Photophoretically levitating devices for atmospheric flight and enhanced lifetimes

Abstract

Photophoretically levitating devices for atmospheric flight of a payload. The devices include oxidation-resistant material. Various architectures of the devices are described, including devices with a plurality of substructures tethered together, devices shaped like grids, devices with curves and concavity, and devices of various polygonal shapes.

Description

PHOTOPHORETICALLY LEVITATING DEVICES FOR ATMOSPHERIC FLIGHT AND ENHANCED LIFETIMESCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and the benefit of the filing of U.S. Provisional Patent Application No. 63 / 677,128, entitled "Photophoretically Levitating Devices for Stratospheric Flight and Enhanced Mesospheric Lifetimes", filed on July 30, 2024, and the specification and claims thereof are incorporated herein by reference.BACKGROUND OF THE INVENTIONField of the Invention

[0002] Embodiments of the present invention relate to propulsion mechanisms for flying devices in the atmosphere of a planet, and in more particular, photophoretically levitating devices.Description of Related Art

[0003] Photophoresis is a phenomenon where a particle suspended in gas or liquid begins to migrate when illuminated because of an imbalance in the momentum transfer between the gas particles and the suspended object due to a heat gradient across the suspended object. Photophoretic forces have gained recent attention as a propulsion mechanism for near-space flight [Schafer (2024); Azadi et al. (2021); Schafer et al. (2022); Cortes et al. (2020)]. The devices that have been proposed are typically centimeters wide, hundreds of nanometers thick, and are expected to stably levitate around altitudes of around 70-90 km in Earth’s atmosphere or in the Martian mesosphere. These devices have area densities around 1 g / m2and could carry 100 mg-scale payloads for sensing and communications. Larger, meter-scale devices have been theorized to carry kg-scale payloads [Benford and Benford (2005); Celenza (2024)].

[0004] Photophoretic levitation devices can be categorized by one of two photophoretic lofting mechanisms that generate sufficient force to levitate the devices when they are illuminated by sunlight. The first is Aa photophoresis, where a difference in the energy accommodation coefficient a over the surface of the device causes a difference in momentum transfer between gas collisions on opposing sides of the device. The second is AT photophoresis, where a difference in the temperature T over thesurface creates a similar variation in momentum transfer. Both mechanisms are strongest when the mean free path A of the surrounding gas is about the same as the characteristic size of the device (the transition regime). In the context of the field of photophoretic forces, the term “characteristic size” refers to the size of a particular dimension of a device, which dimension referred to depends on the device’s geometry. For both Aa and AT photophoresis, the “characteristic size” of a device will be the smallest dimension that is perpendicular to the gradients in accommodation coefficient or temperature on the surface of the structure. The contribution of individual, non-thermally-accommodated gas molecules to the photophoretic force can be quantified as a function of this dimension. At low pressures, where the characteristic size is much smaller than the mean free path (i.e. the free molecular regime), the contribution of individual molecules is highest because the statistical probability of momentum transfer with the structure’s surface is highest. However, the photophoretic force is weak because there are few gas-surface collisions at low pressures. At high pressures, where the characteristic size is much greater than the mean free path (i.e. the continuum regime), the contribution of individual gas molecules is lowest because many gas molecules interfere with each other near the surface, creating a highly thermally-accommodated gas layer around the surface, which minimizes the photophoretic force. As a result, photophoretic forces on any given structure are generally maximized at intermediate pressures, when the mean free path of the surrounding gas is about equal to the characteristic size for that structure (i.e. the transition regime). As such, the value of a structure’s characteristic size depends on the structure’s geometry. For example, in the case of a levitating device shaped as a thin solid disk, the characteristic size may refer to the disk’s radius (or its diameter). If the levitating device was shaped as a thin solid square, the characteristic size would be the square’s side length. If the levitating device was a grid, the smallest dimension of the grid, referred to herein as its “width” (as more thoroughly described later) would be its characteristic size.

[0005] At higher pressures, a AT may cause thermal transpiration (“creep”) flow around the device, which has been shown to increase the pressure at which the forces are maximized, especially when the devices are perforated [Sharipov & Schafer (2024)]. Generally, however, the photophoretic force is proportional to the inverse of the ambient gas pressure Pwhen the size of the device is much larger than A (i.e. in the continuum regime).

[0006] For a device to achieve either Aa or AT photophoretic levitation in the atmosphere using just sunlight, at least one region of the device must maintain a temperature much greater than the ambient gas. The devices proposed here would use highly solar-absorptive and IR-non-emissive optical coatings to selectively absorb sunlight and heat up. At around an altitude of 70 km, the net heat flux away from cm-wide devices reaches a minimum due to the tradeoff between conductive and radiativeheat fluxes [Schafer (2024)]. Because the photophoretic force is proportional to either the temperature between the device and the ambient gas (in the case of Aa photophoresis) or the temperature difference AT on the device’s surface (in the case of AT photophoresis), the force on cm-wide structures is maximized around 70-90 km. Smaller structures can levitate at lower altitudes as well [Keith (2010)].

