Application of heterogeneous vacancy solution theory to characterization of microporous solids

The vacancy solution theory of adsorption is re-formulated here through the mass-action law, and placed in a convenient framework permitting the development of thermodynamic ally consistent isotherms. It is shown that both the multisite Langmuir model and the classical vacancy solution theory expression are special cases of the more general approach when the Flory-Huggins activity coefficient model is used, with the former being the thermodynamically consistent result. The improved vacancy solution theory approach is further extended here to heterogeneous adsorbents by considering the pore-width dependent potential along with a pore size distribution. However, application of the model to numerous hydrocarbons as well as other adsorptives on microporous activated carbons shows that the multisite model has difficulty in the presence of a pore size distribution, because pores of different sizes can have different numbers of adsorbed layers and therefore different site occupancies. On the other hand, use of the classical vacancy solution theory expression for the local isotherm leads to good simultaneous fit of the data, while yielding a site diameter of about 0.257 nm, consistent with that expected for the potential well in aromatic rings on carbon pore surfaces. It is argued that the classical approach is successful because the Flory-Huggins term effectively represents adsorbate interactions in disguise. When used together with the ideal adsorbed solution theory the heterogeneous vacancy solution theory successfully predicts binary adsorption equilibria, and is found to perform better than the multisite Langmuir as well as the heterogeneous Langmuir model. (C) 2001 Elsevier Science Ltd. All rights reserved.

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.

Adsorption of argon on homogeneous graphitized thermal carbon black and heterogeneous carbon surface

In this paper we investigate the effects of surface mediation on the adsorption behavior of argon at different temperatures on homogeneous graphitized thermal carbon black and on heterogeneous nongraphitized carbon black surface. The grand canonical Monte Carlo (GCMC) simulation is used to study the adsorption, and its performance is tested against a number of experimental data on graphitized thermal carbon black (which is known to be highly homogeneous) that are available in the literature. The surface-mediation effect is shown to be essential in the correct description of the adsorption isotherm because without accounting for that effect the GCMC simulation results are always greater than the experimental data in the region where the monolayer is being completed. This is due to the overestimation of the fluid–fluid interaction between particles in the first layer close to the solid surface. It is the surface mediation that reduces this fluid–fluid interaction in the adsorbed layers, and therefore the GCMC simulation results accounting for this surface mediation that are presented in this paper result in a better description of the data. This surface mediation having been determined, the surface excess of argon on heterogeneous carbon surfaces having solid–fluid interaction energies different from the graphite can be readily obtained. Since the real heterogeneous carbon surface is not the same as the homogeneous graphite surface, it can be described by an area distribution in terms of the well depth of the solid–fluid energy. Assuming a patchwise topology of the surface with patches of uniform well depth of solid–fluid interaction, the adsorption on a real carbon surface can be determined as an integral of the local surface excess of each patch with respect to the differential area. When this is matched against the experimental data of a carbon surface, we can derive the area distribution versus energy and hence the geometrical surface area. This new approach will be illustrated with the adsorption of argon on a nongraphitized carbon at 87.3 and 77 K, and it is found that the GCMC surface area is different from the BET surface area by about 7%. Furthermore, the description of the isotherm in the region of BET validity of 0.06 to 0.2 is much better with our method than with the BET equation.

Effects of the juxtaposition of carbonaceous slit pores on the overall transport behavior of adsorbed fluids

It is a common approximation in the modeling of adsorption in microporous carbons to treat the pores as slit pores, whose walls are considered to consist of an infinite number of graphitic layers. In practice, such an approximation is appropriate as long as the number of graphitic layers in the wall is greater than three. However, it is understood that pore walls in microporous carbons commonly consist of three or fewer layers. As well as affecting the solid-fluid interaction within a pore, such narrow walls permit the interaction of fluid molecules through the wall, with consequences for the adsorption characteristics. We consider the effect that a distributed pore-wall thickness model can have on transport properties. At low density we find that the only significant deviation in the transport properties from the infinite pore-wall thickness model occurs in pores with single-layer walls. For a model of activated carbons with a distribution of pore widths and pore-wall thicknesses, the transport properties are generally insensitive to the effects of finite walls, in terms of both the solid-fluid interaction within a pore and fluid-fluid interaction through the pore walls.

