Modeling of gas adsorption equilibrium over a wide range of pressure: A thermodynamic approach based on equation of state

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R I in the temperature range from 25 to 70 C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Adsorption in slit-like pores of activated carbons: Improvement of the Horvath and Kawazoe method

Anew thermodynamic approach has been developed in this paper to analyze adsorption in slitlike pores. The equilibrium is described by two thermodynamic conditions: the Helmholtz free energy must be minimal, and the grand potential functional at that minimum must be negative. This approach has led to local isotherms that describe adsorption in the form of a single layer or two layers near the pore walls. In narrow pores local isotherms have one step that could be either very sharp but continuous or discontinuous benchlike for a definite range of pore width. The latter reflects a so-called 0 --> 1 monolayer transition. In relatively wide pores, local isotherms have two steps, of which the first step corresponds to the appearance of two layers near the pore walls, while the second step corresponds to the filling of the space between these layers. All features of local isotherms are in agreement with the results obtained from the density functional theory and Monte Carlo simulations. The approach is used for determining pore size distributions of carbon materials. We illustrate this with the benzene adsorption data on activated carbon at 20, 50, and 80 degreesC, argon adsorption on activated carbon Norit ROX at 87.3 K, and nitrogen adsorption on activated carbon Norit R1 at 77.3 K.

Mixed gas equilibrium adsorption on zeolites and energetic heterogeneity of adsorption volume

A model for binary mixture adsorption accounting for energetic heterogeneity and intermolecular interactions is proposed in this paper. The model is based on statistical thermodynamics, and it is able to describe molecular rearrangement of a mixture in a nonuniform adsorption field inside a cavity. The Helmholtz free energy obtained in the framework of this approach has upper and lower limits, which define a permissible range in which all possible solutions will be found. One limit corresponds to a completely chaotic distribution of molecules within a cavity, while the other corresponds to a maximum ordered molecular structure. Comparison of the nearly ideal O-2-N-2-zeolite NaX system at ambient temperature with the system Of O-2-N-2-zeolite CaX at 144 K has shown that a decrease of temperature leads to a molecular rearrangement in the cavity volume, which results from the difference in the fluid-solid interactions. The model is able to describe this behavior and therefore allows predicting mixture adsorption more accurately compared to those assuming energetic uniformity of the adsorption volume. Another feature of the model is its ability to correctly describe the negative deviations from Raoult's law exhibited by the O-2-N-2-CaX system at 144 K. Analysis of the highly nonideal CO2-C2H6-zeolite NaX system has shown that the spatial molecular rearrangement in separate cavities is induced by not only the ion-quadrupole interaction of the CO2 molecule but also the significant difference in molecular size and the difference between the intermolecular interactions of molecules of the same species and those of molecules of different species. This leads to the highly ordered structure of this system.

Characterization of micro-mesoporous carbonaceous materials. Calculations of adsorption isotherm of hydrocarbons

In this paper we apply a method recently developed by Do and co-workers(1) for the prediction of adsorption isotherms of pure vapors on carbonaceous materials. The information required for the prediction is the pore size distribution and the BET constant, C, of a corresponding nonporous surface (graphite). The dispersive adsorption force is assumed to be the dominant force in adsorption mechanism. This applies to nonpolar and weakly polar hydrocarbons. We test this predictive model against the adsorption data of benzene, toluene, n-pentane, n-hexane, and ethanol on a commercial activated carbon. It is found that the predictions are excellent for all adsorbates tested with the exception of ethanol where the predicted values are about 10% less than the experimental data, and this is probably attributed to the electrostatic interaction between ethanol molecules and the functional groups on the carbon surfaces.

Adsorption of mixtures containing subcritical fluids on activated carbon

A theoretical analysis of adsorption of mixtures containing subcritical adsorbates into activated carbon is presented as an extension to the theory for pure component developed earlier by Do and coworkers. In this theory, adsorption of mixtures in a pore follows a two-stage process, similar to that for pure component systems. The first stage is the layering of molecules on the surface, with the behavior of the second and higher layers resembling to that of vapor-liquid equilibrium. The second stage is the pore-filling process when the remaining pore width is small enough and the pressure is high enough to promote the pore filling with liquid mixture having the same compositions as those of the outermost molecular layer just prior to pore filling. The Kelvin equation is applied for mixtures, with the vapor pressure term being replaced by the equilibrium pressure at the compositions of the outermost layer of the liquid film. Simulations are detailed to illustrate the effects of various parameters, and the theory is tested with a number of experimental data on mixture. The predictions were very satisfactory.

