3D architectures and applications for macroscopic photophoretically active devices

Abstract

A double-membrane structure includes a pair of membrane layers. At least a portion of each membrane layer has a curved profile; and a gap is defined therebetween the membrane layers. Hollow ligaments extend between the membrane layers across the gap, and each hollow ligament defines a channel open for fluid flow therethrough. The membrane layers each also define holes, some of which are respectively aligned with the channels defined by the hollow ligaments.

Description

[0001] 3D ARCHITECTURES AND APPLICATIONS FOR MACROSCOPIC PHOTOPHORETICALLY ACTIVE DEVICES

[0002] GOVERNMENT SUPPORT

[0003] This invention was made with US government support under 2011754 and 2025158 awarded by the National Science Foundation (NSF). The US government has certain rights in the invention.

[0004] BACKGROUND

[0005] The discussion of the background state of the art, below, may reflect hindsight gained from the disclosed invention(s); and these characterizations are not necessarily admitted to be prior art.

[0006] Photophoresis is a phenomenon where an object immersed in a rarefied gas is heated by a light source, creating gas flows around the object that impart a force to the object. Inspired by naturally occurring aerosol layers in the stratosphere and mesosphere, photophoresis has been proposed as a propulsion mechanism for lofting lightweight engineered structures in the upper atmosphere. Structures can use one of following two kinds of photophoresis to create an upward force when illuminated by sunlight: (1) Act photophoresis (FIG. 1), where a difference in the normal energy accommodation coefficient, a (herein referred to as just the "accommodation coefficient"), between opposing sides of the structure (top and bottom sides 50 and 52) creates a higher transfer of momentum to the side facing downwards from the surrounding gas; and (2) AT photophoresis (FIG. 2), where a difference in the temperature, T, between opposing sides of the structure also creates a higher transfer of momentum to the side facing downwards from the surrounding gas. In either case, the difference in the accommodation coefficient, a, or T is established by the material and optical properties of the structure. Specifically with respect to AT photophoresis, a flow of gas around the structure towards its warm side, called thermal transpiration or thermal creep (FIG. 3), has been shown to amplify the total lofting force on a structure at high pressure, especially if the structure is perforated with holes 20 such that the gas can flow through these perforations.

[0007] Recently, we described advanced designs of photophoretic structures [PCT Pub. App. No. WO 2024 / 020544 Ai and Schafer, B. et al., "Analytical Models for the Design of Photophoretically Levitating Macroscopic Sensors in the Stratosphere," arXiv 2209.08093 (26 November 2022)]. These structures have been shown to photophoretically levitate at reduced pressures when illuminated by as little as one sun [Schafer, B. "Towards photophoretic levitation of macroscopic structures in nearspace," PhD Thesis, Harvard University (2024)]. These structures were inspired, in part, by the "nanocardboard" structures developed by Cortes, J. et al., "Photophoretic Levitation of Macroscopic Nanocardboard Plates," 32 Advanced Materials 1906878 (2020), which comprise hollow alumina shells 16 of the order of 1-cm wide, of the order of 100-pm thick, and with an areal density of roughly 1 g / m2that develop internal temperature gradients when illuminated. These gradients generate upward thrust via thermal transpiration, or thermal "creep" flow, through vertical channels defined within cylinders 13 spaced periodically throughout the structures. In other recent work, we modeled similar structures as two perforated membranes 17 / 18 and 16 / 18 (i.e., face sheets) spaced a set distance apart and connected occasionally by cylindrical ligaments 15 (also referred to as posts or walls) that form channels between the top and bottom face sheets (FIG. 4). A vertical cross-section of the panel, showing the preferential absorption of solar radiation on the bottom face sheet and the preferential emission of thermal-IR radiation on the top sheet, each caused by absorptive 18 and emissive coatings 17 on the sheets, respectively, is shown in FIG. 5. The top emissive coating 17 provides radiative cooling with a low solar emissivity, e, and a high longwave e. The emissive coating 17 can be formed of, e.g., alumina, polymer, glass, nanoparticles, or metamaterials and can be i-pm thick. That work computationally and experimentally showed that a plurality of freestanding perforations (i.e., holes) in the membranes relative to the number of ligaments efficiently achieved a compromise between strong lofting forces and structural performance.

[0008] These structures are some of the most rigid composite structures for their weight ever created, and their mechanical properties can be fine-tuned by changing their microscale dimensions [see Kim, J.-h., etal., "Ultralight and Ultra-stiff Nano-cardboard Panels: Mechanical Analysis, Characterization, and Design Principles," Acta Materialia 248 (2023) 118782]. Applications of these structures range from the aforementioned photophoretic levitation to lightweight functional nanomaterials. Despite their high strength-to-weight ratio, a general limitation of the double-membrane structures is their fragility under macroscopic forces. On the macroscale, the double-membrane structures are effectively two-dimensional (2D) sheets that are subject to buckling and fracture under their own weight as their planar size increases. One solution to this problem is to fabricate structures with three-dimensional profiles, which can increase their bending stiffness by up to a factor of h?, where h is the ratio of the height of the three-dimensional (3D) profile to the thickness of the 2D profile. Structures with 3D profiles are also able to distribute larger point loads across the entire structure than their 2D analogs before failing. Here, 3D architectures and their associated fabrication methods for double-membrane structures, primarily for use in photophoretic levitation, are presented. SUMMARY

[0009] Three-dimensional structures and applications for their use as macroscopic photophoretically active devices are described herein, where various implementations of the apparatus and methods may include some or all of the elements, features, and steps described below.

[0010] A photophoretically levitating macroscopic device comprises a doublemembrane structure. The double-membrane structure includes at least one top face sheet and at least one bottom face sheet, wherein the bottom sheet has greater solarradiation absorptivity than the top surface, wherein each sheet defines a pattern of holes through which gas can flow (i.e., each sheet is a perforated membrane), wherein the sheets are separated by a gap that defines an open volume extending across a plurality of holes in each sheet. Panels with the microscale design can be mounted in or on a support framework; and a device superstructure can be mounted to and can span the support framework to increase the rigidity of the entire device. The structure is photophoretically levitated by delivering the photophoretically levitating macroscopic device to a layer in an atmosphere about a celestial body (e.g., the earth). On the microscale structure, solar radiation is preferentially absorbed by the bottom sheet to heat the bottom sheet to a higher temperature than the top sheet. Heat is transferred from the bottom sheet to the surrounding atmospheric air to warm the air below the structure to a higher temperature than the air above the photophoretically active structure. Air flow from above the top sheet is generated via thermal transpiration through holes in the top sheet, into the gap, and out holes in the bottom sheet. The macroscopic structure is levitated in the atmospheric layer via upward force generated by the thermal transpiration.

