Adsorption, apparent

It is important to note that the experimentally defined or apparent adsorption no AN 2/, while it gives F, does not give the amount of component 2 in the adsorbed layer Only in dilute solution where N 2 0 and = 1 is this true. The adsorption isotherm, F plotted against N2, is thus a composite isotherm or, as it is sometimes called, the isotherm of composition change. 

Equation XI-27 shows that F can be viewed as related to the difference between the individual adsorption isotherms of components 1 and 2. Figure XI-9 [140] shows the composite isotherms resulting from various combinations of individual ones. Note in particular Fig. XI-9a, which shows that even in the absence of adsorption of component 1, that of component 2 must go through a maximum (due to the N[ factor in Eq. XI-27), and that in all other cases the apparent adsorption of component 2 will be negative in concentrated solution. 

The relative adsorptions of the two liquids (CCI4 and CyH g) was found by measuring refractive indices of the initial and final mixtures after contact with the higher area silica. They are found to be almost identical and apparent adsorptions (Table II) are low. 

In their description of metal ion adsorption, Benjamin and Leckie used an apparent adsorption reaction which included a generic relationship between the removal of a metal ion from solution and the release of protons. The macroscopic proton coefficient was given a constant value, suggesting that x was uniform for all site types and all intensities of metal ion/oxide surface site interaction. Because the numerical value of x is a fundamental part of the determination of K, discussions of surface site heterogeneity, which are formulated in terms similar to Equation 4, cannot be decoupled from observations of the response of x to pH and adsorption density. As will be discussed later, It is not the general concept of surface-site heterogeneity which is affected by what is known of x> instead, it is the specific details of the relationship between K, pH and T which is altered. 

Scott HD, Wolf DC, Lavy TL. 1982. Apparent adsorption and degradation of phenol at low concentrations in soil. J Environ Quality 11 107-111. 

EXAMPLE 9.5 Calculating the Adsorption Energy from the Brunauer-Emmett-Teller Isotherm. The BET analysis uses p/p0 rather than p as a variable just as we used this pressure ratio to compare Langmuir adsorption at different temperatures in Example 9.3. What corrections, if any, are needed in the apparent adsorption energy of about 14 kJ mole-1 as calculated in Example 9.3 ... 

Figure 8 illustrates the correlation between the apparent adsorption increase and the onset of precipitation of hafnium hydroxide. 

Experimentally, the investigation of adsorption from solution is much simpler than that of gas adsorption. A known mass of adsorbent solid is shaken with a known volume of solution at a given temperature until there is no further change in the concentration of the supernatant solution. This concentration can be determined by a variety of methods involving chemical or radiochemical analysis, colorimetry, refractive index, etc. The experimental data are usually expressed in terms of an apparent adsorption isotherm in which the amount of solute adsorbed at a given temperature per unit mass of adsorbent - as calculated from the decrease (or increase) of solution concentration - is plotted against the equilibrium concentration. 

Figure 3.4. Apparent adsorption and desorption of boron (B), determined using the continuous flow technique (Sparks et at., 1980b) with no adsorbent. [From Carski and Sparks (1985), with permission.]...

However, two important points should be noted. Firstly, that when one of the ions of an added electrolyte can interact with the surfactant to form an insoluble salt this reaction can remove the adsorbed layer from the particle (see Table I). Secondly, the hydrophobic chain of the surfactant must be compatible with the particle surface. This point is illustrated in Figure 10 which shows the adsorption of dodecanoic acid on to PTFE particles. The adsorption of the C11H23 hydrocarbon chain to PTFE is clearly much less favourable than the adsorption of the, C7F15, fluorocarbon chain in fact, a C7H15 chain, in the form of octanoic acid showed no apparent adsorption on to a PTFE surface. Thus, although both acids have hydrophobic chains, there is clearly a remarkable difference between their affinities for the substrate. 

F/r8 is the amount of gas which would be contained in the volume V if the gas concentration were uniform throughout the volume. That the amount actually present is n° means that local variations in gas concentration must occur the gas concentration within the bulk of the solid is zero, but is greater than c° in the interfacial layer. The difference between n° and V/ig may be called the apparent adsorption... 