[0007] Three issues surround photophoretic levitation at mesospheric altitudes. First, atomic oxygen (AO) concentrations reach a maximum at the 100 km mesopause [Richter et al. (2021)] and may cause substantial material degradation to photophoretic devices. For instance, mylar and alumina oxide are two materials that have been proposed for photophoretically levitating devices. Assuming erosion yields of 2.5 x 10-22cm3 / atom and 3.0 x 10-24cm3 / atom for these materials respectively [de Groh and Banks (2019)], a relative AO velocity of 400 m / s, and an AO concentration of 1011atoms / cm3at an altitude of 80 km, the linear erosion rate of mylar and aluminum oxide are about 100 nm / day and 1 nm / day, respectively. These rates could compromise the structural integrity of the proposed devices on the order of weeks or days.

[0008] Second, deploying and maintaining photophoretic devices in the mesosphere would be difficult. The most plausible deployment method involves raising the devices into the mesosphere via high-altitude balloons. Several high-altitude platforms, such as the Tata Institute of Fundamental Research (TIFR) balloons and NASA “Big 60” and “AESOP-Lite” balloons have been able to reach the stratopause, around 50 km [Kumar et al. (2021); Fairbrother (2021); Littleton (2024)]. Such campaigns are logistically intense and would require the photophoretic devices to begin levitating themselves at 50 km. The current best-performing device prototype could only begin levitating at 60 km [Schafer et al. (2024)].

[0009] Third, nighttime settling of millimeter-scale or larger devices is significant. For instance, a device with area density 1 g / m2would fall from any stratospheric or mesospheric altitude (> 20 km) to the troposphere (< 20 km altitudes) overnight if its size is greater than a few mm. This size dependency is explained by how, generally, smaller structures have much larger drag per unit area than large structures when settling at a given altitude. The drag force is highly dependent on the Reynolds number. Smaller structures generally have smaller Reynolds numbers, which in the case of atmospheric pressures, often mean that the drag on that structure is considered laminar (i.e. viscous or Stokes drag) as opposed to turbulent (i.e. Newtonian drag). The laminar drag per unit area on a structure is proportional to the smaller of the structure’s dimensions normal to the flow [Stokes (1856)], whereas turbulent drag per unit area does not depend on the structure’s size. Hence, for conventional plate-like structures, the drag force per unit area increases as the structure decreases in size. Effectively, the mesospheric or stratospheric flight lifetime of large structures is limited by settling.

[0010] To feasibly deploy photophoretic devices and ensure their longevity in the mesosphere, novel designs and materials are required. Embodiments of the present invention are directed to devices and methods that use AO-resistant materials, either as a core of the devices or a protective layer, to prevent material degradation in the mesosphere. Embodiments are also directed towards a novel design architecture for photophoretic devices that would enable sustained flight in the stratosphere, making deployment feasible, and that would limit overnight settling in the mesosphere and stratosphere.

[0011] Note that this application refers to a number of publications by author(s) and year of publication, and that due to recent publication dates certain publications are not to be considered as prior art vis-a-vis the present invention. Discussion of such publications herein is given for more complete background and is not to be construed as an admission that such publications are prior art for patentability determination purposes.BRIEF SUMMARY OF EMBODIMENTS OF THE PRESENT INVENTION

[0012] Embodiments of the present invention are directed to a photophoretically levitating apparatus for atmospheric flight, the apparatus comprising a first device comprising a plurality of substructures, each substructure comprising a characteristic size about equal to or about less than the mean free path of air molecules at the target flight altitude of the device. At least a portion of each substructure is preferably spaced from an adjacent substructure a distance that is greater than the mean free path of air molecules at the target flight altitude of the device. Each substructure preferably comprises oxidation-resistant material. The thickness of each substructure is preferably about a micron or less. The oxidation-resistant material preferably comprises any of alumina, boron nitride, silicon dioxide, diamond, and self-healing polymers, and any combination thereof. The oxidation-resistant material may be a coating, layer or sheet of or disposed on each substructure. The oxidation-resistant material may be disposed on at least a majority of the surface of each substructure. The oxidationresistant material may also be resistant to high levels of ultraviolet radiation. The plurality of substructures may form or be disposed on a rigid structure. The rigid structure may form a disc shape with at least a majority of the substructures being coplanar. The plurality of substructures may be oriented so as to impart an aligning torque on the first device during flight. The rigid structure may form a hemispherical shape. The plurality of substructures may be oriented so as to impart a force on the first device to cause it to rotate during flight. The rigid structure may form a propeller shape.

[0013] Embodiments of the present invention are directed to formations of such device. In another embodiment, the present invention comprises a second device, for example a second device comprising a plurality of substructures, each substructure comprising a characteristic size about equal to or about less than the mean free path of air molecules at the target flight altitude of the device. At least a portion of each substructure is preferably spaced from an adjacent substructure a distance that is about greater than the mean free path of air molecules at the target flight altitude of the device. The plurality of substructures preferably form or are disposed on a rigid structure. Each substructure preferably comprises oxidation-resistant material disposed on at least a majority of the surface of each substructure. A tether or plurality of tethers disposed on, between or in coordination with the first device and the second device preferably maintain the location of the second device within a distance of the first device. The tether may include a transceiver disposed on either of or both of the first device and second device, by which the tether is maintained by electromagnetic communication. The tether preferably comprises a width that is less than the width of each of the plurality of substructures, and the tethers comprise metal wire or polymer fiber. A payload may be disposed on or otherwise attached to the rigid structure, the payload comprising any of a sensor, GPS trackers, energy storage devices, solar cells, antennas, integrated circuits, microcomputers, LEDS, MEMs, communication device and combinations thereof.

