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.

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.

Interactions of an anionic surfactant with poly(oxyalkylene) copolymers in aqueous solution

The interactions of sodium dodecyl sulfate (SDS) with poly(ethylene oxide)/poly(alkylene oxide) (E/A) block copolymers are explored in this study: With respect to the specific compositional characteristics of the copolymer, introduction of SDS can induce fundamentally different effects to the self-assembly behavior of E/A copolymer solutions. In the case of the E18B10-SDS system (E = poly(ethylene oxide) and B = poly(butylene oxide)) development of large surfactant-polymer aggregates was observed. In the case of B20E610-SDS, B12E227B12-SDS, E40B10E40-SDS, E19P43E19-SDS (P = poly(propylene oxide)), the formation of smaller particles compared to pure polymeric micelles points to micellar suppression induced by the ionic surfactant. This effect can be ascribed to a physical binding between the hydrophobic block of unassociated macromolecules and the non-polar tail of the surfactant. Analysis of critical micelle concentrations (cmc*) of polymer-surfactant aqueous solutions within the framework of regular solution theory for binary surfactants revealed negative deviations from ideal behavior for E40B10E40-SDS and E19P43E19-SDS, but positive deviations for E18B10-SDS. Ultrasonic studies performed for the E19P43E19-SDS system enabled the identification of three distinct regions, corresponding to three main steps of the complexation; SDS absorption to the hydrophobic backbone of polymer, development of polymer-surfactant complexes and gradual breakdown of the mixed aggregates. (C) 2008 Elsevier Inc. All rights reserved.

Formação de micelas mistas entre o sal biliar colato de sódio e o surfactante aniônico dodecanoato de sódio

Mixed-micelle formation between sodium chlolate (NaC) and the anionic surfactant sodium dodecanoate (SDoD) in Tris-HCl buffer solutions, pH 9.00, varying the molar fraction of the surfactants, was investigated by means of electrical conductivity and steady-state fluorescence of pyrene. The critical micelar concentration (cmc) was measured from the equivalent conductance versus the square root of the molar surfactant concentration plots and the regular solution theory (RST) was used to predict the mixing behavior. The I1/I3 pyrene ratio-surfactant concentration plots were used as an additional technique to follow the behavior and the changes in the micropolarity of the mixed micelles.

Interaction between cationic and conventional nonionic surfactants in the mixed micelle and monolayer formed in aqueous medium

Mixed micellization and surface properties of cationic and nonionic surfactants dimethyl decyl-, tetradecyl- and hexadecyl phosphineoxide mixtures are studied using conductivity and surface tension measurements. The models of Rubingh, Rosen, and Clint, are used to obtain the interaction parameter, minimum area per molecule, mixed micelle composition, free energies of mixing and activity coefficients. The micellar mole fractions were always higher than ideal values indicating high contributions of cationics in mixed micelles. Activity coefficients were less than unity indicating synergism in micelles. The negative free energies of mixing showed the stability of the surfactants in the mixed micelles.

