Sorption processes isotherms

Regarding submerged plants, sorption of Cu(II) by Myriophyllum spicatum L. (Eurasian water milfoil) has been shown to be fast and fits isotherm models such as Langmuir, Temkin, and Redlich-Peterson. The maximum sorption capacity (c/lll l j ) of copper onto M. spicatum L. was 10.80 mg/g, while the overall sorption process was best described by the pseudo-second-order equation.115 Likewise, Hydrilla verticillata has been described as an excellent biosorbent for Cd(II). In batch conditions, the qmsx calculated was 15.0 mg/g. Additionally, II. verticillata biomass was capable of decreasing Cd(II) concentration from 10 to a value below the detection limit of 0.02 mg/L in continuous flow studies (fixed-bed column). It was also found that the Zn ions affected Cd(II) biosorption.116... 

The adherence of experimental sorption data to an adsorption isotherm equation provides no evidence as to the actual mechanism of a sorption process. 

There are a good number of sorption/desorption isotherm models which were developed in order to reflect the actual sorption/desorption processes occurring in the natural environment. Some models have a sound theoretical basis however, they may have only limited experimental utility because the assumptions involved in the development of the relationship apply only to a limited number of sorption/desorption processes. Other models are more empirical in their derivation, but tend to be more generally applicable. 

The sorption process generally is studied by plotting the equilibrium concentration of a compound on the adsorbent, as a function of equilibrium concentration in the gas or solution at a given temperature. Adsorption isotherms are graphs obtained by plotting measured adsorption data against the concentration value of the adsorbate. Several mechanisms may be involved in the retention of contaminants on... 

The amount of adsorbed chemical is controlled by both properties of the chemical and of the clay material. The clay saturating cation is a major factor affecting the adsorption of the organophosphorus pesticide. The adsorption isotherm of parathion from an aqueous solution onto montmorillonite saturated with various cations (Fig. 8.32), shows that the sorption sequence (Al > Na > Ca ) is not in agreement with any of the ionic series based on ionic properties. This shows that, in parathion-montmoriUonite interactions in aqueous suspension, such factors as clay dispersion, steric effects, and hydration shells are dominant in the sorption process. In general, organophosphorus adsorption on clays is described by the Freundhch equation, and the values for parathion sorption are 3 for Ca +-kaoUnite, 125 for Ca -montmorillonite, and 145 for Ca -attapulgite. 

Over the valid range of the empirical isotherm equation, the heat of the sorption process is given by ... 

This is easy to explain because values derived from the elution partial isotherm only pay regard to the amount adsorbed in the mesopores and the outer surface area. By contrast, the static method is not able to distinguish between these contributions and the micropore part of adsorption. Therefore the obtained values are higher but have no physical meaning whereas the elution values give a more realistic picture. The results for the standard carbon are very similar to the static values. This means that there are almost no micropores and the sorption processes take place in the mesopores and the outer surface area. This is confirmed by the huge difference in the thermodesorption peak of both materials. 

Sorption is most commonly quantified using distribution coefficients (Kd), which simplistically model the sorption process as a partitioning of the chemical between homogeneous solid and solution phases. Sorption is also commonly quantified using sorption isotherms, which allow variation in sorption intensity with triazine concentration in solution. Sorption isotherms are generally modeled using the empirical Freundlich equation, S = K CUn, in which S is the sorbed concentration after equilibration, C is the solution concentration after equilibration, and Kt and 1 In are empirical constants. Kd and K are used to compare sorption of different chemicals on one soil or sorbent, or of one chemical on several sorbents. Kd and K are also commonly used in solute leaching models to predict triazine interactions with soils under various environmental conditions. 

In order to assess the feasibility of any nuclear waste disposal concept, mathematical models of radionuclide sorption processes are required. In a later section kinetic descriptions of the three common sorption isotherms (3) are compared with experimental data from the mixing-cell tests. For a radionuclide of concentration C in the groundwater and concentration S on the surface of the granite, the net rate of sorption, by a first-order reversible reaction, is given by... 

Normally, when such an experiment is carried out, it may not be possible to cover as wide a range of concentration of the nuclide shown in this hypothetical case Solubility or other constraints may limit the accessible range In the case of tri-valent ions like Eu(III), it is not possible to increase the concentration of the ion much above tracer levels at higher pH because of the possibility of precipitation and the formation of hydrolyzed and polynuclear species which would change the nature of the sorption process We have so far not been able to determine a reproducible sorption isotherm for Eu(III) on our samples of montmorillonite above about pH 5-6. 

The ability of palladium to adsorb or absorb large amounts of hydrogen was known before the end of the last century. Much more precise work has been reported in recent years (I, 2, 3, 18). Such studies accurately showed the dependence of the sorption process on pressure and temperature. The isotherms generally indicated a sudden increase in the sorption of hydrogen at a certain pressure, which was very temperature-dependent. This sudden rise in the amounts sorbed at definite pressures suggested a phase shift in the crystalline structure of the palladium from a hydrogen-poor cr-phase to a hydrogen-rich / -phase. Such... 

