Multisite Langmuir Model Research Articles

Adsorption Equilibrium of n-Paraffins on Binderless 5A Zeolite

The binderless 5A zeolite has higher economy when used in adsorption process to improve utilization efficiency of naphtha. Adsorption isotherms of n-pentane, n-hexane, n-heptane and n-octane on binderless 5A zeolite pellets were determined gravimetrically and analyzed in the temperature ranging from 423 to 573 K. Adsorption thermodynamic parameters were extracted from multisite Langmuir (MSL) model. Heats of adsorption for n-paraffins on 5A zeolite show an increasing trend with carbon number. At small degree of sites filling, the heats of adsorption of n-paraffins on binderless pellets increase from 53.19 kJ mol−1 for n-pentane to 72.34 kJ mol−1 for n-octane.

Analysis of n-C4∼n-C10 mixtures in 5A molecular sieves using IAS theory with multi-site Langmuir isotherms

The Constant-capacity Adsorption Solution (CAS) model for n-C4∼n-C10 mixture was built. Based on the adsorption experimental data, the Multi-site Langmuir (MSL) model was selected to describing the adsorption isotherms of n-C4∼n-C10 monocomponent. The CAS model was derived based on the IAS theory. The adsorption capacities predicted by the CAS model were compared with the experiment data of mixed gas adsorption. The results show the consistency. From the viewpoint of thermodynamics, the interactions between the normal paraffins of different carbon numbers were discovered. CAS model is applicative for the mixed gas in which the monocomponents have the similar adsorption capacities in the adsorbent.

Adsorption of CO2, CH4, and N2in Activated Carbon Honeycomb Monolith

Biomethane generated from renewable sources can be used as a renewable fuel to achieve ambitious targets for biofuels. The development of adsorption-based technologies for purification of biogas requires knowledge of adsorption equilibria and kinetics of pure gases on a specific adsorbent material. In this work, we have measured adsorption equilibria of CO2, CH4, and N2 at (299, 323, 348, 373, and 423) K over a pressure range between (0 and 700) kPa on a carbon honeycomb monolith. The adsorption capacity of the activated carbon honeycomb monolith was CO2 > CH4 > N2. The multisite Langmuir model was employed to fit the data of the pure gases offering the possibility of direct prediction of multicomponent adsorption equilibria. The diffusion of single gases in the microporous structure of the activated carbon honeycomb monolith was studied by diluted breakthrough experiments. The experiments were performed over the same temperature range [(303 to 423) K]. A simplified 1D mathematical model was employed in t...

Characterization and selectivity for methane and carbon dioxide adsorption on the all-silica DD3R zeolite

Clathrasil Deca-dodecasil 3R (DD3R) zeolite was synthesized in this study. Then, adsorption properties of carbon dioxide and methane were examined on the all-silica DD3R zeolite. Pure component adsorption isotherms are reported at temperatures of 273–348 K and pressures as high as 3 MPa. The isotherms follow a typical Type-I shape according to the Brunauer classification. They are well described using Langmuir and multi-site Langmuir models. Isosteric heats of adsorption and Henry’s Law constants of all adsorbates were determined. High selectivity of adsorption for carbon dioxide over methane suggests that the all-silica DD3R is an effective adsorbent or zeolite membrane material that can separate carbon dioxide and methane gaseous mixtures.

Application of the Fractional Statistical Theory of Adsorption (FSTA) to Adsorption of Linear and Flexible k-mers on Two-Dimensional Surfaces

The adsorption of linear and flexible polyatomics on honeycomb, square, and triangular lattices is studied by combining theoretical modeling, Monte Carlo simulations, and experimental results. In the case of flexible k-mers, simulation data are compared with the corresponding ones from the well-known multisite Langmuir model (MSL) of Nitta et al. [J. Chem. Eng. Jpn. 1984, 17, 45], while in the case of rigid k-mers, computational results are correlated from the model for linear adsorbates (MLA) developed by Ramirez-Pastor et al. [Phys. Rev. B 1999, 59, 11027]. On the other hand, it is shown that it is possible to interpret all adsorption isotherms (for linear and flexible adsorbates) by using the recently reported fractional statistical theory of adsorption of polyatomics (FSTA) of Riccardo et al. [Phys. Rev. Lett. 2004, 93, 186101], with an adequate choice of the fundamental parameter of the model, g, being the measure of the statistical exclusion of adsorption minima. In addition, experimental adsorption isotherms for O2 and C3H8 adsorbed in 5A and 13X zeolites, respectively, were analyzed in terms of FSTA. The more general character of FSTA with respect to the existing models and the satisfactory comparison with simulation and experimental results make the new theoretical model an attractive one for the description of adsorption of polyatomic particles with different sizes and shapes.

