Adsorption isotherms mechanism

The preceding derivation, being based on a definite mechanical picture, is easy to follow intuitively kinetic derivations of an equilibrium relationship suffer from a common disadvantage, namely, that they usually assume more than is necessary. It is quite possible to obtain the Langmuir equation (as well as other adsorption isotherm equations) from examination of the statistical thermodynamics of the two states involved. 

An interesting example of a large specific surface which is wholly external in nature is provided by a dispersed aerosol composed of fine particles free of cracks and fissures. As soon as the aerosol settles out, of course, its particles come into contact with one another and form aggregates but if the particles are spherical, more particularly if the material is hard, the particle-to-particle contacts will be very small in area the interparticulate junctions will then be so weak that many of them will become broken apart during mechanical handling, or be prized open by the film of adsorbate during an adsorption experiment. In favourable cases the flocculated specimen may have so open a structure that it behaves, as far as its adsorptive properties are concerned, as a completely non-porous material. Solids of this kind are of importance because of their relevance to standard adsorption isotherms (cf. Section 2.12) which play a fundamental role in procedures for the evaluation of specific surface area and pore size distribution by adsorption methods. 

The water removal mechanism is adsorption, which is the mechanism for ad Class 4 drying agents. The capacity of such materials is often shown in the form of adsorption isotherms as depicted in Figures 9a and 9b. The initial adsorption mechanism at low concentrations of water is beheved to occur by monolayer coverage of water on the adsorption sites. As more water is adsorbed, successive layers are added until condensation or capidary action takes place at water saturation levels greater than about 70% relative humidity. At saturation, ad the pores are fided and the total amount of water adsorbed, expressed as a Hquid, represents the pore volume of the adsorbent. 

Adsorption of dispersants at the soHd—Hquid interface from solution is normally measured by changes in the concentration of the dispersant after adsorption has occurred, and plotted as an adsorption isotherm. A classification system of adsorption isotherms has been developed to identify the mechanisms that may be operating, such as monolayer vs multilayer adsorption, and chemisorption vs physical adsorption (8). For moderate to high mol wt polymeric dispersants, the low energy (equiUbrium) configurations of the adsorbed layer are typically about 3—30 nm thick. Normally, the adsorption is monolayer, since the thickness of the first layer significantly reduces attraction for a second layer, unless the polymer is very low mol wt or adsorbs by being nearly immiscible with the solvent. 

For instance, the time course of SPE demonstrates that the solvent phase surfactant concentration steadily decreases (Fig. 3) [58]. The w/o-ME solution s water content decreases at the same rate as the surfactant [58]. The protein concentration at first increases, presumably due to the occurrence of Steps 2 and 3 above, but then decreases due to the adsorption of filled w/o-MEs by the solid phase (Fig. 3) [58]. Additional evidence supporting the mechanism given above is the occurrence of a single Langmuir-type isotherm describing surfactant adsorption in the solid phase for several SPE experiments employing a given protein type (Fig. 4) [58]. Here, solid-phase protein molecules can be considered as surfactant adsorption sites. Similar adsorption isotherms occurred also for water adsorption [58]. 

C. H. Giles, T. H. MacEwan, S. N. Natchwa and D. Smith, Studies in Adsorption, Part XI A System of Classification of Solution Adsorption Isotherms and its Use in Diagnosis of Adsorption Mechanism and its Measurement of Specific Surface Area of Solids, J. Chem. Soc., p. 3973,1960. 

Adsorption is determined by the depletion method using a Dohrmann DC 80 carbon analyzer. The mineral is contacted with the polymer solution and agitated with a mechanical tumbler for 24 hours, a time which has been verified to be sufficient for adsorption to be complete (9). A more detailed description of experimental procedures is given elsewhere (10). All the data reported in this study are taken in the plateau region of the adsorption isotherm. 

Figure 15.4(A) shows the effect of the R = Zn2+/Al3+ ratio, which determines the charge density of the LDH layer, on the Freundlich adsorption isotherms. K values are far higher than those measured for smectite or other inorganic matrices. The increase in Kf with the charge density (Kf= 215, 228, 325mg/g, respectively, for R = 4, 3 and 2) is supported by a mechanism of adsorption based on an anion exchange reaction. The desorption isotherms confirm that urease is chemically adsorbed by the LDH surface. The aggregation of the LDH platelets can affect noticeably their adsorption capacity for enzymes and the preparation of LDH adsorbant appears to be a determinant step for the immobilization efficiency. [ZnRAl]-urease hybrid LDH was also prepared by coprecipitation with R = 2, 3 and 4 and Q= urease/ZnRAl from 1 /3 up to 2.5. For Q < 1.0,100 % of the urease is retained by the LDH matrix whatever the R value while for higher Q values an increase in the enzyme/LDH weight ratio leads to a decrease in the percentage of the immobilized amount.

Dual nickel, 9 820—821 Dual-pressure processes, in nitric acid production, 17 175, 177, 179 Dual-solvent fractional extraction, 10 760 Dual Ziegler catalysts, for LLDPE production, 20 191 Dubinin-Radushkevich adsorption isotherm, 1 626, 627 Dubnium (Db), l 492t Ductile (nodular) iron, 14 522 Ductile brittle transition temperature (DBTT), 13 487 Ductile cast iron, 22 518—519 Ductile fracture, as failure mechanism, 26 983 Ductile iron... 

