Physical adsorption of gases: the case for absolute adsorption as the basis for thermodynamic analysis

Aspects of Gas Storage: Confined Geometry Effects on the High-Pressure Adsorption Behavior of Supercritical Fluids

During the last decades, major progress was made concerning the understanding of subcritical low-pressure adsorption of fluids like nitrogen and argon at their boiling temperatures in nanoporous materials. It was possible to understand how structural properties affect the shape of the adsorption isotherms. However, within the context of gas storage applications, supercritical high-pressure gas adsorption is important. A key feature here is that the experimentally determined surface excess adsorption isotherm may exhibit a characteristic maximum at a certain pressure. For a given temperature and adsorptive/adsorbent system, the surface excess maximum (and the corresponding adsorbed amount) is related to the storage capacity of the adsorbent. However, there is still a lack of understanding of how key textural properties such as surface area and pore size affect details of the shape of supercritical high-pressure adsorption isotherms. To address these open questions, we have performed a systematic experimental study assessing the effect of pore size/structure on the supercritical adsorption isotherms of pure fluids such as C2H4, CO2, and SF6 over a wider range of temperatures and pressures on a series of model materials exhibiting well-defined pore sizes, i.e., ordered micro- and mesoporous materials (e.g., NaY zeolite, KIT-6 silica, and MCM-48 silica). A fundamental result of our experiments is a unique fluid-independent correlation between the pressure of the surface excess maximum pmax (at a given temperature) and the pore size (by taking into account the kinetic diameter of the fluid and the underlying effective attractive fluid-wall interaction). Summarizing, our results suggest important structure-property relationships, allowing one to determine, for given thermodynamic conditions, important information related to the optimal operating conditions for supercritical adsorption applications. The insights may also serve as a basis for optimizing and tailoring the properties of nanoporous adsorbent materials for gas storage applications.

Effect of Physical Nature (Intact and Powder) of Coal on CO2 Adsorption at the Subcritical Pressure Range (up to 6.4 MPa at 298.15 K)

This study examines the influence of subcritical pressure and the physical nature (intact and powder) of coal samples on CO₂ adsorption capacity and kinetics in the context of CO₂ sequestration in shallow level coal seams. Manometric adsorption experiments were carried out on two anthracite and one bituminous coal samples. Isothermal adsorption experiments were carried out at 298.15 K in two pressure ranges: less than 6.1 MPa and up to 6.4 MPa relevant to gas/liquid adsorption. The adsorption isotherms of intact anthracite and bituminous samples were compared to that of the powdered samples. The powdered samples of the anthracitic samples had a higher adsorption than that of intact samples due to the exposed adsorption sites. The intact and powdered samples of bituminous coal, on the other hand, exhibited comparable adsorption capacities. The comparable adsorption capacity is attributed to the intact samples' channel-like pores and microfractures, where high density CO₂ adsorption occurs. The adsorption-desorption hysteresis patterns and the residual amount of CO₂ trapped in the pores reinforce the influence of the physical nature of the sample and pressure range on the CO₂ adsorption-desorption behavior. The intact 18 ft AB samples showed significantly different adsorption isotherm pattern to that of powdered samples for experiments conducted up to 6.4 MPa equilibrium pressure due to the high-density CO₂ adsorbed phase in the intact samples. The adsorption experimental data fit into the theoretical models showed that the BET model fit better than the Langmuir model. The experimental data fit into the pseudo first order, second order, and Bangham pore diffusion kinetic models showed that the rate-determining steps are bulk pore diffusion and surface interaction. Generally, the results obtained from the study demonstrated the significance of conducting experiments with large, intact core samples pertinent to CO₂ sequestration in shallow coal seams.

