Temperature Dependence of Sorption

High-capacity water sorbent cycles without hysteresis under dry conditions

Sorbents capable of cycling water vapor under dry conditions are critical for applications such as atmospheric water harvesting, desiccation, and heat pumps; however, few existing sorbents demonstrate both hysteresis-free behavior and cycling stability. Here we show that post-synthetic exchange with lithium, sodium, potassium, magnesium, and tetramethylammonium in the metal-organic framework (MOF) SU-102 ([(CH3)2NH2]2[Zr(HL)2]; H4L = ellagic acid) enables high-capacity water sorption under low humidity ranging from 11.1% to 4.3%. The champion material, Mg-SU-102, exhibits sharp water uptake at 4.3% RH, reaches a high maximum gravimetric capacity of 0.41 g/g (with 0.29 g/g at 15% RH), and displays minimal capacity loss over 500 adsorption-desorption cycles, with essentially no hysteresis. We use vibrational Stark spectroscopy to probe the local electric field environment within each ion-exchanged material and show that the trend in relative humidity follows a Hofmeister-type series in which the cation affects the ability for water to solvate the framework pores. We find strong deviation from this trend for the tetramethylammonium material, as the larger cation does not undergo capillary condensation sorption, suggesting that fine control over pore functionality is necessary. Establishing a correlation between water sorption and a Hofmeister-type series provides foundational principles for the design of porous ionic sorbents.

Adsorption Modeling Based on Classical Density Functional Theory and PC-SAFT: Temperature Extrapolation and Fluid Transfer

Adsorption is at the heart of many processes from gas separation to cooling. The design of adsorption-based processes requires equilibrium adsorption properties. However, data for adsorption equilibria are limited, and therefore, a model is desirable that uses as little data as possible for its parametrization, while allowing for data interpolation or even extrapolation. This work presents a physics-based model for adsorption isotherms and other equilibrium adsorption properties. The model is based on one-dimensional classical density functional theory (1D-DFT) and the perturbed-chain statistical associating fluid theory (PC-SAFT). The physical processes inside the pores are considered in a thermodynamically consistent approach that is computationally efficient. Once parametrized with a single isotherm, the model is able to extrapolate to other temperatures and outperforms the extrapolation capabilities of state-of-the-art models, such as the empirical isotherm models from Langmuir or Toth. Furthermore, standard combining rules can be used to transfer parameters adjusted to an adsorbent/fluid pair to other fluids. These features are demonstrated for the adsorption of N2, CH4, and CO2 in metal-organic frameworks. Thereby, the presented model can calculate temperature-dependent isotherms for various fluids by using data limited to a single isotherm as input.

Isoreticular Curves: A Theory of Capillary Condensation To Model Water Sorption within Microporous Sorbents

Metal-organic frameworks have gained traction as leading materials for water sorption applications due to precise chemical tunability of their well-ordered pores. These applications include atmospheric water capture, heat pumps, desiccation, desalination, humidity control, and thermal batteries. However, the relationships between the framework pore structure and the measurable water sorption properties, namely critical relative humidity for condensation, maximal capacity, and pore size or temperature for the onset of hysteresis, have not been clearly delineated. Herein, we precisely formulate these relationships by application of the theory of capillary condensation and macroscopic thermodynamic models to a large data set of MOF water isotherms. These relationships include a concept termed isoreticular curves that relates the critical pressure for pore condensation (α), gravimetric capacity (Qmax), and hydrophilicity (the Gibbs free energy for binding water, ΔG) as Qmax = a1(ΔG/ln α)2 + a2(ΔG/ln α), with constants a1 and a2 dependent upon the density and volume occupied by the linker and secondary building unit, and framework topology. Through this analysis, we propose guidelines for the maximization of sorption capacity at a given relative humidity with minimal hysteresis and discuss the theoretical limits for capacity at low relative humidity. This model provides an explanation for the lack of high-capacity frameworks at low relative humidity, as increasing pore size also causes an increase in relative humidity. We propose a loose upper bound of Qmax = -0.25(1/ln α)2 - 1.75(1/ln α) for the limit of maximal capacity at a given relative humidity in the dry regime. These guidelines are consequential for the design of new materials for water sorption applications.

