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Project titleMagnetic resonance studies of gas diffusion in nanoporous materials: influence of gas-wall interactions

Research area 02 - PHYSICS AND SPACE SCIENCES, 02-204 - Nano- and microstructures

Keywordsdiffusion, gas diffusion, NMR, low temperatures, helium-3, 3He, xenon, 129Xe, hyperpolarisation, porous media, nanopores, mesopores, aerogel, adsorption

Annotation
In modern nanoporous materials, gas diffusivity correlates with their efficiency for gas separation and storage, or for catalysis. It also correlates with their relevance for investigations of helium superfluid phases and phase transitions with perturbing solid impurities, or confining boundaries since these systems essentially behave as low-density gases of quasi-particles at very low temperatures. More generally, liquid and gas diffusion measurement techniques are widely used for the characterization of porous media. Nuclear magnetic resonance (NMR) provides a wealth of non-invasive methods for measuring fluid transport in various kinds of porous systems. Gas diffusion NMR is a mandatory tool to address specific problems, such as finding mean free paths in aerogels and characterizing pore sizes and structure. A precise understanding of all physical processes involved during diffusion measurements is essential to correctly interpret NMR diffusion results obtained in porous media. Gas diffusion in porous media near room temperature is frequently described by diffusion models which take into account the possible presence of adsorbed layers and the spatial structure of pores. However, usual phenomenological models of gas diffusion fail to account for observations made with strongly adsorbed gases or at low temperatures, because the influence of the attractive wall potential on molecular gas dynamics is overlooked in standard diffusion models. Preliminary results obtained for 3He gas diffusion in an ordered aerogel by the KFU team at 4.2 K revealed a significant deviation from the expected behavior, attributed to the increased effect of the aerogel adsorption potential on 3He gas diffusion at low temperatures. This effect of the adsorption potential is believed to manifest itself in an increase of the gas density and in changes of atomic trajectories near the walls in the gas phase. Theoretical background and experimental data lack for gases in porous systems at low temperatures or low gas densities, and the project is designed to address both issues. It aims at discriminating between confinement and wall adsorption effects through NMR investigations of gas diffusion in several well-characterized model porous media over a wide range of temperatures and gas densities for which different adsorption regimes are expected, from no adsorption to multilayer adsorption through Henry’s, Langmuir’s and BET’s regimes. Experimentally, 3He will be mainly used as a probe gas and apparent diffusion will be measured in porous systems such as ordered aerogels, nanopowders, etc., at low temperatures in KFU (Kazan) and at high temperatures in LKB (Paris) using hyperpolarisation methods with laser optical pumping for high sensitivity. Complementary xenon gas diffusion experiments above 170 K are planned in the same porous media to probe diffusion of atoms with stronger adsorption potentials than for 3He. Numerical simulations of diffusion and nuclear spin dynamics will be also intensely used to reliably interpret experimental results and draw strong conclusions. The projects aims to solve the fundamental problem of gas diffusion mechanism determination under the influence of strong adsorption potential at walls of porous media and nanorestrictions on gas dynamics. It also aims at demonstrating that NMR could become one of the accepted characterization tools for pore characterisation by gas diffusion, instead of being limited to assessing diffusion and relaxation in liquids, inside porous media. Besides the achievement of its main objectives, namely the detailed characterization of gas diffusion mechanisms in porous media, the project is expected to yield data and results which might be relevant for different open questions in fundamental physics. One of them is related to recently revisited theories of motion-induced magnetic relaxation and frequency shifts in fluids, beyond the standard Redfield approach. On this topic, the planned NMR measurements in samples with near-planar confinement might provide a benchmark for these theories, which have been triggered by new generations of EDM search experiments.

