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C: Surfaces, Interfaces, Porous Materials, and Catalysis
Visualisation of the Catalysed Nuclear-Spin Conversion of Molecular Hydrogen Using Energy-Selective Neutron Imaging Giovanni Romanelli, Triestino Minniti, Goran Skoro, Maciej Krzystyniak, James D Taylor, Damian Fornalski, and Felix Fernandez-Alonso J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01858 • Publication Date (Web): 15 Apr 2019 Downloaded from http://pubs.acs.org on April 15, 2019
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Visualisation of the Catalysed Nuclear-Spin Conversion of Molecular Hydrogen using Energy-Selective Neutron Imaging † ˇ Giovanni Romanelli,∗,† Triestino Minniti,† Goran Skoro, Maciej Krzystyniak,†,‡
James D. Taylor,† Damian Fornalski,† and Felix Fernandez-Alonso†,¶ †ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom ‡School of Science and Technology, Nottingham Trent University, Clifton Campus, Nottingham, NG11 8NS, UK ¶Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK E-mail:
[email protected] 1
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Abstract We present time-resolved neutron-imaging results on the ortho- to para-hydrogen conversion in the presence of a nanoparticle powder of the ferromagnetic catalyst γFe2 O3 . In particular, we were able to characterise the conversion rate as a function of time and position of molecular hydrogen with respect to the catalyst. Results are reported for liquid and solid molecular hydrogen at 15 K and 10 K, respectively. We discuss how newly generated para-hydrogen poisons the catalyst, thus slowing the process and preventing the full conversion of large quantities of condensed molecular hydrogen, and we underline how the performance of the conversion critically depends on the loading procedure. Moreover, we suggest how a honeycomb distribution of the catalyst in a vessel can boost the conversion rates while minimising the amount of material needed. Finally, we show how state-of-the-art energy-selective imaging using pulsed neutrons can be used to provide molecular specificity beyond what is currently possible for in-situ and operando kinetic studies, with direct industrial applications such as the well-known “boil-off” problem associated with the low-temperature storage of molecular hydrogen.
Introduction Nuclear-spin conversion in molecules remains a fascinating topic from the theoretical point of view, 1 and its experimental characterisation is still a challenging task. The existence of nuclear-spin modifications, i.e., forms of a given molecule with different physical and chemical properties according to the orientation of their nuclear spin, is one of the earliest results of quantum mechanics and a direct consequence of Pauli’s exclusion principle. In particular, molecular hydrogen (H2 ), composed of two hydrogen atoms of half-integer nuclear spin (s), can be found in the ortho-modification (oH2 ), whereby the two spins are parallel forming the s = 1 triplet, or in the para-modification (pH2 ), the singlet state with s = 0. The validity of Pauli’s principle requires for pH2 to exist only in even angular-momentum
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states J = 0, 2, . . . , as opposed to oH2 which can be found only in odd rotational states J = 1, 3 . . . . 2 As a consequence, the ground state of oH2 has about 15 meV excess energy with respect to the pH2 ground state, causing a natural ortho-para Conversion (opC) at low temperatures. 3 At room temperature, the relative populations of the two modifications is related primarily to the triplet-to-singlet ratio of degeneracies (3:1), thus having a mixture of 75% oH2 and 25% pH2, referred to as normal hydrogen (nH2 ). Apart from its fascinating history, reviewed for example in Refs., 2–4 the low-temperature opC has practical consequences on the efficiency of H2 storage. 5–8 The amount of energy released in the conversion of one oH2 molecule, corresponding to a local temperature increase of about 170 K, causes the evaporation of the neighbouring molecules in a process referred to as H2 boil-off. Moreover, a fast opC is crucial in the functioning of leading neutron sources, where pH2 is used to optimise the experimental performances. 9 As the natural conversion from nH2 to high-purity pH2 requires several days, a great effort has been directed to find catalysts that could expedite the conversion. At first, special attention was paid towards paramagnetic powders, 10–12 for Wigner had explained how a strong and inhomogeneous magnetic field is responsible for the nuclear-spin conversion. 13 More recently, experimental studies on ferromagnetic catalysts 14 proved that the opC rate could be improved by ordered magnetic structures as well, and Illisca 15 related such conversion to the interaction of adsorbed molecules with spin waves on the catalyst surface. Fundamental investigations of the opC have been based on thermal-conductivity measurements, 16 infra red 17,18 and Raman spectroscopy, 19,20 and NMR studies. 21 However, in cases when H2 is in the liquid or solid state, often measurements probe the saturated vapour rather than the condensed sample in the vicinity of the catalyst or in the volume of interest. To improve the efficiency of the opC, it has become increasingly important to obtain detailed and direct insight into the process. Nowadays, the focus of the discussion has moved from fundamental systems towards real-life cases of applied interest in technology and industry. To this end, NMR has been used as a spatial and temporal characterisation tool of micro-