[0011] The architectures discussed herein each primarily use panels of the doublemembrane design described above as the foundation for 3D devices. These devices need not be photophoretically active, as they can be useful for a range of nanoscale mechanics applications; however, the most readily apparent application perceived by the inventors is photophoretic levitation. The 3D architectures can be applied to double-membrane structures with any variation in microscale design, such as membranes with no freestanding holes (i.e., every opening in the top and bottom membranes is connected to vertical walls that form channels through the structure) or where the membranes are not perforated at all.

[0012] BRIEF DESCRIPTION OF THE DRAWINGS

[0013] FIG. 1 is a vertical cross-sectional diagram of Aa photophoresis causing an upward force on an isothermal structure that is warmer than the surrounding gas. The top surface 50 of the structure has a lower normal energy accommodation coefficient, a, than the bottom surface 52.

[0014] FIG. 2 is a vertical cross-sectional diagram of AT photophoresis causing an upward force on a structure that has a lower temperature on its top surface 50 than on its bottom surface 52.

[0015] FIG. 3 is a vertical cross-sectional diagram of thermal transpiration flows enhancing AT photophoretic forces at high pressures when perforations (holes) 20 are added to the structure from FIG. 2.

[0016] FIG. 4 is a diagram of a double-membrane structure 22 in which the top membrane layer 16’ and the bottom membrane layer 16” are separated by a hollow gap, which is maintained by vertical cylindrical ligaments 15. Perforations (holes) 20 are defined in the top and bottom membrane layers, some of which are concentric with the cylindrical ligaments.

[0017] FIG. 5 is a vertical cross-section of the double-membrane structure, showing the preferential absorption of solar radiation in the absorbing layer 18 coated on the bottom membrane layer 16” and the preferential emission of thermal-IR radiation on the top membrane layer 16’, which as coated with cooling layer 17.

[0018] FIG. 6 shows stages in a fabrication procedure for producing a photophoretically active structure 22 using a plastically deformable sacrificial template 12 serving as a template.

[0019] FIG. 7 shows a design for a channel 14 with a rectangular vertical cross-section that connects the top and bottom face sheets of a photophoretically active structure.

[0020] FIG. 8 shows a design for a channel 14 with a tapered vertical cross-section that connects the top and bottom membrane layers 16 of a photophoretically active structure. Tapered channels may generate stronger thermal transpiration flows than rectangular channels, and the tapered channels can be fabricated, e.g., using multiphoton lithography.

[0021] FIG. 9 shows a design for a channel 14 with a sinusoidal vertical cross-section that connects the top and bottom face sheets of a photophoretically active structure. Sinusoidal channels also may generate stronger thermal transpiration flows than rectangular channels, and sinusoidal channels also can be fabricated using multiphoton lithography.

[0022] FIG. 10 illustrates a fabrication procedure for producing a curved structure (step 6) using a flat sacrificial template 12 and a top surface coating 25 that contains tensile stress. When the sacrificial template 12 is removed, the tensile stress is released, which causes the entire structure to bend such that it becomes concave on its top surface and convex on its bottom surface. The same effect can be achieved by coating the bottom surface with a material with compressive stress. FIG. 11 shows a profile of a curved photophoretically active structure 22 fabricated using either multiphoton lithography or a plastically deformable template. The curvature varies radially to provide macroscopic stiffness and better support point loads on the structure.

[0023] FIG. 12 shows a profile of a photophoretically levitating macroscopic device 10 in the form of a propeller-shaped array of double-membrane structures 22 fabricated using multiphoton lithography. The array of double-membrane structures 22 with this profile would rotate when photophoretically levitated, providing passive attitude control.

[0024] FIG. 13 shows two sections 23 of a double-membrane structure 22 with circular holes and channels separated by a flexible “hinge” region 24 with rectangular channels in a flattened configuration during fabrication. The structure preferentially curves at the hinge region 24 parallel to the length of the rectangular channels.

[0025] FIG. 14 shows the double-membrane structure 22 of FIG. 7 with the two sections 23 separated by the flexible hinge region 24 with the hinge region 24 in a final curved configuration.

[0026] FIG. 15 shows a profile of a photophoretically levitating macroscopic device 10 as a 3D array of sections 23 of a photophoretically active structure 22 flattened during fabrication and fabricated using an origami approach.

[0027] FIG. 16 shows the photophoretically levitating macroscopic device 10 of FIG. 9 with the sections 23 of the double-membrane structure 22 folded together to form a final 3D profile, wherein the polygon-shaped double-membrane sections 23 are curved.

[0028] FIG. 17 shows another photophoretically levitating macroscopic device 10 with the sections 23 of the double-membrane structure 22 folded together to form a final 3D profile, wherein the polygon-shaped double-membrane sections 23 are flat and where the curves are only at the hinge regions at the intersections of the sections 23.

[0029] FIG. 18 shows double-membrane structures 22 that are fabricated as separate sections 23.

[0030] FIG. 19 shows a lightweight frame 54 to which the double-membrane sections 23 can be attached.

[0031] FIG. 20 shows a side view of a final configuration, where the sections 23 of the double-membrane structure 22 have been attached. The structure 22 is shown right- side-up.

[0032] FIG. 21 shows a side view of the same configuration as FIG. 20, where the structure is upside-down.

[0033] FIG. 22 shows a flattened double-membrane structure 22, including gridlines 26 that define confined open spaces 28 and that, when coated on the top and bottom sides with low and high thermal accommodation coefficient (TAM) materials, respectively, may levitate using both thermal transpiration and Act photophoresis.

[0034] FIG. 23 shows a photophoretically levitating device 10 carrying a payload 46 using metal wire that connects the payload 46 to the bottom of the device 10. The lengths of each wire connection 45 can be adjusted by microelectromechanical actuators to tilt the device 10. If tilted towards oncoming winds 56, the horizontal component of the photophoretic force, Fp, may counteract the drag on the device 10, allowing the device 10 to maintain its position over a fixed point on the ground.