Expected results
In the course of the project, a series of well-designed experiments on the study of the diffusion of 3He and 129Xe will be carried out in model well-characterizated porous media in temperature range 1.5-300 K and various pressures, as well as in planar waffle-structured samples and analogues. As a result, a large array of experimental data will be obtained to study the effects of adsorption on the diffusion of gases and the construction of appropriate diffusion models. The project addresses fundamental issues related to gas diffusion in complex porous systems using a range of NMR tools. Research on this topic already performed by both teams involved in project was triggered by questions arising in the low-temperature community about the modification of properties of superfluid phases of helium in aerogels. Quite clearly, the immediate expected benefit of project’s findings will be an increased knowledge of these aerogels and their interaction with liquid helium for this community. More generally, the expected outcome of project is a deeper understanding of the mechanisms governing gas diffusion in nano- and mesoporous complex systems, as well as in well-defined planar systems, with a large body of experimental data and corresponding benchmarked models. This should positively and durably influence further studies on, and potential applications of gas diffusion in these systems. NMR could therefore become one of the various accepted characterization tools for gas diffusion, whereas it is so far confined to assessing diffusion and relaxation in liquids imbibing porous media. The methodological developments in NMR characterization of restricted diffusion, which will be made to achieve the objectives of project, could find useful applications in different domains. Our problem-solving approach, associating cutting-edge technology, multimodality sample characterization, and intensive supporting computations might for instance be applied in apparent diffusion mapping of HP gases in lung MRI [Rev. Mod. Phys. 89 (2017) 045004, doi: 10.1103/RevModPhys.89.045004]. Experiments with planar samples will allow to verify recently revisited theories of motion-induced magnetic relaxation and frequency shifts in fluids, beyond the standard Redfield approach. Finally, project might also contribute in the long term to highly speculative advances in high-precision fundamental physics searches for deviations from the Standard Model at low energy.

Annotation of the results obtained in 2022
During the third year of the project the series of experimental studies on 3He nuclear magnetic relaxation and diffusion in aerogels proceed with powder aerogel at 4.2 K and magnetic fields up to 0.8 T. The obtained data clearly show the similar 3He relaxation mechanisms in powder aerogel that are dominant in other types of aerogel and emphasize the role of the surface-induced 3He nuclear magnetic relaxation. The measured 3He diffusion dependencies on pressure represent a similar behaviour between all studied aerogel samples. At low pressures the measured 3He diffusion coefficient growths with the pressure increase up to a certain maxima and decreases with the further increase of pressure. This is connected with the presence of adsorbed 3He layer in which the diffusion coefficient is much smaller than in gas phase. At high pressures helium-3 diffusion qualitatively match the ideal gas behaviour. The observed reduced 3He diffusion in powder aerogel also points out on the strong influence of adsorptive potential effects on gaseous 3He atom dynamics at low temperatures. The obtained results line up with the results obtained for oriented aerogels earlier. The numerical diffusion simulation was performed in order to describe the Knudsen self-diffusion at high temperatures in oriented and chaotic aerogels for the cases of diffusion and specular reflections with van der Waals 3He-wall interactions omitted. The obtained results may be used to describe high temperature diffusion results. The oscillator diffusion model was adapted to aerogel structure and the corresponding numerical simulations of 3He diffusion in aerogels was performed. The simulated values of gas densification agree well with the experimentally observed ones. The rough estimates of adsorptive potential effects on helium atom gas dynamics in oriented aerogels are in good agreement with the reduced diffusion and gas densification observed in 4.2 K experiments. However a quantum mechanical approach is required for a better description of diffusion and gas dynamics near walls. The analysis and generalization of all diffusion and relaxation results obtained during al three years of the project was performed. The general pattern of 3He self-diffusion behaviour and nuclear magnetic relaxation in aerogels were revealed as a result of a complex data analysis. It was determined that the adsorbed 0He layer reduces the measured 3He diffusion coefficient in all cases. The accounting for the adsorbed layer using bi-phasic diffusion model allows to obtain the 3He gas diffusion. It is found that the 3He gas diffusion coefficient strongly deviates from the classical Knudsen model when pore sizes become smaller. The common application of the classical Knudsen model to describe small pore diffusion data when adsorption is present may be incorrect. The correlations between 3He gas diffusion, its anisotropy degree, its level of deviation from Knudsen model, the gas density, and the aerogel porosity is found. It was shown that imperfect aerogel fibers alignment do not explain the difference between the observed diffusion anisotropy level and the predicted within the Knudsen model framework. The obtained correlations are in good agreement with the theoretical estimations of the adsorption potential influence on the gas phase.

