Close packed transitions in slit-shaped pores: Density functional theory study of methane adsorption capacity in carbon

An important feature of improving lattice gas models and classical isotherms is the incorporation of a pore size dependent capacity, which has hitherto been overlooked. In this paper, we develop a model for predicting the temperature dependent variation in capacity with pore size. The model is based on the analysis of a lattice gas model using a density functional theory approach at the close packed limit. Fluid-fluid and solid-fluid interactions are modeled by the Lennard-Jones 12-6 potential and Steele's 10-4-3, potential respectively. The capacity of methane in a slit-shaped carbon pore is calculated from the characteristic parameters of the unit cell, which are extracted by minimizing the grand potential of the unit cell. The capacities predicted by the proposed model are in good agreement with those obtained from grand canonical Monte Carlo simulation, for pores that can accommodate up to three adsorbed layers. Single particle and pair distributions exhibit characteristic features that correspond to the sequence of buckling and rhombic transitions that occur as the slit pore width is increased. The model provides a useful tool to model continuous variation in the microstructure of an adsorbed phase, namely buckling and rhombic transitions, with increasing pore width. (C) 2002 American Institute of Physics.

Use of liquid phase adsorption for characterizing pore network connectivity in activated carbon

A simple percolation theory-based method for determination of the pore network connectivity using liquid phase adsorption isotherm data combined with a density functional theory (DFT)-based pore size distribution is presented in this article. The liquid phase adsorption experiments have been performed using eight different esters as adsorbates and microporous-mesoporous activated carbons Filtrasorb-400, Norit ROW 0.8 and Norit ROX 0.8 as adsorbents. The density functional theory (DFT)-based pore size distributions of the carbons were obtained using DFT analysis of argon adsorption data. The mean micropore network coordination numbers, Z, of the carbons were determined based on DR characteristic plots and fitted saturation capacities using percolation theory. Based on this method, the critical molecular sizes of the model compounds used in this study were also obtained. The incorporation of percolation concepts in the prediction of multicomponent adsorption equilibria is also investigated, and found to improve the performance of the ideal adsorbed solution theory (IAST) model for the large molecules utilized in this study. (C) 2002 Elsevier Science B.V. All rights reserved.

Kinetics of adsorption on activated carbon: application of heterogeneous vacancy solution theory

The kinetics of single component adsorption on activated carbon is investigated here using a heterogeneous vacancy solution theory (VST) of adsorption. The adsorption isotherm is developed to account for the adsorbate non-ideality due to the size difference between the adsorbate molecule and the vacant site, while incorporating adsorbent heterogeneity through a pore-width-related potential energy. The transport process in the bidisperse carbon considers coupled mass transfer in both macropore and micropore phases simultaneously. Adsorbate diffusion in the micropore network is modeled through effective medium theory, thus considering pore network connectivity in the adsorbent, with the activation energy for adsorbate diffusion related to the adsorption energy, represented by the Steele 10-4-3 potential for carbons. Experimental data of five hydrocarbons, CO2 and SO2 on Ajax carbon at multiple temperatures, as well as three hydrocarbons on Norit carbon at three temperatures are first fitted by the heterogeneous VST model to obtain the isotherm parameters, followed by application of the kinetic model to uptake data on carbon particles of different sizes and geometry at various temperatures. For the hydrocarbons studied, the model can successfully correlate the experimental data for both adsorption equilibrium and kinetics. However, there is some deviation in the fit of the desorption kinetics for polar compounds such as CO2 and SO2, due to the inadequacy of the L-J potential model in this case. The significance of viscous transport in the micropores is also considered here and found to be negligible, consistent with recent molecular simulation studies. (C) 2002 Elsevier Science Ltd. All rights reserved.

Vacancy solution theory for binary adsorption equilibria in heterogeneous carbon

A heterogeneous modified vacancy solution model of adsorption developed is evaluated. The new model considers the adsorption process through a mass-action law and is thermodynamically consistent, while maintaining the simplicity in calculation of multicomponent adsorption equilibria, as in the original vacancy solution theory. It incorporates the adsorbent heterogeneity through a pore-width-related potential energy, represented by Steele's 10-4-3 potential expression. The experimental data of various hydrocarbons, CO2 and SO2 on four different activated carbons - Ajax, Norit, Nuxit, and BPL - at multiple temperatures over a wide range of pressures were studied by the heterogeneous modified VST model to obtain the isotherm parameters and micropore-size distribution of carbons. The model successfully correlates the single-component adsorption equilibrium data for all compounds studied on various carbons. The fitting results for the vacancy occupancy parameter are consistent with the pressure change on different carbons, and the effect of pore heterogeneity is important in adsorption at elevated pressure. It predicts binary adsorption equilibria better than the IAST scheme, reflecting the significance of molecular size nonideality.

