Adsorption-based atmospheric water harvesting device for arid climates

Water scarcity is a particularly severe challenge in arid and desert climates. While a substantial amount of water is present in the form of vapour in the atmosphere, harvesting this water by state-of-the-art dewing technology can be extremely energy intensive and impractical, particularly when the relative humidity (RH) is low (i.e., below ~40% RH). In contrast, atmospheric water generators that utilise sorbents enable capture of vapour at low RH conditions and can be driven by the abundant source of solar-thermal energy with higher efficiency. Here, we demonstrate an air-cooled sorbent-based atmospheric water harvesting device using the metal−organic framework (MOF)-801 [Zr6O4(OH)4(fumarate)6] operating in an exceptionally arid climate (10–40% RH) and sub-zero dew points (Tempe, Arizona, USA) with a thermal efficiency (solar input to water conversion) of ~14%. We predict that this device delivered over 0.25 L of water per kg of MOF for a single daily cycle.

Supplementary Figure 1 -Photo of experimental setup during night-time adsorption. The MOF layer with its acrylic frame was mounted into cover of an air-tight plastic storage container with the pyromark coated side up for night-time radiative cooling. A ~5 kg metal block was placed inside to secure the apparatus against wind damage. The sides of the air-tight container were modified to fit a fan (0.9 W; 12 VDC) and enable cross flow of ambient air (vapour source). Initially, the black absorber side was covered with aluminium foil to reach thermal equilibrium with the ambient. At the start of the adsorption experiment, the aluminium foil was removed and a temperature drop due to the passive radiative cooling was observed (

Supplementary Note 1: Theoretical modelling framework
A theoretical model based on mass and energy conservation was used to predict the adsorption-desorption dynamics and the extent of regeneration for MOF-801 during the solarassisted desorption process using the following governing equations 1-3 : Eqn (1) describes mass conservation of the vapour during diffusion and adsorption/desorption within the packed MOF layer. Here, , is the local vapour concentration (mol m -3 ), μ / is the average instantaneous rate of vapour adsorption/desorption, is the porosity, and v is the intercrystalline diffusivity of vapour (m 2 s -1 ). The vapour concentration (mol m -3 ) can be expressed from the ideal gas law, = −1 −1 , where , , and denote the pressure (Pa), universal gas constant (J mol -1 K -1 ), and temperature (K). The effective vapour intercrystalline diffusivity, v , in an air-vapour mixture with consideration of both Knudsen and molecular diffusions in tortuous porous media can be estimated as [3][4][5] where vap and K,vap are vapour molecular diffusivity in air and Knudsen diffusivity of vapour, respectively. In Eqns (1) and (2), μ is the vapour concentration within an adsorbent crystal, and the average instantaneous rate of adsorption/desorption, μ / , can be approximated with the linear driving force model [1][2][3]6 .
In Eqn (4), μ , represents the diffusivity of vapour inside an adsorbent crystal (intracrystalline), c is adsorbent crystal radius (m), and eq is the equilibrium vapour concentration corresponding to instantaneous local temperature and vapour pressure. c and μ were characterised experimentally, and eq can be estimated from a linear interpolation of the adsorption isotherms (Supplementary Eqn (2) represents energy conservation within the MOF layer. Here, P represents the average heat capacity (J m -3 K -1 ), is the thermal conductivity (W m -1 K -1 ), and ℎ is the enthalpy of adsorption (J mol -1 ) for MOF-801 and water (~55 kJ mol -1 ), 7 . The effective thermophysical properties were evaluated to include the contributions from the metallic copper foam (~3 W m -1 K -1 , porosity of ~0.95), MOF-801 (specific heat capacity of 760 J kg -1 K -1 , 3 ), and the adsorbed water (assumed to be in a liquid state). In Eqn (2), the advection term is neglected due to the high effective thermal conductivity of the MOF layer owing to the metallic binder (copper foam).
During the solar-assisted desorption, desorbed vapour is transported and condensed via diffusion in air. For the orientation of the device described in Figure 1 a, diffusional vapour transport between the MOF layer and the condenser can be approximated using Fick's law of diffusion where represents the spatial coordinate:

Supplementary Note 2: Packing density and estimation of intercrystalline diffusivities
The effective intercrystalline diffusion is a function of spacing between the packed adsorbent particles and temperature. The characteristic void size of a random packing of spherical particles of uniform size can be estimated using a probability distribution 1,3,8 , on the basis of its average packing porosity ( ) and the porosity corresponding to the maximum packing density of hexagonally packed spheres ( HCP ) as:

