Adsorption isotherms, development

The shape of the adsorption front, the width of the MTZ, and the profile of the effluent concentration depend on the nature of the adsorption isotherm and the rate of mass transfer. Practical bed depths may be expressed as multiples of MTZ, values of 5-10 multiples being economically feasible. Systems that have linear adsorption isotherms develop constant MTZs whereas MTZs of convex ones (such as Type I of Figure 15.1) become narrower, and those of concave systems become wider as they progress through... 

Using a cooperative adsorption isotherm developed by Ling (5) to derive a cooperative absorption isotherm that explicitly relates intracellular potassium content to external potassium concentration, Reisin and Gulati (4) have expressed the cooperative isotherm for the intracellular potassium as a function of Kex/Naex. This isotherm Ka(j is defined... 

The work carried out in [5,62 66] allows the direct extension of the adsorption isotherms developed in the previous section to heterogeneous surfaces. Here, for simplicity, we restrict our study to extend only the adsorption isotherm (57) with n = 1 and za = 0 to random and patchwise surfaces. 

This is one of the oldest empirical adsorption isotherms, developed by Freundlich in 1907. It is useful for adsorption from liquid solutions and also for chemisorption isotherms. 

In concluding this Section we want to emphasize that literature shows a variety of other empirical adsorption isotherms developed for special purposes and using quite different physical pictures and concepts [7.65, 7.66] and also new mathematical techniques like neural networks and/or genetic codes [7.67]. The interested reader is referred to the Proceedings of the most important Int. Conferences in the field of adsorption like COPS, FoA, PBAC, etc., cp. Chap. 1. 

Adsorption-induced reconstruction, surface metal atom, 245 Adsorption isotherms, development, 4/,5 Alcohols, role in photooxidation reaction of water on n-Ti02 electrode, 297-308 Alloy single-crystal surface, thin anodic oxide overlayers, 236-244 Alloy surfaces, chemical reconstruction, 246-247... 

There are also fundamental reasons for the study of protein molecules on surfaces. They are complicated molecules with hydrophilic as well as hydrophobic regions, which can undergo conformational changes upon adsorption. From extensive studies of protein adsorption on hydrophobic materials [cf. ref. 1] it has been concluded that the adsorption isotherms develop plateau values, which correspond to monolayers of varying packing density. In the case of extreme protein concentration, interfacial coagulation [2] has been observed. Studies of simple amphiphiles and their adsorption on metal oxides, on the other hand, has shown that the plateau values of the adsorption isotherms correspond to a bilayer of the amphiphile molecules [3]. There is less information on the adsorption behaviour of proteins. The present paper is based on ellipsometry studies and potential measurements, and we suggest that a bilayer of protein is formed in the case of clean metal surfaces. The first... 

The following several sections deal with various theories or models for adsorption. It turns out that not only is the adsorption isotherm the most convenient form in which to obtain and plot experimental data, but it is also the form in which theoretical treatments are most easily developed. One of the first demands of a theory for adsorption then, is that it give an experimentally correct adsorption isotherm. Later, it is shown that this test is insufficient and that a more sensitive test of the various models requires a consideration of how the energy and entropy of adsorption vary with the amount adsorbed. Nowadays, a further expectation is that the model not violate the molecular picture revealed by surface diffraction, microscopy, and spectroscopy data, see Chapter VIII and Section XVIII-2 Steele [8] discusses this picture with particular reference to physical adsorption. 

Sing (see Ref. 207 and earlier papers) developed a modification of the de Boer r-plot idea. The latter rests on the observation of a characteristic isotherm (Section XVII-9), that is, on the conclusion that the adsorption isotherm is independent of the adsorbent in the multilayer region. Sing recognized that there were differences for different adsorbents, and used an appropriate standard isotherm for each system, the standard isotherm being for a nonporous adsorbent of composition similar to that of the porous one being studied. He then defined a quantity = n/nx)s where nx is the amount adsorbed by the nonporous reference material at the selected P/P. The values are used to correct pore radii for multilayer adsorption in much the same manner as with de Boer. Lecloux and Pirard [208] have discussed further the use of standard isotherms. 

Continuing the formal development of the influence of the adsorption isotherm on the apparent reaction kinetics, we next consider the case of a reac-... 