[0014] In another embodiment, a photophoretically levitating apparatus for atmospheric flight includes a plurality of substructures, each substructure including a characteristic size about equal to or about less than the mean free path of air molecules at the target flight altitude of the apparatus. At least a portion of each substructure is preferably spaced from an adjacent substructure a distance that is greater than the mean free path of air molecules at the target flight altitude of the apparatus. The plurality of substructures preferably form or are disposed on a rigid structure, the rigid structure including tethers disposed on, between or in coordination with each substructure, the tethers capable of maintaining the location of each substructure within a distance of an adjacent substructure. Each substructure preferably comprises oxidation-resistant material disposed as a sheet or coating on at least a majority of the surface of each substructure, and each substructure is preferably formed of a plurality of sheets or coatings of the oxidation-resistant material, and the thickness of each substructure, including the oxidation-resistant material, is about a micron or less. A payload may be disposed on or otherwise attached to the rigid structure, wherein the payload comprises at least one selected from the group of: sensor, GPS trackers, energy storage devices, solar cells, antennas, integrated circuits, microcomputers, LEDS, MEMs, and communication device.

[0015] In another embodiment of the present invention, a photophoretically levitating apparatus for atmospheric flight includes a first device including a rigid structure including a plurality of linesegments. At least a portion or segment of the rigid structure is preferably shaped and sized to have a characteristic size about equal to or about less than the mean free path of air molecules at the target flight altitude of the device. At least a portion or segment of the rigid structure is preferably spaced from an adjacent portion or segment a distance that is greater than the mean free path of air molecules at the target flight altitude of the first device. The oxidation-resistant material is preferably disposed on the rigid structure. The line segments of the rigid structure may form a grid of coplanar intersecting line segments. The line segments may be curved such that the rigid structure comprises a concave shape.

[0016] Objects, advantages and novel features, and further scope of applicability of the present invention will be set forth in part in the detailed description to follow, taken in conjunction with the accompanying drawings, and in part will become apparent to those skilled in the art upon examination of the following, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations described.BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0017] The accompanying drawings, which are incorporated into and form a part of the specification, illustrate one or more embodiments of the present invention and, together with the description, serve to explain the principles of the invention. The drawings are only for the purpose of illustrating one or more embodiments of the invention and are not to be construed as limiting the invention. In the drawings:

[0018] Fig. 1 is a schematic illustration of a disk-shaped structure capable of levitation by Aa photophoresis as traditionally known;

[0019] Fig. 2 is a schematic illustration of a disk-shaped structure capable of levitation by AT photophoresis as traditionally known;

[0020] Fig. 3 is a graph of area lofting force relative to altitude at peak daytime as generated by a thin disk structure with radius 10 pm, Aa =0.3, solar-absorptivity of 1 , and IR-emissivity of 0.01 ;

[0021] Fig. 4 is a schematic illustration showing a perspective view of a disk-shaped Aa-based device coated with an oxidation-resistant coating on both of its top and bottom surfaces according to an embodiment of the present invention, along with a close-up cross-sectional view;

[0022] Fig. 5 is a schematic illustration showing a perspective view of a grid-based design of a device with characteristic size equal to the width of the gridlines according to an embodiment of the present invention, along with a close-up view from the top looking down at a portion of the top surface of such device, along with a close-up cross-sectional view;

[0023] Fig. 6 is an illustration of nine 2 cm x 2 cm grid-based devices that have varying values of grid spacing S and gridline width w, including one device shown with width w = 0;

[0024] Fig. 7 is a graph illustrating the photophoretic force per unit area (including both the grid and the open spaces between the gridlines) of a grid-based structure with fixed total size as a function of the ratio of gridline width w to grid spacing S;

[0025] Fig. 8 is a schematic illustration showing a perspective view of a substructure-based design of a device with characteristic size equal to the width of the substructures according to an embodiment of the present invention, along with a close-up view from the top looking down at a portion of the top surface of such device and a close-up cross-sectional view;

[0026] Fig. 9 is a schematic illustration showing a perspective view of a substructure-based design of a device with characteristic size equal to the radii of the disk-shaped substructures according to an embodiment of the present invention, along with a close-up view from the top looking down at a portion of the top surface of such device and a close-up cross-sectional view;

[0027] Figs. 10A and 10B are schematic illustrations showing a perspective view of a structure that is aligned horizontally with the equilibrium forces acting upon it during the daytime in Fig. 10A and during the nighttime in Fig. 10B;

[0028] Fig. 11 is a schematic illustration showing a perspective view of two device structures: (a) a disk-shaped structure without any spaces or perforations (like that of Figure 1 ) and (b) a gridbased design of a device (like that of Figure 5), both with the upward drag force acting on them as they settle during the nighttime;

[0029] Fig. 12 is a schematic illustration showing a perspective view of a structure that vertically layers multiple devices in a stacked orientation;

[0030] Fig. 13 is a schematic illustration showing a perspective view of a device that contains two parts: a part that generates the photophoretic force (in this case, a grid structure) and a supporting frame that provides structural rigidity to the device;