Low Subcritical CO2 Adsorption-Desorption Behavior of Intact Bituminous Coal Cores Extracted from a Shallow Coal Seam

This study focuses on improving fundamental understanding of low, subcritical CO₂ adsorption-desorption behavior of bituminous coals with the aim to evaluate the utility of shallow-depth coal seams for safe and effective CO₂ storage. Comprehensive data and a detailed description of coal-CO₂ interactions, e.g., adsorption, desorption, and hysteresis behavior of intact bituminous coals at CO₂ pressures <0.5 MPa, are limited. Manometric sorption experiments were performed on coal cores (50 mm dia. and 30- or 60-mm length) obtained from a 30 m deep coal seam located at the Upper Silesian Basin in Poland. Experimental results revealed that the adsorption capacities were correlated to void volume and equilibrium time under low-pressure injection (0.5 MPa). The positive deviation, observed in the hysteresis of adsorption-desorption isotherm patterns, and the increased sample mass at the end of the tests suggested CO₂ pore diffusion and condensation. This behavior is vital for assessing low-pressure CO₂ injection and storage capabilities of shallow coal seams where confining pressure is much lower than that of the deeper seams. Overall, CO₂ adsorption depicts a type II adsorption isotherm and a type H3 hysteresis pattern of the IUPAC classification. Experimental results fitted better to the Brunauer-Emmett-Teller model than the Langmuir isotherm model. CO₂ adsorption behavior of intact cores was also evaluated by characteristic curves. It was found that Curve I favored physical forces, i.e., the presence of van der Waals/London dispersion forces to describe the coal-CO₂ interactions. However, analysis of Curve II indicated that the changing pressure-volume behavior of CO₂ in the adsorbed phase, under low equilibrium pressures, cannot be ignored.

How Important Is the Internal Hydrophobicity of Metal-Organic Frameworks for the Separation of Water/Alcohol Mixtures?

Short-chain alcohols obtained by fermentation will play a key role in the industrial transformation toward green chemistry because of their use as fuel additives and fuels or for their conversion into olefins. The fermentation broth is often a highly diluted aqueous solution that requires separation, for instance, by liquid phase adsorption in nanoporous materials. However, entropy effects that prefer the adsorption of water might significantly reduce the separation efficiency─even in nanoporous materials with internal hydrophobicity. In this paper, we investigate this assumption by a case study on the separation of aqueous alcohol mixtures by liquid phase adsorption in CAU-10─an ultramicroporous metal-organic framework with internal hydrophobicity─using adsorption experiments and grand canonical Monte Carlo simulations to predict both the unary gas adsorption isotherms of ethanol, n-butanol, or water as well as the multicomponent liquid phase adsorption isotherms of their mixtures. It was observed that separation from the liquid phase is commonly driven by entropy effects and strong interactions between the guest molecules─both favoring the adsorption of water and thus complicating the separation of fermentation product by adsorption─while the internal hydrophobicity of CAU-10 is of comparatively little importance.

Membranes Based on PTMSP/PVTMS Blends for Membrane Contactor Applications

In this work, perspective polymeric materials were developed for membrane contactor applications, e.g., for the dissolved oxygen removal from amine CO₂ capture solvents. Several polymeric blends based on poly[1-trimethylsilyl-1-propyne] (PTMSP) and poly[vinyltrimethylsilane] (PVTMS) were studied. The gas and water vapor sorption and permeability coefficients for the PTMSP/PVTMS blend membranes at different PVTMS contents (0-100%) were obtained under temperatures of 30 and 60 °C for the first time. As the PVTMS content increases, the O₂ and CO₂ permeabilities decrease by 160 and 195 times at 30 °C, respectively. The fractional accessible volume of the polymer blends decreases accordingly. The transport of the CO₂ capture solvent vapors through the PTMSP/PVTMS blend membranes were determined in thermo-pervaporation (TPV) mode using aqueous monoethanolamine (30%), N-methyldiethanolamine (40%), and 2-amino-2-methyl-1-propanol (30%) solutions as model amine solvents at 60 °C. The membranes demonstrated high pervaporation separation factors with respect to water, resulting in low amine losses. A joint analysis of the gas permeabilities and aqueous alkanolamine TPV data allowed us to conclude that the polymer blend composition of PTMSP/PVTMS 70/30 provides an optimal combination of a sufficiently high oxygen permeability and the pervaporation separation factor at a temperature of 60 °C.