The degree of uncertainty of 10 per cent or more, inseparable from estimates of specific surface from adsorption isotherms, even those of nitrogen, may seem disappointing. In fact, however, attainment of this level of accuracy is a notable achievement in a field where, prior to the development of the BET method, even the order of magnitude of the specific surface of highly disperse solids was in doubt. The adsorption method still provides the only means of determining the specific surface of a mass of non-... 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

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. 

Adsorption. Adsorption (qv) is an effective means of lowering the concentration of dissolved organics in effluent. Activated carbon is the most widely used and effective adsorbent for dyes (4) and, it has been extensively studied in the waste treatment of the different classes of dyes, ie, acid, direct, basic, reactive, disperse, etc (5—22). Commercial activated carbon can be prepared from lignite and bituminous coal, wood, pulp mill residue, coconut shell, and blood and have a surface area ranging from 500—1400 m /g (23). The feasibiUty of adsorption on carbon for the removal of dissolved organic pollutants has been demonstrated by adsorption isotherms (24) (see Carbon, activated carbon). Several pilot-plant and commercial-scale systems using activated carbon adsorption columns have been developed (25—27). 

The development of microporosity during steam activation was examined by Burchell et al [23] in their studies of CFCMS monoliths. A series of CFCMS cylinders, 2.5 cm in diameter and 7.5 cm in length, were machined from a 5- cm thick plate of CFCMS manufactured from P200 fibers. The axis of the cylinders was machined perpendicular to the molding direction ( to the fibers). The cylinders were activated to bum-offs ranging from 9 to 36 % and the BET surface area and micropore size and volume determined from the Nj adsorption isotherms measured at 77 K. Samples were taken from the top and bottom of each cylinder for pore sfructure characterization. 

The adsorption of hydrocarbons by activated carbon is characterized by the development of adsorption isotherms, adsorption mass and energy balances, and dynamic adsorption zone flow through a fixed bed. 

Contemporary development of chromatography theory has tended to concentrate on dispersion in electro-chromatography and the treatment of column overload in preparative columns. Under overload conditions, the adsorption isotherm of the solute with respect to the stationary phase can be grossly nonlinear. One of the prime contributors in this research has been Guiochon and his co-workers, [27-30]. The form of the isotherm must be experimentally determined and, from the equilibrium data, and by the use of appropriate computer programs, it has been shown possible to calculate the theoretical profile of an overloaded peak. 

One important direetion of study has been to use empirieal adsorption data, together with the preassumed model for loeal adsorption, and attempt to extraet information about the form of x(e) [13,14]. The ehoiee of the model for loeal adsorption, whieh is an important input here, has been eustomarily treated quite easually, assuming that it has rather limited influenee on the form and properties of the evaluated EADFs. Usually, one of so many existing equations developed for adsorption on uniform surfaees is used as the loeal adsorption isotherm. The most often used forms of 0 p, T,e) are the Langmuir [6] and the Fowler-Guggenheim [15] equations for loealized adsorption. Ross and Olivier [4] extensively used the equation for mobile adsorption, whieh results from the two-dimensional version of the van der Waals theory of fluids. The most radieal solution has been... 

For nonlinear systems, however, the evaluation of the flow rates is not straightforward. Morbidelli and co-workers developed a complete design of the binary separation by SMB chromatography in the frame of Equilibrium Theory for various adsorption equilibrium isotherms the constant selectivity stoichiometric model [21, 22], the constant selectivity Langmuir adsorption isotherm [23], the variable selectivity modified Langmuir isotherm [24], and the bi-Langmuir isotherm [25]. The region for complete separation was defined in terms of the flow rate ratios in the four sections of the equivalent TMB unit ... 

Bi-layer adsorption is not uncommon and the development of the bi-layer adsorption isotherm equation is a simple extension of that used for the mono-layer equation. The Langmuir equation for bi-layer adsorption is as follows ... 

The critical parameters for separation by displacement are the displacer concentration, the loading factor (ratio of the sample size to the column saturation capacity) and the column efficiency. The choice of displacer is probably the most critical step. For correct development to occur the adsorption isotherm of the displacer must overlie those of the feed components. The concentration of the i PlAcer controls the separation time and... 

In this chapter, we have chosen from the scientific literature accounts of symposia published at intervals during the period 1920 1990. They are personal choices illustrating what we believe reflect significant developments in experimental techniques and concepts during this time. Initially there was a dependence on gas-phase pressure measurements and the construction of adsorption isotherms, followed by the development of mass spectrometry for gas analysis, surface spectroscopies with infrared spectroscopy dominant, but soon to be followed by Auger and photoelectron spectroscopy, field emission, field ionisation and diffraction methods. 

