Linear sorption isotherm

Wilson, J. N. First theoretical paper on chromatography. Assumed complete equilibration and linear sorption isotherms. Qualitatively defined diffusion, rate of adsorption and isotherm nonlinearity. 

Sorption isotherm curves are graphical relationships showing the partitioning between solid and liquid form where mass adsorbed per unit mass of dry solids (S) is plotted against the concentration (C) of the constituent in solution. K is the sorption equilibrium constant N is a constant describing the intensity of sorption. The linear sorption isotherm can be expressed as follows ... 

Geochemical models of sorption and desorption must be developed from this work and incorporated into transport models that predict radionuclide migration. A frequently used, simple sorption (or desorption) model is the empirical distribution coefficient, Kj. This quantity is simply the equilibrium concentration of sorbed radionuclide divided by the equilibrium concentration of radionuclide in solution. Values of Kd can be used to calculate a retardation factor, R, which is used in solute transport equations to predict radionuclide migration in groundwater. The calculations assume instantaneous sorption, a linear sorption isotherm, and single-valued adsorption-desorption isotherms. These assumptions have been shown to be erroneous for solute sorption in several groundwater-soil systems (1-2). A more accurate description of radionuclide sorption is an isothermal equation such as the Freundlich equation ... 

Freundlich constants and ranges of Kd values for radionuclide sorption on the Rattlesnake Ridge sandstone are given in Table III. The constants K and N were calculated using linear regression. Linear sorption isotherms (N = 1.0) are observed only for strontium, selenium, and radium. 

Most field-scale modeling studies of contaminant plumes make the local equilibrium assumption (LEA) [18,19]. The LEA is based on the premise that the interactions between the contaminant and the aquifer material are so rapid compared to advective residence times that it can be assumed that the interactions are instantaneous [3]. Linear equilibrium sorption assumes that the binding of contaminants to aquifer solids is instantaneous and that the concentration of sorbed contaminant is directly proportional to the concentration of the dissolved contaminant. This can be modeled by a linear sorption isotherm [2] ... 

Carnahan CL, Remer JS (1984) Nonequilibrium and equilibrium sorption with a linear sorption isotherm during mass transport through an infinite porous medium some analytical solutions. J Hydrol 73 227-258... 

The majority of investigations involving polymer-coated acoustic-wave sensors for vapor detection have employed liquid or rubbery, amorphous, solid polymer coatings and have been restricted to vapor concentrations that are well below saturation. As a result, linear sorption isotherms have been found to prevail. Insofar as a sorption isotherm depends on the distribution of analyte between two phases (ambient and coating), models describing the extent of the distribution process are useful in a-priori prediction of coated-sensor performance. 

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. 

Composite Sorption Magnitude and Isotherm Nonlinearity. Accurate assessment of the extent to which the global isotherm for a system is nonlinear is important for accurate portrayal of sorption processes in that system. From a practical point of view, the extrapolation of linear approximations of weakly nonlinear or near-linear sorption isotherms to concentration ranges beyond which they are valid can result in significant errors in projections of contaminant fate and transport (1). From a conceptual point of view, observations of isotherm nonlinearity over specific concentration ranges may be employed in conjunction with models such as the DRM to probe and evaluate the extent to which multiple sorption mechanisms are operative in a particular system. 

Several common local sorption processes have been examined here by way of illustrating such effects sorption by geologically immature soft-carbon organic matter, which results in quasi-linear sorption isotherms, sorption by common mineral phases within concentration regions where linear behavior is exhibited, and sorption by diagenetically altered hard-carbon organic matter... 

Previously, it was assumed that the distribution coefficient (K) was independent of solute concentration. Thus, as the amount of solute is increased, the concentration in the mobile phase and the concentration in the stationary phase both increase in a linear relationship represented as a straight line graph of against Cstat> which has slope K (Figure 2.11). This is often referred to as a linear sorption isotherm. Because the line is straight, the value of K is always the same, regardless of the concentration in the mobile phase. 

Let us consider the impact of this on chromatography by imagining ourselves in three different situations travelling down an HPLC column along with a sample of solute that has just been injected onto the column. As the band-broadening effects described previously start to become obvious, a Gaussian distribution of solute concentrations starts to develop. If there is no effect of concentration on K (a linear sorption isotherm), then all that happens is that the band continues to broaden symmetrically as it travels down the column. A symmetrical Gaussian peak will elute from the column. 

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. 

In general, the following assumptions were made isothermal separation column, no radial concentration gradients, constant plug flow of the mobile phase, and linear sorption isotherm. 

For the case of a linear sorption isotherm, an analytical solution to the above equations, (36) and (37) subject to conditions (28), (29), (38) has been obtained using the integral transform technique by Ramarao and Chatterjee [34], The solution is complex and will not be presented here. A numerical solution to the same equations when the isotherm is non-linear was also obtained by Bandyopadhyay et al. [40],... 

Every chromatographic separation should give sufficient resolution Rs and good reproducibility, which have great importance for qualitative and quantitative analysis. Good reproducibility in LSC can be achieved only in the range of a linear sorption isotherm. In this case the retention time Ir is independent of sample size and sample vol-... 

In the absence of surfactant, HCB sorption by Appling soil yielded linear sorption isotherms, with the observed distribution coefficient (K ) increasing from 385 L/kg to 527 L/kg for mixing periods of 1,3,15, and 22 days. In the presence... 

Most models that handle the transport of organic contaminants within soil are based on the landmark publication of Jury et al. (1983). This model treats soil as a mixture of air, water, and soil particles with the assumption of uniform soil properties, linear sorption isotherms, and equilibrium partitioning between the solid, gas, and liquid phases of soil. 

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