Langmuir-type adsorption isotherms

The result of these investigations leaves the following view of adsorption of ionic surfactants onto hydrophobic surfaces. Measured adsorption isotherms (Langmuir type) and comparisons between particle sizes as measured by soap titration and... 

Ag was used to detennine the adsorption of Ag ions on rutile or anatase T1O2. Atomic absorption and, in some cases, polarography were used to study the adsorption of Ag ions by precipitated silica or pyrogenic silica. The results are found in Surface Technology.VH 9%2) 65y including AG (for specific idsorption) and adsorption isotherms (Langmuir type). 

The model based on formal kinetics was used to model the TPD curves of adsorbed CO molecules, based on the model previously reported [4], The desorption is strongly affected by the fast readsorption of CO on unoccupied Cu+ ions, thus, a quasiequilibrium state is a suitable approximation for the description of adsorption. A Langmuir type of adsorption isotherm was assumed for the CO adsorption on the Cu+ sites in zeolite, without considering lateral interactions among adsorbed molecules. 

Fig. 1 Nonlinear effects in elution chromatography (a) nonlinear adsorption isotherm (b) the corresponding chromatographic peak shapes at N = 10,000 for different injected concentrations (c) the corresponding chromatographic peak shapes at N = 500 for different injected concentrations. Isotherm Langmuir type. Concentrations 2.5, 5.0, 7.5, and 10.0 units. Length of column 10 cm...

In addition to the above technique, the heat of adsorption can also be determined from Langmuir-type adsorption isotherms. Langmuir s adsorption equation pro-... 

The Langmuir-type isotherm can be used (Lakatos et al., 1979), as it is in UTCHEM, to describe polymer adsorption. The Langmuir-type isotherm is given by... 

A plot of F versus C2 gives the adsorption isotherm. Two types of isotherms can be distinguished a Langmuir type for reversible adsorption of surfactants (Figure 18.17) and a high-affinity isotherm (Figure 18.18) for the irreversible... 

The Langmuir Adsorption Isotherm A type of adsorption isotherm commonly observed in adsorption from solutions of surfactants is the Langmuir-type isotherm (Langmuir, 1918), expressed by... 

The Mo adsorption process can be studied by using adsorption isotherms. Langmuir and Freundlich equations are the two major types of isotherms used to describe the Mo adsorption process. The Langmuir equation is based on the kinetic theory of gaseous adsorption onto solids, but is often used to model the adsorption of ions from solution (Ellis and Knezek, 1972). A common form of the Langmuir equation is... 

Laszlo et al. studied the adsorption of phenol and 2.3,4 trichlorophenol from dilute aqueous solutions on a granular activated carbon prepared from PAN by a two-step physical activated process. The adsorption isotherms were Type 1 of the BET classification and followed the Langmuir adsorption equation. The adsorption capacity and the adsorption constant K values, obtained using the Langmuir equation (Table 7.6), were found to depend on the pH of the solution. The results were discussed in terms of the acid-base character of the carbon surface and the acidic character of the two phenols. The effect of pH is more significant in the... 

Adsorption isotherms are by no means all of the Langmuir type as to shape, and Brunauer [34] considered that there are five principal forms, as illustrated in Fig. XVII-7. TVpe I is the Langmuir type, roughly characterized by a monotonic approach to a limiting adsorption at presumably corresponds to a complete monolayer. Type II is very common in the case of physical adsorption... 

Adsorption isotherms in the micropore region may start off looking like one of the high BET c-value curves of Fig. XVII-10, but will then level off much like a Langmuir isotherm (Fig. XVII-3) as the pores fill and the surface area available for further adsorption greatly diminishes. The BET-type equation for adsorption limited to n layers (Eq. XVII-65) will sometimes fit this type of behavior. Currently, however, more use is made of the Dubinin-Raduschkevich or DR equation. Tliis is Eq. XVII-75, but now put in the form... 

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... 

The major surfactant in the foam may usually be considered to be present at the bubble surfaces in the form of an adsorbed monolayer with a substantially constant F, often of the order of 3 X 10" (g mol)/ cm", for a molecular weight of several hundred. On the other hand, trace materials follow the linear-adsorption isotherm Tj = KiCj if their concentration is low enough. For a wider range of concentration a Langmuir or other type of isotherm may be applicable (Davies and Rideal, loc. cit.). 

