Isotherm sorption kinetics

The importance of adsorbent non-isothermality during the measurement of sorption kinetics has been recognized in recent years. Several mathematical models to describe the non-isothermal sorption kinetics have been formulated [1-9]. Of particular interest are the models describing the uptake during a differential sorption test because they provide relatively simple analytical solutions for data analysis [6-9]. These models assume that mass transfer can be described by the Fickian diffusion model and heat transfer from the solid is controlled by a film resistance outside the adsorbent particle. Diffusion of adsorbed molecules inside the adsorbent and gas diffusion in the interparticle voids have been considered as the controlling mechanism for mass transfer. 

In view of these observations, we propose a non-isothermal sorption kinetics model with the following assumptions ... 

The proposed model for non-isothermal sorption kinetics can quantitatively describe uptake0data for adsorption of i-octane on 13X and n-pentane on 5A zeolites. The study indicates that the principal resistance to mass transfer for these systems may be confined at the surface of the zeolite crystals. It is also found that the internal thermal resistance of the assemblage of the micron size zeolite crystals used in the kinetic test is significant which produces a substantial thermal gradient within the assemblage and slows down the heat dissipation from it. 

Angerhofer, M. Calculation of Non-isothermal Sorption Kinetics with the Dusty Gas Model... 

The data of Loukidou et al. (2004) for the equilibrium biosorption of chromium (VI) by Aeromonas caviae particles were well described by the Langmuir and Freundlich isotherms. Sorption rates estimated from pseudo second-order kinetics were in satisfactory agreement with experimental data. The results of XAFS study on the sorption of Cd by B. subtilis were generally in accord with existing surface complexation models (Boyanov et al. 2003). Intrinsic metal sorption constants were obtained by correcting the apparent sorption constants by the Boltzmann factor. A 1 2 metal-ligand stoichiometry provides the best fit to the experimental data with log K values of 6.0 0.2 for Sr(II) and 6.2 0.2 for Ba(II). 

Walters and Guiseppe-Elle [108] studied the sorption of 2,3,7,8-tetrachlorodibenzo-p-dioxin to soils from aqueous methanol mixtures and evaluated the applicability of the cosolvent theory to such sorption. Sorption kinetics were influenced by the fraction of methanol in the liquid phase and the soil type. Linear equilibrium sorption isotherms were... 

In a similar study (Comans et al., 1990), the reversibility of Cs+ sorption on illite was studied by examining the hysteresis between adsorption and desorption isotherms and the isotopic exchangeability of sorbed Cs+. Apparent reversibility was found to be influenced by slow sorption kinetics and by the nature of the competing cation. Cs+ migrates slowly to energetically favorable interlayer sites from which it is not easily released. 

In the ethylenediammonium forms of these two preparations there was a sensitive dependence of uptake upon molecular dimensions under the experimental conditions used (72) and distinctions between the crystals of the two exchange capacities. The free distance between pairs of siliceous layers of the sorbate free fluorhectorites was 2.8 A. When guest molecules are taken up, this distance within limits increases enough to accommodate the guest. Thus, among the paraffins isobutane and 2,3-dimethylbutane were taken up. However, paraffins with quaternary carbons (neo-Cs, 2,2-di-CH3-C4, 2,2,4-tri-CH.3-C5) were not. The important dimension is the difference in height of these species (4.65 and 5.9 A). The sorption of n-paraffins (minimum thickness 4.0 A) occurred more rapidly than that of isoparaffins. Isotherms and kinetics of uptake are illustrated for n-octane in Figure 12 (72). 

Figure 12. Isotherms and kinetics of sorption for Vroctane in ethylenediammonium forms of synthetic fluorhectorites of exchange capacities 90 (a and c) and 150 (h and d) milliequivalents per 100 grams ( ) sorption points, (O) desorption points (73). Qt, Qoo are amounts sorbed at time t and at equilibrium,...