Alginate Ag for Composite Hollow Fiber Membrane: Formation and Ethylene/Ethane Gas Mixture Separation

Membranes based on natural polymers, in particular alginate, are of great interest for various separation tasks. In particular, the possibility of introducing silver ions during the crosslinking of sodium alginate makes it possible to obtain a membrane with an active olefin transporter. In this work, the creation of a hollow fiber composite membrane with a selective layer of silver alginate is proposed for the first time. The approach to obtaining silver alginate is presented in detail, and its sorption and transport properties are also studied. It is worth noting the increased selectivity of the material for the ethylene/ethane mixture (more than 100). A technique for obtaining a hollow fiber membrane from silver alginate has been developed, and its separating characteristics have been determined. It is shown that in thin layers, silver alginate retains high values of selectivity for the ethylene/ethane gas pair. The obtained gas transport properties demonstrate the high potential of using membranes based on silver alginate for the separation of an olefin/paraffin mixture.

The Rigid Adsorbent Lattice Fluid Model: Thermodynamic Consistency and Relationship to the Real Adsorbed Solution Theory

The Rigid Adsorbent Lattice Fluid model has been shown to comply with all the requirements for thermodynamic consistency in the case of an adsorbent that does not undergo structural changes. This is achieved by introducing a correction to the reduced density function that multiplies the combinatorial term. A procedure to calculate the predicted adsorbed mixture activity coefficients has been presented that allows the production of excess Gibbs energy plots at a constant reduced grand potential. The predicted nonideality is structurally consistent with the Non-Ideal Adsorbed Solution Theory of Myers in terms of both its dependence on concentration and reduced grand potential. The ability to generate excess Gibbs energy values allows linking the new Rigid Adsorbent Lattice Fluid model to the traditional Real Adsorbed Solution Theory providing an alternative approach to predicting multicomponent adsorption based solely on pure component data.

Hydrophobic Ag-Containing Polyoctylmethylsiloxane-Based Membranes for Ethylene/Ethane Separation in Gas-Liquid Membrane Contactor

The application of gas-liquid membrane contactors for ethane-ethylene separation seems to offer a good alternative to conventional energy-intensive processes. This work aims to develop new hydrophobic composite membranes with active ethylene carriers and to demonstrate their potential for ethylene/ethane separation in gas-liquid membrane contactors. For the first time, hybrid membrane materials based on polyoctylmethylsiloxane (POMS) and silver tetrafluoroborate, with a Si:Ag ratio of 10:0.11 and 10:2.2, have been obtained. This technique allowed us to obtain POMS-based membranes with silver nanoparticles (8 nm), which are dispersed in the polymer matrix. The dispersion of silver in the POMS matrix is confirmed by the data IR-spectroscopy, wide-angle X-ray diffraction, and X-ray fluorescence analyses. These membranes combine the hydrophobicity of POMS and the selectivity of silver ions toward ethylene. It was shown that ethylene sorption at 600 mbar rises from 0.89 cm³(STP)/g to 3.212 cm³(STP)/g with an increase of Ag content in POMS from 0 to 9 wt%. Moreover, the membrane acquires an increased sorption affinity for ethylene. The ethylene/ethane sorption selectivity of POMS is 0.64; for the membrane with 9 wt% silver nanoparticles, the ethylene/ethane sorption selectivity was 2.46. Based on the hybrid material, POMS-Ag, composite membranes were developed on a polyvinylidene fluoride (PVDF) porous support, with a selective layer thickness of 5–10 µm. The transport properties of the membranes were studied by separating a binary mixture of ethylene/ethane at 20/80% vol. It has been shown that the addition of silver nanoparticles to the POMS matrix leads to a decrease in the ethylene permeability, but ethylene/ethane selectivity increases from 0.9 (POMS) to 1.3 (9 wt% Ag). It was noted that when the POMS-Ag membrane is exposed to the gas mixture flow for 3 h, the selectivity increases to 1.3 (0.5 wt% Ag) and 2.3 (9 wt% Ag) due to an increase in ethylene permeability. Testing of the obtained membranes in a gas-liquid contactor showed that the introduction of silver into the POMS matrix makes it possible to intensify the process of ethylene mass transfer by more than 1.5 times.

