Nonlinear Sorption Isotherms Research Articles

Calculation of adsorption isotherms from chromatographic peak shapes

Abstract Jonsson, J.A. and Lovkvist, P., 1989. Calculation of adsorption isotherms from chromatographic peak shapes. Chemometrics and Intelligent Laboratory Systems , 5: 303–310. A numeric method is presented for the calculation of a nonlinear sorption isotherm from the shape of a chromatographic peak in the presence of significant dispersion effects (nonideal, nonlinear chromatography). The algorithm involves an initial guess for a reasonable isotherm function, and a reasonable value for D , the diffusion coefficient. This permits the calculation (by numerical solution of the pertinent nonlinear partial differential equation) of a new peak. Using the properties of the original peak and of the calculated peak, new estimates for the isotherm function and for D can be calculated. These calculations are repeated until the discrepancy between consecutive iterations is judged to be insignificant. The procedure was tested with computer-generated peaks and shown to converge to the expected isotherm curve after few iterations even if the initial guesses of isotherm shape and D are relatively coarse. A preliminary application to an experimentally measured chromatographic peak is also presented.

Diffusion and Sorption of Cesium, Strontium, and Iodine in Water-Saturated Cement

Diffusion and sorption in cementitious materials are important factors influencing radionuclide migration in radioactive waste disposal. Four different experimental techniques have been used to study these processes for Cs+, Sr2+, and I− ions in Sulphate Resisting Portland Cement paste saturated with water. The results of different experimental methods are compared and their relative merits discussed. The observations can be rationalized only by taking into account departures from the usual simple description of transport in porous media. These are that the cement pore structure has fast and slow diffusivity networks, that all ions do not have the same diffusibility, and that some ions (in this case I−) have nonlinear sorption isotherms. When these factors are taken into account, the present observations are also found to be compatible with the results of other studies.The most appropriate values of characteristic parameters for diffusion and sorption in this system are deduced.

Determination of adsorption isotherms from chromatographic measurements, using the peak maxima method

Methods for the calculation of a non-linear sorption isotherm from chromatographic data in the presence of significant dispersion effects were compared using chromatographic peaks, generated by a computer from a known Langmuir isotherm. The most accurate and also most easily applied method involves the use of the retention volume at the peak maximum to calculate the slope of the isotherm at the concentration which corresponds to the height of the peak. The so-called method of “elution on a characteristic point” is only accurate when the peak-shaping effects of non-linearity are overwhelming compared with those of dispersion. This condition was not generally met, not even in cases when the diffuse flanks of peaks of various sizes coincided. An equation for non-ideal, non-linear chromatographic peaks developed by other authors under the assumption that the non-linearity effects are small was fitted to the peaks studied. As expected, this is an accurate method for the determination of the isotherm at low concentrations. At higher concentrations, large deviations from the correct isotherm were observed, also when satisfactory fittings were obtained.

Surface Resistance Limited Sorption Kinetics in Zeolite Crystals with a Non-Linear Sorption Isotherm

Surface Resistance Limited Sorption Kinetics in Zeolite Crystals with a Non-Linear Sorption Isotherm

Kinematic Models for Soil Moisture and Solute Transport

The kinematic theory of soil moisture and solute transport in the vertical direction for unsaturated groundwater recharge is considered. The general theory of kinematic models is reviewed and applied for an isolated wetting event wherein the soil starts at and eventually drains to field capacity. Analytical expressions are developed for the water content and moisture flux as a function of depth and time. The approach is extended for an arbitrary sequence of surface flux or water content boundary conditions. The transport of a solute with a general nonlinear sorption isotherm is also considered. It is shown that for the general isotherm the vertical displacement of a solute isochore during an arbitrary wetting sequence depends only on the total depth of water infiltrated and not on how the infiltration rate varies with time.

Relationship between the retention volume and some experimental parameters in gas-liquid chromatography

A general equation for the retention volume in GLC is discussed which takes the nonlinear sorption isotherm and solubility in the adsorbed liquid layers into consideration. The experimental conditions for the observation of a nonlinear sorption isotherm are discussed theoretically and confirmed by experiments. It is established that the retention volume depends on the sample volume at the lowest and highest concentrations. The concentration effects of the retention volumes are studied and an equation for the calculation of this effect is established. A new extrapolating chromatographic parameter — specific retention volume for infinitely diluted solutions is proposed. The new effect representing the influence of the adsorbed liquid layers on solubility is described. It is shown that the solubility in the adsorbed liquid layer is less than in the bulk liquid.

Plate model of a chromatographic column in the case of a nonlinear sorption isotherm

Plate model of a chromatographic column in the case of a nonlinear sorption isotherm