On the steady-state assumption and its application to the rotating disk voltammetry of adsorbed enzymes

Rotating disk voltammetry is routinely used to study electrochemically driven enzyme catalysis because of the assumption that the method produces a steady-state system. This assumption is based on the sigmoidal shape of the voltammograms. We have introduced an electrochemical adaptation of the King-Altman method to simulate voltammograms in which the enzyme catalysis, within an immobilized enzyme layer, is steadystate. This method is readily adaptable to any mechanism and provides a readily programmable means of obtaining closed form analytical equations for a steady-state system. The steady-state simulations are compared to fully implicit finite difference (FIFD) simulations carried out without any steady-state assumptions. On the basis of our simulations, we conclude that, under typical experimental conditions, steady-state enzyme catalysis is unlikely to occur within electrode-immobilized enzyme layers and that typically sigmoidal rotating disk voltammograms merely reflect a mass transfer steady state as opposed to a true steady state of enzyme intermediates at each potential.

Thickness and stability of adsorbed film in cylindrical mesopores

The adsorbed film in small cylindrical mesopores is studied by using MCM-41 samples of uniform cylindrical channels as model systems. It is found that at a given relative pressure, the smaller the pore radius, the thicker the adsorbed film is, as postulated by Broekhoff and De Beer. Thermodynamics analysis established that the stability of the adsorbed film is determined by interface curvature and the potential of interaction between adsorbate and adsorbent. A semiempirical equation is proposed to describe the state of stable adsorbed films in cylindrical mesopores. It is also shown to be useful in calculations of pore size distributions of mesoporous solids.

Turbulent spots in boundary layers in a free-piston shock-tunnel flow

In this paper, experiments to detect turbulent spots in the transitional boundary layers, formed on a flat plate in a free-piston shock tunnel how, are reported. Experiments indicate that thin-film heat-transfer gauges are suitable for identifying turbulent-spot activity and can be used to identify parameters such as the convection rate of spots and the intermittency of turbulence.

Molecular Lego (R): non-centrosymmetric alignment within interdigitating layers

(E)-N-Hexadecyl-4-[2-(4-octadecyloxynaphthyl) ethenyl] quinolinium bromide, which has a wide-bodied chromophore and terminal n-alkyl groups, adopts a U-shape when spread at the air-water interface but a stretched conformation when compressed to ca. 35 mN m(-1). The high-pressure phase has a narrow stability range prior to collapse but may be extended from 40 to 60 mN m(-1) by co-spreading the dye in a 1 : 1 ratio with docosanoic acid. The mixed Langmuir-Blodgett (LB) film has a monolayer thickness of 4.6 +/- 0.2 nm which decreases to 2.5 +/- 0.1 nm layer(-1) in the bulk, the reduction arising from an interdigitating layer arrangement, both top and bottom. It is the first example of LB-Lego(R) and, in addition, represents the only fully interdigitating structure with non-centrosymmetrically aligned chromophores. They are tilted 38 degrees from the substrate normal. The second-harmonic intensity increases quadratically with the number of layers, i.e. as I-(N)(2 omega) = (I(1)N2)-N-2 omega, with a second-order susceptibility of chi ((2))(zzz) = 30 pm V-1 at 1064 nm for refractive indices of n(omega) = 1.55 and n(2 omega) = 1.73, d = 2.5 nm layer(-1) and phi = 38 degrees. Angle resolved X-ray photoelectron spectra (XPS) of these films provide no evidence of the bromide counterion, which suggests that it is replaced by OH 2 or HCO3-, which occur naturally in the aqueous subphase, or C21H43COO- from the co-deposited fatty acid. This probably applies to all cationic dyes deposited by the LB technique.

Surface diffusion of adsorbed molecules in porous media: Monolayer, multilayer, and capillary condensation regimes

This review provides an overview of surface diffusion and capillary condensate flow in porous media. Emphasis has been placed on the distinction between purely surface diffusion, multilayer surface diffusion, and, capillary condensate flow.

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).

Study on diffusion and flow of benzene, n-hexane and CCl4 in activated carbon by a differential permeation method

In this paper the diffusion and flow of carbon tetrachloride, benzene and n-hexane through a commercial activated carbon is studied by a differential permeation method. The range of pressure is covered from very low pressure to a pressure range where significant capillary condensation occurs. Helium as a non-adsorbing gas is used to determine the characteristics of the porous medium. For adsorbing gases and vapors, the motion of adsorbed molecules in small pores gives rise to a sharp increase in permeability at very low pressures. The interplay between a decreasing behavior in permeability due to the saturation of small pores with adsorbed molecules and an increasing behavior due to viscous flow in larger pores with pressure could lead to a minimum in the plot of total permeability versus pressure. This phenomenon is observed for n-hexane at 30degreesC. At relative pressure of 0.1-0.8 where the gaseous viscous flow dominates, the permeability is a linear function of pressure. Since activated carbon has a wide pore size distribution, the mobility mechanism of these adsorbed molecules is different from pore to pore. In very small pores where adsorbate molecules fill the pore the permeability decreases with an increase in pressure, while in intermediate pores the permeability of such transport increases with pressure due to the increasing build-up of layers of adsorbed molecules. For even larger pores, the transport is mostly due to diffusion and flow of free molecules, which gives rise to linear permeability with respect to pressure. (C) 2002 Elsevier Science Ltd. All rights reserved.