Publications

1. Kuzmin V.V., Safiullin K.R., Stanislavovas A.A., Baibekov E.I., Tagirov M.S. Diffusion Anisotropy of Gaseous Helium-3 in Ordered Aerogels at Low Temperatures The Journal of Physical Chemistry B, №127, с.1459−1470 (year - 2023) https://doi.org/10.1021/acs.jpcb.2c08251

Annotation of the results obtained in 2020
A detailed understanding of all physical processes during NMR diffusion measurements are essential for the correct interpretation of experimental data obtained in porous media. Right now there is a lack of theoretical descriptions and experimental data for gas diffusion at low temperatures and low gas densities. The main goal of this project is to assess the effect of nanoporous media adsorption potential on gas diffusion at low temperatures by means of NMR technique. The series of oriented Al2O3 aerogel with various densities (82-920 mg/cm3 or 77-98% porosity) samples has been prepared. The samples have been characterized by EPR, TEM/SEM and gas adsorption methods. The most dense aerogels were fabricated from low density aerogels by a soaking in water and a further drying technique. According to EPR data all aerogel samples have a signal (perhaps free radical) at g~2 that corresponds to approximately 1e13 per mg concentration. EPR spectra of two samples also show the presence of Fe at g~4 with 5e12 per mg concentration, probably Fe substitutes some Al atoms in Al2O3 matrix. The obtained concentrations of impurities correspond to properties of relatively pure samples . 3He gas adsorption measurements on aerogels allowed to determine the surface values and the surface-to-volume ratios for all samples. 3He and 4He monolayer capacities are also obtained from helium gas adsorption data. 3He NMR relaxation and diffusion experiments were planned for three aerogel samples at 1.5 and 4.2 K temperatures in moderate magnetic fields (up to 0.8 T). The linear dependence of helium-3 T1 on helium-3 amount in the probe cell with samples have been obtained. T1 vs helium-3 amount dependencies normalized to monolayer capacities coincide at different temperatures for samples prepared from the same batch piece. This behaviour indicates on the surface relaxation mechanism of gaseous 3He. The preadsorption of helium-4 has allowed us to eliminate the influence of surface relaxation, it has led to the increase of T1 relaxation times by orders of magnitude. At this condition other rather weak relaxation mechanisms take place. The most probable relaxation mechanism that accounts for helium-3 diffusion in inhomogeneous magnetic field created by aerogel matrix was suggested. The model that suggests areas with high densities of paramagnetic impurities (leads to fast T1 relaxation) in aerogels is proposed, it implies the T1 relaxation is determined by helium diffusion time to such areas. It has been shown that studies of T1 pressure dependencies may reveal the effective mean-free paths of 3He in aerogels within the frame of the suggested model. The measured 3He diffusion pressure dependencies are similar for three samples: it increases with pressure at low pressure values and then starts to decrease at high pressures. It is connected with the presence of adsorbed helium-3 layer as its diffusion is much slower than in gas. At high pressures diffusion data qualitatively follows the expectations for ideal gas. The obtained effective helium-3 mean-free paths are considerably low than expected from Knudsen model. Presumably it points out on the strong effect of adsorption potential on helium dynamics in gas phase at low temperatures. Preliminary work on preparation of numerical simulations of 3He adsorption in simulation cell that consists the part of aerogel fiber has been done using RASPA software package. It is necessary for further correct interpretation of experimental data or verification of theoretical approaches. The gamma-Al2O3 fiber structure and void structures have been optimized for faster simulations. The series of preliminary 3He adsorption isotherms in simulation cell with fiber structure were obtained at 8-30 K. The tested and optimized simulation parameters will allow us to perform simulations of aerogel adsorption potential effects on gaseous helium-3 properties in a wide range of temperatures. Diffusion studies of 3He in helium mixture in aerogel at temperatures above 1.5 K have been also performed within the frame of this project. The angular 3He diffusion dependence has been obtained for 2.5% mixture in 597 mg/cm3 aerogel at 1.63 K. The analysis of reasons of the angular dependence and reduced helium-3 diffusion have included the accounting for Knudsen diffusion and superfluid helium excitations. It revealed that Knudsen diffusion is not responsible for obtained experimental data. Possible mechanisms of helium-3 diffusion anisotropy that involve 3He-roton collisions and possible changes of roton properties have been suggested. The possibility of bulk-like rotons anisotropy, anisotropic roton mode broadening and layer roton modes have been discussed. The results are published in Journal of Physics: Condensed Matter (doi:10.1088/1361-648X/abc4f1). The 3He/4He/129Xe gas management/handling/cleaning/storage system has been prepared for further well-controlled 3He and 129Xe gas diffusion experiments with porous samples at high magnetic fields (up to 9 T) and wide range of temperature (1.8-300 K). The sensitivity, signal-to-noise ratio, field homogeneity of high-field NMR setup have been tested in 3He phantom sample (cell with mixture of helium-3 and oxygen) at room temperature.

