Benjamin C. Schafer

Lightweight nanofabricated structures could photophoretically loft payloads in near-space. Proposed structures range from microscale engineered aerosols¹, to centimetre-scale thin disks with variations in surface accommodation coefficients^2,3, to sandwich structures with nanoscale thickness^4,5 that might be extended to metre-scale width^6,7. Quantitative understanding of how structural and surface properties determine photophoretic lofting forces is necessary to develop a practical flying device. Here we focus on thermal transpiration as the most promising photophoretic mechanism for lofting large devices⁸ and present a hybrid analytical-numerical model of the lofting force on a structure that consists of two perforated membranes spaced a small distance apart. We identify optimal structural parameters, including device size, membrane perforation density and distribution of the vertical ligaments that connect the two membranes, each as a function of atmospheric altitude. Targeting these optimal parameters, we fabricate structures with a heterogeneous ligament distribution, which efficiently compromises between structural rigidity and photophoretic performance. We measure how lofting forces generated by these structures depend on pressure using gases with three different molecular weights. We observed photophoretic levitation of a 1-cm-wide structure at an air pressure of 26.7 Pa when illuminated by 750 W m^-2, about 55% the intensity of sunlight. Lastly, we describe the preliminary design of a 3-cm-radius device with 10-mg payload capacity at 75-km altitudes and discuss horizontal motion control, overnight settling, and applications in climate sensing, communications and Martian exploration.

The radiometric force exerted on a thin perforated membrane and the heat flux from the membrane to a surrounding gas are calculated by the direct simulation Monte Carlo method over wide ranges of the gas rarefaction and membrane porosity. Ab initio potentials are used to model the intermolecular collisions. We find that perforations increase the force several times in the viscous regime of flow but decrease the force in the free-molecular and transitional regimes. The influence of the accommodation coefficients is studied by applying the Cercignani–Lampis model. The effects of gas species, degree of non-equilibrium, and environment temperature are found to have relatively small effects on dimensionless quantities such that the reported results can be applied to wide ranges of these factors and, hence, to numerous practical situations such as the levitation of centimeter-scale membranes at upper atmospheric altitudes.

The photophoretic force exerted on an illuminated membrane vanishes when its size is much larger than the molecular mean-free-path. Perforations in the membrane can increase the force, but they make modeling the gas flow more difficult. In the present letter, a new model of gas interaction with a perforated surface is proposed. The direct simulation Monte Carlo method is used to calculate the flow-field and photophoretic force exerted on a perforated membrane, showing a significant increase in the force at high rarefaction parameters. This effect could be used to levitate membranes of a few centimeters in size at mesospheric altitudes.

Photophoretic forces could levitate thin 10 centimeter-scale structures in Earth's stratosphere indefinitely. We develop analytical models of the thermal transpiration force on a bilayer sandwich structure in the stratosphere. Lofting is maximized when the layers are separated by an air gap equal to the mean free path (MFP), when about half of the layers' surfaces consist of holes with radii < MFP, and when the top layer is solar-transmissive and infrared-emissive while the bottom layer is solar-absorptive and infrared-transmissive. We use the models to design a 10 cm diameter device with sufficient strength to withstand forces that might be encountered in transport, deployment, and flight. The device has a payload of about 285 mg at an altitude of 25 km; enough to support bidirectional radio communication at over 10 Mb/s and limited navigation. Such devices could be useful for atmospheric science or telecommunications on Earth and Mars. Structures a few times larger might have payloads of a few grams.

We introduce a class of ultra-light and ultra-stiff sandwich panels designed for use in photophoretic levitation applications and investigate their mechanical behavior using both computational analyses and micro-mechanical testing. The sandwich panels consist of two face sheets connected with a core that consists of hollow cylindrical ligaments arranged in a honeycomb-based hexagonal pattern. Computational modeling shows that the panels have superior bending stiffness and buckling resistance compared to similar panels with a basketweave core, and that their behavior is well described by Uflyand-Mindlin plate theory. By optimizing the ratio of the face sheet thickness to the ligament wall thickness, panels maybe obtained that have a bending stiffness that is more than five orders of magnitude larger than that of a solid plate with the same area density. Using a scalable microfabrication process, we demonstrate that panels as large as 3x3 cm^2 with a density of 20 kg/m^3 can be made in a few hours. Micro-mechanical testing of the panels is performed by deflecting microfabricated cantilevered panels using a nanoindenter. The experimentally measured bending stiffness of the cantilevered panels is in very good agreement with the computational results, demonstrating exquisite control over the dimensions, form, and properties of the microfabricated panels.

N-Substituted pyridinium salts constitute one of the most valuable reagent classes in organic synthesis, due to their versatility and ease of use. Herein we report a preliminary synthesis and detailed structural analysis of several N-(1-ethoxyvinyl)pyridinium triflates, an unusual class of pyridinium salts with potentially broad use as a reagent in organic synthesis. Treatment of pyridines with trifluoromethane sulfonic acid and ethoxyacetylene generates stable, isolable adducts which have been extensively characterized, due to their novelty. Three-dimensional structural stability is perpetuated by an array of C–H•••O hydrogen bonds involving oxygen atoms from the –SO₃ groups of the triflate anion, and hydrogen atoms from the aromatic ring and vinyl group of the pyridinium cation. Predictions from density functional theory calculations of the energy landscape for rotation about the exocyclic C–N bond of 2-chloro-1-(1-ethoxyvinyl)pyridine-1-ium trifluoromethanesulfonate (7) and 1-(1-ethoxyvinyl)pyridine-1-ium trifluoromethanesulfonate (16) are also reported. Notably, the predicted global energy minimum of 7 was nearly identical to that found within the crystal structure.