Migration of additives from thermoplastic polymers

A homologous series of ultra-violet stabilisers containing 2-hydroxybenzophenone (HBP) moiety as a uv absorbing chromophore with varying alkyl chain lengths and sizes were prepared by known chemical synthesis. The strong absorbance of the HBP chromophore was utilized to evaluate the concentration of these stabilisers in low density polyethylene films and concentration of these stabilisers in low density polyethylene films and in relevant solvents by ultra-violet/visible spectroscopy. Intrinsic diffusion coefficients, equilibrium solubilities, volatilities from LDPE films and volatility of pure stabilisers were studied over a temperature range of 5-100oC. The effects of structure, molecular weight and temperature on the above parameters were investigated and the results were analysed on the basis of theoretical models published in the literature. It has been found that an increase in alkyl chain lengths does not change the diffusion coefficients to a significant level, while attachment of polar or branched alkyl groups change their value considerably. An Arrhenius type of relationship for the temperature dependence of diffusion coefficients seems to be valid only for a narrow temperature range, and therefore extrapolation of data from one temperature to another leads to a considerable error. The evidence showed that increase in additive solubility in the polymer is favoured by lower heat of fusions and melting points of additives. This implies the validity of simple regular solution theory to provide an adequate basis for understanding the solubility of additives in polymers The volubility of stabilisers from low density polyethylene films showed that of an additive from a polymer can be expressed in terms of a first-order kinetic equation. In addition the rate of loss of stabilisers was discussed in relation to its diffusion, solubility and volatility and found that all these factors may contribute to the additive loss, although one may be a rate determining factor. Stabiliser migration from LDPE into various solvents and food simulants was studied at temperatures 5, 23, 40 and 70oC; from the plots of rate of migration versus square root time, characteristic diffusion coefficients were obtained by using the solution of Fick's diffusion equations. It was shown that the rate of migration depends primarily on partition coefficients between solvent and the polymer of the additive and also on the swelling action of the contracting media. Characteristic diffusion coefficients were found to approach to intrinsic values in non swelling solvents, whereas in the case of highly swollen polymer samples, the former may be orders of magnitude greater than the latter.

Cobalt incorporation in calcite: Thermochemistry of (Ca,Co)CO3 solid solutions from density functional theory simulations

The incorporation of cobalt in mixed metal carbonates is a possible route to the immobilization of this toxic element in the environment. However, the thermodynamics of (Ca,Co)CO3 solid solutions are still unclear due to conflicting data from experiment and from the observation of natural ocurrences. We report here the results of a computer simulation study of the mixing of calcite (CaCO3) and spherocobaltite (CoCO3), using density functional theory calculations. Our simulations suggest that previously proposed thermodynamic models, based only on the range of observed compositions, significantly overestimate the solubility between the two solids and therefore underestimate the extension of the miscibility gap under ambient conditions. The enthalpy of mixing of the disordered solid solution is strongly positive and moderately asymmetric: calcium incorporation in spherocobaltite is more endothermic than cobalt incorporation in calcite. Ordering of the impurities in (0001) layers is energetically favourable with respect to the disordered solid solution at low temperatures and intermediate compositions, but the ordered phase is still unstable to demixing. We calculate the solvus and spinodal lines in the phase diagram using a sub-regular solution model, and conclude that many Ca1-xCoxCO3 mineral solid solutions (with observed compositions of up to x=0.027, and above x=0.93) are metastable with respect to phase separation. We also calculate solid/aqueous distribution coefficients to evaluate the effect of the strong non-ideality of mixing on the equilibrium with aqueous solution, showing that the thermodynamically-driven incorporation of cobalt in calcite (and of calcium in spherocobaltite) is always very low, regardless of the Co/Ca ratio of the aqueous environment.

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.

Multicomponent supercritical adsorption in microporous activated carbon materials

In this paper, a new technique for predicting multicomponent adsorption equilibria of supercritical fluids in microporous carbons is presented. In difference from adsorption on a surface, which is a function of the fluid-solid interaction only, adsorption in porous media is influenced by the proximity of the pore walls, resulting in the enhancement in adsorption affinity. The degree of this enhancement is different for different adsorbates, and it increases with a decrease in pore size. The theory is applied to a number of carbonaceous systems with good success.

Percolation Phenomena in Micropore Adsorption: Influence on Single and Multicomponent Adsorption Equilibria

A novel and simple method for determination of micropore network connectivity of activated carbon using liquid phase adsorption is presented in this paper. The method is applied to three different commercial carbons with eight different liquid phase adsorptives as probes. The effect of the pore network connectivity on the prediction of multicomponent adsorption equilibria was also studied. For this purpose, the Ideal Adsorbed Solution Theory (IAST) was used in conjuction with the modified DR single component isotherm. The results of comparison with experimental data show that incorporation of the connectivity, and consideration of percolation processes associated with the different molecular sizes of the adsorptives in the mixture, can improve the performance of the IAST in predicting multicomponent adsorption equilibria.

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.

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.

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.