[0035] FIG. 24 shows stacked double-membrane structures 22 with conductive material 30 and 32 on the horizontal layers. The alumina scaffold 16 is non-conductive, and a voltage from a voltage source 34 is applied to the alternating layers of conductive material 30 and 32.

[0036] FIG. 25 shows the photophoretically levitating device 10 of FIG. 23 that maintains a voltage (V) from a voltage source 34 between the top membrane 16’ and bottom membrane 16” of the microscale double-membrane structure 22. This voltage supplies a current (I) to the payload 46 through the metal wires 45 that bond to the double-membrane structure 22.

[0037] FIG. 26 shows a phased array of macroscopic photophoretically levitating devices 10. The spacing among devices determines the array’s communication frequency.

[0038] In the accompanying drawings, like reference characters refer to the same or similar parts throughout the different views. The drawings are not necessarily to scale; instead, an emphasis is placed on illustrating particular principles in the exemplifications discussed below. For any drawings that include text (words, reference characters, and / or numbers), alternative versions of the drawings without the text are to be understood as being part of this disclosure; and formal replacement drawings without such text may be substituted therefor.

[0039] DETAILED DESCRIPTION

[0040] The foregoing and other features and advantages of various aspects of the invention(s) will be apparent from the following more particular description of various concepts and specific implementations within the broader bounds of the invention(s). Various aspects of the subject matter introduced above and discussed in greater detail below may be implemented in any of numerous ways, as the subject matter is not limited to any particular manner of implementation. Examples of specific implementations and applications are provided primarily for illustrative purposes.

[0041] Unless otherwise herein defined, used, or characterized, terms that are used herein (including technical and scientific terms) are to be interpreted as having a meaning that is consistent with their accepted meaning in the context of the relevant art and are not to be interpreted in an idealized or overly formal sense unless expressly so defined herein. For example, if a particular composition is referenced, the composition may be substantially (though not perfectly) pure, as practical and imperfect realities may apply; e.g., the potential presence of at least trace impurities (e.g., at less than i or 2%) can be understood as being within the scope of the description. Likewise, if a particular shape is referenced, the shape is intended to include imperfect variations from ideal shapes, e.g., due to manufacturing tolerances. Percentages or concentrations expressed herein can be in terms of weight or volume.

[0042] Although the terms, first, second, third, etc., maybe used herein to describe various elements, these elements are not to be limited by these terms. These terms are simply used to distinguish one element from another. Thus, a first element, discussed below, could be termed a second element without departing from the teachings of the exemplary implementations.

[0043] Spatially relative terms, such as “above,” “below,” “left,” “right,” “in front,” “behind,” maybe used herein for ease of description to describe the relationship of one element to another element, as illustrated in the figures. It will be understood that the spatially relative terms, as well as the illustrated configurations, are intended to encompass different orientations of the apparatus in use or operation in addition to the orientations described herein and depicted in the figures. For example, if the apparatus in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary term, “above,” may encompass both an orientation of above and below. The apparatus maybe otherwise oriented e.g., rotated 90 degrees or at other orientations), and the spatially relative descriptors used herein should be interpreted accordingly. The term, “about,” can mean within ± 10% of the value recited. In addition, where a range of values is provided, each subrange and each individual value between the upper and lower ends of the range is contemplated and therefore disclosed.

[0044] Further still, in this disclosure, when an element is referred to as being “on,” “connected to,” “coupled to,” “in contact with,” etc., another element, it maybe directly on, connected to, coupled to, or in contact with the other element or intervening elements may be present unless otherwise specified.

[0045] Some of the terminology used herein is for the purpose of describing particular implementations and is not intended to limit more generic exemplifications of the invention. As used herein, singular forms, such as those introduced with the articles, “a” and “an,” are intended to include the plural forms as well, unless the context indicates otherwise. Additionally, the terms, “includes,” “including,” “comprises” and “comprising,” specify the presence of the stated elements or steps but do not preclude the presence or addition of one or more other elements or steps. Additionally, the various components identified herein can be provided in an assembled and finished form; or some or all of the components can be packaged together and marketed as a kit with instructions (e.g., in written, video, or audio form) for assembly and / or modification by a customer to produce a finished product.

[0046] Curved structures:

[0047] As shown in FIG. 6, a process for fabricating a curved double-membrane structure 22 can start with a plastically deformable template 12 (step o), and the plastically deformable template 12 is curved via bending— e.g., plastically deforming the plastically deformable template 12 by pressing it into or onto a curved cavity of a mold (step 1). Multiphoton lithography (where two distinct light beams can be directed from different locations into a pool of resin, wherein the resin polymerizes or otherwise solidifies where the two light beams intersect) can be used to create a curved template 12 without the need for bending, so this approach would start at step 1. Other forms of additive (3D) printing can also be used to produce the curved template 12. Channels 14 are etched through the curved template 12 using, e.g., deep-reactive ion etching (DRIE) (step 2). An alumina shell 16, which later forms the membrane layers 16’ and 16” is then deposited on the etched template 12 (step 3). Next, an absorption layer 18 is deposited, e.g., via sputtering or electron-beam evaporation, on the alumina shell 16 on the bottom of the template 12 (step 4). Top-layer holes 20 are then etched through the alumina shell 16 deposited on the template 12 (step 5). Bottom-layer holes 20 are then etched through the layers 16 and 18 deposited on the template 12 (step 6). Finally, the template 12 is etched away, e.g., using 02plasma (step 7), leaving the alumina shell 16, as membrane layers, and an absorption layer 18 thereon, wherein the channels 14 are defined as the interior volume within the hollow ligaments 15 extending between the membrane layers 16. The channels 14 can have an internal diameter smaller than the mean free path of the surrounding gas— e.g., less than 500 pm or 1 mm, in particular exemplifications, 1-100 pm.

[0048] The plastically deformable template 12 can be formed, e.g., of an epoxy-based photoresist and can be 20-500 pm (e.g., about 100 pm) thick. The atomic-layer deposited alumina layer 16 can be 100-nm thick with a thermal conductivity of 1.8 Wnr1K’1. The absorption layer 18 can be a 200-nm thick multilayer of chromium and aluminum, which is highly solar absorptive (eib= 0.9) and infrared transmissive (eib= 0) with an areal density of 0.5 g / m2.