Separation of Methane and Nitrogen by Adsorption on Carbon Molecular Sieve

Adsorption equilibrium of methane and nitrogen on CMS 3K from Takeda Corp. were gravimetrically measured at 298, 308, and 323 K and at pressures up to 2000 kPa. The most adsorbed gas is methane followed by nitrogen. The adsorption loading at 550 kPa and 308 K is 1.73 mol/kg for methane and 0.91 mol/kg for nitrogen. Experimental data were fitted with the multisite Langmuir model. Single component uptake of these gases at low pressures was used to determine the adsorption kinetics. Adsorption of nitrogen is much faster than methane, although this gas is preferentially adsorbed. The adsorption rate of both gases was controlled by a surface barrier resistance at the mouth of the micropore combined with micropore diffusion. Breakthrough curves of pure gases and their binary mixtures were measured at ambient temperature. A bi‐LDF (Linear Driving Force) model was used to predict the fixed‐bed behavior. Large differences in the adsorption kinetics were observed: at 308 K the LDF constant ratio was Kμ,N2 /Kμ,CH4 =133, although because of much higher adsorption of methane, the overall kinetic selectivity was 1.9 at 308 K. The data obtained in this work can be used for adsorption separation processes modeling for methane purification from nitrogen‐contaminated streams.

Determination of Azeotropic Behavior in Adsorbed Mixtures

An analogy between vapor adsorbed equilibrium and vapor liquid equilibrium is made to determine the condition where azeotropes are observed, using a relationship between infinite dilution activity coefficients and pure component pressures in the reference state. The range of conditions where azeotropic behavior is expected in vapor-adsorbed equilibrium (VAE) was determined for the multisite Langmuir model for a mixture of two components with molecules of different size, and for CO2-C3H8 on NaX using an empirical model (Siperstein and Myers, 2001), which has been shown to correlate accurately experimental data.

Statistical Thermodynamics Models for Polyatomic Adsorbates: Application to Adsorption of n-Paraffins in 5A Zeolite

Experimental adsorption isotherms of five n-paraffins (ethane, propane, butane, pentane, and hexane) in 5A zeolite were described by means of a statistical thermodynamics model for linear adsorbates (MLA) developed by Ramirez-Pastor et al. (1999) and compared with the well-known multisite Langmuir model (MSL) of Nitta et al. (1984). The experimental data, obtained by different authors in a wide range of temperatures and pressures, were correlated by using an algorithm of multiple fitting. Two main conclusions were drawn from the analysis of experimental data: (i) for small molecules (ethane, propane), MLA is the more accurate model, validating the hypothesis of the linear rigid character of the adsorbate and reinforcing previous results obtained from the analysis of computational experiments developed for dimers and linear trimers; (ii) for large molecules (n-butane, n-pentane, n-hexane), the better performance of the MSL model suggests that the admolecules adsorb in a nonlinear structure. The isosteric heat of adsorption dependence on the number of carbons obtained from our study, ranging between 23.84 kJ/mol for ethane and 59.26 kJ/mol for hexane, showed a very good agreement with previous results reported in the literature, confirming the consistency of our analysis.

Adsorption Equilibrium of Methane, Carbon Dioxide, and Nitrogen on Zeolite 13X at High Pressures

High-pressure adsorption of methane, carbon dioxide, and nitrogen on zeolite 13X was measured in the pressure range (0 to 5) MPa at (298, 308, and 323) K and fitted with the Toth and multisite Langmuir models. Isosteric heats of adsorption were (12.8, 15.3, and 37.2) kJ/mol for nitrogen, methane, and carbon dioxide respectively, which indicate a very strong adsorption of carbon dioxide. The preferential adsorption capacity of CO2 on zeolite 13X was much higher than for the other gases, indicating that zeolite 13X can be used for methane purification from natural gas or for carbon dioxide sequestration from flue gas.