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reactor chambers, 22 and fluorescence microscopy has shown the nucleation and growth of H2 nano-bubbles at the electrode-solution interface during electrochemical water splitting. 23 Neutron scattering is amongst the most-suitable techniques to look at hydrogen in materials. 24,25 Neutrons can penetrate deep into bulk materials, and allow in-situ and operando non-destructive investigations. Moreover, the scattering cross section of oH2 and pH2 differ dramatically for thermal neutrons, 26,27 as shown in Figure 1 (top panel) and discussed in the Materials and Methods section. Such pronounced difference makes energy-selective neutron transmission a unique technique to characterise the amount of H2 modifications in unknown mixtures. 28 We show here the results of a time-resolved neutron-imaging study characterising the opC in condensed H2 , both in the liquid and solid states, and in the presence of nano-particles of γ-Fe2 O3 acting as a catalyst. The catalyst was chosen because of its technological interest, 29 for example in its crucial use in neutron sources, 28,30 such as the ISIS pulsed neutron and muon source in the UK and the European Spallation Source in Sweden, where high levels of pH2 are required to allow for state-of-the-art scientific investigations. Experimental conditions were chosen so as to be representative of industrial applications, with the aim to provide additional insight into H2 storage, and how to minimise the boil-off problem.
Materials and Methods Materials A sample of γ-Fe2 O3 was purchased form Sigma Aldrich, 31 with average particle size of ca. 50 nm. Before the experiment, the catalyst was loaded in a stainless-steel cylindrical container and heated in a furnace up to ca. 200 ◦ C under vacuum of ca. 10−5 mbar. At about 170 ◦
C, a pressure increase was observed for about 1 hour, to be related to the desorption of
water and the activation of the catalyst. After the activation, a surface area of ca. 30 m2 /g was obtained from a Brunauer-Emmett-Teller analysis of the Ar adsorption isotherm. Pure 4
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H2 was commercially available from CK gas, 32 with a purity of 99.9995% (information from the cylinder’s label, cylinder serial number E968215) and was stored in a cylinder at room temperature for several weeks, therefore considered a source of nH2 .
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E [meV] Figure 1: Top: Tabulated scattering cross sections of the hydrogen molecule in the para (green triangles) and ortho form (red squares) from Ref. 27 The latter is compared with its average value over the IMAT flux, represented by the red dashed line. Middle: Measured total cross section of nano-sized γ-Fe2 O3 . Bottom: The absolute neutron flux on IMAT as a function of the incident neutron energy. The energy-dependent neutron cross sections for oH2 and pH2 were available from the literature, 26,27 and have been remeasured recently 28 on the VESUVIO spectrometer at ISIS. 33 The cross section of the catalyst was measured also on VESUVIO by filling a 0.2-mmwalled aluminium container with a 1-mm-thick powder sample of the same batch of powder used in the imaging experiment. At the same time as neutron transmission, mass-selective neutron spectroscopy, 34 from the spectra recorded by the forward-scattering detectors on VESUVIO, confirmed the successful activation of the catalyst as the amount of hydrogen from water was below the level of detection of the instrument. 35 The energy-dependent transmission spectrum was obtained following the procedures in Ref. 28,36 Because of the 5
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difficult determination of the effective density during the measurement, the logarithm of the transmission was normalised to unity in the energy region between 100 meV and 10 eV, then multiplied by the value of the free scattering cross section for Fe2 O3 , 33.66 barn, so as to satisfy the epithermal-neutron limit. 37,38 As a result of the measurement, we found that the scattering cross section of the nano-particles, shown in Figure 1 (middle panel), increases more-than-exponentially with energies lower than ca. 50 meV (wavelengths larger than ca. 1.4 ˚ A), as it is expected from the small-angle and magnetic scattering off iron-oxide nano-particles. 39