[0031] Fig. 14 is a schematic illustration showing a perspective view of a device with a hexagonal grid, which produces the same effect as a square grid; and

[0032] Fig. 15 is a schematic illustration showing a perspective view of a device of carrying an arbitrary payload, the payload attached to the base of the part of the device that provides structural rigidity to the device;

[0033] Fig. 16 is a schematic illustration showing a perspective view of a curved device, which can passively align itself horizontally when its attitude is perturbed; and

[0034] Fig. 17 is a schematic illustration showing a perspective view of multiple devices that are virtually tethered together in a group, and where the individual devices maintain position and orientation by means of gravitational, magnetic, electric, or gyroscopic orientation.DETAILED DESCRIPTION OF THE INVENTION

[0035] Embodiments of the present invention employ photophoresis for levitation. Fig. 1 illustrates a disk-shaped device 10 that levitates by Aa photophoresis, which figure is provided in order to explain the basic principles of photophoresis. A higher accommodation coefficient a on bottom surface 12 of device 10 produces an upward force E on device 10. The Aa is produced by using different materials on the top 14 and bottom 12 of device 10. The characteristic size of device 10 is its radius r since in this example, device 10 is disk-shaped. As used in this application and the claims, the term “characteristic size” shall have the meaning described of that term in the Background section of this application, which in the case of the disk-shape described in this paragraph, happens to be its radius. Here and in other designs, one may consider the characteristic size of a device to be about equal to the mean free path of the surrounding gas at the pressure where the photophoretic force F is maximized. The characteristic size of a device depends on the device’s geometry.

[0036] Fig. 2 illustrates a disk-shaped device 20 that levitates by AT photophoresis. Fig. 2 is provided in order to explain the basic principles of photophoresis. A higher temperature T on the bottom of device 20 produces an upward force E on device 20. The AT can be produced by using different optical coatings on the top and bottom of device 20, and the core structural element can be made via atomic layer deposition of alumina or other ceramic. Holes 22 in top 14 and bottom 12 surfaces enhance the lofting force E by thermal transpiration flows at high pressure. The characteristic size of this device is its radius r.

[0037] The lofting force of devices such as those illustrated in Figs. 1 and 2 is a function of the altitude of the device. The graph of Fig. 3 shows the area lofting force as a function of altitude at peak daytime generated by a thin disk with radius 10 pm, Aa = 0.3, solar-absorptivity of 1 , and IR-emissivity of 0.01.The Materials of Device 100

[0038] Referring to Figs. 4-17, embodiments of the present invention are directed to device100. Device 100 comprises any material conducive to photophoretic levitation. As described in the Background and throughout this application, photophoretic levitation is primarily a result of the shape, size, orientation and particular dimensions of device 100 (its architecture), rather than the composition of the material itself. Forthat reason, the term “photophoretically active material”, when used in this specification and in the claims, shall not be interpreted to be a particular material, but simply refers to a material that forms or is included on or in device 100. Device 100 may comprise any material. While certain materials may be preferred to be employed in device 100, for example because such material is more appropriate for the manufacturing process, for the particular architecture of device 100 or for economic reasons, there is no such material that, by its chemical / compositional nature, is inherently “photophoretic”. Accordingly, any use of the term “photophoretically active material” or “photophoretic material” should not be interpreted to limit the scope of the invention to any particular material or type of material.

[0039] Embodiments of the present invention preferably comprise oxidation-resistant materials120. This prevents the problems discussed in the background above of material degradation by AO in the mesosphere, weaker oxidants like ozone in the stratosphere, and photodegradative mechanisms. Referring to Fig. 4 as an example, Aa-based levitating device 100, which in this example comprises a solid disk shape, is coated with an oxidation-resistant material 120 on both bottom surface 102 and top surface 104. Bottom surface 102 has been deposited in such a way that it has a higher accommodation coefficient than top surface 104.

[0040] The oxidation-resistant materials 120 used in the present invention include but are not limited to alumina / aluminum oxide, diamond, silicon dioxide, boron nitride, polymers containing functional groups with self-healing properties (e.g. fluorinated polymers), and polymers doped with self- healing nanoparticles such as titanium dioxide or silicon oxide, and any combination thereof. The oxidation-resistant material(s) 120 employed depend on the desired characteristics, commercial availability, the particular construction of Aa-based structure 100 and its particular application. In someembodiments, top surface 104 may comprise a different oxidation-resistant material than that disposed on bottom surface 102.

[0041] This application and the claims may refer to oxidation-resistant material 120 as a material distinctly from the photophoretically active material or the material that forms the rigid structure of device 100. However, oxidation-resistant material 120 may also be the same material as the photophoretically active material or the material that forms the rigid structure of device 100.Dimensions of Device 100

[0042] To attain Aa-based levitation, device 100 preferably comprises a plurality of thin sheets and / or coatings with total thickness of all the sheets or coatings together ranging from about tens of nm to about one mm. As used in this context in this application and the claims, the term “thickness” refers to the distance from the “bottom” to the “top” of a subject device, for example referring to Fig. 4, the distance as measured between the surface of bottom 102 to the surface of top 104 of device 100. As used in this application and claims, the terms “sheet” and “coat” may be used interchangeably. If one is viewing device 100 as it would levitate in operation, its radius would be generally and hypothetically directed normal to or horizontal relative to the direction of gravity. The “top” 104 would be that surface of device 100 furthest from the earth below it and its “bottom” 102 would be that surface of device 100 closest to earth below it. From that perspective, the “thickness” could also be referred to as the “height” or “vertical distance” of such device, for example device 100, as viewed in this manner.