Physicochemical Properties, Equilibrium Adsorption Performance, Manufacturability, and Stability of TIFSIX-3-Ni for Direct Air Capture of CO2

The use of adsorbents for direct air capture (DAC) of CO2 is regarded as a promising and essential carbon dioxide removal technology to help meet the goals outlined by the 2015 Paris Agreement. A class of adsorbents that has gained significant attention for this application is ultramicroporous metal organic frameworks (MOFs). However, the necessary data needed to facilitate process scale evaluation of these materials is not currently available. Here, we investigate TIFSIX-3-Ni, a previously reported ultramicroporous MOF for DAC, and measure several physicochemical and equilibrium adsorption properties. We report its crystal structure, textural properties, thermal stability, specific heat capacity, CO2, N2, and H2O equilibrium adsorption isotherms at multiple temperatures, and Ar and O2 isotherms at a single temperature. For CO2, N2, and H2O, we also report isotherm model fitting parameters and calculate heats of adsorption. We assess the manufacturability and process stability of TIFSIX-3-Ni by investigating the impact of batch reproducibility, binderless pelletization, humidity, and adsorption-desorption cycling (50 cycles) on its crystal structure, textural properties, and CO2 adsorption. For pelletized TIFSIX-3-Ni, we also report its skeletal, pellet, and bed density, total pore volume, and pellet porosity. Overall, our data enable initial process modeling and optimization studies to evaluate TIFSIX-3-Ni for DAC at the process scale. They also highlight the possibility to pelletize TIFSIX-3-Ni and the limited stability of the MOF under humid and oxidative conditions as well as upon multiple adsorption-desorption cycles.

Kaolin-Derived Porous Silico-Aluminate Nanoparticles as Absorbents for Emergency Disposal of Toluene Leakage

To rapidly eliminate toluene from aqueous environments during leakage accidents, this paper synthesized porous silico-aluminate nanoparticles (SANs) via a hydrothermal method, using cost-effective and non-toxic natural kaolin as the basic raw material. The morphology and structure of the porous SANs were characterized using scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), and BET-specific surface area tests. The effects of different conditions, such as the dosage of porous SANs, initial concentration of toluene, temperature, capture time, and pH, on the adsorption performance of porous SANs were analyzed. The as-prepared SANs exhibited a high removal efficiency and rapid adsorption performance toward toluene in aqueous solution. Finally, the kinetics of the adsorption of toluene in aqueous solution by porous SANs were investigated. The mechanism of the adsorption of toluene by porous SANs was further discussed. These findings provide a cost-effective and highly efficient absorbent for the emergency disposal of toluene leakage accidents.

Bridging the Adsorption Data and Adsorption Process by Introducing a Polynomial Structure To Accurately Describe IUPAC Isotherms, Stepwise Isotherms, and Stepwise Breakthrough Curves

Porous heterogeneous adsorbents, those composed of multiple pore structures and surface chemical adsorption sites, can result in various gas or vapor adsorption isotherms, including five types of IUPAC adsorption isotherms and stepwise adsorption isotherms that have been difficult to model using a single adsorption equilibrium model. The limitation of the above equilibrium model further restricts the calculations of complex stepwise breakthrough curves. To bridge the adsorption data and adsorption process, it is important to first develop a simple model or method to describe these isotherms of various complex adsorption systems. In this work, assuming that the effect of the diffusion rate can be neglected under the static condition and the adsorption process is discontinuous, the number of adsorption isotherm inflection points can be used to represent the changed number of adsorption interactions. With the introduction of the polynomial structure, a series of empirical or semi-empirical polynomial adsorption models were developed. The N-site polynomial Langmuir-Freundlich equation could accurately fit common type I, II, III, IV, and V adsorption isotherms and complex stepwise adsorption isotherms covering various adsorbates, such as volatile organic compounds (VOCs), toxic industrial chemicals (TICs), water vapor, and carbon dioxide, as well as different adsorbents, such as metal/covalent organic frameworks (MOFs/COFs), zeolites, and porous carbons. Similarly, the introduction of a polynomial structure, such as the N-site polynomial Yoon-Nelson equation, was also successful in the description of interesting stepwise breakthrough curves. This work provides a more accurate adsorption equilibrium model to characterize all types of isotherms. As a foundation model, it is expected to be used to simulate the gas-solid adsorption process inside the fixed and fluidized beds packed with porous adsorbents.

Controlling Adsorption of Diblock Copolymer Nanoparticles onto an Aldehyde-Functionalized Hydrophilic Polymer Brush via pH Modulation

Sterically stabilized diblock copolymer nanoparticles with a well-defined spherical morphology and tunable diameter were prepared by RAFT aqueous emulsion polymerization of benzyl methacrylate at 70 °C. The steric stabilizer precursor used for these syntheses contained pendent cis-diol groups, which means that such nanoparticles can react with a suitable aldehyde-functional surface via acetal bond formation. This principle is examined herein by growing an aldehyde-functionalized polymer brush from a planar silicon wafer and studying the extent of nanoparticle adsorption onto this model substrate from aqueous solution at 25 °C using a quartz crystal microbalance (QCM). The adsorbed amount, Γ, depends on both the nanoparticle diameter and the solution pH, with minimal adsorption observed at pH 7 or 10 and substantial adsorption achieved at pH 4. Variable-temperature QCM studies provide strong evidence for chemical adsorption, while scanning electron microscopy images recorded for the nanoparticle-coated brush surface after drying indicate mean surface coverages of up to 62%. This fundamental study extends our understanding of the chemical adsorption of nanoparticles on soft substrates.