HCP HCP
HCP HCP The average porosity ( ) was calculated from the measured MOF layer density ( layer ) and the estimated particle density ( p ) of the activated MOF-801 (1400± 20 kg m -3 ) using Eqn (7). The porosity of the MOF-801 layer is determined to be 0.67.
The characteristic void size ( p ) based on this distribution can be estimated as, = 2 c avg , where c is the MOF crystal radius, and avg is defined as: The average crystal diameter of MOF-801 (~1 μm) was characterised using a scanning electron microscope (6010LA SEM, JEOL), as shown in Supplementary Figure 4, and assumed uniform for the estimation of the void size.
The effective intercrystalline diffusivity can be computed using Eqn (3), where the Knudsen diffusivity is K,vap = ( p /3)√8 / , and the p is ~0.34 μm for the porosity of 0.67 and uniform crystal diameter of 1 μm. The diffusion coefficient of vapour in air at atmospheric pressure as a function of temperature can be obtained using the following relation 4 ,

Supplementary Note 3: Adsorption isotherms and estimation of intracrystalline diffusivities of MOF-801
Vapour adsorption isotherms of MOF-801 were characterised using an adsorption analyser (Q5000 SA, TA instruments) at 15, 25, 45, 65, and 85°C ( Supplementary Figure 6 a). The adsorption isotherm at 105°C was predicted using the characteristic curve based on the 85°C isotherm, vapour uptake as a function of adsorption potential: = ln( sat / ). 9 The vapour adsorption isotherm of MOF-801 before and after water harvesting cycles is also shown in Supplementary Figure 6 b, indicating the hydrothermal stability of MOF-801.
Using the dynamic adsorption behaviour (i.e., rate of mass adsorbed as a function of time), intracrystalline vapour diffusivity of MOF-801 was estimated using the following relation 10 where we assume homogeneous pore structure, constant spherical adsorbent crystals of radius ( c ), and constant surface concentration and diffusivity ( μ ), where / is the fractional water uptake with = 0 at = 0 and = eq as ⟶ ∞ for a sufficiently small pressure and uptake step. The effective intracrystalline (Fickian) diffusivity of MOF-801 at 25 and 65°C were estimated by fitting Eqn (10) with the experimental measurements, as shown Supplementary Figure 6 c and d, respectively. For the macroscopic modelling framework outlined, it is essential to define a characteristic intracrystalline diffusivity 3 , therefore, constant intracrystalline diffusivities at 25°C or 65°C (25% RH) were used for the theoretical prediction.

Supplementary Note 4: Optimisation of MOF layer
To enable sufficient vapour diffusion kinetics along with reasonably high water production, findings from our recent study 3 suggests that the optimum packing porosity for the MOF-801 based water harvesting device is ~0.7. Using the theoretical framework presented and characterised properties, adsorption-desorption dynamics for MOF-801 were simulated, as shown in Supplementary Figure 7, and used as a guideline for selecting the optimum MOF layer thickness.
Supplementary Figure 7 -Adsorption-desorption dynamics of MOF-801 in ambient air at 30% RH. Predicted adsorption-desorption dynamics with a packing porosity of 0.67, desorption heat flux of 1 kW m -2 , natural convective heat transfer coefficient of 10 W m -2 K -1 , ambient temperature of 25°C, and thicknesses of 1, 3, and 5 mm. MOF-801 is initially equilibrated at 30% RH (25°C), and the partial vapour pressure rapidly increased from 30% RH to 100% RH (at 25°C) for condensation/water harvesting at 25°C with a desorption heat flux of 1 kW m -2 . Durations of solar exposure for 1, 3, and 5 mm thick MOF layer are 0.8, 2.1, and 4 hours, respectively. After desorption, solar exposure is stopped and the surrounding RH reverted to 30% RH for water adsorption from air. The temperature profile of a 5 mm thick MOF layer is also shown. Based on the predicted performance for the porosity of 0.67, the MOF layer thickness should be ~3 mm to enable complete saturation under the limited time window for adsorption (approximately under 8 hours in 20-40% RH environment). For simplicity, constant intracrystalline diffusion coefficient of 3E-17 m 2 s -1 is used for the simulation (Supplementary Figure 6 c) and sufficiently fast air freestream velocity is assumed to keep the RH of 30% at the MOF layer.