[0049] As discussed in our previous work (PCT Pub. App. No. WO 2024 / 020544 Al), curved photophoretically levitating macroscopic devices can self-align when tilted away from their stable axis. This self-alignment is caused by a restoring force on the sides of the tilted structure 22 that are perturbed from their stable positions. Expanding on this idea, we propose the following general approaches to fabricate curved doublemembrane layers 22: (1) using a flat plastically deformable sacrificial template 12 on which is deposited the structure’s materials and then curving the template 12, (2) forming a curved template 12, e.g., via additive manufacturing and depositing the structure’s materials thereon, and (3) depositing structural materials with internal stresses that curve upon being freed from their substrate.

[0050] The first approach involves fabricating a plastically deformable sacrificial template 12 on which to deposit the membrane material (FIG. 6). The membranes can be made of any sufficiently rigid, conformally deposited material, such as alumina, to form a shell 16 via atomic layer deposition (ALD). The desired optical coatings 17 and 18 can then be deposited on either or both sides of the double-membrane structure 22, and the template 12 can then be etched away to leave the hollow alumina shell 16 (FIG. 6). In previous embodiments disclosed in PCT Pub. App. No. WO 2024 / 020544 Al, we described a structure 22 that has a plurality of freestanding holes 20 not connected to vertical cylindrical ligaments 15 between the top and bottom membrane layers 16, and the remaining holes 20 are concentric with hollow vertical ligaments 15 (i.e., aligned with the internal channels defined inside the hollow ligaments 15) between the membrane layers 16. In a curved double-membrane structure 22 made with a plastically deformable template 12, the locations of the holes 20 with the ligaments 15 can be made using photolithography or deep-reactive ion etching (DRIE), and the freestanding holes 20 can be made using reactive ion etching (RIE) and / or wet etching techniques on the surface layers’ optical coatings 17 and 18 and ALD material 16, before removing the sacrificial template 12.

[0051] The hollow ligaments 15 form a thermal bridge that reduces the temperature difference between the membrane layers 16, though the ligaments 15 are designed via their composition and structure to attempt to minimize their thermal conductivity. Consequently, the thermal transpiration through the internal channels 14 of the ligaments 15 will generally offer less lifting force than thermal transpiration through holes 20 in the membrane layers 16 that are remote from and not circumscribed by ligaments 15. Although the function of the ligaments 15 is primarily for structural support and membrane separation, thermal transpiration through the internal channels 14 of the ligaments 15 will nevertheless provide a degree of lifting force.

[0052] Candidate materials for plastically deformable templates 12 include but are not limited to polyimides, such as KAPTON polyimide films, epoxy-based photoresists such as those in the SU-8 family, and other thin, flexible polymer films. The SU-8 photoresists are easily etchable using photolithography but become resistant to most common solvents after hard-baking and are usually removed using oxygen plasma etching. To curve a plastically deformable template 12 into the desired 3D shape, a monomer can first be spin-coated on a flat substrate to the desired 2D thickness. The substrate can then be dissolved or etched, freeing the template 12. The template 12 can then be cut and molded to the desired shape before hard-baking to fully polymerize it. At the end of the fabrication procedure, the template 12 can be removed with oxygen plasma etching, which removes organic-based materials.

[0053] Another example of fabricating curved sacrificial templates 12 uses multiphoton lithography. This technique builds 3D structures with as low as 150-nm resolution by polymerizing layers of a monomer precursor in situ. Common multiphoton lithography monomer resins include SU-8 photoresists, acrylates, and other epoxy resins. Due to the resolution being larger than the typical alumina shell thickness of 100 nm, multiphoton lithography is best suited for fabricating arbitrarily shaped sacrificial templates 12 on which the alumina shell 16 is deposited, rather than the shell 16 itself, though this is also a viable method. In addition to creating curved macroscopic structures, multiphoton lithography can be used to create arbitrarily shaped ligaments 15 that connect the two membrane layers 16 in a double-membrane structure 22. Previously reported fabrication methods in this domain limit vertical posts and channels 14 to being perpendicular to the horizontal membrane layers 16. The doublemembrane structure’s mechanical properties and photophoretic lofting force, however, can be improved by using curved vertical connections. For instance, studies have demonstrated that channels 14 with tapered and sinusoidal cross sections (FIGS. 8 and 9, respectively) can produce stronger photophoretic flows via thermal transpiration than channels 14 with rectangular cross sections (FIG. 7). Curved-wall channels 14 and ligaments 15 can also prevent buckling in curved membrane layers 16 better than straight-wall channels 14 and ligaments 15 under the same bending load.

[0054] As an alternative to using a curved template 12 on which the double-membrane structure 22 is deposited, the membrane 16, itself, can be deposited on a flat template 12; but with sufficient internal material stresses such that the final structure, itself, curves when detached from the template 12 (FIG. 10). For instance, to create a doublemembrane structure 22 with a concave top surface, the double-membrane structure 22 can be fabricated on a flat sacrificial template 12; but before the template 12 is removed, the top membrane layer 16’ of the double-membrane structure 22 can be coated with a film 25 with internal tensile stress. When the template 12 is removed, the tensile stress in the film coating 25 of the double-membrane structure 22 can cause the entire panel to curve such that the top membrane layer 16’ is concave. The same effect can be achieved with a bottom membrane layer 16” and an absorptive coating 18 that have internal compressive stress.

[0055] Curved double-membrane structures 22 can be used to build much more rigid photophoretically levitating macroscopic devices 10 (see FIGS. 23 and 25) than their flat counterparts for the same payload weight 46. For instance, consider a curved double-membrane structure 22 that has a radially varying curvature (FIG. 11). When viewed right-side-up, the inner portion has a convex profile while the outer portion has a concave profile. By curving the profile radially, the photophoretically levitating macroscopic device 10 can have macroscopic bending stiffness up to 2 / 13 greater than a flat device, where h is the ratio of the height of the 3D profile to the thickness of the 2D profile. This and all other structures reported herein can be bonded to the support structures, e.g., the device superstructure 42 shown in FIG. 25, and as discussed in the previous application (i.e., PCT Pub. App. No. WO 2024 / 020544 Al) for added macroscopic rigidity.

[0056] As another example, a propeller-like design can be made using multiphoton lithography (see FIG. 12). The benefit of this device is that thermal transpiration air flowthrough double-membrane structures 22 that are configured and joined in an angled arrangement as “vanes” will cause the entire device to rotate and thus better maintain its attitude.