Cadmium complexation by bacteriogenic iron oxides from a subterranean environment

This study quantifies the metal sorption characteristics of subterranean bacteriogenic iron oxides (BIOS) and their organic phases (intermixed intact and fragmented bacteria). A Cd 2+ ion-selective electrode was used to generate high-resolution metal sorption data as a function of increasing pH. A multisite Langmuir model, along with a linear programming regression method (LPM), was applied to fit experimental data. This approach found two discrete Cd 2+ binding sites for the BIOS with average −log 10 equilibrium constants (p K S, j ) of 1.06±0.19 and 2.24±0.28. Three discrete sites were obtained for the bacterial fraction, with p K S, j values of −0.05±0.12, 1.18±0.02, and 3.81±0.16. This indicated that the BIOS surface had a lower affinity for Cd 2+ than that of the bacteria. p K S, j values for the BIOS were similar to those reported for pure iron oxide phases, while the organic fraction p K S, j spectrum was consistent with previous spectra for intact bacteria. Individual binding site densities of 0.04±0.01 and 0.05±0.02 and 0.29±0.05, 0.11±0.01, and 0.09±0.02 μmol/mg of BIOS corresponded to the iron oxide mixture and bacteria fraction, respectively. These values indicated high concentrations of strong affinity Cd 2+ complexing groups on the bacterial surface. Comparison of total site densities of 0.08±0.02 and 0.48±0.06 μmol/mg of BIOS for the mixture and the bacterial phase, respectively, suggested a nonadditive character for the BIOS surface reactivity. This was emphasized by a higher affinity for Cd 2+, as well as an increase in total site concentration observed for the bacterial phase. LPM was able to distinguish between the BIOS mixture and its organic fraction Cd 2+ complexation characteristics. This approach is therefore a useful tool for the study of natural sorbent materials controlling metal partitioning in contaminated and pristine environments.

Binary and Ternary Adsorption Kinetics of Gases in Carbon Molecular Sieves

In two recent studies from this laboratory, a dual resistance model with chemical potential gradient as the driving force for transport and empirical correlations to account for the strong concentration dependence of the thermodynamically corrected transport parameters was proposed and verified for the uptake of oxygen, nitrogen, and their mixtures in the micropores of Bergbau Forschung and Takeda carbon molecular sieve (CMS) samples. In this paper, the same model has been further verified with integral uptakes of carbon dioxide, methane, their binary mixtures, as well as their ternary mixtures with nitrogen in the two CMS samples. Inadequacy of the Langmuir model and IAS−Langmuir combination for these gases has been discussed in detail. It has been demonstrated that, for these gases, the multisite Langmuir model is much more effective in fitting the unary equilibrium data and predicting the mixture isotherms in CMS.

Improved Multisite Langmuir Model for Mixture Adsorption Using Multiregion Adsorption Theory

Prediction of mixed gas adsorption by the multisite Langmuir (MSL) theory is significantly improved by incorporating the multiregion adsorption (MRA) theory. The new model, called the multiregion multisite Langmuir (MR-MSL) model, is thermodynamically consistent. MR-MSL uses the same pure-component isotherm parameters as MSL does, and no new parameters are introduced. Eight binary systems and one ternary system are used to test the MR-MSL model. For systems containing like components (such as mixtures of hydrocarbons and that of O2 + N2), MR-MSL yielded only minor improvements over MSL. This is true regardless of the magnitude of the differences in the pure-component MSL parameters among different components. For highly nonideal mixtures, MR-MSL results in very substantial improvements. It is also capable of predicting the azeotropic behavior of the adsorption of CO2 + C3H8 on H-mordenite and the correct azeotropic compositions. For such systems, it is also shown that surface heterogeneity needs to be considered.

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 thermodynamically 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.

Binary diffusion of unequal sized molecules in zeolites

Multicomponent diffusivities in zeolites are predicted using the framework of the theory of irreversible thermodynamics, for which the information on equilibrium mixture adsorption isotherms is a critical requirement. Two thermodynamically consistent mixture isotherms, a multi-site Langmuir model and a modified Dubinin-type expansion facilitate quantification of the thermodynamic effect. In both these isotherms, saturation capacities of the species are allowed to differ. The ratio of saturation capacities in a binary mixture represents, to a first approximation, the inverse of the ratio of molecular sizes. In this work, thermodynamic interactions based on the two isotherm models are isolated from kinetic interactions due to surface mobilities which may also depend on concentration, and applied to study the concentration dependence of the effective Fickian diffusivities of components in a binary mixture. For the special case of zero cross terms in the phenomenological diffusion coefficient matrix and constant surface mobilities, size difference and the choice of isotherm are both shown to have significant effects on binary diffusion in mixtures of unequal sized molecules. For the multi-site Langmuir isotherms, co-diffusion enhances while counter-diffusion diminishes diffusivity, as expected. The thermodynamic effect of the Dubinin-type isotherm, however, shows a different behavior for the effect of one species on the other. The size effect is amplified in the case of counter-diffusion, and leads to possible enhancement in diffusivity even in counter-diffusion.