Neutron imaging Neutron radiography and tomography experiments were performed on the IMAT instrument at ISIS 40 in an aluminium container with cross-sectional area 6 cm (vertical) x 5 cm (horizontal), and sample thickness of 0.14 cm along the the neutron-beam direction. The container was inserted in a closed-circuit refrigerator (CCR) that was kept at the nominal temperature of 10 K during all measurements, and connected to a gas panel outside of the IMAT blockhouse. The gas panel was provided with a turbomolecular pump for gas extraction, 4 stainless-steel buffers of 1-litre volume each, and connected to the source of nH2 . The spectrum of the incident neutron beam was centred in the region 1–30 meV by tuning the two double-disk choppers along the IMAT incident path. An absolute measurement of the neutron flux was obtained using a GS01 monitor, 41 and it is shown in Figure 1 (bottom panel). A series of radiographs were acquired using the neutron camera described in Reference 42 with the 50-mm lens and a resulting square field of view of side ca. 20 cm. A pinhole of 20 mm was used to reduce the beam divergence, providing a value of the collimation ratio of 500, and the distance of the camera from the centre of the sample was 31 cm. An absorbing “Siemens star” test pattern was placed on the surface of the container and within the working CCR, and the spatial resolution of the measurement was evaluated to be 472.5 µm using the modulated transfer function method. 41 The spatial resolution when the CCR 6
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was not operational had been evaluated as 255 µm, and we conclude that the deterioration of the resolution is a consequence of the compressor-induced vibrations to which the CCR and the sample were subject. While these values of the resolution proved to be suitable for our experiment, we notice, for future investigations, that an imaging-specific cryogenic apparatus could be designed so as to minimise the vibration-induced effects to the resolution. Radiographs were acquired every 2 seconds during the gas-loading process of ca. ten minutes, and every 30 seconds during the rest of the measurement, of the order of tens of hours. Radiographs were corrected by the dark field (electronic noise in the camera) and normalised to the flat field (a radiography of the empty CCR). Both flat and dark fields were recorded for the 2 and 30 seconds, and the image processing was performed with two pieces of software, ImageJ 43 and Octopus. 44
Determination of oH2 concentration Average values of all cross sections were evaluated using the measured IMAT flux as a weighting function, and the values σ ¯C = 216 ± 9 barn per Fe2 O3 formula unit, and σ ¯o = 52.1 barn and σ ¯p = 2.95 barn per hydrogen molecule were obtained, for the catalyst, oH2 , and pH2 respectively. For each pixel in the camera, the corrected intensity was interpreted using a Beer-Lambert law with average cross sections, and a time dependent concentration of oH2 , o(t), and pH2 , p(t) = 1 − o(t),
T = T0 exp [−n ((1 − o)σp + oσo ) d] ,
(1)
where T0 = TAl TC , and TAl and TC the transmission of the aluminium container and the catalyst, respectively. The time-dependent concentration of oH2 could then be determined as o(t) =
− ln (T /T0 ) /nd − σp . σo − σp
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Results
Figure 2: A neutron tomography (left) and radiography (right) of the sample container partially loaded with the catalyst in region II, and empty in region I.
Molecular hydrogen adsorption Experiments were performed on H2 at 15 K and 10 K, in the liquid and solid phases, both in the bulk and partially adsorbed on the γ-Fe2 O3 catalyst. Figure 2 shows a 3D rendering of the sample container together with the catalyst employed in the experiment, obtained using neutron tomography, together with a frontal radiography. It is possible to recognise two regions within the container: the top region (I) empty, and the bottom region (II) partially filled with the catalyst. In region I, H2 could condense in its bulk forms, while in region II H2 was readily adsorbed in the proximity of the catalyst and onto its surface. The gas loading into the container was monitored by neutron radiographs every 2 seconds, and a video of the process is available online as Supplementary Information. Before the loading, the container was evacuated and kept at 15 K, at liquid H2 temperature. Figure 3 shows a series of radiographs collected during H2 loading in the container and in the presence of the catalyst, providing a unique physical insight into the adsorption and conversion kinetics at much lower scales. in Figure 3(A–C), the gas is adsorbed onto and in the proximity of the surface of the catalyst, first on the outer borders and then migrating to and covering the centre of region II. After saturating the surface of the catalyst, H2 starts to fill the rest of 8
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Figure 3: A series of 2-second-long neutron radiographs during the H2 loading process at 15 K: no H2 loaded (A), adsorption onto the catalyst (B, C), filling of the rest of the container with liquid H2 (D), filled container with change in contrast in region II because of the opC (E, F). the container in its bulk liquid phase. In fact, the filling proceeds upwards, accordingly to the hydrostatic approximation for the top surface of the liquid, and effects from the liquid surface tension are evident near the border of the container (D). In Figure 3(E–F), the container was completely filled, and the effect of the opC due to the catalyst in region II can be observed in the bottom-right corner of the images: the change in the neutron cross section from tens of barns (oH2 ) to almost vanishing values (pH2 ) corresponds to a lower contrast in the radiography, and the image becomes clearer.
