Two-dimensional mobile films of gases on solids: Adaptation of three-dimensional equations of state to physical adsorption of single gases on homogeneous surfaces

The generalized van der Waals theory for dense fluids, presented in terms of statistical thermodynamics by Vera and Prausnitz, is adapted to physical adsorption of single gases on homogeneous solid surfaces. Using the procedure of Vera and Prausnitz, new three-dimensional equations of state and their two-dimensional analogues are derived. Furthermore, the adsorption isotherms are obtained from the two-dimensional equations of state by using well-known thermodynamic relations.     

On Ritchie's equation for adsorption kinetics of gases on solids

Ritchie's equation for the kinetic adsorption isotherm has been derived on the basis of the theory describing the kinetics of adsorption of gases on energetically heterogeneous solid surfaces. This eqation has also been generalized to the kinetics of adsorption of multicomponent gas mixtures.

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Water adsorption and desorption on microporous solids at elevated temperature

Summary An accurate gravimetric method was used to explore water adsorption/desorption isotherms between 105 and to 250°C for a number of synthetic and natural porous solids including controlled pore glass, activated carbon fiber monoliths, natural zeolites, pillared clay, and geothermal reservoir rocks. The main goal of this work was to evaluate water adsorption results, in particular temperature dependence of hysteresis, for relatively uniform, nano-structured solids, in the context of other state-of-the-art experimental and modeling methods including nitrogen adsorption, spectroscopy, neutron scattering, and molecular simulation. Since no single method is able to provide a complete characterization of porous materials, a combination of approaches is needed to achieve progress in understanding the fluid-solid interactions on the way to developing a predictive capability.     

Physical adsorption of gases on energetically heterogeneous solids II. Theoretical extension of a generalizedLangmuir equation and its application for analysing adsorption data

The generalizedLangmuir equation proposed in part I is extended to monolayer adsorption with lateral interactions and to multilayer adsorption on heterogeneous surfaces with random distribution of adsorption sites. New differential functions, useful for interpreting the adsorption data, are introduced to study the mathematical and physical properties of this equation. These functions are applied to study three gas adsorption systems available from the literature.

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Gasadsorption auf energetisch heterogenen Feststoffen, 2. Mitt.: Die theoretische Erweiterung einer generalisierten Langmuir-Gleichung und ihre Anwendung zur Analyse von Adsorptionsdaten

Zusammenfassung Die generalisierteLangmuir-Gleichung, die in der 1. Mitt. beschrieben wurde, wird für die einlagige Adsorption mit lateralen Wechselwirkungen und für die viellagige Adsorption auf heterogenen Oberflächen mit einer Zufallsverteilung von Adsorptionsplätzen erweitert. Es werden neue Differentialfunktionen zur Untersuchung der mathematischen und physikalischen Eigenschaften dieser Gleichung eingeführt, die sich als fruchtbringend zur Interpretation von Adsorptionsdaten erweisen. Diese Funktionen werden zur Untersuchung von drei Gasadsorptionssystemen aus der Literatur herangezogen.

     

Physical adsorption of gases on energetically heterogeneous solids I. GeneralizedLangmuir equation and its energy distribution

A generalizedLangmuir equation is proposed for describing the monolayer adsorption of single gases on heterogeneous solids. The special cases of this equation are:Langmuir-Freundlich, Tóth andFreundlich type adsorption isotherms. The energy distribution function corresponding to this equation produces all types of simple energy distributions, i.e., symmetrical distribution, decreasing exponential distributions and asymmetrical distributions showing widening in the directions of low and high adsorption energies.

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Gasadsorption auf energetisch heterogenen Feststoffen, 1. Mitt.: Eine generalisierteLangmuir-Gleichung und ihre Energieverteilung

Zusammenfassung Es wird eine generalisierteLangmuir-Gleichung zur Beschreibung der einlagigen Adsorption eines einzelnen Gases auf heterogenen Feststoffen beschrieben. Die speziellen Fälle dieser Gleichung sind:Langmuir-Freundlich-, Tóth- undFreundlich-Typ der Adsorptionsisotherme. Die Energieverteilung, die dieser Gleichung entspricht, gibt alle Typen einer einfachen Verteilung wieder, z. B. eine symmetrische Verteilung, eine abfallende exponentielle Verteilung und asymmetrische Verteilungen mit Erweiterung in die Richtung von niedriger oder hoher Adsorptionsenergie.

     

On the physical adsorption of gases on carbon materials from molecular simulation

In this paper we present a series of work covering a range of aspects relating molecular simulation to experiment. The importance of surface mediation type effects to the adsorption of simple and complex gases is demonstrated. Coupled with the adsorption of simple gases is their projection area when used for surface area determination. The pressure dependence of a projection area is demonstrated for argon at 77 and 87.3 K. A simple model is used to account for the degree of graphitisation of a surface is demonstrated and used to account for the isosteric heat behaviour of non-graphitised carbon blacks. Turning from surfaces to porous solids, an alternative treatment of experiment data (either sub or super critical) is presented that avoids the ambiguity of excess amounts adsorbed. Using this method one is able to obtain pore size distributions and amounts adsorbed without relying on such things as helium expansion volumes. Since this type of method is usually applied to composite solids we also demonstrate the correct method for calculating the heat of adsorption using independent sets of simulations. The final topic covered in this paper is an example of the information that can be gained from the heat capacity of an adsorbed phase.     

