Langmuir-type isotherm

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...

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... 

Kinetic characteristics of the deposition study of the deposition isotherms Langmuir type localized deposition on almost energetically equivalent deposition sites. Lateral Interactions are exerted between the adsorbed species. 

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). 

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... 

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... 

Langmuir-Type Relations For systems composed of solutes that individually follow Langmuir isotherms, the traditional iTuilti-component Langmuir equation, obtained via a kinetic derivation, is... 

Figure 9. Peak Distortion by a Langmuir Type Isotherm...

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 ... 

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. 

Langmuir isotherm. Figure 3.43 shows a Langmuir-type isotherm. This isotherm is described with the following equation ... 

Figure 5 also shows the effect of the ionophore concentration of the Langmuir type binding isotherm. The slope of the isotherm fora membrane with 10 mM of ionophore 1 was roughly three times larger than that with 30 mM of the same ionophore. The binding constant, K, which is inversely proportional to the slope [Eq. (3)], was estimated to be 4.2 and 11.5M for the membranes with 10 mM and 30 mM ionophore 1, respectively. This result supports the validity of the present Langmuir analysis because the binding constant, K, should reflect the availability of the surface sites, the number of which should be proportional to the ionophore concentration, if the ionophore is not surface active itself In addition, the intercept of the isotherm for a membrane with 10 mM of ionophore 1 was nearly equal to that of a membrane with 30 mM ionophore 1 (see Fig. 5). This suggests the formation of a closest-packed surface molecular layer of the SHG active Li -ionophore 1 cation complex, whose surface concentration is nearly equal at both ionophore concentrations. On the other hand, a totally different intercept and very small slope of the isotherm was obtained for a membrane containing only 3 mM of ionophore 1. This indicates an incomplete formation of the closest-packed surface layer of the cation complexes due to a lack of free ionophores at the membrane surface, leading to a kinetic limitation. In this case, the potentiometric response of the membrane toward Li+ was also found to be very weak vide infra).

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. 

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... 

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. 

The fitting of space relaxation data using Eq. (1) to this mechanistic scheme (space relaxation data are always isothermal, because transient temperature effects are not relevant for the amplitude change of a concentration disturbance this is just an advantage of wavefront analysis of reaction kinetics), reported in (3, 5, 12), supposing a Langmuir type chemisorption for (CO) and (I O) has confirmed that (see Figure 10, 11) ... 

An assumed instantaneous distribution between the adsorbed and free solute is modelled by a Langmuir-type adsorption isotherm, where... 

A Langmuir type adsorption isotherm is given in Fig. 4.2a. As is shown in Fig. 4.2b the evaluation of the equilibrium adsorption constant and of rmax is readily obtained from experimental data by plotting Eq. (4.10a) in the reciprocal form... 

Instead of ion-exclusion, size exclusion has been used in the separation of NH4S04 from a protein [41]. In that case, the adsorption isotherms were found to be simply linear. A hydrophobic interaction separation has been used for desalting in the case of phenylalanine and NaCl [41]. NaCl shows almost no interaction with the packing and consequently has a linear adsorption isotherm. The phenylalanine, on the other hand, showed a classical Langmuir-type adsorption isotherm. 

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