An Upper Bound Visualization of Design Trade-Offs in Adsorbent Materials for Gas Separations: CO2 , N2 , CH4 , H2 , O2 , Xe, Kr, and Ar Adsorbents

Abstract

The last 20 years have seen many publications investigating porous solids for gas adsorption and separation. The abundance of adsorbent materials (this work identifies 1608 materials for CO₂ /N₂ separation alone) provides a challenge to obtaining a comprehensive view of the field, identifying leading design strategies, and selecting materials for process modeling. In 2021, the empirical bound visualization technique was applied, analogous to the Robeson upper bound from membrane science, to alkane/alkene adsorbents. These bound visualizations reveal that adsorbent materials are limited by design trade-offs between capacity, selectivity, and heat of adsorption. The current work applies the bound visualization to adsorbents for a wider range of gas pairs, including CO₂ , N₂ , CH₄ , H₂ , Xe, O₂ , and Kr. How this visual tool can identify leading materials and place new material discoveries in the context of the wider field is presented. The most promising current strategies for breaking design trade-offs are discussed, along with reproducibility of published adsorption literature, and the limitations of bound visualizations. It is hoped that this work inspires new materials that push the bounds of traditional trade-offs while also considering practical aspects critical to the use of materials on an industrial scale such as cost, stability, and sustainability.

Keywords: adsorbent design; adsorption; bound visualization; gas separation; metal organic framework; zeolite imidazolate framework.

Figure 1

Example upper bound plot of CO₂ uptake versus CO₂/N₂ selectivity. Each point is an adsorbent material, and the best materials lie in the upper‐right region of the plot above the upper bound, highlighted in solid colors.

Figure 2

Distribution of heat of adsorption values for each gas (data gathered as described in Sections 7 and 19). A larger bubble indicates more materials at the given heat of adsorption value. Crosses indicate the 10^th percentile for the minimum heat of adsorption.

Figure 3

Number of adsorbent materials recorded for each gas pair, organized in the format selective gas/non‐selective gas. Less than 50 adsorbents for the Xe/O₂/N₂, Kr/O₂/N₂, Xe/Ar and Kr/Ar gas pairs were found, so are not included.

Figure 4

Type‐1 ethylene isotherm of Zeolite 13X^{[ 15 ]} compared to the step isotherm of nonporous [Cu—H].^{[ 16 ]} Zeolite 13X shows a loading of 4.1 mol kg⁻¹ at 300 kPa, while [Cu‐H] has a loading of 3.5 mol kg⁻¹ at the same pressure. This makes the capacity of Zeolite 13X appear better than [Cu‐H]. However, an example pressure swing between 300 kPa and 100 kPa reveals a working capacity of 0.4 mol kg⁻¹ for Zeolite 13X, while a much larger working capacity of 3.5 mol kg⁻¹ for [Cu—H]. This illustrates the difference between static capacity and working capacity.

Figure 5

CO₂ heat of adsorption as a function of CO₂ loading on a range of amine‐modified porous polymers, illustrating how the value recorded at saturation capacity is not always representative of the entire range. For example, at 298K and 100 kPa, PP‐2‐PEI adsorbs 2.7 mol kg⁻¹, giving a heat of adsorption of −34.5 kJ mol⁻¹ and not accounting for the heat of adsorption up to −47 kJ mol⁻¹. Reproduced with permission.^{[ 24 ]} Copyright 2019, Elsevier.

Figure 6

Carbon dioxide – nitrogen empirical bounds illustrating the trade‐off between A) CO₂ uptake versus CO₂/N₂ selectivity (upper bound), B) CO₂ uptake versus CO₂ heat of adsorption (lower bound) and C) CO₂/N₂ selectivity versus CO₂ heat of adsorption (lower bound). The legend applies to all figures in this manuscript, unless stated otherwise.

Figure 7

Comparison of CO₂/N₂ selectivity values reported using the IAST method (blue squares) and the uptake ratio method (cyan stars), illustrating that IAST predictions tend to report higher selectivity values than the uptake ratio.

Figure 8

CO₂/N₂ bound movement from 2010 to the current day—A) uptake versus selectivity, B) uptake versus heat of adsorption, and C) selectivity versus heat of adsorption. Symbols represent material class; Square—porous, star—porous with metal site, circle—MOF,triangle—MOF with metal site, diamond—nonporous. In C), the 2018 bound cannot be seen as it did not move from 2018 to 2022.