A 0.5-gram mass of either the organo-treated or inorganic cation exchanged zeolite and 50 mL of 10 mM/L arsenate or chromate aqueous solutions were placed into Erlenmeyer flasks and mechanically shaken in reciprocating mode to attain equilibrium. Different equilibrium periods for individual zeolite modifications and both aqueous oxyanions species have been established. The adsorption isotherm experiments were conducted using above mass/ volume ratio of samples with an initial metal concentrations ranged from 0.5 to 100 mM/L at laboratory temperature. The... 

Hysteresis is observed not only in the sorption isotherms but also in calorimetric measurements of heat of wetting at different moisture contents, and it is thus a combined entropy and enthalpy phenomenon. A reliable explanation for this effect is not currently available, but there is speculation that it is due to the stresses which are induced as the cellulose swells. Since the swelling of cellulose is not completely reversible, mechanical recovery is incomplete and hysteresis will therefore be present both in the internal stress-strain curve of the sample, and also in the water adsorption isotherm. 

To determine which mechanism is operative, it is necessary to obtain information on the extent of adsorption of the polymer (adsorption isotherm), the effect of the adsorbed polymer on the... 

The fits of experimental data to a Langmuir (or another) adsorption isotherm does not constitute evidence that adsorption is the actual mechanism that accounts for the loss of the sorbate from the solution. Very frequently adsorption to a surface is followed by additional interactions at the surface, e.g., a surfactant undergoes two-dimensional association subsequent of becoming adsorbed or charged ions tend to repel each other within the adsorbed layer. 

The adsorption isotherm of sodium dodecyl sulfate (SDS) on alumina at pH = 6.5 in 0.1 M NaCI (Fig. 4.11a) is characteristic of anionic surfactant adsorption onto a positively charged oxide. As shown by Somasundaran and Fuerstenau (1966) and by Chandar et al. (1987), the isotherm can be divided into four regions. These authors give the following explanation for the adsorption mechanism ... 

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

Where there is a wide distribution of pore sizes and, possibly, quite separately developed pore systems, a mean size is not a sufficient measure. There are two methods of finding such distributions. In one a porosimeter is used, and in the other the hysteresis branch of an adsorption isotherm is utilised. Both require an understanding of the mechanism of capillary condensation. 

One should realize that adsorption isotherms are purely descriptions of macroscopic data and do not definitively prove a reaction mechanism. Mechanisms must be gleaned from molecular investigations (e.g., the use of spectroscopic techniques). Thus the conformity of experimental adsorption data to a particular isotherm does not indicate that this is a unique description of the experimental data, and that only adsorption is in operation. 

In the mechanism of the anodic iron dissolution, described in this section, the formation process of the intermediate of ferrous hydroxocomplexes, Eqn. 9-21a, is in the quasi-equilibrium state so that the Nemst equation applies between the adsorption coverage, 6p oa-, of the intermediate FeOH [d and the overvoltage, t). Accordingly, for the range of relatively low coverages of adsorption to which Langmuir s adsorption isotherm applies, we obtain Eqn. 9-22 ... 

Adsorption/Desorption Mechanisms Isotherm Hysteresis Loops... 

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... 

Based on their molecular properties as well as the properties of the solvent, each inorganic or organic contaminant exhibits an adsorption isotherm that corresponds to one of the isotherm classifications just described. Figure 5.1 illustrates these isotherms for different organic contaminants, adsorbed either from water or hexane solution on kaolinite, attapulgite, montmorillonite, and a red Mediterranean soil (Yaron et al. 1996). These isotherms may be used to deduce the adsorption mechanism. 

Retention of organic contaminants on subsurface solid phase constituents in general is not completely reversible, so that release isotherms differ from retention isotherms. As a consequence, the extent of sorption depends on the nature of the sorbent. Subsurface constituents as well as the types of bonding mechanisms between contaminants and the sohd phase are factors that control the release of adsorbed organic contaminants. Saltzman et al. (1972) demonstrated the influence of soil organic matter on the extent of hysteresis. Adsorption isotherms of parathion showed hysteresis (or apparent hysteresis) in its adsorption and desorption in a water solution. In contrast, smaller differences between the two processes were observed when the soils were pretreated with hydrogen peroxide (oxidized subsamples) to reduce initial organic matter content. The parathion content of the natural... 

The adsorption data is often fitted to an adsorption isotherm equation. Two of the most widely used are the Langmuir and the Freundlich equations. These are useful for summarizing adsorption data and for comparison purposes. They may enable limited predictions of adsorption behaviour under conditions other than those of the actual experiment to be made, but they provide no information about the mechanism of adsorption nor the speciation of the surface complexes. More information is available from the various surface complexation models that have been developed in recent years. These models represent adsorption in terms of interaction of the adsorbate with the surface OH groups of the adsorbent oxide (see Chap. 10) and can describe the location of the adsorbed species in the electrical double layer. 

The adsorption isotherms of three basic drngs, the anxiolytic bnspirone hydrochloride, the antidepressant doxepin hydrochloride, and the Ca + blocker diltiazem hydrochloride, were fitted to the Bilangmnir model, as shown in Figure 10.12 [27]. This finding snggested that the adsorption took place on two different types of sites and that there were two different adsorption mechanisms. 

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