Tin and americium were so extensively sorbed under all conditions that isotherm data could not be obtained. These elements are not significantly mobile in the Mabton Interbed aquifer. Values of Freundlich constants for technetium, radium, uranium, neptunium, and plutonium are given in Table IV. The Freundlich equation did not fit the selenium sorption data very well probably because of slow sorption kinetics or precipitation. Precipitation was also observed for technetium at 23°C for concentrations above 10 7M. This is about the same solubility observed for technetium in the sandstone isotherm measurements. Linear isotherms were observed only in the case of radium sorption. In general, sorption on the Mabton Interbed was greater than on the Rattlesnake Ridge sandstone. This is probably due to the greater clay content of the Mabton standard. 

Rate-limited sorption can also be modeled assuming a kinetic rate expression coupled with a nonlinear equilibrium expression. If we assume a Freundlich isotherm and a first-order rate expression, we can use the following equation to model sorption kinetics [21] ... 

If we assume a Langmuir isotherm, with sorption kinetics described by a second-order rate constant (kf) that depends on both dissolved contaminant concentration and number of available sorption sites, the following expression results [3,21] ... 

Shah, B. A., A. V. Shah, and R. R. Singh. 2009. Sorption isotherms and kinetics of chromium uptake from wastewater using natural sorbent material. Int. J. Environ. Sci. Technol. 6 77-90. 

The phenomenon of polymer swelling, owing to sorption of small molecules, was known even before Staudinger reported [1] in 1935 that crosslinked poly(styrene) swells enormously in certain liquids to form two-component polymer gels. The physical state of such systems varies with the concentration (C) and molecular structure of the sorbed molecules thus, the system undergoes transition at constant temperature from a rigid state (glassy or partially crystalline) at C < Cg to a rubbery state at Cg (the transition state composition). When C > Cg and the second component is a liquid, its subsequent sorption proceeds quickly to gel-saturation and of course a solution is produced if the polymer lacks covalently bonded crosslinks or equivalent restraints. Each successive physical state exhibits its own characteristic sorption isotherm and sorption kinetics. 

Sorption of monomethyl arsonic acid (MMAA), dimethyl arsinic acid (DMAA), and arsenate on anaerobic bottom sediments from the Menominee River, Wisconsin are described by Langmuir Isotherms. These results were Incorporated Into a kinetic model of arsenic species transforamtlon which takes sorption Into account. Model predictions were found to be sensitive to the sediment water content and r, the adsorptive capacity of the sediment. Demethylatlon of MMAA and DMAA was observed In sediment Incubation experiments. The predictions of the sorption/kinetic model were In good agreement with the results of the Incubation experiments. 

Sorption Kinetics. The adsorption and desorption data were analyzed in terms of a model based on the following main assumptions. Micropore diffusion within the sieve crystals is the rate-controlling process. Diffusion may be described by Fick s law for spherical particle geometry with a constant micropore diffusivity. The helium present in the system is inert and plays no direct role in the sorption or diffusion process. Sorption occurs under isothermal conditions. Sorption equilibrium is maintained at the crystal surface, which is subjected to a step change in gas composition. These assumptions lead to the following relation for the amount of ethane adsorbed or desorbed by a single particle as a function of time (Crank, 4). 

The effects of pH on sorption isotherms have been studied extensively particularly with oxide surfaces (Anderson and Rubin, 1981 Sposito, 1984), but pH effects in sorption kinetic studies have not received equal attention. In contrast, pH effects in mineral-dissolution kinetic experiments have received a great deal of attention (e.g., Chou and Wollast, 1984 Stumm, 1986 Stone, 1987a,b). 

Regardless whether sorption research is motivated by environmental, plant nutritional or other concerns, system description requires certain types of information. At a minimum, it is usually helpful to know the amount of sorbate retained by the sorbent and the partitioning of sorbate between solid and solution. Isotherms are quite adequate for this purpose. If movement of ions is of concern, the rate of sorption (or sorption kinetics) becomes important. 