The chromatographic resolution of bi-naphthol enantiomers was considered for simulation purposes [18]. The chiral stationary phase is 3,5-dinitrobenzoyl phenyl-glycine bonded to silica gel and a mixture of 72 28 (v/v) heptane/isopropanol was used as eluent. The adsorption equilibrium isotherms, measured at 25 °C, are of bi-Langmuir type and were proposed by the Separex group ... 

As with the Langmuir adsorption isotherm, which in shape closely resembles Michaelis-Menten type biochemical kinetics, the two notable features of such reactions are the location parameter of the curve along the concentration axis (the value of Km or the magnitude of the coupling efficiency factor) and the maximal rate of the reaction (Vmax). In generic terms, Michaelis-Menten reactions can be written in the form... 

Such a model should be as simple as possible, without however missing any of the underlying thermodynamic and physicochemical factors which cause electrochemical promotion. In particular it will be shown that even the use of Langmuir-type adsorption isotherms, appropriately modified due to the application of potential (or equivalently by the presense of promoters) suffice to describe all the experimentally observed rules G1 to G7 as well as practically all other observations regarding electrochemical promotion including the effect of potential on heats of adsorption as well as on kinetics and reaction orders. 

Knox and Piper (13) assumed that the majority of the adsorption isotherms were, indeed, Langmuir in form and then postulated that all the peaks that were mass overloaded would be approximately triangular in shape. As a consequence, Knox and Piper proposed that mass overload could be treated in a similar manner to volume overload. Whether all solute/stationary phase isotherms are Langmuir in type is a moot point and the assumption should be taken with some caution. Knox and Piper then suggested that the best compromise was to utilize about half the maximum sample volume as defined by equation (15), which would then reduce the distance between the peaks by half. They then recommended that the concentration of the solute should be increased until dispersion due to mass overload just caused the two peaks to touch. 

Figure 5.19 shows an idealized form of the adsorption isotherm for physisorption on a nonporous or macroporous solid. At low pressures the surface is only partially occupied by the gas, until at higher pressures (point B on the curve) the monolayer is filled and the isotherm reaches a plateau. This part of the isotherm, from zero pressures to the point B, is equivalent to the Langmuir isotherm. At higher pressures a second layer starts to form, followed by unrestricted multilayer formation, which is in fact equivalent to condensation, i.e. formation of a liquid layer. In the jargon of physisorption (approved by lUPAC) this is a Type II adsorption isotherm. If a system contains predominantly micropores, i.e. a zeolite or an ultrahigh surface area carbon (>1000 m g ), multilayer formation is limited by the size of the pores. 

From the asymmetrical concentration profile with front tailing (see Figure 2.4b), it can correctly be deduced that (1) the adsorbent layer is already overloaded by the analyte (i.e., the analysis is being run in the nonlinear range of the adsorption isotherm) and (2) the lateral interactions (i.e., those of the self-associative type) among the analyte molecules take place. The easiest way to approximate this type of concentration profile is by using the anti-Langmuir isotherm (which has no physicochemical explanation yet models the cases with lateral interactions in a fairly accurate manner). 

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]. 

Plots of an amount of material adsorbed versus pressure at a fixed temperature are known as adsorption isotherms. They are generally classified in the five main categories described by Brunauer and his co-workers (4). In Figure 6.2 adsorbate partial pressures (P) are normalized by dividing by the saturation pressure at the temperature in question (P0). Type I is referred to as Langmuir-type adsorption and is characterized by a monotonic approach to a limiting amount of adsorption, which presumably corresponds to formation of a monolayer. This type of behavior is that expected for chemisorption. 

Note the similarity of this expression to that for 9a, derived by the Langmuir adsorption isotherm. (ES)/(E0) plays a role analogous to 04, while S0 plays a role akin to the gas pressure. Although the expression is formally similar, we do not mean to imply that the two types of catalytic reactions proceed by similar molecular steps. 

Adsorption of lysozyme on these mesoporous carbon materials was studied at a solution pH of 11 [152]. All the adsorption isotherms were of a Langmuir type (see Figure 4.11A), resulting in monolayer adsorption capacities of 3.8, 9.8, 15.9, and 22.9 pmol g 1 for CMK-1, CMK-3, CMK-3-130, and CMK-3-150, respectively. These values are compared with the structural parameters of the CMK materials (Figure 4.11B). There is no clear relation between the adsorption capacity and the surface area (Figure 4.11B(a)). In sharp contrast, positive correlation between the adsorption... 

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