[0057] Origami double-membrane structures:

[0058] Macroscopic rigidity can also be improved by folding / curving conventional “two- dimensional” structures into 3D structures, much like origami. The end devices of this approach are effectively the same as those from the previous section, as the doublemembrane design can be curved or bent into any arbitrary configuration. Because the bending stiffness of double-membrane structures 22 can be fine-tuned by changing their design parameters, including the shape and size of the ligaments 15 connecting the top and bottom layers and positioned therebetween, the thickness of the top and bottom layers, and the material composition of the shell 16. One use of this approach has two rigid, flat sections 23 of a double-membrane structure 22 separated by a small “hinge” region 24 that can have high flexibility (as shown in FIGS. 13 and 14). The rigid sections 23 can define a hexagonal hole pattern, and the hinge region 24 can define a basketweave or offset rectangular hole pattern, where each pattern is discussed in Kim J.-h., et al. (referenced above). The hinge region 24 is configured to bend / curve via a hinge-like motion.

[0059] The thin hinge regions 24 allow for forming origami -like structure orientations when curved, allowing the creation of intricate 3D designs. These designs can be held in place by performing surface-activated bonding at the edges of the rigid regions that touch when curved. They can also be held in place by coating the touching regions with a material that has high-tensile strength, ALD alumina.

[0060] An exemplary useful origami photophoretically levitating macroscopic device 10 includes five 2D hexagonal double-membrane sections 23 surrounding a similar pentagonal double-membrane section 23, with each of these double-membrane sections 23 separated by the hinge regions 24, described above (FIGS. 15-17). The 2D doublemembrane sections 23 are typically about 1 cm in horizontal width (in the orientation shown in FIG. 15). The five hexagonal double-membrane sections 23 fold inward to form part of a truncated icosahedron, as shown in FIGS. 16, a pattern typically associated with soccer balls (i.e., “football” balls in most countries outside the US and Canada). A similar device 10 fabricated with flat double-membrane sections 23 is shown in FIG. 17, with the main difference here being that the curvature of the macroscale device results from the hinge region 24 and is not part of the photophoretically active sections 23, themselves, though it could be.

[0061] Lastly, 3D structures can be made by assembling standalone photophoretically active panels in the form of the double-membrane sections 23 into a larger device. For instance, to recreate the soccer-ball-shaped device from the previous paragraph, the six rigid double-membrane sections 23 can be fabricated independently as flat panels (FIG. 18), then hooked or bonded to either each other or to a frame 54 with the hemispherical shape (FIGS. 19-21). The thin frame 54 may make assembly easier and can be fabricated via multiphoton lithography.

[0062] Thermal transpiration and Aa photophoresis:

[0063] An unexplored method of increasing the lofting force on a macroscopic photophoretically levitating device 10 is to use both thermal transpiration flows and Aa photophoretic forces. Double-membrane structures 22 that levitate using either mechanism, but not both, have been demonstrated. Structures that levitate using Aa photophoretic forces are limited by the requirement that their smaller horizontal dimension must be smaller than the mean free path of the surrounding gas. To eschew this requirement, such photophoretically levitating macroscopic devices 10 can adopt a 2D grid-like shape, where the width of the gridlines 26 (of a double-membrane structure 22) is smaller than the mean free path of the gas, and the width of the open spaces 28 between the gridlines 26 is larger than the mean free path of the gas (see FIG. 22).

[0064] Macroscopic structures that have been shown to levitate using Aa photophoretic forces alone, such as the mylar disks of Azadi, et al. [Azadi, M., et al., "Controlled Photophoretic Levitation of Nanostructured Thin Films for Near-Space Flight," Science Advances eabeii27 (2021)], are typically a few cm wide and a few-100-nm thick, and are susceptible to buckling and crumpling under their own weight. Larger structures made of the same materials would be even less rigid. To loft structures of this size, a curved double-membrane design can be used to impart structural rigidity and amplify the total lofting force by generating thermal transpiration flows. Payload integration:

[0065] Payloads, including atmospheric sensors and telecommunications components, can be integrated onto / into photophoretically levitating devices for various applications. Because such payloads would likely weigh as much as if not more than the rest of the device, they can hang from the bottom of the photophoretically active portion to gravitationally align the entire device 10 (FIG. 23). Metal wires 45, such as 25-pm diameter aluminum or gold wire, can have linear densities on the order of 1-10 mg per meter and can support several grams before breaking, making them excellent candidates for tethering payloads to levitating structures. Depending on the materials used and their thicknesses, wire bonds can be made directly to the levitating structures, as in the case of aluminum wires to the alumina membranes 16 that we have observed in recent tests. Alternatively, metal bonding pads on the order of 100-nm thick and with planar dimensions at least twice as wide as the diameter of the wire can be deposited on the levitating device. Similar wire bonds can be made on the payload 46, or the payload 46 can be attached with a small drop of adhesive.

[0066] Stacked layers of double-membrane structures:

[0067] Stacked layers of double-membrane structures 22 can provide a new class of micro-lattice structures with applications such as lightweight energy-storage devices and multi-stage Knudsen pumps.

[0068] Photophoretically levitating devices and other ultra -lightweight aerial platforms have severe size, weight, and power (SWaP) requirements and can benefit from lightweight power-storage systems. Energy storage can be built into double-membrane structures 22 by coating the top and bottom surfaces of the double-membrane structures 22 with a conductive material 30 and 32, such as silver, gold, or indium tin oxide (ITO), and establishing a voltage difference between the two membrane layers 16 of the double-membrane structure 22 to thereby form a capacitor. If the ligaments 15 that separate the two sides remain non-conductive (as in the case of alumina), the structure effectively becomes a capacitor. The energy storage of the device 10 can be multiplied by stacking conductive double-membrane layers 30 and 32 of opposite voltage (positive layers and negative layers) on top of one another, creating a capacitor bank 36 (see FIG. 24). To maximize energy storage density, the stacked layers can be positioned as close as possible without permitting arcing.