The apparent adsorption may, alternatively, be defined by measuring the amount of gas which has to be added to the system at constant T, p to increase the volume V back to V°. The apparent adsorption is then equal to the extra amount of gas which can be accommodated in a volume V° at a given 7, p when the solid is introduced. It can, therefore, be expressed in terms of the local deviations of the concentration, c, of adsorptive molecules, from the bulk concentration c° ... 

The first term represents the amount of gas excluded by the solid, while the second is the extra amount of gas accommodated because of the accumulation of gas in the neighbourhood of the solid surface. If the adsorption is very weak the first term may exceed the second and the apparent adsorption may be negative (V > V°). 

In the case of adsorption from solution, the apparent adsorption of a solute at the liquid-solid interface is usually evaluated by measuring the decrease in its concentration when brought into contact with the adsorbent. The adsorption isotherm is then plotted as the apparent adsorption of the solute against the equilibrium concentration. 

The number of transfer units is related to the apparent adsorption rate constant by... 

With very low adsorption rates (small n values), a fraction of solute is eluted at the retention time of the nonretained compound. This effect is increased by the column overloadings this phenomenon, called the split-peak effect [7.211. can be used to determine the apparent adsorption rate constant [21—25 [. 

Another problem in model applications is the adsorption on a nonuniform adsorbent. The immobilization of polyclonal antibodies will lead to different populations of binding sites, and the measurements will only give an apparent adsorption rate constant [22], The properties of the adsorbent surface are also greatly affected by the procedure used for protein immobilization. It may be important to select coupling methods that orient the covalently attached protein... 

The effect of the amount of monoclonal antibody immobilized to the Sepharose matrix was further investigated by Fowell and Chase [54]. Batch experiments were used to determine the apparent adsorption rate constant k. d. A marked increase in the fc value is observed as the amount of antibody immobilized is decreased. The values of fc vary from 1.3 x 103 dm3 mol l-s l for the support of high capacity to 7.0 x 105 dm3-moM s l for the support of low capacity. A marked increase of the efficiency of the adsorption process was also observed when using the frontal analysis techniques. This effect has been explained by the improved adsorption properties of the low-capacity immunoadsorbent. 

The mI contribution can also be determined from experiments with columns of the same size packed with immunoadsorbents of varying capacities (22). Because of the low amount of monoclonal antibody available, these experiments were performed by immobilizing various quantities of polyclonal anti-HSA antibody on the silica matrix. The results for an 83.3 mm s-1 flow rate are summarized in Table 2. An important decrease of the apparent adsorption rate constant is observed when the column capacity is increased. 

In contrast with the results of Fig. 5. important deviations between the theoretical profile and the experimental one are observed for adsorption studies on the polyclonal antibody [23], even at low HSA feeding concentrations. The frontal elution model given by Eq. (7) with k d = 0 correlates well with the first part of the breakthrough curve, but later a deviation is observed even at very low feeding HSA concentrations. In this case, the simplified model assuming a uniform adsorbent surface is not appropriate. The polyclonal antibody is made of different populations of antibodies of various affinities. With polyclonal immunoadsorbents, the values of ka in Table 2 are to be considered as apparent adsorption rates. 

Table 2 lists the two parameters n and Qx necessary to describe the model as determined with columns differing by the density of immobilized polyclonal antibody. As previously described, from the variation of the column capacity one can evaluate the contribution to the transport to the binding sites (I/nmt = 0.040) and calculate the effective adsorption rate constant ka. The results agree with those obtained from frontal analysis. The value of the apparent adsorption rate constant k is close to the value of Aa for experiments carried out both at high flow rates and with an immunoadsorbent column of low capacity 22). In this case, the rate-controlling step is the biospecific interaction. 

The main problem in the determination of association rates at the gas-liquid interface is the interplay of the mass transport effects and the biospecific sorption process. The experimental studies show that both effects are involved in the binding of antigen to the antibody attached to a surface. The variations of the value of the apparent adsorption rate constant with various experimental conditions reveal the importance of the nonideal effects in such experiments. To determine the effective rate of interaction, it is important both to minimize the diffusion resistances and to estimate this contribution by increasing the amount of information. Studies with varying flow rates, particle sizes, ligand densities. 

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