Reference surface excess isotherms for carbon dioxide adsorption on ammonium ZSM-5 at various temperatures

This work is part of the effort at the Facility for Adsorbent Characterization and Testing (FACT lab) at the National Institute of Standards and Technology (NIST) to develop reference materials, reference data, and measurement best practices for adsorption metrology. High-pressure surface excess isotherms for CO2 adsorption on NIST Reference Material 8852 (ammonium ZSM-5) at 15 °C, 25 °C, and 35 °C are reported, expanding on a FACT Lab-organized international interlaboratory study on this sorbent/sorbate pair at 20 °C. The range of temperatures of the present study is of interest for many CO2 adsorption measurements and applications. Measurements were made using five different adsorption instruments, both manometric and gravimetric. Excellent agreement in the measured isotherms among the instruments was found. An empirical reference equation of the form,

$${n}_{ex,ref}({P}_{eq})=\frac{c}{\{{1+\mathrm{exp}[\left(-\mathrm{ln}\left(P\right)+a\right)/b ]\}}^{b }} ,$$ n e x , r e f ( P eq ) = c { 1 + exp [ - ln P + a / b ] } b ,

[nex,ref is surface excess uptake (mmol/g); Peq is equilibrium pressure (MPa); P is (Peq)/(1 MPa)]; a, b, c are constants] and the 95% uncertainty interval were determined for the isotherms at each of the temperatures. Lastly, the isosteric heat of adsorption is estimated from absolute isotherms derived from the surface excess reference data.

Supercritical methane adsorption measurement on shale using the isotherm modelling aspect

In shale gas reservoirs, adsorbed gas accounts for 85% of the total shale gas in place (GIP). The adsorption isotherms of shale samples are significant for understanding the mechanisms of shale gas storage, primarily for assessing the GIP and developing an accurate gas flow behaviour. Isothermal adsorption experiments primarily determine the adsorption capacity of methane in shale gas reservoirs. However, experimental data is limited due to the heterogeneous properties of shale and extreme reservoir conditions at high pressures and temperatures. This work discusses the effect of total carbon (TOC), pore size distributions, and mineralogical properties on adsorption capacity. In this study, the gravimetric adsorption isotherm measurement method was applied to obtain the adsorption isotherms of methane on four shale core samples from Eagle Ford reservoirs. Four shale core samples with TOC of 9.67% to 14.4% were used. Adsorption experiments were conducted at a temperature of 120 °C and to a maximum pressure of 10 MPa. The data obtained experimentally were compared with adsorption isotherm models to assess each model's applicability in describing the shale adsorption behaviour. A comparison of these models was performed using fitting and error analysis. It was observed that the calculated absolute adsorption of supercritical methane is higher than the excess adsorption. The percentage of differences between the absolute and excess adsorption is more significant at a pressure higher than the critical methane pressure of 9.6%. Sample EF C has the highest adsorption capacity of 1.308 mg g⁻¹, followed by EF D 1.194 mg g⁻¹, EF B 0.546 mg g⁻¹, and EF A 0.455 mg g⁻¹. Three statistical error analyses, average relative error (ARE), the Pearson chi-square (χ²) test and root mean square error (RMSE) deviation were used to assess the applicability of each model in describing the adsorption behaviour of shale samples. The order of adsorption isotherm fitting with experimental data is Toth > D–R = Freundlich > Langmuir. Error analysis shows that the Toth model has the lowest values compared to other models, 0.6% for EF B, 2.5% for EF C, and 2.2% for EF A and EF D, respectively.

Adsorption isotherm can be used to depict the adsorption in shale.

Improving Reproducibility in Hydrogen Storage Material Research

Research into new reversible hydrogen storage materials has the potential to help accelerate the transition to a hydrogen economy. The discovery of an efficient and cost-effective method of safely storing hydrogen would revolutionise its use as a sustainable energy carrier. Accurately measuring storage capacities - particularly of novel nanomaterials - has however proved challenging, and progress is being hindered by ongoing problems with reproducibility. Various metal and complex hydrides are being investigated, together with nanoporous adsorbents such as carbons, metal-organic frameworks and microporous organic polymers. The hydrogen storage properties of these materials are commonly determined using either the manometric (or Sieverts) technique or gravimetric methods, but both approaches are prone to significant error, if not performed with great care. Although commercial manometric and gravimetric instruments are widely available, they must be operated with an awareness of the limits of their applicability and the error sources inherent to the measurement techniques. This article therefore describes the measurement of hydrogen sorption and covers the required experimental procedures, aspects of troubleshooting and recommended reporting guidelines, with a view of helping improve reproducibility in experimental hydrogen storage material research.