[0069] If the conductive material of layers 30 and 32 is optically transparent, a capacitive structure can also photophoretically levitate. Because the temperature gradient within a levitating structure is sourced from its optical coatings, a transparent conductor, such as indium tin oxide, would not interfere with this mechanism. A stack of capacitive structures would not be suitable for levitation because the photophoretic lofting mechanism relies on unobstructed air conduction between one doublemembrane layer 16 and the ambient environment. Regardless, energy storage can easily be built into a macroscopic levitating device 10, either across many single-layer doublemembrane structures 22 or as a voltage difference between the two membrane layers 16’ and 16” (FIG. 25). This voltage can serve as supply power to the payload via electric current in the metal wires 45 that connect the double-membrane structure 22 and a payload package 46.

[0070] Without conductive layers 30 and 32, stacked double-membrane structures 22 can be used as lightweight Knudsen pumps. Knudsen pumps are also known as thermal transpiration pumps; and they use thermal transpiration, wherein gas molecules drift from a warm side to a cool side of the pump. The double-membrane design is effectively a single-stage Knudsen pump. To be used as a multi-stage Knudsen pump, multiple double-membrane structures 22 can be stacked on top of each other, and the stack of horizontal layers can have temperatures that alternate between hot and cold. These temperature gradients can be established using resistive heaters embedded in alternate horizontal layers.

[0071] Phased arrays:

[0072] We previously described a photophoretically levitating macroscopic device (see PCT Pub. App. No. WO 2024 / 020544 Al). A photophoretically levitating macroscopic device 10 of the present design is shown in FIG. 25. The device 10 is capable of lofting a transceiver that can communicate wirelessly to a remote receiver. The photophoretically levitating macroscopic device 10 includes an array of hexagonal double-membrane structures 22 mounted in a PAS support framework 40. A payload weight 46 is attached to a rigid shaft 44 and angled with a MEMS actuator 48 secured to a pyramidal device superstructure 42 to adjust the tilt angle of the array of photophoretically active structures 22. To make these photophoretically levitating macroscopic devices 10 and the structures 10 and 22 mentioned elsewhere in this disclosure more useful to the fields of wireless telecommunications and reconnaissance, multiple photophoretically levitating macroscopic devices 10 can be lofted in an array in the upper atmosphere, as shown in FIG. 26. If the spacing among the photophoretically levitating macroscopic devices 10 is consistent (e.g., >10 cm as shown in FIG. 26), one has a phased array, where the array, itself, acts as a highly directional antenna with higher bandwidth than the sum of the individual photophoretically levitating macroscopic devices 10. Changing the space between the photophoretically levitating macroscopic devices 10 changes the communication wavelength of the array. Using the navigation features disclosed in PCT Pub. App. No. WO 2024 / 020544 Al, the spacing among photophoretically levitating macroscopic devices 10 can be tuned with a resolution as low as the width of the photophoretically levitating macroscopic devices 10, about 10 cm. The phased array can, therefore, communicate at wavelengths above 10 cm (below a frequency of 3 GHz). Non-uniform spacing of the photophoretically levitating macroscopic devices 10 in the array can also be useful to the fields of augmented and virtual reality (AR / VR) by allowing multispectral sensing of nearby objects and / or the ground and using the data gathered by that sensing to alter the imagery and / or other sensory input generated as part of the augmented or virtual reality via an AR / VR device.

[0073] In one exemplification, two or more macroscopic photophoretically levitating devices 10, of either flat or curved PAS geometry, each include a communicating payload, and are arranged in a regularly spaced array so as to communicate as a phased array at a frequency tunable by the spacing among devices 10.

[0074] Additional examples consistent with the present teachings are set out in the following numbered clauses:

[0075] 1. A photophoretically levitating macroscopic device, including a double-membrane structure, comprising: a pair of membrane layers, including a first and second membrane layer, wherein a gap is defined between the membrane layers, wherein at least a portion of the membrane layers have a curved profile, and wherein an outer surface of the second membrane layers is coated with an absorption layer that is solar-radiation absorptive and that facilitates photophoretic levitation of the double-membrane structure, wherein the absorption layer has greater solarradiation absorptivity than the first and second membrane layers; and hollow ligaments extending between the first and second membrane layers across the gap, wherein each hollow ligament defines a channel open for fluid flow there through, and wherein the membrane layers each define holes, some of which are respectively aligned with the channels defined by the hollow ligaments.

[0076] 2. The photophoretically levitating macroscopic device of clause 1, further comprising a payload comprising a power source, a sensor, and a communication device.

[0077] 3. The photophoretically levitating macroscopic device of clause 1 or 2, wherein the first membrane layer is transparent to solar radiation.

[0078] 4. The photophoretically levitating macroscopic device of any of clauses 1-3, wherein the first membrane layer is coated with an emissive layer that has a greater thermal emissivity than the absorption layer. 5. The photophoretically levitating macroscopic device of any of clauses 1-4, wherein the photophoretically levitating macroscopic device includes a plurality of the double-membrane structures.

[0079] 6. The photophoretically levitating macroscopic device of any of clauses 1-5, wherein the double-membrane structure functions as a Knudsen pump.

[0080] 7. The photophoretically levitating macroscopic device of any of clauses 1-6, wherein the plurality of double-membrane structures are oriented in a propellerlike orientation such that, when levitating, the photophoretically levitating macroscopic device rotates.

[0081] 8. The photophoretically levitating macroscopic device of any of clauses 1-7, wherein the gap between the first and second membrane layers spans a range from 5 to 500 pm orthogonal to the orientation of the membrane layers.

[0082] 9. The photophoretically levitating macroscopic device of clause 8, wherein the first and second membrane layers have a greatest dimension in a range from 1 mm to 2 cm.

[0083] 10. The photophoretically levitating macroscopic device of any of clauses 1-19, wherein the first and second membrane layers comprise alumina.

[0084] 11. The photophoretically levitating macroscopic device of any of clauses 1-10, wherein the absorption layer comprises a composition selected from carbon nanotubes, graphene, carbon black, chromium, aluminum oxide, and a combination of a plurality of these compositions.

[0085] 12. The photophoretically levitating macroscopic device of any of clauses 1-11, wherein the first and second membrane layers each have a thickness of 20-200 nm.

[0086] 13. The photophoretically levitating macroscopic device of any of clauses 1-12, wherein the first and second membrane layers further define holes that are nonintersecting with any channels defined by the hollow ligaments.

[0087] 14. The photophoretically levitating macroscopic device of any of clauses 1-13, wherein the channels defined by the hollow ligaments have a diameter in a range from 1 to 100 pm measured parallel to the orientation of the first and second membrane layers.