[0043] Device 100 preferably comprises thin sheets having a dimension of at least tens of microns, but more preferably a dimension of about several millimeters to about several meters. The dimension referred to in this context refers to the distance from one end of the entire device 100 to its opposite other end (which for a disk device would be its diameter). Multi-layer combinations of these materials could attain the desired optical properties and / or substantial (on the order of 0.1) values of Aa. In some embodiments, the entirety of device 100 is formed of oxidation-resistant materials 120, that is, in such case, the photophoretically active material is also the oxidation-resistant material. In some embodiments, only certain components of the levitating structure is formed of oxidation-resistant materials, for example, as a coating, layer, particular sheets, embedded material etc. Preferably, at least a majority of device 100 is formed of oxidation-resistant materials when measured in terms of its physical dimensions, for example, that the oxidation-resistant material is disposed on a majority of the surface area of device 100. In some embodiments, each oxidation-resistant material 120 is deposited sequentially with a variety of techniques, including physical vapor deposition, chemical vapor deposition, thermal evaporation, spin-coating, and blade-coating.

[0044] To generate AT forces, including those enhanced by thermal transpiration that flows through or around device 100, a thermally insulating material 122 is preferably disposed on device 100 between its top 104 and bottom 102. This may be performed by atomic layer deposition (ALD) of aluminum oxide [Kim et al. (2023); Cortes et al. (2020)], but more AO-resistant materials such as silicon dioxide (ALD) could be deposited instead. Materials for which ALD is not an option can be used as a protective coating over existing architectures. For example, a mylar or aluminum oxide-based thin disk structure could be coated with a layer of CVD diamond or PVD platinum.Architectures of Device 100Devices 100 Comprising Grid-like Architectures

[0045] To enable photophoretic levitation of macroscopic payloads at various altitudes in a planetary atmosphere, embodiments of the present invention are directed to various architectures of the structure of device 100. To that end, device 100 may comprise grid 130, for example as illustrated in Figs. 5, 13, 15 and 16. Referring to Fig. 5, the width w of gridlines 132 is the characteristic size. In this particular example, width w of gridlines 132 preferably range from about 100nm to about 0.1 meters, depending on the desired altitude of levitation as explained herein. This device could be fabricated with existing nanofabrication methods, including but not limited to photolithography or laser cutting. Device 100 comprising grid 130 is well-suited for Aa photophoresis, but could be extended to AT photophoresis by introducing a thermally-insulating layer between top 104 and bottom 102 surfaces of device 100. This architecture takes advantage of the fact that photophoretic forces are maximized when the characteristic size of device 100 is about the same size as the mean free path A of the surrounding gas. The characteristic size need not be the macroscopic size of the entire structure. This structure can therefore levitate when the mean free path A of the surrounding air is much smaller than the macroscopic size of the entire device. Aa-based structures with characteristic sizes less than or approximately equal to A within a given range of altitudes will generate a constant, maximized Aa force per unit area within that range of altitudes due to the inverse relationship between altitude and conductive energy loss to the environment [Keith (2010)]. This fact explains why aerosols can stably levitate at a range of atmospheric altitudes, ranging from the stratosphere to the thermosphere [Cheremisin (2019)].

[0046] Referring to Fig. 5, spacing S between gridlines 132 is preferably much larger than A, such that gridlines 132 are always in the free-molecular or transition regimes when device 100 is levitating. The whole device 100 is preferably much larger than A, but because the spaces S between gridlines 132 are much larger than the widths w of gridlines 132, most of the horizontal area of device100 is open space. Provided that the spacing S between the gridlines is large enough, there may be no theoretical limit to the macroscopic size of device 100. Similarly, so long as the width w of gridlines 132 is small enough, device 100 may be levitated at any atmospheric altitude. Fig. 6 shows nine examples of devices 100 that have varying values of w and S. Fig. 7 predicts that for a given structure size, some value of w / S, likely w / S < 1 , will maximize the photophoretic force per unit area of the structure. Referring to Fig. 7, as w / S approaches infinity, the force per unit area is expected to approach that of a solid plate structure with no holes or perforations.

[0047] In an example of device 100 intended to levitate at an altitude of about 30 km, device100 comprises a grid-like structure 130 comprising gridlines 132 with width w of about 10 pm, about the mean free path at that altitude. The spacing between gridlines 132 is preferably much greater than this distance, but assuming it is about five times larger (50 pm) for example, device 100 is about 80% open space.Devices 100 Comprising Substructures

[0048] Device 100 may also comprise various substructures 142 tethered together. For example, Fig. 8 illustrates design 140 that comprises individually levitating substructures 142 tethered together by tether 144, to form device 100 with payload capacity equal to the sum of the individual substructures 142. In this example, substructures 142 comprise a square shape. Such substructures 142 can have any number shapes, including but not limited to polygonal shapes (including rectangles, squares, triangles), circular shapes, and any combination thereof. Preferably, tether 144 comprises a thin yet strong material, including but not limited to metal wire or polymer fiber. Substructures 142 preferably have a characteristic size less than or approximately equal to A at the desired levitation altitudes, but the spacing among them is much larger than A. The exact arrangement of the substructures is defined by tethers 144, which allows for intricate 2D or 3D designs which would, for instance, enhance the photophoretic lofting force by changing the direction of gas flows, assist in attitude adjustment, change the drag force on device 100, or actively reposition substructures 142 to enable dynamic sensing applications or communications. The values of substructure 142 width and spacing S shown could allow this device 100 to levitate at an altitude of about 30 km.