Density functional theory analysis of the influence of pore wall heterogeneity on adsorption in carbons

Density functional theory for adsorption in carbons is adapted here to incorporate a random distribution of pore wall thickness in the solid, and it is shown that the mean pore wall thickness is intimately related to the pore size distribution characteristics. For typical carbons the pore walls are estimated to comprise only about two graphene layers, and application of the modified density functional theory approach shows that the commonly used assumption of infinitely thick walls can severely affect the results for adsorption in small pores under both supercritical and subcritical conditions. Under supercritical conditions the Henry's law coefficient is overpredicted by as much as a factor of 2, while under subcritical conditions pore wall heterogeneity appears to modify transitions in small pores into a sequence of smaller ones corresponding to pores with different wall thicknesses. The results suggest the need to improve current pore size distrubution analysis methods to allow for pore wall heterogeneity. The density functional theory is further extended here to allow for interpore adsorbate interactions, and it appears that these interaction are negligible for small molecules such as nitrogen but significant for more strongly interacting heavier molecules such as butane, for which the traditional independent pore model may not be adequate.

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

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.

Analysis of adsorption data of graphitized thermal carbon black with a DFT-lattice gas theory

In this paper we analyzed the adsorption of gases and vapors on graphitised thermal carbon black by using a modified DFT-lattice theory, in which we assume that the behavior of the first layer in the adsorption film is different from those of second and higher layers. The effects of various parameters on the topology of the adsorption isotherm were first investigated, and the model was then applied in the analysis of adsorption data of numerous substances on carbon black. We have found that the first layer in the adsorption film behaves differently from the second and higher layers in such a way that the adsorbate-adsorbate interaction energy in the first layer is less than that of second and higher layers, and the same is observed for the partition function. Furthermore, the adsorbate-adsorbate and adsorbate-adsorbent interaction energies obtained from the fitting are consistently lower than the corresponding values obtained from the viscosity data and calculated from the Lorentz-Berthelot rule, respectively.

Effects of adsorbate-adsorbate interaction in the description of adsorption isotherm of hydrocarbons in micro-mesoporous carbonaceous materials

In this paper, we present a model accounting for the adsorbate-adsorbate interaction in the adsorbed phase in the description of adsorption of pure vapors on carbonaceous materials. The details of the adsorbate-adsorbate interaction of a particular species are obtained from the analysis of its adsorption data on non-porous carbon black. The predictability of the model is tested against the adsorption isotherm data for benzene, toluene, n-pentane, n-hexane, carbon tetrachloride, methanol and ethanol on microporous activated carbon. It was found that the model prediction for non-polar adsorbates are satisfactory while it under-predicts for polar adsorbates, which is attributed to their additional interaction with functional groups. (C) 2002 Elsevier Science B.V. All rights reserved.

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.

Removal of sulfamethoxazole from solution by raw and chemically treated walnut shells

Purpose: The sorption of sulfamethoxazole, a frequently detected pharmaceutical compound in the environment, onto walnut shells was evaluated. Methods: The sorption proprieties of the raw sorbent were chemically modified and two additional samples were obtained, respectively HCl and NaOH treated. Scanning electron microscopy, Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, and thermogravimetric (TG/DTG) techniques were applied to investigate the effect of the chemical treatments on the shell surface morphology and chemistry. Sorption experiments to investigate the pH effect on the process were carried out between pH 2 and 8. Results: The chemical treatment did not substantially alter the structure of the sorbent (physical and textural characteristics) but modified the surface chemistry of the sorbent (acid–base properties, point of zero charge—pHpzc). The solution pH influences both the sorbent’s surface charge and sulfamethoxazole speciation. The best removal efficiencies were obtained for lower pH values where the neutral and cationic sulfamethoxazole forms are present in the solution. Langmuir and Freundlich isotherms were applied to the experimental adsorption data for sulfamethoxazole sorption at pH 2, 4, and 7 onto raw walnut shell. No statistical difference was found between the two models except for the pH 2 experimental data to which the Freundlich model fitted better. Conclusion: Sorption of sulfamethoxazole was found to be highly pH dependent in the entire pH range studied and for both raw and treated sorbent.