[0088] 15. The photophoretically levitating macroscopic device of any of clauses 1-14, wherein the ligaments are non-cylindrical. 16. The photophoretically levitating macroscopic device of clause 15, wherein the ligaments have a shape selected from tapered, sinusoidal, or jagged.

[0089] 17. The photophoretically levitating macroscopic device of any of clauses 1-16, wherein the double-membrane structure serves as a capacitor.

[0090] 18. The photophoretically levitating macroscopic device of clause 17, further comprising a layer of electrically conductive material coated on the first and second membrane layers, wherein the ligaments are electrically non-conductive, and wherein the double-membrane structure is configured to maintain a substantial voltage difference between the first and second membrane layers.

[0091] 19. The photophoretically levitating macroscopic device of clause 18, wherein an outer surface of the second membrane layer includes an absorption layer that is solar-radiation absorptive and that facilitates photophoretic levitation of the double-membrane structure, wherein the membrane layer that includes the absorption layer has greater solar-radiation absorptivity than the other membrane layer, and wherein the double-membrane structure is incorporated into a photophoretically levitating macroscopic device, and wherein the electrically conductive material is transparent to visible and / or infrared radiation.

[0092] 20. The photophoretically levitating macroscopic device of any of clauses 19, wherein the electrically conductive material is indium tin oxide.

[0093] 21. The photophoretically levitating macroscopic device of clause 19, wherein the electrically conductive material has an electrical conductivity at least as great as the electrical conductivity of indium tin oxide.

[0094] 22. The photophoretically levitating macroscopic device of any of clauses 1-21, wherein the membrane layers have the curved profile at a hinge section central to the double-membrane structure, wherein the hinge section is configured to curve via a hinge-like motion.

[0095] 22. A method for forming a double-membrane structure of a photophoretically levitating macroscopic device, the method comprising: providing a curved template, wherein at least a portion of the curved template is curved; forming channels through the curved template; depositing a shell layer on the curved template, including along the formed channels; depositing a solar-radiation absorptive composition on the shell layer on a first side of the curved template; forming holes through the shell layer and through the solar-radiation adsorptive composition on the first side of the curved template and on a second side of the curved template opposite the first side; and removing the curved template while maintaining the shape of the shell layer and the solar-radiation adsorptive composition to form a doublemembrane structure with membrane layers joined via hollow ligaments.

[0096] 23. The method of clause 22, wherein the curved template is formed by plastically bending a plastically deformable template.

[0097] 24. The method of clause 22, wherein the curved template is formed via additive manufacturing.

[0098] 25. The method of any of clauses 22-24, wherein the curved template comprises a polyimide or an epoxy-based photoresist.

[0099] 26. The method of any of clauses 22-25, wherein the shell comprises alumina or silica.

[0100] 27. The method of any of clauses 22-26, wherein the solar-radiation absorptive composition is selected from carbon nanotubes, graphene, carbon black, chromium, aluminum oxide, and a combination of a plurality of these compositions.

[0101] 28. The method of any of clauses 22-27, wherein the curved template is removed via etching with oxygen plasma.

[0102] 29. The method of any of clauses 22-28, wherein the channels are formed via deep- reactive ion etching.

[0103] 30. The method of any of clauses 22-29, wherein the solar-radiation absorptive composition is deposited via at least one of the following: sputtering, physical vapor deposition, chemical vapor deposition, or electron beam evaporation.

[0104] 31. The method of any of clauses 22-30, wherein the holes are formed via at least one of the following: reactive ion etching, wet etching, ion beam milling, or laser cutting.

[0105] 32. A method for photophoretic levitation, comprising: exposing a photophoretically levitating macroscopic device of clause 1 to solar radiation and a surrounding gas; absorbing energy from the solar radiation in the adsorption layer; and utilizing transpiration and Act photophoretic forces to levitate the doublemembrane structure.

[0106] 33. The method of clause 32, wherein the entirety or regions of the doublemembrane structure have dimensions approximately equal to or smaller than the mean free path of the surrounding gas.

[0107] In describing implementations herein, specific terminology is used for the sake of clarity. For the purpose of description, specific terms are intended to at least include technical and functional equivalents that operate in a similar manner to accomplish a similar result. Additionally, in some instances where a particular implementation includes a plurality of system elements or method steps, those elements or steps maybe replaced with a single element or step. Likewise, a single element or step may be replaced with a plurality of elements or steps that serve the same purpose. Further, where parameters for various properties or other values are specified herein for implementations, those parameters or values can be adjusted up or down by i / iooth, i / 5Oth, 1 / 20*, 1 / 10*, 1 / 5*, i / 3rd, 1 / 2, 2 / 3*, 3 / 4*, 4 / 5*, 9 / ioth, 19 / 20*, 49 / 5Oth, 99 / 100*, etc. (or up by a factor of 1, 2, 3, 4, 5, 6, 8, 10, 20, 50, 100, etc.), or by rounded- off approximations thereof or within a range of the specified parameter up to or down to any of the variations specified above (e.g., for a specified parameter of 100 and a variation of 1 / 100th, the value of the parameter maybe in a range from 0.99 to 1.01), unless otherwise specified. Further still, where methods are recited and where steps / stages are recited in a particular order— with or without sequenced prefacing characters added for ease of reference— the steps / stages are not to be interpreted as being temporally limited to the order in which they are recited unless otherwise specified or implied by the terms and phrasing.

[0108] While this invention has been shown and described with references to particular implementations thereof, those skilled in the art will understand that various substitutions and alterations in form and details maybe made therein without departing from the scope of the invention. Further still, other aspects, functions, and advantages are also within the scope of the invention; and all implementations of the invention need not necessarily achieve all of the advantages or possess all of the characteristics described above. Additionally, steps, elements, and features discussed herein in connection with one implementation can likewise be used in conjunction with other implementations. The contents of references, including reference texts, journal articles, patents, patent applications, etc., cited throughout the text are hereby incorporated by reference in their entirety for all purposes; and all appropriate combinations of implementations, features, characterizations, and methods from these references and the present disclosure may be included in implementations of this invention. Still further, the components and steps identified in the Background section are integral to this disclosure and can be used in conjunction with or substituted for components and steps described elsewhere in the disclosure within the scope of the invention.