Enthalpic and Liquid-Phase Adsorption Study of Toluene-Cyclohexane and Toluene-Hexane Binary Systems on Modified Activated Carbons

The liquid-phase adsorption of toluene in cyclohexane and hexane solutions on modified activated carbons was evaluated; the energy involved in the interaction between these solutions and the solids was determined by immersion enthalpies of pure solvents and their mixtures, and the contribution of the system constituents was calculated by differential enthalpies. The thermal treatment generated modifications that favored adsorption and interaction with the evaluated solutions, since it increased the textural parameters and the basic character of the samples. Cyclohexane could create greater competition with the adsorption sites compared to hexane, but it favored the increase in adsorption capacities (0.416 to 1.026 mmol g⁻¹) and the interactions with the solid evaluated through the immersion enthalpies. The immersion enthalpies of pure solvents (−16.36 to −112.7 J g⁻¹) and mixtures (−25.65 to −104.34 J g⁻¹) had exothermic behaviors that were decreasing due to the possible displacement of solvent molecules when increasing the solute concentration in the mixtures. The differential enthalpies for toluene were negative (−18.63 to −2.14 J), mainly due to the π–π interaction with the solid, while those of the solvent–solid component tended to be positive values (−4.25 to 55.97 J) due to the displacement of the solvent molecules by those of toluene.

Measurement and interpretation of unary supercritical gas adsorption isotherms in micro-mesoporous solids

Gas adsorption at high pressures in porous solids is commonly quantified in terms of the excess amount adsorbed. Despite the wide spectrum of adsorbent morphologies available, the analysis of excess adsorption isotherms has mostly focused on microporous materials and the role of mesoporosity remains largely unexplored. Here, we present supercritical CO2 adsorption isotherms measured at $$T=308$$ T = 308  K in the pressure range $$p=0.02{-}21$$ p = 0.02 - 21  MPa on three adsorbents with distinct fractions of microporosity, $$\phi_2$$ ϕ 2 , namely a microporous metal-organic framework ($$\phi_2=70$$ ϕ 2 = 70 %), a micro-mesoporous zeolite ($$\phi_2=38$$ ϕ 2 = 38 %) and a mesoporous carbon ($$\phi_2<0.1$$ ϕ 2 < 0.1 %). The results are compared systematically in terms of excess and net adsorption relative to two distinct reference states–the space filled with gas in the presence/absence of adsorbent–that are defined from two separate experiments using helium as the probing gas. We discuss the inherent difficulties in extracting from the supercritical adsorption isotherms quantitative information on the properties of the adsorbed phase (its density or volume), because of the nonuniform distribution of the latter within and across the different classes of pore sizes. Yet, the data clearly reveal pore-size dependent adsorption behaviour, which can be used to identify characteristic types of isotherm and to complement the information obtained using the more traditional textural analysis by physisorption.

Computational Investigation of Correlations in Adsorbate Entropy for Pure-Silica Zeolite Adsorbents

Vast numbers of unstudied hypothetical porous frameworks continue to spark interest in optimizing adsorption and catalytic processes. Evaluating the use of such materials depends on the accessibility of thermodynamic metrics such as the free energy, which, in turn, depend on the satisfactory estimation or calculation of the adsorption entropy, which often remains elusive. Previous works using simulations and experimental data have demonstrated relationships between the entropy and system descriptors, allowing for sensible predictions based on more-easily obtained physical parameters. However, the resultant conclusions were either based on experimental data for industrially relevant alkanes or lacked a significant sample size. In this paper, we evaluate correlations between gas-phase and adsorbed-phase entropies for a larger and more chemically diverse set of adsorbate molecules by using force fields and statistical mechanical expressions to calculate those entropies. In total, we perform calculations for 37 molecules across 10 chemical categories available in the TraPPE force field set, as adsorbed in five siliceous zeolites. Our results show that linear correlations between the gas- and adsorbed-phase entropies persist for the larger and diverse set of adsorbate molecules studied here, proving a broader applicability and justifying the use of simple correlations for many adsorbates and, presumably, adsorbent materials.

