Non-isothermal sorption

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. 

The basic mathematical model for a calculation of concentration vs. time dependences in sorbent beds accounts for non-isothermal sorption in biporous sorbent particles. It considers mass and energy balances in the interparticle void space of the bed and in the macro- and micropores of sorbent particles. Thus, it comprises three spatial coordinates, besides time, (0 < t < co) (i) the height z along the bed, (0 < z < L) (ii) the radial direction r in macropores of particles, (0 < r < Rp) and (hi) the radial direction p in their micropores, (0 < p < Rzi). Different geometries may exist in each single direction but in each of those geometries the transport equations are one-dimensional. For zeolite-based biporous particles, sorption in the macropores is negligible. These pores serve as transport pores, only. Sorption takes place, exclusively, in micropores. 

Basmadjian, D, and Wright, D.W., Non-isothermal sorption of ethane-carbon dioxide mixtures in beds of 5A molecular sieves, Chem. Eng. Sci., 36(5), 937-940 (1981). 

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

Of the various equilibrium and non-equilibrium sorption isotherms or sorption characteristics models, the most popular are the Langmuir and Freundlich models. The correct modeling of an adsorbate undergoing both transport and adsorption through a clay soil-solid system necessitates the selection of an adsorption isotherm or characteristic model which best suits the given system. The use of an improper or inappropriate adsorption model will greatly affect the... 

Usually the retention volume is obtained using peak maxima to define the retention times. In this treatment, since bulk absorption only is assumed, band broadening effects and the existence of a non-linear sorption isotherm are not considered, as these usually reflect some surface adsorption, resulting in skewed peaks. 

Lipsky and Landowne dissolved both the polar phase (PEG) and the non polar phase in the same solvent and carried out both precoating and coating simultaneously. They found that this procedure reduced or eliminated tailing due to non-linear sorption isotherms, and attributed the effect to deactivation of the support. 

We have considered the analysis of single component systems under isothermal conditions as well as non-isothermal conditions. In these analyses, the local equilibrium between the fluid and adsorbed phases (eqs. 9.2-44 and 9.3-8) was invoked. This is valid when the rates of adsorption and desorption of adsorbate molecules at sorption sites are much faster than the rates of diffusion in the fluid and... 

The simplest monofunctional carboxylic acids retain their boiling points at standard atmospheric pressure without undergoing decomposition and, hence, can be analyzed directly by GC. However, owing to the relatively high polarities of carbonyl compounds, a typical problem of their GC analysis with standard non-polar phases is the non-linear sorption isotherm. As a result, these compounds yield broad non-symmetrical peaks, which lead to poor detection limits and unsatisfactory reproducibility of their retention indices. The recommended stationary phases for direct analysis of free carboxylic acids are polar polyethylene glycols (Carbowax 20M, DBWax, SP-1000, FFAP, etc.). However, these phases have lower thermal stability as compared with... 

Large standard deviations of RIs of arenecarboxylic acids (benzoic, phenylacetic, etc.) on standard non-polar phases are explained by the high asymmetry of their chromatographic peaks. This effect cannot be eliminated by the use of inert chromatographic systems, special techniques of injection, or the appUcation of modem WCOT columns. It depends on the typical non-linear sorption isotherm polar sorbate-non-polar phase and, hence, the conversion of these polar analytes into less polar derivatives is strongly recommended. 

Andrade et al. investigated the transport properties and the solvent induced-crystallization phenomena in poly(ethylene terephthalate) (PET) and PET clay nanocomposites, prepared by melt intercalation. Results of non-isothermal crystallization showed that cold crystallization temperature, and percent of crystallinity of nanocomposites are higher than those of pure PET. The sorption of all die solvents is accompanied by a large-scale stmctural rearrangement, leading to the induced crystallization of the original amorphous state. The solvent induced crystallization caused an increasing of more than four times the percent of crystallinity. 

Generally the above expressions adequately describe sorption isotherms of the type reported in Fig. 1, giving good agreement with experimental results in non-... 

Sorption. Capture of neutral organics by non-living particulates depends on the organic carbon content of the solids (9). Equilibrium sorption of such "hydrophobic" compounds can be described by a carbon-normalized partition coefficient on both a whole-sediment basis and by particle size classes. The success of the whole-sediment approach derives from the fact that most natural sediment organic matter falls in the "silt" or "fine" particle size fractions. So long as dissolved concentrations do not exceed 0.01 mM, linear isotherms (partition coefficients) can be used. At higher concentrations, the sorptive capacity of the solid can be exceeded, and a nonlinear Freundlich or Langmuir isotherm must be invoked. 

Nevertheless, surfactant sorption isotherms on natural surfaces (sediments and biota) are generally non-linear, even at very low concentrations. Their behaviour may be explained by a Freundlich isotherm, which is adequate for anionic [3,8,14,20,30], cationic [7] and non-ionic surfactants [2,4,15,17] sorbed onto solids with heterogeneous surfaces. Recently, the virial-electrostatic isotherm has been proposed to explain anionic surfactant sorption this is of special interest since it can be interpreted on a mechanistic basis [20]. The virial equation is similar to a linear isotherm with an exponential factor, i.e. with a correction for the deviation caused by the heterogeneity of the surface or the energy of sorption. 

The Adsorption of Cs+on Clays - an ion with a simple solution chemistry (no hydrolysis, no complex formation) - can be remarkably complex. Grutter et al. (1990) have studied adsorption and desorption of Cs+ on glaciofluvial deposits and have shown that the isotherms for sorption and exchange on these materials are nonlinear. Part of this non-linearity can be accounted for by the collaps of the c-spacing of certain clays (vermiculite, chlorite). As illustrated in Fig. 4.23 the Cs+ sorption on illite and chlorite is characterized by non-linearity. 

Prediction of the breakthrough performance of molecular sieve adsorption columns requires solution of the appropriate mass-transfer rate equation with boundary conditions imposed by the differential fluid phase mass balance. For systems which obey a Langmuir isotherm and for which the controlling resistance to mass transfer is macropore or zeolitic diffusion, the set of nonlinear equations must be solved numerically. Solutions have been obtained for saturation and regeneration of molecular sieve adsorption columns. Predicted breakthrough curves are compared with experimental data for sorption of ethane and ethylene on type A zeolite, and the model satisfactorily describes column performance. Under comparable conditions, column regeneration is slower than saturation. This is a consequence of non-linearities of the system and does not imply any difference in intrinsic rate constants. 

Because of non-adherence of the site sorption mode to a strict Langmuir mechanism, as noted previously, Eq. (18), as well as Eqs. (20) or (20 a), must, at the quantitative level, be validated experimentally. This can be done most conveniently by varying the partial pressure of one component at various constant partial pressures of the other. Sorption data of this type have recently been reported for PMMA-C02, C2H4 at 35 °C69 70). As shown in Fig. 7, the agreement between experiment and calculation from the pure component isotherms, though not perfect, is nevertheless quite impressive. 

In this paper we report experimental and theoretical results on the sorption of methane and krypton on 5A zeolite. The sorption of methane in the 5A cavity is reported to be non-localized (9.), whereas that of krypton is localized at a cavity site and window site (10). The multicomponent form of the isotherm of Schirmer et al. is used to interpret the experimental data and to predict mixture equilibria at other concentrations. 

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