[0049] Fig. 9 illustrates another example of substructures 142 tethered together by tethers. In this example, substructures 142 comprise a solid disk shape with characteristic size equal to the radii of the disk-shaped substructures.

[0050] Tethers 144 that connect substructures 142 need not all be in the same or a single plane. For instance, the structure in Fig. 12 shows multiple layers of structures 100 tethered by tethers 144 in a 3D orientation, where the vertical spacing between layers of structures 100 is much larger than the mean free path of the gas.

[0051] As a matter of terminology, it should be noted that the term “substructure” (referring to substructures 142) and device 100 can be used interchangeably in some instances, for example when a series of devices 100 are tethered together as illustrated in Figs. 8, 9, and 12. In such case, each entire device 100 is technically also a substructure of the larger device.

[0052] Tethers among substructures 142 can be maintained virtually by communications among the substructures, for example as illustrated in Fig. 17. Communications may be performed with transceivers onboard each substructure, which direct the substructures to cluster together. However, the ideal spacing among adjacent substructures is always much greater than the mean free path. The orientation and position of each substructure is maintained gravitationally, magnetically, electrically, or gyroscopically with an additional weight, magnet, or gyroscope onboard each substructure. Both the communications and orientation components could be used on any of the designs from Figs. 1 , 2, 4-6, 7-16 and any of these designs could comprise the substructures of the virtually tethered cluster of Fig. 17.Additional Examples

[0053] The following examples are additional examples of implementations of what is described above.

[0054] In one embodiment of the present invention, device 100 intended to employ Aa photopheresis comprises a thin structure in which the majority of the structure is comprised of a highly AO-resistant material, including but not limited to: diamond, silicon dioxide, boron nitride, and self- healing polymer, and any combination thereof.

[0055] In another embodiment, device 100 intended to employ Aa photopheresis is formed such that its interior comprises a non-AO-resistant material that provides the desired mechanical or optical properties of the larger device, and the exterior of the device comprises a coating of AO-resistant material, including but not limited to: diamond, silicon dioxide, boron nitride, and self-healing polymer, and any combination thereof.

[0056] In both of the foregoing examples, the Aa between top 104 and bottom 102 surface of device 100 may be formed by one of the following processes: deposition of a material on one side with substantively higher surface roughness than the other side, or laser ablation of the surface to increase roughness, and any combination thereof.

[0057] In another example of the present invention, device 100 intended to employ AT-based photopheresis comprises two (potentially perforated) face sheets on the order of about 100 nm-thick separated by a thermally-insulated gap on the order of about 100 pm thick, and the face sheets are made of an oxidation resistant material, including but not limited to: diamond, silicon dioxide, boron nitride, and self-healing polymer, and any combination thereof.

[0058] In another example of device 100 comprising grid 130, the grid spacing s is much larger than the mean free path of the ambient gas at target flight altitudes, and the gridline width w is about the same or less than the mean free path at target flight altitudes. Target flight altitudes ranges from 0 km (sea level) to about 100 km, and the corresponding mean free paths at these altitudes range from about 100 nm to about 0.1 m.

[0059] In another example as illustrated in Fig. 8, device 100 comprises grid 130 and two or more regions of substructures 142 intended to employ Aa-based photopheresis tethered together with tethers 144 of wire, fiber, or other thin material. The smallest horizontal dimension of substructures 142 (perhaps describable as its “width”) is about the same or less than the mean free path of the ambient gas at the target flight altitude and the spacing among substructures is greater than the mean free path at the target flight altitude.

[0060] If device 100 has a grid-design, the grid pattern need not be square. For instance, Fig.14 shows a device with hexagonal grid elements, which has similar lofting characteristics as the device in Fig. 13, but with different material properties (e.g. bending stiffness and localized stresses).

[0061] The profile of the entire device need not be two-dimensional. For instance, the curved device shown in Fig. 16 has a grid design curved into the shape of a hemisphere, which would passively align itself horizontally when flying. Substructures (or panels) of the devices shown in Figs. 1 , 2, 4-6, 7- 16 can be bent, folded, or otherwise combined into any arbitrary three-dimensional design that benefits the flight characteristics.

[0062] Device 100 may comprise payload 200, including but not limited to atmospheric sensors (e.g. temperature, pressure, gas composition, radiometric sensors, wind speed anemometers),communications devices, GPS, and reflective elements. Fig. 15 shows a possible means of integrating an arbitrary payload with an arbitrary levitating device; namely, by tethering the payload to the base of the levitating portion of the device using wire, fiber, or other thin material.

[0063] Device 100, whether such comprises grid 130 or substructures 142, may also be configured in a three-dimensional (3D) arrangement to improve structural rigidity, attitude control, or total photophoretic force.