Supplementary Note 5: Water harvesting cyclesexperiments and predictions
Using the theoretical framework outlined and characterised properties, computational simulations were carried out using COMSOL Multiphysics to evaluate the extent of regeneration during the solar-assisted water harvesting (Supplementary Figure 9 and Supplementary Figure 10). Temperature (MOF layer, environmental, dew point, and condenser) and solar flux profiles, and photos of condensed droplets of the water harvesting (adsorption-desorption) cycles for the cycle numbers 1, 3, and 4 are shown in Supplementary Figure 8. Note that cycles 1 to 3 were carried out under global horizontal irradiance (GHI), and cycles 4 and 5 were carried out with 1.8x optical concentration with direct normal irradiance (DNI). For the cycle 4 and 5, due to buoyancy-assisted condensation with tilting of the stage, the regeneration was significantly faster than the predictions as evident in the change in temperature slope shown in Supplementary Figure 10 after ~45 minutes of desorption. The thermal efficiency of the water harvesting cycle is defined as where water , ℎ fg , and solar are predicted amount of harvested water, latent heat, and input solar energy, respectively. For the non-concentrated cycle number 2, thermal is predicted to be ~3% (with GHI) and for the concentrated cycle number 5, thermal is predicted to be ~14% (with GNI times optical concentration of 1.8x). The efficiency for the concentrated cycle was evaluated on the basis of the time at which a change in the slope of the MOF temperature was observed. Despite the near complete desorption, at the time of the slope change, the simulation predicts ~0.1 kg kg -1 of residual uptake (Supplementary Figure 10). This is due to fact that the simulation does not take into account the enhanced vapour transport due to buoyancy. Furthermore, the enhanced rate of desorption driven by the enhanced vapour transport (lower interface vapour pressure) is evident from the lower MOF layer temperature observed in comparison to the simulations. This can also be qualitatively deduced from the significantly greater amount of water condensation on the viewport compared to the non-concentrated cycles.

Supplementary Note 6: Water quality analysis
Results shown in Supplementary Figure 12 indicate that zirconium concentration in both the collected and control water was found to be indistinguishable and less than 1 ppb (part per billion), indicating that the metal ions (Zr) from MOF-801 did not leach the harvested water. The largest difference in composition was found in concentrations of iron and copper (which are both absent in MOF-801 compound) due to oxidation reactions occurring during the cycling experiments. While the concentration of iron (~3 ppb) in the harvested water was negligible, the concentration of copper (~2.6 ppm) can be eliminated through material choices. Copper was chosen in this study for its high thermal conductivity and ease of machinability (i.e., milling and fabrication of chambers), which enabled an isothermal condenser. In a practical system, we envision the use of galvanized steel as a candidate material for the condenser and thermal binder. The FT-IR spectra indicated that signature of organic linkers (fumaric acid) was absent.

Supplementary Note 7: Thermal analysis for passive operation
Our proposed approach can harvest water solely based on solar-thermal energy without any additional input of electrical energy (i.e., in a passive manner) for remote/arid climates. In this section, we present thermal analysis which shows that complete passive solar-thermal operation is realistic without any additional input of energy 3 . During day-time operation, the dissipation of heat from the condenser to the ambient can also be managed by passive means of buoyant convection and the natural flow of air. Though, it is a common practice to assume ambient temperature condensers for thermodynamic analysis, we show a simple analysis to indicate that passive operation is possible. We start by developing an energy balance during the steady-state operation which can be expressed as dissipation condensation gain Q Q Q  (12) where ̇d issipation is the rate of heat dissipation from a finned heatsink to the ambient, ̇c ondensation is the rate of heat released during the condensation of water, and ̇g ain is the rate of heat addition from the MOF layer to the condenser. Eqn (12) can be expressed as dissipation heatsink condenser ambient water fg gain condenser MOF condenser In Eqn (13), ℎ, , and are the heat transfer coefficient in W m -2 K -1 , heat transfer area in m 2 , and temperature, respectively. ̇w ater is the rate of condensation. Here, we assume an equal area of the MOF layer and condenser. In order to estimate the required heat transfer coefficient (ℎ dissipation ) to enable passive operation, we assume a reasonable area ratio ( heatsink / condenser ) of 20, 11 , and a temperature difference of 5 K between the condenser and the ambient. ̇ is estimated based on complete desorption in 1 hour (~1E-4 kg m -2 s -1 or ~0.36 L m -2 hour -1 ). Based on the experimentally measured temperatures shown in Figure 3b, for MOF = 100°C, ambient = 35°C and ℎ gain = 10 W m -2 K -1 , condenser can be maintained at 40°C with an ℎ dissipation of only ~10 W m -2 K -1 . This confirms that passive operation is achievable with buoyant convection and the naturally occurring flow of air.