a height where the light received generates a force that exactly balances their weight. After several seconds of successful levitation, we typically increased the light intensity at a rate of ~0.3
Using our model for the photophoretic force on a disk, we can predict the possibility of photophoretic flight at different altitudes in the atmosphere. As the altitude increases from 0 to 100 km, ambient temperature and pressure change markedly (see the Supplementary Materials and fig. S4), which affects the temperature difference between the disk and ambient. In our model, we also accounted for different radiation environments seen by the top and bottom of the disk at altitudes above 30 km. Conservatively, we assumed a 3 K effective temperature for deep space, seen by the top side of the disk, and 255 K for Earth, seen by the bottom side (39).
As shown in Fig. 4, our theoretical model predicts the possibility of sunlight-powered levitation in a wide range of altitudes between 50 and 100 km if the accommodation coefficient of the surfaces can reach Δα = 0.5 and the thermal infrared emissivity is reduced to ϵ = 0.5. Moreover, the disks can lift up to 10 mg of payload under natural sunlight, sufficient to carry smart dust sensors presented in the literature (40). Thermal accommodation coefficient value for air on clean glass and air on glass coated with molecularly thin polymer is reported to be 0.19 and 0.43, respectively (41), which means that Δα = 0.5 is realistic with carefully treated surfaces. The use of selective absorbers has been shown to reduce the emissivity to as low as ϵ~0.1 (42), which would allow levitation even for incident light intensities below full natural sunlight intensity (see fig. S9). At high altitudes (>20 km), the sunlight intensity is approximately 0.136
Contour plots of (A) areal density of the object able to be levitated (B) payload that can be lifted using mylar-CNT (white area represents no levitation for mylar areal density). (C) Temperature and (D) temperature difference between the disk and ambient for different sizes at different altitudes with ∆α = 0.5, ϵ = 0.5, and under natural sunlight
To prevent the tumbling of the microflyer due to winds or other disturbances at high altitudes, the payload can be suspended by, e.g., a carbon fiber thread from the disk to lower its center of mass and suppress the tilting of the sample. Moreover, controllable tilting and horizontal movement of the samples can be achieved in such structures by shifting the position of the payload along the thread that suspends the payload from the disk. Another possibility for further improvement of payload capacity is using an array of microflyers, with potentially hundreds of microflyers connected by ultrathin carbon fibers, which can potentially increase the payload into the gram range.
In summary, this work demonstrated an approach to photophoretic levitation of macroscopic structures that does not require a temperature gradient within the object, offering a path to the development of affordable photophoretic microflyers for the mesosphere. We developed a theoretical model for thin disks, which showed agreement with the experiments done using low-cost fabrication methods. The levitation tests were successful at pressures of ~10 Pa and incident light intensity of
Our experimentally validated model predicts that the same approach can be used in the near space at altitudes between 50 and 100 km. Such microflyers can use sunlight or a laser beam from any direction to stay levitated for extended periods of time, allowing, for example, the mapping of wind flows at these high altitudes by tracking the location of these flyers using a radar or lidar. There is a large opportunity to further increase the force by increasing the difference in accommodation coefficients and reducing the infrared emissivity. Such improvements will allow the microflyers to carry payloads of up to 10 mg, which can consist of thin substrate or smart dust sensors for weather and climate applications, such as measuring temperature, pressure, or carbon dioxide levels.
MATERIALS AND METHODS
Sample fabrication process
We started with a thin sheet of commercially available mylar film with a nominal thickness of 0.5 μm (Dupont). Using a 1-cm2 sample and a precision scale (PerkinElmer AD4 model), we measured the areal density to be ~0.7 g/m2, which agrees with the theoretical value expected from the nominal density of mylar of 1.39 kg/m3. To deposit the CNT layer, we used a 0.2 weight % water-based single-wall CNT with 1- to 2-nm diameter and 5- to 30-μm length (NanoAmor) and diluted it with deionized (DI) water by a volumetric ratio of 3:1 (DI Water/CNT). We then stretched a sheet of this mylar thin film of a Si wafer and put it on a hot plate at 50°C. By dropcasting the CNT solution on the sheet and letting the water evaporate, we created a CNT layer on the mylar sheet, then peeled the mylar sheet off of the Si substrate, and cut circular samples of the desired diameter using a razor blade. Weight measurements of the CNT-covered samples showed their areal density to be ~1 g/m2.
Testing methods
The experimental setup used a 10-liter custom-designed cylindrical acrylic vacuum chamber. The acrylic allowed for easy illumination of the sample from any direction and allows for video capture from any direction. Despite the 25-mm thick walls and properly sealed junctions, the chamber leaked a substantial amount of air through its walls (a known downside of acrylic chambers), making it impossible to reach high-vacuum base pressures. A two-stage vacuum pump with a 1500-Hz turbo pump resulted in base pressures ranging from 7 to 200 Pa (~0.05 to 1.5 torr) by using the roughing-turbo combination or only the roughing pump.
To create a light trap that has a local minimum in the center and a ring of maximum intensity, we used eight LED arrays, each rated for 100 W of input power (LOHAS LH-XP-100W-6000k). These LEDs, as shown in fig. S1, were mounted on two pieces of aluminum connected to four heat sinks with forced convection cooling from four fans, capable of removing ~1000 W in total. All thermal interfaces were enhanced using silver paste (Arctic Silver 5 Polysynthetic Thermal Compound). In all experiments, a metallic mesh with a transparency of 74% (McMaster item no. 9238T51) was used as a “launchpad” and was placed several centimeters away from any inner surface of the vacuum chamber to avoid ground or wall effects. Figure S1 shows a side view of the chamber, the eight-LED-array assembly, and the launchpad. To study the residual ground effect of the launchpad, we also created and tested an 85% transparent mesh by removing approximately one half of the wires of the 74% mesh. The experimental results showed no measurable difference in the height versus input power to the LEDs, suggesting that the effect of the mesh is negligible.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/7/7/eabe1127/DC1
This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.
REFERENCES AND NOTES
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