Measurement of Physicochemical Properties and CO2, N2, Ar, O2, and H2O Unary Adsorption Isotherms of Purolite A110 and Lewatit VP OC 1065 for Application in Direct Air Capture

Direct air capture (DAC) using solid adsorbents has gained significant attention as a carbon dioxide removal (CDR) technology to help limit global temperature rise to below 2 °C. One large area of focus is the development of new adsorbent materials for DAC. However, the necessary data needed to employ these materials in process models for adsorbent screening are rarely available. Here, we showcase Purolite A110, a commercially available amine-functionalized polymeric resin, as a new candidate adsorbent for DAC and compare its properties to a current benchmark, Lewatit VP OC 1065. For both materials, we report their chemical features and composition, skeletal, particle, and bed density, total pore volume, particle porosity, BET area, thermal stability, and specific heat capacity. We determine their equilibrium sorption properties by measuring the volumetric CO2 isotherms at 288, 298, 308, 333, 343, 353, and 393 K, N2 and H2O isotherms at 288, 298, and 308 K, and Ar and O2 isotherms at 298 K. For CO2, N2, and H2O, we also present the corresponding isotherm model fitting parameters and heats of adsorption. These data can help facilitate process modeling and optimization studies to properly assess these adsorbents at scale.

Cooperativity in Sorption Isotherms

We present a general theory of cooperativity in sorption isotherms that can be applied to sorbent/gas and sorbent/solution isotherms and is valid even when sorbates dissolve into or penetrate the sorbent. Our universal foundation, based on the principles of statistical thermodynamics, is the excess number of sorbates (around a probe sorbate), which can capture the cooperativities of sigmoidal and divergent isotherms alike via the ln-ln gradient of an isotherm (the excess number relationship). The excess number relationship plays a central role in deriving isotherm equations. Its combination with the characteristic relationship (i.e., a succinct summary of the sorption mechanism via the dependence of excess number on interfacial coverage or sorbate activity) yields a differential equation whose solution is an isotherm equation. The cooperative isotherm equations for convergent and divergent cooperativities derived from this novel method can be applied to fit experimental data traditionally fitted via various isotherm models, with a clear statistical thermodynamic interpretation of their parameters..

Sorption from Solution: A Statistical Thermodynamic Fluctuation Theory

Given an experimental solid/solution sorption isotherm, how can we gain insight into the underlying sorption mechanism on a molecular basis? Classifying sorption isotherms, for both completely and partially miscible solvent/sorbate systems, has been useful, yet the molecular foundation of these classifications remains speculative. Isotherm models, developed predominantly for solid/gas sorption, have been adapted to solid/solution isotherms, yet how their parameters should be interpreted physically has long remained ambiguous. To overcome the inconclusiveness, we establish in this paper a universal theory that can be used for interpreting and modeling solid/solution sorption. This novel theory shares the same theoretical foundation (i.e., the statistical thermodynamic fluctuation theory) not only with solid/gas sorption but also with solvation in liquid solutions and solution nonidealities. The key is the Kirkwood-Buff χ parameter, which quantifies the net self-interaction (i.e., solvent-solvent and sorbate-sorbate interactions minus solvent-sorbate interaction) via the Kirkwood-Buff integral in the same manner as the solvation theory and, unlike the Flory χ, is not limited to the lattice model. We will demonstrate that the Kirkwood-Buff χ is the key not only to isotherm classification but also to generalizing our recent statistical thermodynamic gas (vapor) isotherm, which is capable of fitting most of the solid/solution isotherm types.

Unusual Temperature Dependence of Water Sorption in Semicrystalline Hydrogels

Water vapor sorption is a ubiquitous phenomenon in nature and plays an important role in various applications, including humidity regulation, energy storage, thermal management, and water harvesting. In particular, capturing moisture at elevated temperatures is highly desirable to prevent dehydration and to enlarge the tunability of water uptake. However, owing to the thermodynamic limit of conventional materials, sorbents inevitably tend to capture less water vapor at higher temperatures, impeding their broad applications. Here, an inverse temperature dependence of water sorption in poly(ethylene glycol) (PEG) hydrogels, where their water uptake can be doubled with increasing temperature from 25 to 50 °C, is reported. With mechanistic modeling of water-polymer interactions, this unusual water sorption is attributed to the first-order phase transformation of PEG structures, and the key parameters for a more generalized strategy in materials development are identified. This work elucidates a new regime of water sorption with an unusual temperature dependence, enabling a promising engineering space for harnessing moisture and heat.