As a final cautionary note, erroneous results can be replicated by replicating experimental conditions. Such erroneous results can usually be detected by careful comparison to all information available. At minimum, batch sorption kinetics studies should be conducted in parallel with isotherm studies. It is also beneficial to use multiple start concentrations and multiple sorbents. 

Farnworth [14] reported a numerical model describing the combined heat and water-vapor transport through clothing. The assumptions in the model did not allow for the complexity of the moisture-sorption isotherm and the sorption kinetics of fibers. Wehner et al [30] presented two mechanical models to simulate the interaction between moisture sorption by fibers and moisture flux through the void spaces of a fabric. In the first model, diffusion within the fiber was considered to be so rapid that the fiber moisture content was always in equilibrium with the adjacent air. In the second model, the sorption kinetics of the fiber were assumed to follow Fickian diffusion. In these models, the effect of heat of sorption and the complicated sorption behavior of the fibers were neglected. 

The assumptions in his model do not allow for the complexity of the moisture sorption isotherm and the sorption kinetics of fibers. Wehner et a.I [67] presented... 

These observations on PVC/penetrant systems suggest a correlation of sorption kinetics with the generalized isotherm for swelling penetrants in glassy polymers, as shown schematically in Figure 9. For sorption into an initially penetrant-free glassy... 

Figure 9. Relation of sorption kinetics to generalized sorption isotherm. (Schematic.)...

Accordingly, it would seem prudent in any study of vapor sorption kinetics, involving a highly swelling organic liquid, to test whether the conditions are, in fact, isothermal by application of the Armstrong-stannett analysis. 

The performance of all the four alumina samples were measured with respect to the sorption kinetics of of tertiary butyl catechol from styrene. The performance of all the four samples is given in Table 6. Adsorption isotherms of TBC on AD-101, alkali treated, acid treated and commercial adsorbent are given in Figure 4. 

Abstract Infrared spectroscopic methodsfor the measurement of adsorption and adsorption kinetics of some aromatics (benzene, ethylbenzene, p-xylene), pyridine, and paraffins in solid microporous materials such as zeolites (MOR, ZSM-5, silicalite-1) are described as well as the evaluation of the spectroscopically obtained data. The adsorption isotherms are of the Langmuir-Freundlich type. Isosteric heats of adsorption, transport diffusivities, and activation energies of diffusion as deduced from the spectroscopic measurements are compared with literature data as far as available, and they are found to be in reasonable agreement with results provided by independent techniques. Special attention is paid to sorption and sorption kinetics of binary mixtures, especially the problems of co- and counter-diffusion. ... 

Fundamentals of sorption and sorption kinetics by zeohtes are described and analyzed in the first Chapter which was written by D. M. Ruthven. It includes the treatment of the sorption equilibrium in microporous sohds as described by basic laws as well as the discussion of appropriate models such as the Ideal Langmuir Model for mono- and multi-component systems, the Dual-Site Langmuir Model, the Unilan and Toth Model, and the Simphfied Statistical Model. Similarly, the Gibbs Adsorption Isotherm, the Dubinin-Polanyi Theory, and the Ideal Adsorbed Solution Theory are discussed. With respect to sorption kinetics, the cases of self-diffusion and transport diffusion are discriminated, their relationship is analyzed and, in this context, the Maxwell-Stefan Model discussed. Finally, basic aspects of measurements of micropore diffusion both under equilibrium and non-equilibrium conditions are elucidated. The important role of micropore diffusion in separation and catalytic processes is illustrated. 

The maximum adsorption capacity for H2S from natural gas, obtained at ambient conditions and a flow rate of 0.4 L/min, is found to be 4.9 mg/g. Chemisorption of H2S on the surface is suggested by the sorption kinetics. The sorption isotherm shows a multilayer adsorption, which fits BET equation... 

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