Effects of surface chemistry on aromatic compound adsorption from dilute aqueous solutions by activated carbon

Adsorption of one nondissociating and four dissociating aromatic compounds onto three untreated activated carbons from dilute aqueous solutions were investigated. All adsorption experiments were preformed in pH-controlled solutions. The experimental isotherms were analyzed using the homogeneous Langmuir model. The surface chemical properties of the activated carbons were characterized using a combination of water adsorption, X-ray photoemission spectroscopy, and mass titration. These data give rise to a new insight into the adsorption mechanism of aromatic solutes, in their molecular and ionic forms, onto untreated activated carbons. It was found that, for the hydrophilic activated carbons, the dominant adsorption forces were observed to be dipolar interactions when the solutes were in their molecular form whereas dispersive forces, such as pi-pi interactions, were most likely dominant in the case of the basic hydrophobic carbons. However, when the solutes were in their ionic form adsorption occurs in all cases through dispersive forces.

Conformational changes in SP-B as a function of surface pressure

X-ray reflectivity of bovine and sheep surfactant-associated protein B (SP-B) monolayers is used in conjunction with pressure-area isotherms and protein models to suggest that the protein undergoes changes in its tertiary structure at the air/water interface under the influence of surface pressure, indicating the likely importance of such changes to the phenomena of protein squeeze out as well as lipid exchange between the air-water interface and subphase structures. We describe an algorithm based on the well-established box- or layer-models that greatly assists the fitting of such unknown scattering-length density profiles, and which takes the available instrumental resolution into account. Scattering-length density profiles from neutron reflectivity of bovine SP-B monolayers on aqueous subphases are shown to be consistent with the exchange of a large number of labile protons as well as the inclusion of a significant amount of water, which is partly squeezed out of the protein monolayer at elevated surface pressures.

Adsorption of supercritical fluids in non-porous and porous carbons: analysis of adsorbed phase volume and density

In this paper, we revisit the surface mass excess in adsorption studies and investigate the role of the volume of the adsorbed phase and its density in the analysis of supercritical gas adsorption in non-porous as well as microporous solids. For many supercritical fluids tested (krypton, argon, nitrogen, methane) on many different carbonaceous solids, it is found that the volume of the adsorbed phase is confined mostly to a geometrical volume having a thickness of up to a few molecular diameters. At high pressure the adsorbed phase density is also found to be very close to but never equal or greater than the liquid phase density. (C) 2003 Elsevier Science Ltd. All rights reserved.

Analysis of multicomponent adsorption kinetics on activated carbon

An integrated mathematical model for the kinetics of multicomponent adsorption on microporous carbon was developed. Transport in this bidisperse solid is represented by balance equations in the macropore and micropore phases, in which gas-phase diffusion dominates the mass transfer in the macropores, with the phenomenological diffusivities represented by the generalized Maxwell-Stefan (GMS) formulation. Viscous flow also contributes to the macropore fluxes and is included in the MS expressions. Diffusion of the adsorbed phase controls the mass transfer in the micro ore phase, p which is also described in a similar way by the MS method. The adsorption isotherms are represented by a new heterogeneous modified vacancy solution theory formulation of adsorption, which has proved to be a robust method for adsorption on activated carbons. The model is applied to the coadsorption and codesorption of C2H6 and C3H8 on Ajax and Norit carbon, as well as the displacement on Ajax carbon. The effect of the viscous flow in the macropore phase is not significant for the cases studied. The model accurately predicts the overshoot behavior and rollup of C2H6 during coadsorption. The prediction for the heavier compound C3H8 is always satisfactory, though at higher C3H8 mole fraction, the overshoot extent of C2H6 is overpredicted, possibly due to neglect of heat effects.

Prediction of multilayer adsorption and capillary condensation phenomena in cylindrical mesopores

MCM-41 periodic mesoporous silicates with a high degree of structural ordering are synthesized and used as model adsorbents to study the isotherm prediction of nitrogen adsorption. The nitrogen adsorption isotherm at 77 K for a macroporous silica is measured and used in high-resolution alpha(s)-plot comparative analysis to determine the external surface area, total surface area and primary mesopore volume of the MCM-41 materials. Adsorption equilibrium data of nitrogen on the different pore size MCM-41 samples (pore diameters from 2.40 to 4.92 nm) are also obtained. Based on the Broekhoff and de Boer' thermodynamic analysis, the nitrogen adsorption isotherms for the different pore size MCM-41 samples are interpreted using a novel strategy, in which the parameters of an empirical expression, used to represent the potential of interaction between the adsorbate and adsorbent, are obtained by fitting only the multilayer region prior to capillary condensation for C-16 MCM-41. Subsequently the entire isotherm, including the phase transition, is predicted for all the different pore size MCM-41 samples without any fitting. The results show that the prediction of multilayer adsorption and total adsorbed amount are in good agreement with the experimental isotherms. The predictions of the relative pressure corresponding to capillary equilibrium (coexistence) transition agree remarkably with experimental data on the adsorption branch even for hysteretic isotherms, confirming that this is the branch appropriate for pore size distribution analysis. The impact of pore radius on the adsorption film thickness and capillary coexistence pressure is also investigated, and found to agree with the experimental data. (C) 2003 Elsevier Inc. All rights reserved.