Publications

1. Safiullin K., Kuzmin V., Stanislavovas A., Alakshin E., Klochkov A., Tagirov M. Anisotropic reduced diffusion in dilute liquid 3He-4He mixture in ordered aerogel Journal of Physics: Condensed Matter, Volume 33, Number 6, 065101 (year - 2021) https://doi.org/10.1088/1361-648X/abc4f1

Annotation of the results obtained in 2021
The series of 3He NMR relaxation and diffusion experiments were performed during the second year of the project using the planned two oriented aerogels and the 95% porosity chaotic SiO2 aerogel at temperatures of 4.2 and 1.5 K in magnetic fields up to 0.8 T. The obtained data point out on the similar relaxation mechanism of helium-3 in all studied aerogels: relaxation of gaseous helium-3 is a surface-induced. The preadsorbtion of helium-4 allows to exclude helium-3 adsorption that leads to the increase in T1 by an order of magnitude. In this case the influence of a surface relaxation is negligible and other, weaker, relaxation mechanisms dominate. The measured helium-3 diffusion coefficients in all studied samples have similar pressure dependencies. At low pressures the helium-3 diffusion coefficient increases with pressure, then achieves its maximum value and then decreases at high pressures. This is connected with the presence of an adsorbed helium-3 that has much slower diffusion that gaseous helium. At high pressures the diffusion of helium-3 approaches the expectations for the ideal gas diffusion. The obtained effective mean free path values for gaseous 3He are significantly lower than predicted by Knudsen diffusion model. This fact implies on the strong adsorption potential influence on the 3He gas dynamics at low temperatures. The chaotic aerogel with 95% porosity was characterized. NMR experiments on helium-3 relaxation times and diffusion measurements were also performed using this sample. The obtained results correlate with the experimental results obtained for oriented aerogels. The correlation between the 3He gas diffusion coefficients and the basic aerogel samples parameters was studied. For this purpose the electron microscopy studies were additionally performed on the used oriented aerogels and the data on the fiber alignment degree, fiber thickness, and other parameter were obtained. The experimental study of helium-3 NMR relaxation in one of the oriented aerogel samples was performed at 10 and 20 K temperatures. The obtained pressure dependencies of 3He relaxation times suggest the similar relaxation mechanisms of helium-3 that occurs at 4.2 K. The numerical simulations of helium-3 adsorption on aerogel fiber was performed for 4.2-30 K temperatures. It was found that the classical approach is not correct to use in this temperature range. The numerical simulations of 3He diffusion were also performed to account for Knudsen self-diffusion at higher temperatures in oriented and chaotic aerogels. These simulations excluded the van der Waals interactions. The obtained results may be used to describe the gas diffusion in aerogels at high temperatures.

Publications

1. Stanislavovas, A., Kuzmin, V., Safiullin, K., Alakshin E., Klochkov A., Kutuzov, M., Tagirov, M. The3He nuclear magnetic relaxation in nematically ordered Al2O3aerogels: Effects of 4He and nitrogen pre-plating Journal of Physics Condensed Matter, Volume 33, Number 19, Article 195805 (year - 2021) https://doi.org/10.1088/1361-648X/abe475