Understanding Sorption Mechanisms Directly from Isotherms

Currently, more than 100 isotherm models coexist for the six IUPAC isotherm types. However, no mechanistic insights can be reached when several models, each claiming a different mechanism, fit an experimental isotherm equally well. More frequently, popular isotherm models [such as the site-specific models like Langmuir, Brunauer-Emmett-Teller (BET), and Guggenheim-Anderson-de Boer (GAB)] have been applied to real and complex systems that break their basic assumptions. To overcome such conundrums, we establish a universal approach to model all isotherm types, attributing the difference to the sorbate-sorbate and sorbate-surface interactions in a systematic manner. We have generalized the language of the traditional sorption models (such as the monolayer capacity and the BET constant) to the model-free concepts of partitioning and association coefficients that can be applied across the isotherm types. Through such a generalization, the apparent contradictions, caused by applying the site-specific models alongside with cross-sectional area of sorbates for the purpose of surface area determination, can be eliminated straightforwardly.

Exceptionally high selectivity in the separation of light hydrocarbons by adsorption on MIL-127(Fe) and on a (9,9) carbon nanotube

Porous solids with channel sizes that are not much above the size of small hydrocarbons can yield extremely large adsorption selectivity. Our Grand Canonical Monte-Carlo simulations indicate exceptionally high selectivity for the separation of methane, ethane and propane from natural gas. At 250 K the C₃H₈/CH₄ separation on MIL-127 at low pressure has a selectivity of more than 1000 and the C₃H₈/CH₄ separation on CNT (9,9) is even above 2000. This is due to the strong molecule lattice interaction in narrow channels which leads to large enthalpies of adsorption. The Arrhenius law for the Henry coefficients is analysed in order to show that the effect is due to this enthalpy rather than to steric reasons.

Bioengineered textiles with peptide binders that capture SARS-CoV-2 viral particles

The use of personal protective equipment (PPE), face masks and ventilation are key strategies to control the transmission of respiratory viruses. However, most PPE provides physical protection that only partially prevents the transmission of viral particles. Here, we develop textiles with integrated peptide binders that capture viral particles. We fuse peptides capable of binding the receptor domain of the spike protein on the SARS-CoV-2 capsid to the cellulose-binding domain from the Trichoderma reesei cellobiohydrolase II protein. The hybrid peptides can be attached to the cellulose fibres in cotton and capture SARS-CoV-2 viral particles with high affinity. The resulting bioengineered cotton captures 114,000 infective virus particles per cm2 and reduces onwards SARS-CoV-2 infection of cells by 500-fold. The hybrid peptides could be easily modified to capture and control the spread of other infectious pathogens or for attachment to different materials. We anticipate the use of bioengineered protective textiles in PPE, facemasks, ventilation, and furnishings will provide additional protection to the airborne or fomite transmission of viruses.

Surface Area Estimation: Replacing the Brunauer-Emmett-Teller Model with the Statistical Thermodynamic Fluctuation Theory

Surface area estimation using the Brunauer-Emmett-Teller (BET) analysis has been beset by difficulties. The BET model has been applied routinely to systems that break its basic assumptions. Even though unphysical results arising from force-fitting can be eliminated by the consistency criteria, such a practice, in turn, complicates the simplicity of the linearized BET plot. We have derived a general isotherm from the statistical thermodynamic fluctuation theory, leading to facile isotherm fitting because our isotherm is free of the BET assumptions. The reinterpretation of the monolayer capacity and the BET constant has led to a statistical thermodynamic generalization of the BET analysis. The key is Point M, which is defined as the activity at which the sorbate-sorbate excess number at the interface is at its minimum (i.e., the point of strongest sorbate-sorbate exclusion). The straightforwardness of identifying Point M and the ease of fitting by the statistical thermodynamic isotherm have been demonstrated using zeolite 13X and a Portland cement paste. The adsorption at Point M is an alternative for the BET monolayer capacity, making the BET model and its consistency criteria unnecessary. The excess number (i) replaces the BET constant as the measure of knee sharpness and monolayer coverage, (ii) links macroscopic (isotherms) to microscopic (simulation), and (iii) serves as a measure of sorbate-sorbate interaction as a signature of sorption cooperativity in porous materials. Thus, interpretive clarity and ease of analysis have been achieved by a statistical thermodynamic generalization of the BET analysis.