Gas Adsorption in Novel Environments, Including Effects of Pore Relaxation

Adsorption experiments have been interpreted frequently with simplified model geometries, such as ideally flat surfaces and slit or cylindrical pores. Recent explorations of unusual environments, such as fullerenes and metal-organic-framework materials, have led to a broadened scope of experimental, theoretical and simulation investigations. This paper reviews a number of such studies undertaken by our group. Among the topics receiving emphasis are these: universality of gas uptake in pores, relaxation of a porous absorbent due to gas uptake and the novel phases of gases on a single nanotube, all of which studies have been motivated by recent experiments

Design of High Pressure Differential Volumetric Adsorption Measurements with Increased Accuracy

High pressure adsorption measurements for light gases on volumetric equipment are prone to error. Differential units reduce the sensitivity to leakage, gas compressibility, and temperature gradients, but remain highly sensitive to volume uncertainties, the calibration of which is difficult in the presence of low-density, microporous samples. Calibration error can be reduced using a high initial pressure differential and large calibration volume; however, systematic error is prevalent in the literature. Using both analytical and multivariate error analysis, we demonstrate that calibration of the differential unit with the differential pressure transducer significantly decreases volume sensitivity. We show that hydrogen adsorption to GX-31 superactivated carbon at 298 K and 80 bar can be measured with a 7 % error in measurement (i.e. within 0.05 wt% for a 100 mg sample), even when experimental volume calibration is determined only within ~1 %. This represents approximately a 2-7 fold increase in sensitivity relative to previous reports using differential measurements. We also provide a framework for optimizing the design of a volumetric adsorption unit. For virtually any system design, the improved differential methods offer a significant increase in precision relative to the conventional volumetric measurement (from 10- to over 250-fold, depending on the precision of the pressure transducer). This improvement further enhances advantages of the differential unit, in addition to advantages that arise for treating gas compressibility and temperature fluctuations

Effect of Time, Temperature, and Kinetics on the Hysteretic Adsorption-Desorption of H₂, Ar, and N₂ in the Metal-organic Framework Zn₂(bpdc)₂(bpee)

The intriguing hysteretic adsorption-desorption behavior of certain microporous metal-organic frameworks (MMOFs) has received considerable attention and is often associated with a gate-opening (GO) effect. Here, the hysteretic adsorption of N2 and Ar to Zn2(bpdc)2(bpee) (bpdc = 4,4\u27-biphenyldicarboxylate; bpee = 1,2-bipyridylethene) shows a pronounced effect of allowed experimental time at 77 and 87 K. When the time allowed is on the order of minutes for N2 at 77 K, no adsorption is observed, whereas times in excess of 60 h is required to achieve appreciable adsorption up to a limiting total coverage. Given sufficient time, the total uptake for N2 and Ar converged at similar reduced temperatures, but the adsorption of Ar was significantly more rapid than that of N2, an observation that can be described by activated configurational diffusion. N2 and Ar both exhibited discontinuous stepped adsorption isotherms with significant hysteresis, features that were dependent upon the allowed time. The uptake of H2 at 77 K was greater than for both N2 and Ar but showed no discontinuity in the isotherm, and hysteretic effects were much less pronounced. N2 and Ar adsorption data can be described by an activated diffusion process, with characteristic times leading to activation energies of 6.7 and 12 kJ/mol. Fits of H2 adsorption data led to activation energies in the range 2-7 kJ/mol at low coverage and nonactivated diffusion at higher coverage. An alternate concentration-dependent diffusion model is presented to describe the stepwise adsorption behavior, which is observed for N2 and Ar but not for H2. Equilibrium is approached very slowly for adsorption to molecularly sized pores at low temperature, and structural change (gate opening), although it may occur, is not required to explain the observations

Corresponding States Interpretation of Adsorption in Gate-Opening Metal-Organic Framework Cu(dhbc)2(4,4\u27-bpy)