Finite, three-dimensional adsorbed phase growth in activated carbon mesopores

The role of PACs (primary adsorption centers) in the mesopore (i.e., transport) region of activated carbons during adsorption of polar species, such as water, is unclear. A classical model of three-dimensional adsorption on finite PACs is presented. The model is a preliminary, theoretical investigation into adsorption on mesopore PACs and is intended to give some insight into the energetic and physical processes at work. Work processes are developed to obtain isotherms and three-dimensional sorbate growth on PACs of varying size and energetic characteristics. The work processes allow two forms of adsorbed phase growth: densification at constant boundary and boundary growth at constant density. Relatively strong sorbate-sorbent interactions and strong surface tension favor adsorbed phase densification over boundary growth. Conversely, relatively weak sorbate-sorbent interactions and weak surface tension favor boundary growth over densification. If sorbate-sorbate interactions are strong compared to sorbate-sorbent interactions, condensation with hysteresis occurs. This can also give rise to delayed boundary growth, where all initial adsorption occurs in the monolayer only. The results indicate that adsorbed phase growth on PACs may be quite complex.

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.

Skin-friction measurements in high-enthalpy hypersonic boundary layers

Skin-friction measurements are reported for high-enthalpy and high-Mach-number laminar, transitional and turbulent boundary layers. The measurements were performed in a free-piston shock tunnel with air-flow Mach number, stagnation enthalpy and Reynolds numbers in the ranges of 4.4-6.7, 3-13 MJ kg(-1) and 0.16 x 10(6)-21 x 10(6), respectively. Wall temperatures were near 300 K and this resulted in ratios of wall enthalpy to flow-stagnation enthalpy in the range of 0.1-0.02. The experiments were performed using rectangular ducts. The measurements were accomplished using a new skin-friction gauge that was developed for impulse facility testing. The gauge was an acceleration compensated piezoelectric transducer and had a lowest natural frequency near 40 kHz. Turbulent skin-friction levels were measured to within a typical uncertainty of +/-7%. The systematic uncertainty in measured skin-friction coefficient was high for the tested laminar conditions; however, to within experimental uncertainty, the skin-friction and heat-transfer measurements were in agreement with the laminar theory of van Driest (1952). For predicting turbulent skin-friction coefficient, it was established that, for the range of Mach numbers and Reynolds numbers of the experiments, with cold walls and boundary layers approaching the turbulent equilibrium state, the Spalding & Chi (1964) method was the most suitable of the theories tested. It was also established that if the heat transfer rate to the wall is to be predicted, then the Spalding & Chi (1964) method should be used in conjunction with a Reynolds analogy factor near unity. If more accurate results are required, then an experimentally observed relationship between the Reynolds analogy factor and the skin-friction coefficient may be applied.

Determination of the effect of lipophilicity on the in vitro permeability and tissue reservoir characteristics of topically applied solutes in human skin layers

In order to establish the relationship between solute lipophilicity and skin penetration (including flux and concentration behavior), we examined the in vitro penetration and membrane concentration of a series of homologous alcohols (C2-C10) applied topically in aqueous solutions to human epidermal, full-thickness, and dermal membranes. The partitioning/distribution of each alcohol between the donor solution, stratum corneum, viable epidermis, dermis, and receptor phase compartments was determined during the penetration process and separately to isolated samples of each tissue type. Maximum flux and permeability coefficients are compared for each membrane and estimates of alcohol diffusivity are made based on flux/concentration data and also the related tissue resistance (the reciprocal of permeability coefficient) for each membrane type. The permeability coefficient increased with increasing lipophilicity to alcohol C8 (octanol) with no further increase for C10 (decanol). Log vehicle:stratum corneum partition coefficients were related to logP , and the concentration of alcohols in each of the tissue layers appeared to increase with lipophilicity. No difference was measured in the diffusivity of smaller more polar alcohols in the three membranes; however, the larger more lipophilic solutes showed slower diffusivity values. The study showed that the dermis may be a much more lipophilic environment than originally believed and that distribution of smaller nonionized solutes into local tissues below a site of topical application may be estimated based on knowledge of their lipophilicity alone.