Effects of carbon surface chemistry and solution pH on the adsorption of binary aromatic solutes

Adsorption of p-cresol, nitrobenzene and p-nitrophenol on treated and untreated carbons is investigated systematically. The effects of carbon surface chemistry and solution pH are studied and discussed. All adsorption experiments were carried out in pH-controlled solutions to examine the adsorption properties of the adsorption systems where the solutes are in molecular as well as ionic forms. Using the homogeneous Langmuir equation, the single solute parameters are determined. These parameters are then used to predict the binary solute adsorption isotherms and gain further insights into the adsorption process. (C) 2002 Elsevier Science Ltd. All rights reserved.

Refined method of potential enhancement in the equilibria characterization of activated carbon. Comparison with GCMC and DFT

In this paper, we present a technique for equilibria characterization of activated carbon having slit-shaped pores. This method was first developed by Do (Do, D. D. A new method for the characterisation of micro-mesoporous materials. Presented at the International Symposium on New Trends in Colloid and Interface Science, September 24-26, 1998 Chiba, Japan) and applied by his group and other groups for characterization of pore size distribution (PSD) as well as adsorption equilibria determination of a wide range of hydrocarbons. It is refined in this paper and compared with the grand canonical Monte Carlo (GCMG) simulation and density functional theory (DFT). The refined theory results in a good agreement between the pore filling pressure versus pore width and those obtained by GCMG and DFT. Furthermore, our local isotherms are qualitatively in good agreement with those obtained by the GCMC simulations. The main advantage of this method is that it is about 4 orders of magnitude faster than the GCMC simulations, making it suitable for optimization studies and design purposes. Finally, we apply our method and the GCMG in the derivation of the PSD of a commercial activated carbon. It was found that the PSD derived from our method is comparable to that derived from the GCMG simulations.

High-pressure adsorption of supercritical gases on activated carbons: An improved approach based on the density functional theory and the bender equation of state

Adsorption of nitrogen, argon, methane, and carbon dioxide on activated carbon Norit R1 over a wide range of pressure (up to 50 MPa) at temperatures from 298 to 343 K (supercritical conditions) is analyzed by means of the density functional theory modified by incorporating the Bender equation of state, which describes the bulk phase properties with very high accuracy. It has allowed us to precisely describe the experimental data of carbon dioxide adsorption slightly above and below its critical temperatures. The pore size distribution (PSD) obtained with supercritical gases at ambient temperatures compares reasonably well with the PSD obtained with subcritical nitrogen at 77 K. Our approach does not require the skeletal density of activated carbon from helium adsorption measurements to calculate excess adsorption. Instead, this density is treated as a fitting parameter, and in all cases its values are found to fall into a very narrow range close to 2000 kg/m(3). It was shown that in the case of high-pressure adsorption of supercritical gases the PSD could be reliably obtained for the range of pore width between 0.6 and 3 run. All wider pores can be reliably characterized only in terms of surface area as their corresponding excess local isotherms are the same over a practical range of pressure.

Pore characterization of carbonaceous materials by DFT and GCMC simulations: A review

A review is given of the pore characterization of carbonaceous materials, including activated carbon, carbon fibres, carbon nanotubes, etc., using adsorption techniques. Since the pores of carbon media are mostly of molecular dimensions, the appropriate modem tools for the analysis of adsorption isotherms are grand canonical Monte Carlo (GCMC) simulations and density functional theory (DFT). These techniques are presented and applications of such tools in the derivation of pore-size distribution highlighted.

The structural characterization of carbon molecular sieve membrane (CMSM) via gas adsorption

The microstructure of a carbon molecular sieve membrane (CMSM) is characterized using adsorption equilibrium information. The pore size distributions of the CMSM derived from N-2 and CH4 adsorption isotherm are found to be consistent with each other and in agreement with the results of gas permeation experiments as well as the general characteristics of such molecular sieve materials. (C) 2003 Elsevier B.V. All rights reserved.