The universal adsorption theory (UAT) extends the principle of corresponding states for gas compressibility to describe the excess density of an adsorbed phase at comparable reduced conditions. The UAT helps to describe experimental trends and provide predictive capacity for extrapolation from one adsorption isotherm to that of a different adsorbate. Here, we extend the UAT to a flexible metal-organic framework (MOF) as a function of adsorbate, temperature, and pressure. When considered via the UAT, the adsorption capacity and GO pressure of multiple gases to Cu(dhbc)2(4,4\u27-bpy) [H2dhbc=2,5-dihydroxybenzoic acid, bpy=bipyridine] show quantifiable trends over a considerable temperature and pressure range, despite the chemical and structural heterogeneity of the adsorbent. Exceptions include quantum gases (such as H2) and prediction of maximum capacity for large and/or polar adsorbates. A method to derive the heat of gate opening and heat of expansion from experimental trends is also presented, and the parameters can be treated as separable and independent over the temperature and pressure range studied. We demonstrate the relationship between the UAT and the common Dubinin analysis, which was not previously noted

Effect of Time, Temperature, and Kinetics on the Hysteretic Adsorption–Desorption of H₂, Ar, and N₂ in the Metal–Organic Framework Zn₂(bpdc)₂(bpee)

The intriguing hysteretic adsorption–desorption behavior of certain microporous metal–organic frameworks (MMOFs) has received considerable attention and is often associated with a gate-opening (GO) effect. Here, the hysteretic adsorption of N₂ and Ar to Zn₂(bpdc)₂(bpee) (bpdc = 4,4′-biphenyldicarboxylate; bpee = 1,2-bipyridylethene) shows a pronounced effect of allowed experimental time at 77 and 87 K. When the time allowed is on the order of minutes for N₂ at 77 K, no adsorption is observed, whereas times in excess of 60 h is required to achieve appreciable adsorption up to a limiting total coverage. Given sufficient time, the total uptake for N₂ and Ar converged at similar reduced temperatures, but the adsorption of Ar was significantly more rapid than that of N₂, an observation that can be described by activated configurational diffusion. N₂ and Ar both exhibited discontinuous stepped adsorption isotherms with significant hysteresis, features that were dependent upon the allowed time. The uptake of H₂ at 77 K was greater than for both N₂ and Ar but showed no discontinuity in the isotherm, and hysteretic effects were much less pronounced. N₂ and Ar adsorption data can be described by an activated diffusion process, with characteristic times leading to activation energies of 6.7 and 12 kJ/mol. Fits of H₂ adsorption data led to activation energies in the range 2–7 kJ/mol at low coverage and nonactivated diffusion at higher coverage. An alternate concentration-dependent diffusion model is presented to describe the stepwise adsorption behavior, which is observed for N₂ and Ar but not for H₂. Equilibrium is approached very slowly for adsorption to molecularly sized pores at low temperature, and structural change (gate opening), although it may occur, is not required to explain the observations

Gas Adsorption in Novel Environments, Including Effects of Pore Relaxation

Adsorption experiments have been interpreted frequently with simplified model geometries, such as ideally flat surfaces and slit or cylindrical pores. Recent explorations of unusual environments, such as fullerenes and metal-organic-framework materials, have led to a broadened scope of experimental, theoretical and simulation investigations. This paper reviews a number of such studies undertaken by our group. Among the topics receiving emphasis are these: universality of gas uptake in pores, relaxation of a porous absorbent due to gas uptake, and the novel phases of gases on a single nanotube, all of which studies have been motivated by recent experiments

A Generalized Adsorption-Phase Transition Model to Describe Adsorption Rates in Flexible Metal Organic Framework RPM3-Zn

Flexible gate-opening metal organic frameworks (GO-MOFs) expand or contract to minimize the overall free energy of the system upon accommodation of an adsorbate. The thermodynamics of the GO process are well described by a number of models, but the kinetics of the process are relatively unexplored. A flexible GO-MOF, RPM3-Zn, exhibits a significant induction period for opening by N2 and Ar at low temperatures, both above and below the GO pressure. A similar induction period is not observed for H2 or O2 at comparable pressures and temperatures, suggesting the rate of opening is strongly influenced by the gas-surface interaction rather than an external stress. The induction period leads to severe mass transfer limitations for adsorption and over-prediction of the gate-opening pressure. After review of a number of existing adsorption rate models, we find that none adequately describe the experimental rate data and similar timescales for diffusion and opening invalidate prior reaction-diffusion models. Statistically, the rate data are best described by a compressed exponential function. The resulting fitted parameters exceed the expectations for adsorption but fall within those expected for phase transition. By treating adsorption as a phase transition, we generalize the Avrami theory of phase transition kinetics to describe adsorption in both rigid and flexible hosts. The generalized theory is consistent with observed experimental trends relating to induction period, temperature, pressure, and gas-substrate interaction