Molecular-Hydrogen Conversion Regions of interest (ROIs) in the neutron radiographs were defined, and the contrast of the image was related to the time evolution of the oH2 concentration, o(t). As an example, Figure 4 shows o(t) at 15 K in the case of the bulk liquid without any catalyst (A), in the bulk liquid in region I near the catalyst (B), and in region II within the catalyst (C). In all cases, experimental data are compared to model solid lines discussed below. In the cases B and C, dashed lines correspond to the short loading period when vacuum was replaced by nH2 . At low temperatures, the natural conversion of oH2 to pH2 in the bulk liquid phase can 9
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be described by a second-order conversion rate with respect to the oH2 concentration, o,
−
do o(o − oe ) = k2 dt 1 − oe
(3)
where o ≡ o(t), oe = o(t → ∞) is the equilibrium concentration, and k2 is the natural conversion rate constant. The natural conversion of oH2 in the condensed phases is a slow process, primarily caused by the simultaneous change of the rotational state J = 1 → 0 and the nuclear-spin change s = 1 → 0. The transition between two states of different parity requires the presence of a non-vanishing gradient of an external magnetic field. For bulk H2 , this is provided by a rotating triplet, that is a neighbouring oH2 , making the opC of second order in o. Bulk H2 with no catalyst was condensed at 15 K and 0.66 bar in the liquid, and 10 K and 0.4 bar in the solid. Values of the conversion rate constants were found to be k2 = 0.0143(7) hour−1 · o−1 for the liquid, and k2 = 0.0124(7) hour−1 · o−1 for solid H2 . Characteristic conversion times τ ' 1/k2 were reported to be ca. 79 hours. 5,45 In particular, Milenko and Sibileva 46 have compiled a detailed table of rate constants for liquid H2 , as a function of temperature and pressure, reporting k2 = 0.0125(4) hour−1 · o−1 at 16.6 K and 0.3 bar, that compares well with our value. We notice that, while the two results are in qualitative agreement, a slightly lower rate constant in the case of Refs. 5,45,46 can be ascribed to the common procedure based on thermal conductivity measurements whereby a batch of sample is extracted from the saturation vapour. As such batch is measured in a separated container, the chance of back-conversion of pH2 to oH2 is increased, as recently discussed in Ref. 28 The conversion rate of H2 gas in the presence of a catalyst is expressed as a first-order reaction of the form −
do = k1 o. dt
(4)
However, the experimental data in Figure 4(C) from region II are well reproduced using a zero-order equation whereby the conversion rate does not depend upon the concentration of
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time [s] Figure 4: Time evolution of the oH2 concentration in the case of bulk liquid H2 at 15 K and no catalyst (A), bulk liquid H2 in region I near the catalyst (B), and H2 in region II adsorbed onto the surface of catalyst and in its proximity (C). oH2 . This is typical of kinetic reactions for saturated catalyst surfaces, 47 as one could expect when low-density H2 gas is replaced with its condensed forms. The rate constant is such that after ca. 20 minutes the catalyst has fully converted the oH2 in its vicinity, k0 = 1.41(7) hour−1 · o, in good agreement with the results in Ref. 30 When looking at the liquid H2 in region I (centimetres away from the catalyst, curve B in Figure 4), the conversion rate after ca. 1 hour is well described by the first-order Equation 4, with a constant rate k1 = 0.62(3) hour−1 and a characteristic conversion rate of ca. 100 minutes. However, within the first hour the data are better reproduced by a zero-order conversion, with k0 = 0.28(1) hour−1 · o. The boost in the conversion rate with respect to the bulk liquid seems to be related to the fast diffusion of H2 in its liquid phase, and no dependence upon the distance of the ROI in region I from the catalyst was observed.