The role of molecular modelling and simulation in the discovery and deployment of metal-organic frameworks for gas storage and separation

Metal-organic frameworks (MOFs) are highly tuneable, extended-network, crystalline, nanoporous materials with applications in gas storage, separations, and sensing. We review how molecular models and simulations of gas adsorption in MOFs have informed the discovery of performant MOFs for methane, hydrogen, and oxygen storage, xenon, carbon dioxide, and chemical warfare agent capture, and xylene enrichment. Particularly, we highlight how large, open databases of MOF crystal structures, post-processed to enable molecular simulations, are a platform for computational materials discovery. We discuss how to orient research efforts to routinise the computational discovery of MOFs for adsorption-based engineering applications.

Determination of the absolute CH4 adsorption using simplified local density theory and comparison with the modified Langmuir adsorption model

Accurately determining the adsorbed amount of CH₄ on shale is significant for understanding the mechanisms of shale gas storage and shale methane recovery from shale gas reservoirs. Excess CH₄ adsorption is measured using the thermogravimetric method. Simplified local density (SLD) theory is applied to calculate the adsorbed CH₄ density to obtain the absolute adsorption. Moreover, the modified Langmuir adsorption model is employed to fit the excess adsorption to describe the absolute adsorption. The adsorbed CH₄ density from the SLD model is affected by the system pressure and temperature, while such density obtained from the modified Langmuir model is only a function of temperature. Compared to the modified Langmuir model, the SLD model can better capture the adsorbed CH₄ density, which allows accurate determination of the absolute CH₄ adsorption.

Accurately determining the adsorbed amount of CH₄ on shale is significant for understanding the mechanisms of shale gas storage and shale methane recovery from shale gas reservoirs.

Quasi-Two-Dimensional Phase Transition of Methane Adsorbed in Cylindrical Silica Mesopores

Using Monte Carlo and molecular dynamics simulations, we examine the adsorption of methane in cylindrical silica mesopores in an effort to understand a possible phase transition of adsorbed methane in MCM-41 and SBA-15 silica that was previously identified by an unexpected increase in the adsorbed fluid density following capillary condensation, as measured by small-angle neutron scattering (SANS) [Chiang, W-S., et al., Langmuir 2016, 32, 8849]. Our initial simulation results identify a roughly 10 % increase in the density of the liquidlike adsorbed phase for either an isotherm with increasing pressure or an isobar with decreasing temperature and that this densification is associated with a local maximum in the isosteric enthalpy of adsorption. Subsequent analysis of the simulated fluid, via computation of bond-orientational order parameters of specific annular layers of the adsorbed fluid, showed that the layers undergo an ordering transition from a disordered, amorphous state to one with two-dimensional hexagonal structure. Furthermore, this two-dimensional restructuring of the fluid occurs at the same thermodynamic state points as the aforementioned densification and local maximum in the isosteric enthalpy of adsorption. We thus conclude that the densification of the fluid is the result of structural reorganization, which is signaled by the maximum in the isosteric enthalpy. Owing to the qualitative similarity of the structural transitions in the simulated and experimental methane fluids, we propose this hexagonal reorganization as a plausible explanation of the densification observed in SANS measurements. Lastly, we speculate how this structural transition may impact the transport properties of the adsorbed fluid.