Equilibrium between solution and adsorbed or sorbed phases is a condition commonly used to evaluate adsorption or sorption processes in soils or soil-clay minerals. As previously stated, equilibrium is defined as the point at which the rate of the forward reaction equals the rate of the reverse reaction. Two major techniques commonly used to model soil adsorption or sorption equilibrium processes are (1) the Freundlich approach and (2) the Langmuir approach. Both involve adsorption or sorption isotherms. A sorption isotherm describes the relationship between the dissolved concentration of a given chemical species (adsorbate) in units of micrograms per liter (pg L 1), milligrams per liter (mg L-1), microequivalents per liter (pequiv L-1), or millimoles per liter (mmol L-1), and the sorbed quantity of the same species by the solid phase (adsorbent) in units of adsorbate per unit mass of adsorbent (solid) (e.g., pg kg-1, mg kg-1, peq kg-1, or mmol kg 1) at equilibrium under constant pressure and temperature. Sorption isotherms have been classified into four types, depending on their general shape (Fig. 4.13) ... 

Mesoporous melamine-formaldehyde and phenolic-formaldehyde resins were synthesized in the process of polymerization in the presence of fumed silica as an inorganic template. The surface and structural characteristics of the obtained sorbents were investigated using XPS technique and sorption from gas phase. The parameters characterizing porous structure of the synthesized resins in a dry state were determined from nitrogen adsorption/desorption isotherms. The sorption processes of benzene and water vapor accompanied by simultaneous swelling of both polymers were also studied. 

The ion-exchange kinetics accompanied by association-dissociation in this model differ, on the one hand, fiom nonlinear sorption processes where the isotherm shape is responsible for the concentration profiles in the bead and for the kinetic rate [63] and, on the other, from conventional ion exchange where the kinetic rate and concentration profiles Cb, Ca are governed by the diffusivity factor D, /Db [16]. In the model both the selectivity (Kb /K b) and the diffusivity (Df/D factors play a role in the IE process. 

Equations 1 and 4 are equivalent only when the diffusion and sorption processes are ideal, i.e. when the diffusion coefficient is a constant and when Henry s law, which states that there is a linear relation between the external concentration or vapor pressure and the equilibrium concentration in the material, is obeyed (or, in other words, when the sorption isotherm is linear). In this case. Equation 1 may be interpreted to give... 

The basic transport mechanism through a polymeric membrane is the solution diffusion as explained in Section 4.2.1. As noted, there is a fundamental difference in the sorption process of a rubbery polymer and a glassy polymer. Whereas sorption in a mbbery polymer follows Henry s law and is similar to penetrant sorption in low molecular weight liquids, the sorption in glassy polymers may be described by complex sorption isotherms related to unrelaxed volume locked into these materials when they are quenched below the glass transition temperature, Tg. The various sorption isotherms are illustrated in Figure 4.6 [47]. 

The merits of isotherm analyses by the BET method and other theories are probably best outlined by Adamson (9). We have analyzed our results in terms of several sorption theories (9) and have concluded that those based on the sorption potential are most informative. Polanyi first proposed that the sorption process is dictated by the sorption potential e, where... 

Our results for water are given (Figure 4) for sorbed concentration F, linearized in the form of Equation 3. Least-squares analyses of our isotherms in this form show an excellent linearity typical coefficients of determination are 0.937 (N2), 0.973 (CO2), and 0.997 (H2O). Such a relationship allows us to reproduce the adsorption branch of the isotherms with respect to various coordinates (i.e, Figures 1, 2, 3) well within the experimental accuracy over the entire range of the experiment (0.001 Fq to 1.0 Pq). This result is a boon in several respects (1) interpolation to intermediate concentrations is accurate and straightforward (2) interlaboratory comparisons can be obtained easily at virtually any pressure and (3) further insight into the sorption process is available. 

Nitrogen sorption isotherms at 77 K were calculated by means of the simulated 3D networks. Besides the Kelvin equation, necessary for determining the critical radius of curvature Rc, at which condensation and evaporation would occur, it is also necessary to consider specific menisci interactions and network effects that can influence the sorption phenomena [5, 7]. The existence of an adsorbed layer is indeed of great importance on the outcome of a sorption process, but for simplicity it will not be considered in this treatment. 

Both thin-layer techniques were developed by Schmidt, Siegenthaler et al. [3.55, 3.67, 3.68] and allow an independent and precise measurement of q(E,p) and iXE.fi) isotherms. From the q-T plot, the electrosorption valency can be directly determined as illustrated in Fig. 3.12 [3.97, 3.105]. The electrosorption valency was found to be Y = z m both UPD systems indicating the absence of cosorption and competitive sorption processes in the systems studied. 

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... 

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