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Discussion Para-Hydrogen Poisoning Cunningham et al. showed how the relative concentration of pH2 and oH2 on the catalyst surface and in the gas are not expected to be the same. 12,48 In fact, the adsorption of oH2 on the catalyst is more convenient due to the polarised J = 1 shape of the molecule, as opposed to the isotropic J = 0 case of pH2 . In the light of this process, it is interesting to see in Figure 4 how, after about 1500 seconds, a very little amount of oH2 could be found in the proximity of the catalyst (region II), despite the huge reservoir available in the nearby bulk liquid (region I). We suggest that the adsorption of oH2 on the catalyst surface extends beyond the first adsorption shell, and that converted molecules remain in the proximity of the catalyst, thus saturating its surface and preventing an easy exchange with the rest of the bulk liquid. The increased H2 residence time on the catalyst surface with increasing density was discussed previously, e.g., in Refs., 2,49 and optimal strategies for opC in H2 gas are based on repeated adsorption and desorption of a single H2 monolayer. While this procedure is not practicable for condensed phases of H2 , the poisoning is expected to be reduced by flowing H2 through the catalyst. 49 In this sense, newly generated pH2 acts as a poisoning for the catalyst, slowing the opC kinetics. The assumption of a single adsorption layer in the context of opC for H2 gas was recently debated for paramagnetic catalysts based on transition metals, 21 but otherwise is considered as a good assumption for iron oxide. 12 However, in the case of large quantities of condensed H2 with respect to the amount of catalyst, as for example in the ISIS H2 moderators where liquid H2 is at 20 K and 8 bar, 9,50 the presence of saturation and poisoning of the catalyst can prevent a complete conversion to pH2 . 28
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Loading Procedures Further measurements were performed on solid H2 in the presence of the catalyst, and we discuss below how the overall conversion in the container critically depends on the loading and freezing procedures. First, it is important to notice how region II is crossed by dendritelike tunnels (for example in Figure 3). These structures, not present at the moment of the loading of the powder in the container, are the result of the loading and evacuation of the gas, as a consequence of the mechanical force from the transient pressure difference, and changed in shape for every measurement. Within these tunnels, having diameters on the millimetre scale, the rate of the opC has intermediate values between those within the catalyst, and in the bulk. Therefore, despite the fact that no dependence of the conversion rate was observed for the liquid in region I, the conversion rate is boosted within the bulk liquid surrounded by the catalyst. On industrial scales, one needs to maximise the conversion performances while minimising the amount of catalyst used. In this context, we suggest the use of a solid support with a honeycomb structure onto which a high-surface-area catalyst can be deposited, allowing H2 flow within the tunnels, so as to provide an increase in the conversion time and efficiency with respect to the case where the catalyst is deposited, for example, at the bottom of the vessel. We notice how special inks highly loaded with ironoxide nanoparticles were recently produced 51 that can be used in 3D printing to obtain thin-walled porous structures. The measurement of the catalytic conversion for solid H2 was attempted several times, for spatial features in the H2 density distribution were observed depending on the loading procedure. Figures 5(A–C) show the result of the loading of H2 gas within a container at 10 K, as opposed to Figure 5(D–F) where the loading took place at 15 K at liquid H2 temperature, then the sample was cooled and solidified at 10 K. In the first case, region I appears to be particularly structured and inhomogeneous, possibly because the sudden solidification was followed, in the regions where the catalysis was faster, by enhanced boil-off processes. There appears to be a spatial correlation between the inhomogeneous structures in region I, and 13
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Figure 5: A series of radiographs for solid H2 conversion following different loading procedures: loading at 10 K (A–C), or loading at 15 K, then cooling at 10 K (D–F). Figures correspond to ca. 1 hour after loading (A, D), 7 hours (B, E), and 14 hours (C, F). The yellow-box region in (F) was subdivided in smaller ROIs, from top to bottom, for which o(t) is shown in Figure 6. Labels S1–S4 approximately correspond to the similarly-labelled curves in Figure 6. the dendrite-like structures in region II were we have noticed an accelerated opC. On the other hand, in the case of loading at 15 K and following cooling to 10 K, Figure 5(D–F) show a much more homogeneous H2 sample where one can appreciate a vertical gradient in the oH2 concentration, as discussed below.
