Adsorption isotherms Langmuir type isotherm

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). 

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... 

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]. 

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. 

Furthermore, in 3.3 we turn to reactive binary ion-exchange. An equilibrium binding reaction (adsorption) with a Langmuir-type isotherm is considered. Formation of sharp propagating concentration fronts is studied via an unconventional asymptotic procedure [1]. 

The Langmuir isotherm is based on the simplest model that involves the following assumptions (1) the adsorption energy of all sites is the same and is unaffected by adsorption on neighboring sites, (2) the adsorption is immobile, (3) each site accommodates only one adsorbed particle, and (4) adsorbed atoms (molecules) do not interact with each other. Figure 10.2a shows that the Langmuir-type isotherm for... 

Type I isotherms (e.g. ammonia on charcoal at 273 K) show a fairly rapid rise in the amount of adsorption with increasing pressure up to a limiting value. They are referred to as Langmuir-type isotherms and are obtained when adsorption is restricted to a monolayer. Chemisorption isotherms, therefore, approximate to this shape. Type I isotherms have also been found for physical adsorption on solids... 

In many cases, the adsorption of surfactants on hydrophobic surfaces may follow a Langmuir-type isotherm,... 

As we have seen previously, the separation mechanism in pervaporation is explained by an adsorption-diffusion process. In this way, the selective adsorption of the components in the zeolite will be responsible for the selectivity in the separation. Adsorption is an exothermic nonactivated process. In general, the isotherm of adsorption on zeohtes follows a single site Langmuir-type isotherm [74]. 

Early work (Kemp and Rideal, 1934 Lindau and Rhodius, 1935) showed that the concentration dependence of adsorption followed a Langmuir-type isotherm, and recent studies have confirmed this in many cases (Dillman and Miller, 1973 Brash and Lyman, 1969). Thus the adsorbed film is believed to be monomolecular and its concentration is frequently found to approach a plateau value as the solution concentration is increased, consistent with the saturation of available sites. In addition to the plateau value concentration (capacity), two other quantities, the thickness of the adsorbed film and the initial slope of the isotherm are often used to characterize polymer adsorption. The thickness data supplements interfacial concentrations to give clues about molecular conformation. For proteins, the interfa-... 

Sorption in micropores can be described by the Dubinin-Radushkevic formalism that has been adapted by Stoeckli et al. This is a largely empirical approach and it should be emphasized that the use of a combination of Langmuir types isotherm leads to similar quantitative results. For evaluation of the distribution of micropores, one can either rely on high-resolution measurements of mostly nitrogen adsorption as suggested by Horvath and Kawazoe or use a combination of probe molecules of different minimum kinetic diameter. More recently, approaches based on density functional theory are put forward. 

The second simulation project was aimed at describing experiments in which retention results from surface adsorption characterized by a Langmuir-type isotherm. In this simulation, the characteristic parameters are Z , Z, Zs, and R. Zs is the distribution coefficient between the surface and the carrier gas at vanishing surface coverage. R is defined as the ratio % = Minj/totot where Minj is the ness of the probe injected and Mtot is the mass of the probe which would fully saturate the adsorbing surface. The surface simulation work shows that at infinite dilution... 

Therefore, the basic correlations for situations present in the different sections of the SMB process, combined with a simplified short-cut approach, will be presented. Without knowing the adsorption equilibria, an operating point can be generated with a minimum number of experiments. All considerations made in the following are valid only for Langmuir-type isotherms. 

Most adsorption takes place in a layer adjacent to the soUd-solution interface. If there are negligible interactions between species adsorbed on adjacent surface sites, adsorption can be described quantitatively by a Langmuir type isotherm Lads kC ... 

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... 

Li (2007) observed that the adsorption of a hydrophobically associating water-soluble polymer, AP-2, did not follow the Langmuir-type isotherm. Figure 5.37 shows that the adsorption increased to a maximum and then decreased as the polymer concentration was increased. The reason is probably that the hydrophobic polymer has an adsorption layer of multiple molecules on rock surfaces. When the polymer concentration is increased, the adsorption layer becomes thicker because of more adsorption. When the polymer concentration is further increased, the molecular interaction in the liquid is stronger than that between the adsorbed molecules and rock surfaces. Then the adsorbed molecules may leave the rock surfaces and redissolve into the liquid. Thus, the adsorption decreases. 

Effect of Salinity on Adsorption and Recovery Factor UTCHEM uses the Langmuir-type isotherm equation to describe surfactant adsorption. The adsorption is directly proportional to the coefficient 83 in the equation, which is defined as 83 = 831 + 832 x C e, where Cse is the effective salinity. We can see that by changing 832, we can change the level of salinity sensitivity. Higher salinity leads to higher surfactant adsorption. 

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... 

With most surfactants, a Langmuir-type isotherm is obtained, as illustrated in Figure 19.3, where F increases gradually with increase of and eventually reaches a plateau value F which corresponds to saturation adsorption. 

The activity of an adsorbed electron donor for the interfacial electron transfer depends on both its ability to be oxidized by the photogenerated hole (Fig. 1 ) j and its adsorption properties. The first is a thermodynamic, the second a kinetic requirement. Kinetic experiments performed at various concentrations of the electron donor can give information on its adsorption properties. Different authors have reported, that the rate of the photocatalytic oxidation of an electron donor at the Ti02 surface varied as a function of the dissolved concentration of the electron donor according to a Langmuir-type isotherm (l ig. 

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... 

Thermal regeneration of a fixed-bed adsorber is based on the fact that the adsorption process is exothermic therefore, heating the saturated adsorbent will result in desorption. The dynamics of the desorption process is very similar to that of adsorption, and can be modeled, for a Langmuir-type isotherm, by the Thomas solution (Vermeulen et al., 1973) ... 

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... 

---