Claims

CLAIMSWhat is claimed is:

1. A photophoretically levitating macroscopic device, including a double-membrane structure, comprising: a pair of membrane layers, including a first and second membrane layer, wherein a gap is defined between the membrane layers, wherein at least a portion of the membrane layers have a curved profile, and wherein an outer surface of the second membrane layers is coated with an absorption layer that is solar-radiation absorptive and that facilitates photophoretic levitation of the double-membrane structure, wherein the absorption layer has greater solarradiation absorptivity than the first and second membrane layers; and hollow ligaments extending between the first and second membrane layers across the gap, wherein each hollow ligament defines a channel open for fluid flow there through, and wherein the membrane layers each define holes, some of which are respectively aligned with the channels defined by the hollow ligaments.

2. The photophoretically levitating macroscopic device of claim 1, further comprising a payload comprising a power source, a sensor, and a communication device.

3. The photophoretically levitating macroscopic device of claim 1, wherein the first membrane layer is transparent to solar radiation.

4. The photophoretically levitating macroscopic device of claim 1, wherein the first membrane layer is coated with an emissive layer that has a greater thermal emissivity than the absorption layer.

5. The photophoretically levitating macroscopic device of claim 1, wherein the photophoretically levitating macroscopic device includes a plurality of the double-membrane structures.

6. The photophoretically levitating macroscopic device of claim 1, wherein the double-membrane structure functions as a Knudsen pump.

7. The photophoretically levitating macroscopic device of claim 1, wherein the plurality of double-membrane structures are oriented in a propeller-likeorientation such that, when levitating, the photophoretically levitating macroscopic device rotates.

8. The photophoretically levitating macroscopic device of claim 1, wherein the gap between the first and second membrane layers spans a range from 5 to 500 pm orthogonal to the orientation of the membrane layers.

9. The photophoretically levitating macroscopic device of claim 8, wherein the first and second membrane layers have a greatest dimension in a range from 1 mm to 2 cm.

10. The photophoretically levitating macroscopic device of claim 1, wherein the first and second membrane layers comprise alumina.

11. The photophoretically levitating macroscopic device of claim 1, wherein the absorption layer comprises a composition selected from carbon nanotubes, graphene, carbon black, chromium, aluminum oxide, and a combination of a plurality of these compositions.

12. The photophoretically levitating macroscopic device of claim 1, wherein the first and second membrane layers each have a thickness of 20-200 nm.

13. The photophoretically levitating macroscopic device of claim 1, wherein the first and second membrane layers further define holes that are non-intersecting with any channels defined by the hollow ligaments.

14. The photophoretically levitating macroscopic device of claim 1, wherein the channels defined by the hollow ligaments have a diameter in a range from 1 to 100 pm measured parallel to the orientation of the first and second membrane layers.

15. The photophoretically levitating macroscopic device of claim 1, wherein the ligaments are non-cylindrical.

16. The photophoretically levitating macroscopic device of claim 15, wherein the ligaments have a shape selected from tapered, sinusoidal, or jagged.

17. The photophoretically levitating macroscopic device of claim 1, wherein the double-membrane structure serves as a capacitor.

18. The photophoretically levitating macroscopic device of claim 17, further comprising a layer of electrically conductive material coated on the first and second membrane layers, wherein the ligaments are electrically non-conductive, and wherein the double-membrane structure is configured to maintain a substantial voltage difference between the first and second membrane layers.

19. The photophoretically levitating macroscopic device of claim 18, wherein an outer surface of the second membrane layer includes an absorption layer that is solar-radiation absorptive and that facilitates photophoretic levitation of the double-membrane structure, wherein the membrane layer that includes the absorption layer has greater solar-radiation absorptivity than the other membrane layer, and wherein the double-membrane structure is incorporated into a photophoretically levitating macroscopic device, and wherein the electrically conductive material is transparent to visible and / or infrared radiation.

20. The photophoretically levitating macroscopic device of claim 19, wherein the electrically conductive material is indium tin oxide.

21. The photophoretically levitating macroscopic device of claim 19, wherein the electrically conductive material has an electrical conductivity at least as great as the electrical conductivity of indium tin oxide.

22. The photophoretically levitating macroscopic device of claim 1, wherein the membrane layers have the curved profile at a hinge section central to the doublemembrane structure, wherein the hinge section is configured to curve via a hinge-like motion.

22. A method for forming a double-membrane structure of a photophoretically levitating macroscopic device, the method comprising: providing a curved template, wherein at least a portion of the curved template is curved; forming channels through the curved template; depositing a shell layer on the curved template, including along the formed channels; depositing a solar-radiation absorptive composition on the shell layer on a first side of the curved template;forming holes through the shell layer and through the solar-radiation adsorptive composition on the first side of the curved template and on a second side of the curved template opposite the first side; and removing the curved template while maintaining the shape of the shell layer and the solar-radiation adsorptive composition to form a doublemembrane structure with membrane layers joined via hollow ligaments.

23. The method of claim 22, wherein the curved template is formed by plastically bending a plastically deformable template.

24. The method of claim 22, wherein the curved template is formed via additive manufacturing.

25. The method of claim 22, wherein the curved template comprises a polyimide or an epoxy-based photoresist.

26. The method of claim 22, wherein the shell comprises alumina or silica.

27. The method of claim 22, wherein the solar-radiation absorptive composition is selected from carbon nanotubes, graphene, carbon black, chromium, aluminum oxide, and a combination of a plurality of these compositions.

28. The method of claim 22, wherein the curved template is removed via etching with oxygen plasma.

29. The method of claim 22, wherein the channels are formed via deep-reactive ion etching.

30. The method of claim 22, wherein the solar-radiation absorptive composition is deposited via at least one of the following: sputtering, physical vapor deposition, chemical vapor deposition, or electron beam evaporation.

31. The method of claim 22, wherein the holes are formed via at least one of the following: reactive ion etching, wet etching, ion beam milling, or laser cutting.

32. A method for photophoretic levitation, comprising: exposing a photophoretically levitating macroscopic device of claim 1 to solar radiation and a surrounding gas; absorbing energy from the solar radiation in the adsorption layer; andutilizing transpiration and Act photophoretic forces to levitate the doublemembrane structure.

33. The method of claim 32, wherein the entirety or regions of the double-membrane structure have dimensions approximately equal to or smaller than the mean free path of the surrounding gas.

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