Multisite Langmuir Model Applied to the Interpretation of Sorption of n-Paraffins in 5A Zeolite

Adsorption equilibrium isotherms of n-paraffins from methane to decane on 5A zeolites (crystals and pellets) were compiled in a wide range of temperature and pressure. The data were correlated using the MSL (multisite Langmuir) model for homogeneous surfaces. It is shown that it is possible to correlate all adsorption isotherms by maintaining thermodynamic consistency on model parameters. However, for paraffins with more than seven carbons it is necessary to account for the effects of lateral interaction of adsorbed molecules. The heat of adsorption for C1−C10 paraffins linearly increases with the carbon number, ranging from 4.6 kcal/mol for methane up to 23.2 kcal/mol for n-decane.

Pure and Binary Gas Adsorption Equilibria and Kinetics of Methane and Nitrogen on 4A Zeolite by Isotope Exchange Technique

The Isotope Exchange Technique (IET) was used to simultaneously measure pure and binary gas adsorption equilibria and kinetics (self-diffusivities) of CH4 and N2 on pelletized 4A zeolite. The experiment was carried out isothermally without disturbing the adsorbed phase. CH4 was selectively adsorbed over N2 by the zeolite because of its higher polarizability. The multi-site Langmuir model described the pure gas and binary adsorption equilibria fairly well at three different temperatures. The selectivity of adsorption of CH4 over N2 increased with increasing pressure at constant gas phase composition and temperature. This curious behavior was caused by the differences in the sizes of the adsorbates. The diffusion of CH4 and N2 into the zeolite was an activated process and the Fickian diffusion model described the uptake of both pure gases and their mixtures. The self-diffusivity of N2 was an order of magnitude larger than that for CH4. The pure gas self-diffusivities for both components were constants over a large range of surface coverages (0 < θ < 0.5). The self-diffusivities of CH4 and N2 from their binary mixtures were not affected by the presence of each other, compared to their pure gas self-diffusivities at identical surface coverages.

Influence of adsorbate size and adsorbent heterogeneity of IAST

AbstractThe ideal adsorbed solution theory (IAST) can introduce serious errors in the calculation of multicomponent gas adsorption equilibria from the corresponding pure gas adsorption isotherms when the adsorbate sizes and the degree of adsorbent heterogeneity for adsorption of the components differ substantially. The multisite Langmuir and heterogeneous Langmuir models were used to evaluate the extent of these errors. It is shown that large diferences in adsorbate sizes and degrees of heterogeneity of adsorption of the components of a mixture can cause the formation of an adsorption azeotrope that cannot be described by IAST.

Equilibrium and kinetics of adsorption of Freon‐12 at infinite dilution

AbstractEquilibrium and kinetic data for adsorption of trace CF2Cl2 (Freon‐12) from various carrier gases on BPL activated carbon are reported. Coadsorption of the bulk carrier gas can severely reduce the equilibrium adsorption capacity and adsorptive mass‐transfer coefficient of strongly adsorbed CF2Cl2. The difference in size between CF2Cl2 and the bulk carrier gas molecules plays a major role in establishing the binary or multicomponent equilibrium adsorption properties. The multisite (single and multicomponent) Langmuir model, which accounts for differences in adsorbate sizes, provides a reasonable framework for describing the size effects. The adsorptive mass transfer of CF2Cl2 under the experimental conditions investigated is dominated by surface diffusion into the pores of the activated carbon. The surface diffusivity is a strong function of the extent of coverage and strength of adsorption of the bulk components.

Gas Adsorption on Silicalite

Isotherms for adsorption of H2, CH4, N2, CO, Ar, CO2, and Kr were measured at two temperatures (∼32.0 and ∼69.0°C) over a pressure range of 0-18.0 atm on silicalite. The isosteric heats of adsorption for these gases at the limit of zero coverage increased as the polarizability of the adsorbate increased. An enhancement in the heat was introduced for CO2, CO, and N2 adsorption due to the presence of permanent poles in these gases. All isotherms were Type I, but the Henry's Law constants and the overall shapes were very different for the gases. The homogeneous multisite Langmuir model described the isotherms very well. The variations in isosteric heats of adsorption as functions of adsorbate loadings were very small for all gases, indicating that silicalite was an energetically homogeneous adsorbent for the adsorption of these gases.