[0064] In another embodiment, device 100 comprises thin, photophoretically active material segments spaced apart by a distance greater than the mean free path at the target flight altitude. These segments, typically less than a micron thick, generate upward photophoretic forces through a differential absorption coefficient (Aa) between their top and bottom surfaces. The arrangement of segments can take any periodic pattern, with two preferred configurations: a grid-like structure with open spaces between the lines or tethered substructures separated by open spaces. The materials used are resistant to photooxidation, addressing challenges from ozone, atomic oxygen, and ultraviolet radiation in high altitudes. Candidate materials include alumina, silica, diamond, self-healing polymers, or composites with conformal coatings of these materials. The design also allows for attachment to a rigid frame for structural stability, enabling complex 3D shapes like hemispheres or propellers, which can enhance flight stability. Payloads, including sensors, GPS trackers, and communication devices, can be integrated into the structure for atmospheric data collection and other applications. The device comprises segments of photophoretically active material spaced apart by a defined distance, generally greater than the mean free path of air molecules at the intended flight altitude. Each segment is generally narrower than the mean free path and separated by open space, enabling photophoretic levitation. Segments are composed of thin films with thicknesses typically on the order of a micron or less. These segments generate upward photophoretic forces via a difference in accommodation coefficients (Aa) between their top and bottom surfaces. The pattern of segments to open space can be periodic and take any form, but two preferred configurations include: (1) grid-like patterns, where the gridlines are the photophoretically active material, and spaces between them are open; and (2) disjointed substructures, tethered together by a thin connecting material (e.g., wires or fibers) but separated by open spaces. The materials are designed to be resistant to photooxidation, ozone (stratosphere), atomic oxygen (mesosphere), and high levels of ultraviolet radiation. Candidate materials include alumina, silica, boron nitride, diamond, self-healing polymers, or conformally coated composites of these. The photophoretically active segments may attach to a rigid frame to maintain structural integrity.Frames need not be two-dimensional and may form arbitrarily-shaped 3D devices. Examples include:hemispherical shapes, which impart aligning torque during flight; propeller-like shapes, which enable rotation during flight, providing stability. An arbitrary payload can attach to either the levitating segments or the frame. Payloads may include: sensors (e.g., pressure, temperature, wind speed); GPS trackers, energy storage devices, solar cells, antennas, integrated circuits, microcomputers, LEDs, or MEMS; and components for collecting climate data or communicating with other devices, ground stations, deployment craft, or satellites.References

[0065] References to prior publications made herein are to the following references, none of which shall be construed as an admission that such renders the invention claims unpatentable:1 . Bargatin, I., Lu, Z. & Azadi, M. Systems and methods for photophoretic propulsion for flight. (2022). US20220380039A1 .2. Lu, Z., Aldan, G., Levin, D., Campbell, M. F. & Bargatin, I. Lightweight photophoretic flyers with germanium coatings as selective absorbers. Phys. Rev. Appl. 21 , 044019 (2024).3. Azadi, M. et al. Controlled levitation of nanostructured thin films for sun-powered nearspace flight. Sci. Adv. 7, eabel 127 (2021).4. Keith, D. W. Photophoretic levitation of engineered aerosols for geoengineering. Proc. Natl. Acad. Sci. U.S.A. 107, 16428-16431 (2010).5. Schafer, B. C., Kim, J., Vlassak, J. J. & Keith, D. W. 3D architectures and applications for photophoretically active devices. PPA 63 / 598,876 filed 1 1 / 14 / 2023.6. Celenza, T., Eskenazi, A. & Bargatin, L 3D photophoretic aircraft made from ultralight porous materials can carry kg-scale payloads in the mesosphere. Preprint at https: / / doi.org / 10.48550 / arXiv.2301 .04281 (2023).7. Schafer, B. C., Kim, J., Vlassak, J. J. & Keith, D. W. Analytical models forthe design of photophoretically levitating macroscopic sensors in the stratosphere. Preprint at https: / / arxiv.org / abs / 2209.08093 (2022).8. Schafer, B., Kim, J., Vlassak, J. & Keith, D. Photophoretically levitating macroscopic structures. WO Application PCT / US23 / 70703 filed 7 / 21 / 2023.9. Kim, J. et al. Ultralight and ultra-stiff nano-cardboard panels: Mechanical analysis, characterization, and design principles. Acta Mater. 248, 118782 (2023).10. Cortes, J. et al. Photophoretic Levitation of Macroscopic Nanocardboard Plates. Adv. Mater. 32, 1906878 (2020).11 . Schafer, B. C. Towards photophoretic levitation of macroscopic structures in nearspace. PhD Thesis, Harvard University (2024).12. Sharipov, F. & Schafer, B. C. Radiometric forces exerted on a perforated membrane. Phys. Fluids. 36, 117155 (2024).

[0066] Note that in the specification and claims, “about” or “approximately” means within twenty percent (20%) of the numerical amount cited.