Characterization of Methane Excess and Absolute Adsorption in Various Clay Nanopores from Molecular Simulation

In this work, we use grand canonical Monte Carlo (GCMC) simulation to study methane adsorption in various clay nanopores and analyze different approaches to characterize the absolute adsorption. As an important constituent of shale, clay minerals can have significant amount of nanopores, which greatly contribute to the gas-in-place in shale. In previous works, absolute adsorption is often calculated from the excess adsorption and bulk liquid phase density of absorbate. We find that methane adsorbed phase density keeps increasing with pressure up to 80 MPa. Even with updated adsorbed phase density from GCMC, there is a significant error in absolute adsorption calculation. Thus, we propose to use the excess adsorption and adsorbed phase volume to calculate absolute adsorption and reduce the discrepancy to less than 3% at high pressure conditions. We also find that the supercritical Dubinin-Radushkevich (SDR) fitting method which is commonly used in experiments to convert the excess adsorption to absolute adsorption may not have a solid physical foundation for methane adsorption. The methane excess and absolute adsorptions per specific surface area are similar for different clay minerals in line with previous experimental data. In mesopores, the excess and absolute adsorptions per specific surface area become insensitive to pore size. Our work should provide important fundamental understandings and insights into accurate estimation of gas-in-place in shale reservoirs.

Net, excess and absolute adsorption in mixed gas adsorption

The formulation of a thermodynamic framework for mixtures based on absolute, excess or net adsorption is discussed and the qualitative dependence with pressure and fugacity is used to highlight a practical issue that arises when extending the formulations to mixtures and to the Ideal Adsorbed Solution Theory (IAST). Two important conclusions are derived: the correct fundamental thermodynamic variable is the absolute adsorbed amount; there is only one possible definition of the ideal adsorbed solution and whichever starting point is used the same final IAST equations are obtained, contrary to what has been reported in the literature.

Differential Heat of Adsorption and Isosteres

Heat of adsorption is a basic thermodynamic property extensively used not only for understanding thermal effects and heat management in industrial gas storage and separation processes but also for development and validation of adsorption models and materials force fields. Despite a long history of theoretical studies and a vast experimental literature, controversies often arise in the thermodynamic analysis of heat effects due to various assumptions used to describe gas adsorption and inconsistencies between direct calorimetric measurements and isosteric heat obtained from various adsorption isotherms. Here we present a rigorous theoretical procedure for predicting isosteric heat without any assumption about the geometry of porous adsorbents or operating conditions. Quantitative relations between the differential heat and various isosteres have been established with the grand-canonical Monte Carlo simulation for gas adsorption in amorphous as well as crystalline porous materials. The inconsistencies and practical issues with conventional methods for the analysis of the heat effect have been clarified in the context of the exact results for model systems. Via the resolution of a number of controversies about heat analysis, we hope that the new theoretical procedure will be adopted for both fundamental research and industrial applications of gas adsorption processes.

Enthalpic Contribution of Ni(II) in the Interaction between Carbonaceous Material and Aqueous Solution

Solid adsorbents were prepared from corn cob that was modified with a solution of HNO3 6 M at different contact times. The solids are characterized by physical N2 adsorption at 77 K to know their surface area by applying the BET model and surface chemistry is determined using the Bohem method. Once we have prepared the adsorbents we determine the immersion enthalpy, ΔHim, of the solids in Ni(II) aqueous solutions of different concentrations between 20 and 800 mg·L−1, with values for ΔHim between 10.0 and 35.3 J·g−1. From the results obtained for the immersion enthalpy in function of the ion Ni(II) concentration we calculate the contribution to the immersion enthalpy that corresponds to the ion when it is treated with the system adsorbent-solution as a mixture in which the solid, the solvent, and the adsorbate are involved. The solution thermodynamics allows for establishing the enthalpic changes that bring the ion in function of the concentration and the intensity of the interaction of solid-metal ion that is favored by the presence of acid groups in the solid.

Net, excess and absolute adsorption and adsorption of helium

The definitions of absolute, excess and net adsorption in microporous materials are used to identify the correct limits at zero and infinite pressure. Absolute adsorption is shown to be the fundamental thermodynamic property and methods to determine the solid density that includes the micropore volume are discussed. A simple means to define when it is necessary to distinguish between the three definitions at low pressure is presented. To highlight the practical implications of the analysis the case of adsorption of helium is considered in detail and a combination of experiments and molecular simulations is used to clarify how to interpret adsorption measurements for weakly adsorbed components.