Estudo da tratabilidade laboratorial e optimização experimental do tratamento de águas residuais de indústrias lácteas

O presente trabalho experimental teve como objectivos estudar a tratabilidade dum efluente lácteo utilizando a técnica de coagulação/floculação e avaliar a possibilidade de utilização do carvão activado granulado (CAG) Aquasorb 2000 como adsorvente para a remoção de compostos orgânicos presentes nos efluentes lácteos pré–tratados por coagulação/floculação, funcionando como um tratamento de polimento. No estudo da tratabilidade do efluente por coagulação/floculação investigou-se a influência de determinadas variáveis como o tipo e dose de coagulante e pH, a fim de encontrar as melhores condições operatórias. A utilização da referida técnica visou a redução do valor de concentração de alguns parâmetros: carência química de oxigénio (CQO); fósforo total e turvação, tendo sido utilizados efluentes desta indústria recolhidos em diferentes datas e após tratamento biológico, designados por A, B, C e D apresentando características diferentes. Sendo que o efluente A apresentava valores de CQO, fósforo total e turvação de 500 mg O2/L;32 mg P/L e 40 NTU respectivamente, o efluente B 1400 mg O2/L; 120 mg P/L e 80 NTU respectivamente, o efluente C 12300 mg O2/L; 87 mg P/L e 350 NTU respectivamente e o efluente D 340 mg O2/L; 33 mg P/L e 42 NTU respectivamente. Os coagulantes estudados foram hidróxido de cálcio (HC), sulfato de alumínio (SA) e tricloreto de ferro (TF). Verificou-se que o coagulante com maior eficácia nos efluentes estudados foi o TF. As maiores remoções de CQO, fósforo total e turvação, 89%, 99,9% e 99%, respectivamente, foram obtidas para o efluente C, com uma dosagem de TF de 4 g/L e com um pH entre 6 e 7. Entre os efluentes estudados este era o que apresentava valores iniciais mais elevados para qualquer um destes parâmetros. As melhores percentagens de remoção obtidas com o HC, para a CQO, fósforo total e turvação foram de 59%, 99% e 91%, respectivamente, com uma dosagem de HC de 1 g/L e com um pH entre 10 e 11,5 foram conseguidas no tratamento do efluente D, com o qual se alcançaram também as melhores remoções de CQO, fósforo total e turvação de 65%, 99% e 87%, respectivamente, quando se utilizou o coagulante SA, com uma dosagem de 2 g/L e com um pH entre 7 e 7,5. Relativamente ao volume de lamas produzido neste processo pela utilização dos diferentes coagulantes no tratamento dos efluentes referidos concluiu-se que o coagulante que gera menor volume de lamas é o HC, sendo o SA aquele que origina um maior volume. Submeteu-se posteriormente o efluente D, pré-tratado por coagulação/floculação, a um processo de adsorção em batch utilizando o CAG Aquasorb 2000, onde se conseguiu uma remoção de CQO de 48%, alcançando para este parâmetro o valor de 63 mg O2/L, nas condições operatórias que correspondem a uma massa de CAG de 12,5 g/L e um tempo de contacto de 3 horas. Quanto aos custos associados com os coagulantes, o que menores custos apresenta é o HC (150 €/ton), seguido pelo TF (250 €/ton) e por ultimo o SA (340 €/ton). Sendo que o efluente quando tratado com TF e SA é necessário uma correcção do pH do meio para que estes coagulantes actuem eficazmente, em que essa correcção de pH é realizada com hidróxido de sódio (540 €/ton). Realizaram-se ainda estudos de equilíbrio de adsorção com o carvão activado referido e o azul-de-metileno usando diferentes concentrações deste (50 mg/L; 100 mg/L e 200 mg/L) e diferentes massas de CAG (0,1g; 0,2g; 0,3g; 0,4g e 0,5g). A temperatura a que se realizaram estes ensaios foi de 28,7ºC e o volume de azul-de-metileno foi de 200 mL. Verificou-se que os melhores resultados obtidos foram para uma concentração de adsorvato de 100 mg/L. Ajustaram-se os modelos de Langmuir e Freundlich às isotérmicas obtidas tendo correlações mais elevadas para a concentração de 100 mg/L de corante (azul de metileno), sendo o modelo de Freundlich aquele que melhor se ajustou apresentando uma correlação quadrática de 0,9744 e os seguintes parâmetros Kf = 6,59 e n = 5,33, enquanto que o de Langmuir apresentou uma correlação quadrática de 0,9583 e os seguintes parâmetros qmáx = 83,3 mg/g de adsorvente e K = 20 L/mg de adsorvato.. Verificou-se que a capacidade de adsorção promovida pelo CAG, em relação ao azul-demetileno, obtida experimentalmente, 83,3 mg/g, é muito inferior à capacidade de adsorção teoricamente prevista pela ficha técnica deste carvão, 280 mg/g a uma temperatura de 25ºC, o que pode indiciar que o carvão utilizado não estaria nas melhores condições.