Figure 9

Carbon dioxide–methane empirical bounds illustrating the trade‐off between A) CO₂ uptake versus CO₂/CH₄ selectivity (upper bound), B) CO₂ uptake versus CO₂ heat of adsorption (lower bound) and C) CO₂/CH₄ selectivity versus CO₂ heat of adsorption (lower bound).

Figure 10

Carbon dioxide–hydrogen empirical bounds illustrating the trade‐off between A) CO₂ uptake versus CO₂/H₂ selectivity (upper bound), B) CO₂ uptake versus CO₂ heat of adsorption (lower bound) and C) CO₂/H₂ selectivity versus CO₂ heat of adsorption (lower bound).

Figure 11

Methane–hydrogen empirical bounds illustrating the trade‐off between A) CH₄ uptake versus CH₄/H₂ selectivity (upper bound), B) CH₄ uptake versus CH₄ heat of adsorption (lower bound) and C) CH₄/H₂ selectivity versus CH₄ heat of adsorption (lower bound).

Figure 12

Methane–nitrogen empirical bounds illustrating the trade‐off between A) CH₄ uptake versus CH₄/N₂ selectivity (upper bound), B) CH₄ uptake versus CH₄ heat of adsorption (lower bound) and C) CH₄/N₂ selectivity versus CH₄ heat of adsorption (lower bound).

Figure 13

Nitrogen–methane empirical bounds illustrating the trade‐off between A) N₂ uptake versus N₂/CH₄ selectivity, B) N₂ uptake versus N₂ heat of adsorption and C) N₂/CH₄ selectivity versus N₂ heat of adsorption. Bound curves have not been fitted because of the lack of materials.

Figure 14

Nitrogen–oxygen empirical bounds illustrating the trade‐off between A) N₂ uptake versus N₂/O₂ selectivity (upper bound), B) N₂ uptake versus N₂ heat of adsorption (lower bound) and C) N₂/O₂ selectivity versus N₂ heat of adsorption (lower bound).

Figure 15

Oxygen–nitrogen empirical bounds illustrating the trade‐off between A) O₂ uptake versus O₂/N₂ selectivity (upper bound), B) O₂ uptake versus O₂ heat of adsorption (lower bound) and C) O₂/N₂ selectivity versus O₂ heat of adsorption (lower bound).

Figure 16

Xenon–krypton empirical bounds illustrating the trade‐off between A) Xe uptake versus Xe/Kr selectivity (upper bound), B) Xe uptake versus Xe heat of adsorption (lower bound) and C) Xe/Kr selectivity versus Xe heat of adsorption (lower bound).

Figure 17

Number of 298 K isotherms for each material/gas combination identified in this literature search.

Figure 18

Zeolite 13X CO₂ 298 K isotherm reproducibility. Darker gradient indicates higher activation temperature, with orange indicating an unknown activation temperature. “?” indicates an unknown activation temperature or duration.

Figure 19

Zeolite 13X N₂ 298 K isotherm reproducibility. Darker gradient indicates higher activation temperature, with orange indicating an unknown activation temperature. “?” indicates an unknown activation temperature or duration.

Figure 20

Zeolite 13X CH₄ 298 K isotherm reproducibility. Darker gradient indicates higher activation temperature, with orange indicating an unknown activation temperature. “?” indicates an unknown activation temperature or duration.

Figure 21

CO₂ isotherms at 298 K on Zeolite 13X purchased from Zeochem.^{[ 90} , ¹⁵⁸ , ¹⁵⁹ , ¹⁶⁰ , ^{161 ]} The narrow range of activation conditions suggests that isolating synthesis/source alone is not sufficient to remove variability.

Figure 22

A) Reference isotherm experiments for CO₂ on ZSM‐5, with a 95% confidence interval of 0.075 mol kg⁻¹. Reproduced with permission under Creative Commons license CC BY 4.0.^{[ 156 ]} Copyright 2018, Springer. B) Reference isotherm experiments for CH₄ on Zeolite Y, with a 95% confidence interval of 0.09 mol kg⁻¹. Reproduced with permission under Creative Commons license CC BY 4.0.^{[ 167 ]} Copyright 2020, Springer.

Figure 23

Zeolite 13X (bought from Sigma‐Aldrich) TGA curve at a ramp rate of 10 °C min^‐1, showing a significant mass loss between 80 °C and 400 °C.

Figure 24

Adsorbent criteria star diagram, illustrating the major considerations for designing and selecting an appropriate adsorbent material.