Unravelling the Water Adsorption Mechanism in Hierarchical MOFs: Insights from In Situ Positron Annihilation Lifetime Studies

Atmospheric water harvesting with metal–organic frameworks (MOFs) is a new technology providing a clean, long-term water supply in arid areas. In-situ positron annihilation lifetime spectroscopy (PALS) is proposed as a valid methodology for the mechanistic understanding of water sorption in MOFs and the selection of prospective candidates for desired applications. DUT-67-Zr and DUT-67-Hf frameworks are used as model systems for method validation because of their hierarchical pore structure, high adsorption capacity, and chemical stability. Both frameworks are characterized using complementary techniques, such as nitrogen (77 K) and water vapor (298 K) physisorption, SEM, and PXRD. DUT-67-Zr and DUT-67-Hf are investigated by PALS upon exposure to humidity for the first time, demonstrating the stepwise pore filling mechanism by water molecules for both MOFs. In addition to exploring the potential of PALS as a tool for probing MOFs during in situ water loading, this work offers perspectives on the design and use of MOFs for water harvesting.

two 511 keV gamma-photons that are emitted when the wavefunctions of positrons and electrons overlap.Positron annihilation lifetime is a measure of the time elapsed since positron implantation until its annihilation with one electron.The elapsed time is governed by the probability of how often a positron meets an electron (electron density distribution) at the trapping site.
On one hand, free (unbound) positrons can annihilate with electrons from the bulk or from defects.Since this probability depends on the size of the defective site, the distinguishability between these traps (monovacancy, vacancy cluster) is based on the value of the positron lifetime.On the other hand, positrons can also bind with electrons in porous solids with free space > ~ 2 Å [2] and on inner pore walls while forming the so-called 'positronium (Ps)' atom before annihilation.Ps has two states that depend on the spin alignment of electron and positron; parapositronium (p-Ps) and ortho-positronium (o-Ps).p-Ps is a singlet state with antiparallel spins and it decays into two-511 keV photons with 0.125 ns lifetime in vacuum.While o-Ps is a triplet state with parallel spins and annihilates into three photons with an intrinsic lifetime of 142 ns in vacuum.The short-lived and self-annihilating p-Ps is weakly affected by the surrounding media [3] hence it cannot be used for measuring the size of free volumes (pores).It is common in the literature to fix τ 1 to 125 ps (theoretical lifetime of p-Ps) in order to minimize the uncertainties associated with the pore-related components.However, this approach may be flawed as τ 1 could also include contributions from the spaces between the chains in the organic linkers, which might depend on humidity level.Due to the limited timing resolution (240 ps), distinguishing between the very similar lifetimes of p-Ps and unbound positrons between the chains is not feasible.As a result, we made the decision to keep τ 1 as a free parameter in our analysis.It is worth noting that both τ 1 and τ 2 are independent of the pore structure and are therefore excluded from the discussion in the main text.
The sufficiently long-lived o-Ps is capable of approaching the pore wall many times before annihilation and its lifetime is significantly reduced depending on the size of the probed free volumes.This is because trapped o-Ps in free volumes annihilates by the 2-gamm mode when the positron involved in o-Ps finds an electron in the pore wall with an antiparallel spin.This process is known as pick-off annihilation [4].The pick-off annihilation probability (reciprocal of o-Ps lifetime) is therefore large for small free volumes.This means that this collisionally-reduced o-Ps lifetime provides the physical basis for probing free volumes by PALS [5].The correlation between o-Ps lifetime and pore size has been first described in the Tao-Eldrup (TE) model [6,7], which is valid only for spherical micropores (R > 1 nm).Later, the TE-model had been extended to include larger pores of different pore shapes and at any temperature in the Rectangular TE (RTE) model [4] and in the Extended TE (ETE) model [8].According to the TE model, the Ps atom is supposed to be trapped in holes of spherical shape surrounded by an infinite potential well.As mentioned above, the TE model is valid to probe hole radii < 1nm because of the huge difference between the ground state and the excited states which restricts the TE calculation to the Ps atom populating the ground state only.The relation between the measured o-Ps lifetime ( o-Ps ) and pore radius (R) [6,9] is expressed as; -1 (1) The 0.5 ns is the spin-averaged lifetime of the Ps, and the empirically determined δ ) 1.66 Å describes the penetration of the Ps wave function into the hole "walls".

Figure S1 .Figure S2 .
Figure S1.Examples of the relative humidity monitored by the humidity sensor during PALS measurements.Values right to the figure show the average RH.Target RH values are marked with the orange dotted lines.

Figure S6 .
Figure S6.TG of as-synthesized DUT-67-Hf under the flow of synthetic air.

Table S1 .
Saturated salt solution and relative humidity values used for in situ PALS measurement.