Development of an adsorption differential volumetric apparatus for accurate measurement of mass transfer in nanoporous materials

The volumetric technique is a widely used macroscopic method to measure gas adsorption kinetics in nanoporous materials, however, there are some common pitfalls in measurement practices which can lead to significant deviation in the diffusivity. Apart from this, the traditional single-branch volumetric systems show severe limitations for accurate kinetic measurements at different pressure levels. This work aims to contribute to the use of the volumetric technique for reliable and accurate pure gas adsorption kinetic studies. The main objective of the work is to develop a novel adsorption differential volumetric apparatus (ADVA-1) which can achieve accurate kinetic measurements over the pressure range from vacuum to atmospheric pressure. The thesis comprises review, modelling, and experimental studies. A review of common practices in volumetric kinetic experiments over the past 20 years was conducted to identify the major pitfalls. The main findings include the dominant use of inappropriate experimental conditions and inappropriate theoretical models, as well as the lack of information on the experimental conditions and the fitting of the data. The good practices of volumetric kinetic measurements were demonstrated. These results will be used to provide guidelines on diffusion measurements in porous solids through the IUPAC work group. While the theoretical model for studying isothermal diffusion systems with volumetric experiments had been well established, two models for the interpretation of more complex rate limiting mechanisms were developed in this work. Firstly, a non-isothermal diffusion model was developed by considering the heat transfer resistance on the surface of the adsorbent solid and the temperature dependence of the adsorption equilibrium. Both numerical and analytical solutions were derived. The conditions under which useful diffusion information can be extracted were identified. Secondly, the biporous diffusion model for a finite volume system developed by Lee in 1978 was restored and adapted to volumetric experiments. For both models, the forms of the response curves, including the limiting cases, were demonstrated. As the focus of this work, the ADVA-1 was designed, built, and commissioned. The key features of the ADVA-1 are: 1. The differential configuration allows the use of a small-scale differential pressure transducer (±3.5 kPa) to measure adsorption kinetics. A high signal-to-noise ratio can therefore be achieved in the whole pressure range (from vacuum to 130 kPa). 2. Small cell volumes lead to the high sensitivity of the system, which enables the use of a small amount of sample for the kinetic tests. 3. Fast data acquisition modules allow the determination of time constants of a few seconds. The protocol for volume calibration, adsorption kinetic measurements, and equilibrium determination were established. To demonstrate the new system, it was employed to study the adsorption kinetics on two commercial adsorbents, zeolite 4A and 5A pellets. The campaign started with relatively simple isothermal diffusion systems and then moved on to more complex systems. The adsorption kinetics of N2 and Ar on zeolite 4A pellets were firstly investigated to validate the apparatus and the approach. The N2-4A system was studied between 5 to 35 ℃, while the Ar-4A system was studied between –10 to 35℃. These systems were chosen for their weak adsorption feature to demonstrate the sensitivity of the ADVA-1, which gives a good signal-to-noise ratio even with a single pellet in the entire pressure range. The study confirmed the dominance of micropore diffusional resistance, and an isothermal diffusion model was shown to reproduce accurately the observed kinetics using reduced pressure plots. The results were validated with literature values. A collaborative diffusion mechanism study of CO₂ and N₂ on zeolite 5A pellets was conducted using the ADVA-1 and a zero-length column (ZLC) system. The CO₂-5A isotherms were determined between 20 and 100℃, and kinetic tests were performed between 0 and 60℃. N2-5A adsorption experiments were performed between –15 and 15℃. The dominance of macropore diffusional resistance for the CO₂-5A system was confirmed by ZLC experiments using different carrier gases and different pellet sizes. ADVA-1 experiments further confirmed the macropore diffusion control at different pressures and temperatures for both CO₂ and N₂. Despite only ~25mg samples and inert metal beads were used, heat effects were identified for high pressure experiments by changing the sample configuration. The low-pressure CO₂-5A isothermal data were combined with the ZLC data to obtain the effective macropore diameter and the effective tortuosity, which are physical properties of the sample. Then a systematic analysis of the ADVA-1 CO₂ and N₂ data at all pressures was conducted using the non-isothermal diffusion model, and satisfactory fittings were obtained using consistent heat transfer related parameters. The analysis revealed that, with increasing pressure, the system moved from isothermal diffusion control to combined diffusion and heat transfer control, and finally to complete heat limit. With the macropore diffusion control correlation and the effective macropore diameter obtained, the ADVA-1 and ZLC experiments at different conditions yielded consistent values of the effective tortuosity, thus validating the approach. The non-isothermal analysis of 5A systems also highlighted the importance of experimental checks for isothermal condition and the use of an appropriate model. It was shown that CO₂-5A non-isothermal kinetic curves exhibited similar shapes as the isothermal curves. The isothermal model was able to provide reasonable fittings, but the error in the diffusional time constant saw dramatic increase with pressure. In addition, a case study for the non-isothermal model demonstrated that, to get closer to isothermal behaviour, the experiments should be performed at lower pressure and lower temperature. The ADVA-1 was proven to be a useful tool for accurate diffusion mechanism study and the approaches for studying different cases were demonstrated