Automatic gravimetric apparatus for recording the adsorption isotherms of gases or vapours onto solids

The assembly described was built with the aim of obtaining high resolution and precision, together with automaticity. It was designed around a symmetrical commercial vacuum microbalance (Setaram), its main features being the following:(1) Controlled “residual” vacuum during outgassing of the sample.(2) Two possible procedures for the introduction of the adsorbate: either a conventional — but automated — point by point procedure (with discontinuous introduction of gas or vapour) or a continuous procedure, specially suited for high resolution work.(3) Measurement of pressure (0–1 atm) by a silica Bourdon gague (Texas Instruments) of 10^?5 accuracy.(4) Direct recording of the isotherms on a XY recorder.(5) Constant level (± 0.5 mm) cryogenic bath (liquid nitrogen or argon) of low consumption (4 liters per 15 hours).(6) Liquid thermostat for adsorption temperatures between ? 30 and + 100°C.(7) Temperature control (up to 50°C) of the whole assembly (manifolds, balance, gauges) allowing to handle condensable vapours.Several examples are given, illustrating the versatility and resolution of the systems. For instance, it allowed to detect, for the first time, a distinct substep at the top of the nitrogen/graphite and argon/graphite isotherms at 77 K. This is now explained by a sudden localization or “freezing” of the monolayer near its completion.     

Shell models of two-dimensional Coulomb crystals: assessment and comparison with the three-dimensional case

Three shell models, differing in accuracy and computational cost, are formulated for two-dimensional Coulomb crystals. Offering a new means of predicting and analyzing properties of these species, the new models also provide new insights into their previously derived three-dimensional counterparts. In particular, analysis of the individual components of the energy error points out to the neglect of the positional relaxation as the main source of the differences between the approximate and exact energies. Within the realm of shell models, the two-dimensional case turns out to be somewhat more challenging than the three-dimensional one. Due to the lack of exact closed-form expressions for the optimal shell radii, it is computationally more expensive and the energy predictions at the same level of approximation are less accurate (as indicated by the maximum relative energy error of 0.15% vs. that of 0.03% found for spherical Coulomb crystals).     

Net adsorption: a thermodynamic framework for supercritical gas adsorption and storage in porous solids

The thermodynamic treatment of adsorption phenomena is based on the Gibbs dividing surface, which is conceptually clear for a flat surface. On a flat surface, the primary extensive property is the area of the solid. As applications became more significant, necessitating microporous solids, early researchers such as McBain and Coolidge implemented the Gibbs definition by invoking a reference state for microporous solids. The mass of solid is used as a primary extensive property because surface area loses its physical meaning for microporous solids. A reference state is used to fix the hypothetical hyperdividing surface typically using helium as a probe molecule, resulting in the commonly used excess adsorption; experimentalists measure this reference state for each new sample. Molecular simulations, however, provide absolute adsorption. Theoreticians perform helium simulations to convert absolute to excess adsorption, mimicking experiments for comparison. This current structure of adsorption thermodynamics is rigorous (if the conditions for reference state helium measurements are completely disclosed) but laborious. In addition, many studies show that helium, or any other probe molecule for that matter, does adsorb, albeit to a small extent. We propose a novel thermodynamic framework, net adsorption, which completely circumvents the use of probe molecules to fix the reference state for each microporous sample. Using net adsorption, experimentalists calibrate their apparatus only once without any sample in the system. Theoreticians can directly calculate net adsorption; no additional simulations with a probe gas are necessary. Net adsorption also provides a direct indication of the density enhancement achieved (by using an adsorbent) over simple compression for gas (e.g., hydrogen) storage applications.     

High-resolution physical adsorption on supported borosilicate MFI zeolite membranes: comparison with powdered samples

We have performed physical adsorption measurements to analyze the structure of intact MFI membranes with a nominal Si:B ratio of 12.5:1. Argon adsorption isotherms of membranes at 77 K are nearly identical to isotherms of corresponding zeolite powders throughout most of the domain of relative pressures, the exception being the micropore-filling region (between 10⁻⁵ and 10⁻⁴ relative pressure). The isotherm in the micropore-filling region is steeper by a factor of 4–5 for the borosilicate membranes than it is for a powder made under the same conditions, while the saturation loadings are found to be similar. This implies a difference in how the zeolite pores fill with argon – either thermodynamic or kinetic in origin – and that fluxes for argon permeation through such powder and membrane samples may differ. Our membrane adsorption measurements reveal no hysteresis and hence no mesoporsity in the zeolite membranes. This finding, from adsorption measurements, stands in contrast to recent alkane permeation measurements on these membranes, which suggest the presence of mesopores. We reaffirm the conclusion, found in previous work, that zeolite membranes can be approximated as a zeolite powder plus a support for the purposes of adsorption characterization.     

pH dependence of adsorption of n-dodecyl-beta-D-maltoside on solids

Adsorption of surfactants on solids plays an important role in industrial operations such as separation, lubrication, flotation, dispersion, chemical mechanical polishing, and enhanced oil recovery. In this work, adsorption of a typical biodegradable nonionic surfactant, n-dodecyl-beta-d-maltoside, on solids was studied to explore its potential applications. Even though it is a nonionic surfactant, significant pH-dependence was revealed for the adsorption on alumina in the range from pH 4 to 7. The adsorption density was found to be proportional to the concentration of surface AlOH group among Al(OH(2))(+) and AlO(-) groups. The equilibriums among the surface species are governed by pH through surface ionization reactions. The surface AlOH group evidently determines the formation of hydrogen bonding between the surfactant molecules and the solid surface and thus the adsorption. Similar correlation was also found in the case of hematite. The results help to understand the mechanism of adsorption of sugar-based surfactant on solids.