Catalysed Conversion for Solid H2 The region within the yellow box in Figure 5(F), with dimensions 3.6 cm (heigh) and 1.6 cm (width), was subdivided along the vertical direction in 2-mm-height ROIs, and the time evolution of the oH2 concentration was studied. Results are reported in Figure 6, with the curves from top to bottom in the plot strictly corresponding to the regions from top to bottom in the radiography. In this example, H2 was first condensed in the liquid form at 15 K, then solidified at 10 K. The phase change is clearly recognised at about 1100 seconds (vertical dashed line) because of the ca. 10% increase in the bulk density from liquid to solid. In the bulk region farthest from 14
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time [s] Figure 6: The time evolution of oH2 concentration in the ROIs within the yellow box of Figure 5(F). Curves S1–S4 approximately correspond to the regions within the yellow box labelled accordingly. the catalyst, the conversion rate can be modelled by a second-order equation, with a rate constant k2 = 0.0149(7) hour−1 · o−1 , faster than in the case of the solid without a catalyst (curve S1). On the contrary, on the bottom of the plot, the conversion within the catalyst was found compatible with a first-order conversion, and a rate constant of k1 = 5.8(3) hour−1 (curve S4). Because of the lack of mobility of H2 molecules and the lower values of o(t), the surface of the catalyst does not appear to suffer from saturation, making this case more similar to the catalytic conversion of the gas. All the intermediate cases between S1 and S4 in Figure 6 can be modelled as a combination of a first-order solution at shorter times (as in S4) and a second-order solution for longer times (as in S1). Two example curves obtained in this way are labelled S2 and S3 in the figure. While k1 stays approximately constant for all cases, the conversion rate at longer times becomes faster as the ROI approaches the catalyst. Moreover, the initial oH2 concentration after freezing varies continuously as a function of such distance, as opposed to the case of the liquid where, on the time scale of a radiography (30 seconds), no gradient of the oH2 concentration could be observed. Furthermore, the equilibrium value oe that best 15
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reproduces the experimental data is a function of the sample position within the container, with larger equilibrium values for batches nearer the catalyst. As mentioned, the opC in the bulk solid requires two neighbour oH2 molecule, a condition that becomes more unlikely for lower values of o(t), that is for longer times or for ROIs nearer to the catalyst, making the conversion slower.
Conclusions We have presented a characterisation of the ortho-para conversion of molecular hydrogen in the presence of a nanoparticle powder of γ-Fe2 O3 , with an unprecedented level of simultaneous spatial and temporal detail. We have found that, at experimental conditions similar to those encountered in industrial and engineering applications, the conversion rate critically depends upon the spatial distribution of the catalyst and the loading procedure. We have discussed how, upon saturation of the catalyst surface, the newly generated pH2 poisons the catalysis; and we show how the conversion rate for solid H2 markedly depends upon the distance from the catalyst. Finally, we have found that liquid H2 in dendrite-like tunnels within the catalyst, with diameter of the order of the millimetre, shows a boosted conversion rate with respect to the liquid slightly outside of the catalyst, and we have suggested that catalytic vessels can be designed so as to take advantage of this phenomenon, for example by positioning the catalyst in the vessel over a honeycomb support. Moreover, we have shown how state-of-the-art energy-selective imaging using pulsed neutrons provides molecular specificity in kinetic processes, allowing for in situ and operando investigations of direct interest for engineering and industry.
Acknowledgements We would like to thank Dr F Orlandi for useful discussions, and all the Sample Environment Group at ISIS for their precious support in preparing the experiment. The authors gratefully 16
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acknowledge the UK Science & Technology Facilities Council for financial support and access to beam time at the ISIS Facility.
Supporting Information Available: A video of molecular-hydrogen adsorption onto the catalyst surface and into the container at 15 K is available as Supporting Information, and was obtained by combining the series of radiographs collected on IMAT over several hours. This material is available free of charge via the Internet http://pubs.acs.org.
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