Conventional bulk measurements of adsorption are performed by determining the amount of gas adsorbed at equilibrium as a function of pressure, at a constant temperature [23-25], These bulk adsorption isotherms are commonly analyzed using a kinetic theory for multilayer adsorption developed in 1938 by Brunauer, Emmett and Teller (the BET Theory) [23]. BET adsorption isotherms are a common material science technique for surface area analysis of porous solids, and also permit calculation of adsorption energy and fractional surface coverage. While more advanced analysis methods, such as Density Functional Theory, have been developed in recent years, BET remains a mainstay of material science, and is the recommended method for the experimental measurement of pore surface area. This is largely due to the clear physical meaning of its principal assumptions, and its ability to handle the primary effects of adsorbate-adsorbate and adsorbate-substrate interactions. 

As noted above, adsorption isotherms are largely derived empirically and give no information on the types of adsorption that may be involved. Scrivner and colleagues39 have developed an adsorption model for montmorillonite clay that can predict the exchange of binary and ternary ions in solution (two and three ions in the chemical system). This model would be more relevant for modeling the behavior of heavy metals that actively participate in ion-exchange reactions than for organics, in which physical adsorption is more important. 

In a separate study, Igwe and Abia46 determined the equilibrium adsorption isotherms of Cd(II), Pb(II), and Zn(II) ions and detoxification of wastewater using unmodified and ethylenediamine tetraacetic acid (EDTA)-modified maize husks as a biosorbent. This study established that maize husks are excellent adsorbents for the removal of these metal ions, with the amount of metal ions adsorbed increasing as the initial concentrations increased. The study further established that EDTA modification of maize husks enhances the adsorption capacity of maize husks, which is attributed to the chelating ability of EDTA. Therefore, this study demonstrates that maize husks, which are generally considered as biomass waste, may be used as adsorbents for heavy metal removal from wastewater streams from various industries and would therefore find application in various parts of the world where development is closely tied to affordable cost as well as environmental cleanliness.46... 

The Langmuir Equation for the Case Where Two or More Species May Adsorb. Adsorption isotherms for cases where more than one species may adsorb are of considerable significance when one is dealing with heterogeneous catalytic reactions. Reactants, products, and inert species may all adsorb on the catalyst surface. Consequently, it is useful to develop generalized Langmuir adsorption isotherms for multicomponent adsorption. If 0t represents the fraction of the sites occupied by species i, the fraction of the sites that is vacant is just 1 — 0 where the summation is taken over all species that can be adsorbed. The pseudo rate constants for adsorption and desorption may be expected to differ for each species, so they will be denoted by kt and k h respectively. 

The theoretical and (model) experimental work referred to above has largely been concerned with linear homopolymers adsorbed on regular surfaces. However, there is a vast literature of experimental studies on more complex systems. Unfortunately, in many cases the systems are either ill-defined and/or only adsorption isotherms have been established for drawing general conclusions or comparison with theory such studies are of little use. On the theoretical side, clearly the work needs to be extended towards these more complex systems. In particular, developments are required in the following areas (starts have already been made in some cases) ... 

In this paper we present results for a series of PEO fractions physically adsorbed on per-deutero polystyrene latex (PSL) in the plateau region of the adsorption isotherm. Hydro-dynamic and adsorption measurements have also been made on this system. Using a porous layer theory developed recently by Cohen Stuart (10) we have calculated the hydrodynamic thickness of these adsorbed polymers directly from the experimental density profiles. The results are then compared with model calculations based on density profiles obtained from the Scheutjens and Fleer (SF) layer model of polymer adsorption (11). 

The other molecular probe method is the single-probe method (SP method), which is separately proposed by Avnir and Jaroniec,93 and Pfeifer et al.108-112 In the SP method, a single adsorption isotherm is analyzed using a modified FHH theory. The FHH model was developed independently by Frenkel,113 Halsey,114 and Hill,115 and describes the multilayer adsorption coverage. Since the SP method uses only one probe molecule, this method is more convenient than the MP method. However, there are many theoretical limitations in applying the SP method to determination of the surface fractal dimension. Therefore, it is really necessary to discuss whether the SP method is an adequate tool to investigate the surface fractal dimension or not before applying the SP method to certain system. 

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