[0067] Embodiments of the present invention can include every combination of features that are disclosed herein independently from each other. Although the invention has been described in detail with particular reference to the disclosed embodiments, other embodiments can achieve the sameresults. Variations and modifications of the present invention will be obvious to those skilled in the art and it is intended to cover in the appended claims all such modifications and equivalents. The entire disclosures of all references, applications, patents, and publications cited above are hereby incorporated by reference. Unless specifically stated as being “essential” above, none of the various components or the interrelationship thereof are essential to the operation of the invention. Rather, desirable results can be achieved by substituting various components and / or reconfiguration of their relationships with one another. The terms, “a”, “an”, “the”, and “said” mean “one or more” unless context explicitly dictates otherwise.

Claims

CLAIMSWe claim:

1. A photophoretically levitating apparatus for atmospheric flight, the apparatus comprising a first device comprising: a plurality of substructures, each substructure comprising a characteristic size about equal to or about less than the mean free path of air molecules at the target flight altitude of the device, wherein at least a portion of each substructure is spaced from an adjacent substructure a distance that is greater than the mean free path of air molecules at the target flight altitude of the device, and wherein each substructure comprises oxidation-resistant material.

2. The apparatus of claim 1 , wherein the thickness of each substructure is about a micron or less.

3. The apparatus of claim 1 , wherein the oxidation-resistant material comprises at least one material selected from the group of: alumina, boron nitride, silicon dioxide, diamond, and self-healing polymers.

4. The apparatus of claim 1 , wherein the oxidation-resistant material is a coating, layer or sheet of or disposed on each substructure.

5. The apparatus of claim 1 , wherein the oxidation-resistant material is disposed on at least a majority of the surface of each substructure.

6. The apparatus of claim 1 , wherein the oxidation-resistant material is also resistant to high levels of ultraviolet radiation.

7. The apparatus of claim 1 , wherein the plurality of substructures form or are disposed on a rigid structure.

8. The apparatus of claim 7, wherein the rigid structure forms a disc shape and at least a majority of the substructures are coplanar.

9. The apparatus of claim 7, wherein the plurality of substructures are oriented so as to impart an aligning torque on the first device during flight.

10. The apparatus of claim 7, wherein the rigid structure forms a hemispherical shape.

11. The apparatus of claim 7, wherein the plurality of substructures are oriented so as to impart a force on the first device to cause it to rotate during flight.

12. The apparatus of claim 7, wherein the rigid structure forms a propeller shape.

13. The apparatus of claim 1 , further comprising: a second device, the second device comprising: a plurality of substructures, each substructure comprising a characteristic size about equal to or about less than the mean free path of air molecules at the target flight altitude of the device, wherein at least a portion of each substructure is spaced from an adjacent substructure a distance that is about greater than the mean free path of air molecules at the target flight altitude of the device, wherein the plurality of substructures form or are disposed on a rigid structure, and wherein each substructure comprises oxidation-resistant material disposed on at least a majority of the surface of each substructure; and a tether disposed on, between or in coordination with the first device and the second device, the tether capable of maintaining the location of the second device within a distance of the first device.

13. The apparatus of claim 12, wherein the tether comprises a transceiver disposed on either of or both of the first device and second device, by which the tether is maintained by electromagnetic communication.

14. The apparatus of claim 12, wherein the tether comprises a width that is less than the width of each of the plurality of substructures, and the tethers comprise metal wire or polymer fiber.

15. The apparatus of claim 1 , further comprising a payload disposed on or otherwise attached to the rigid structure, wherein the payload comprises at least one selected from the group of: sensors, GPS trackers, energy storage devices, solar cells, antennas, integrated circuits, microcomputers, LEDS, MEMs, and communication devices.

16. A photophoretically levitating apparatus for atmospheric flight, the apparatus comprising:a plurality of substructures, each substructure comprising a characteristic size about equal to or about less than the mean free path of air molecules at the target flight altitude of the apparatus, wherein at least a portion of each substructure is spaced from an adjacent substructure a distance that is greater than the mean free path of air molecules at the target flight altitude of the apparatus, wherein the plurality of substructures form or are disposed on a rigid structure, the rigid structure comprising tethers disposed on, between or in coordination with each substructure, the tethers capable of maintaining the location of each substructure within a distance of an adjacent substructure, wherein each substructure comprises oxidation-resistant material disposed as a sheet or coating on at least a majority of the surface of each substructure, wherein each substructure is formed of a plurality of sheets or coatings of the oxidation-resistant material, and wherein the thickness of each substructure, including the oxidation-resistant material, is about a micron or less.

17. The apparatus of claim 16, further comprising a payload disposed on or otherwise attached to the rigid structure, wherein the payload comprises at least one selected from the group of: sensor, GPS trackers, energy storage devices, solar cells, antennas, integrated circuits, microcomputers, LEDS, MEMs, and communication device.

18. A photophoretically levitating apparatus for atmospheric flight, the apparatus comprising a first device comprising: a rigid structure comprising a plurality of line segments, at least a portion or segment of the rigid structure shaped and sized to have a characteristic size about equal to or about less than the mean free path of air molecules at the target flight altitude of the device, wherein at least a portion or segment of the rigid structure is spaced from an adjacent portion or segment a distance that is greater than the mean free path of air molecules at the target flight altitude of the first device; and oxidation-resistant material disposed on the rigid structure.

19. The apparatus of claim 18, wherein the line segments of the rigid structure form a grid of coplanar intersecting line segments.

20. The apparatus of claim 18, wherein the line segments are curved such that the rigid structure comprises a concave shape.

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