Non-linear Sorption

Note Kd is assumed to be a linear sorption coefficient. A non-linear sorption coefficient (Kf) could be calculated if a value for N is known or could be estimated. 

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. 

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. 

WASP/TOXIWASP/WASTOX. The Water Quality Analysis Simulation Program (WASP, 3)is a generalized finite-difference code designed to accept user-specified kinetic models as subroutines. It can be applied to one, two, and three-dimensional descriptions of water bodies, and process models can be structured to include linear and non-linear kinetics. Two versions of WASP designed specifically for synthetic organic chemicals exist at this time. TOXIWASP (54) was developed at the Athens Environmental Research Laboratory of U.S. E.P.A. WASTOX (55) was developed at HydroQual, with participation from the group responsible for WASP. Both codes include process models for hydrolysis, biolysis, oxidations, volatilization, and photolysis. Both treat sorption/desorption as local equilibria. These codes allow the user to specify either constant or time-variable transport and reaction processes. 

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 data are "normalized" with regard to the ion exchange capacity C of the sorbents. The sorption curves of the illite and of the < 40-pm chlorite are strongly non-linear, whereas that of the montmorillonite approaches linearity. 

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. 

In this equation dW/dt is the rate of sorption, k. is the experimental rate constant for sorption, W, is the equilibrium sorption, W is the amount of sorption at time t = t, and h is the experimental rate constant for desorption. Thus, the sorption rate was found to be proportional to the square of the concentration of unoccupied sites, and the desorption rate was proportional to the square of the concentration of occupied sites. These rate equations are not general solutions to Fick s law of diffusion. The experimental rate constants for sorption were found to be non-linearly dependent on methanol pressure and seemed to correlate with the amount of surface sorbed methanol in different ways for coals of various rank. 

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. 

The calculation of Kd shown above assumes a linear relationship between the concentration sorbed and the concentration of the chemical in the aqueous phase (i.e., a linear isotherm). If sorption was known to be non-linear, the Freundlich constant, N, would need to be known or an estimate of it would need to be made. Generally values of N range from 0.7 to 1.2. 

Hygro-themo-chemo-mechanical behaviour of concrete is of great practical importance in many fields of civil engineering. Modelling these phenomena, especially in fresh concrete structures or concrete elements exposed to fire, is a complex problem. Several non-linear phenomena, like heat and mass sources associated with hydration or dehydration processes, phase changes, hysteresis of sorption isotherms, material properties dependent on moisture content, tem-... 

Sorption of organic contaminants onto aquifer solids is frequently described as a partitioning process, where the hydrophobic organic compound partitions into natural organic material associated with the aquifer solids [8]. Sorption can be characterized as either an equilibrium or rate-limited phenomenon. Equilibrium sorption can be modeled as either a linear or non-linear process. Equilibrium sorption may be assumed when the flow of groundwater and other processes affecting contaminant transport are slow compared to the rate of sorption. In this event the sorption of the contaminant can be considered instantaneous. If we assume equilibrium sorption, the relationship between sorbed and aqueous contaminant concentrations may be described by a sorption isotherm. 

Figure 12. Normalized, -weighted arsenic EXAFS spectra (soiid lines in a) and Fourier transforms (solid lines in b) of As(V) sorbed to S-Mn02 and birnessite and in an Mn(ll)-As(V) precipitate. Non-linear, least-squares fits to raw EXAFS data are plotted as dotted lines. The spectra of all sorption samples appear very similar, but sorption sample spectra are distinct from the model precipitate. Peak positions in FTs are not corrected for phase-shift effects, and are therefore approximately 0.5 A shorter than the true distance. From Foster et al. (submitted) reprinted with permission.

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