Adsorption concentration-dependent

The first term on the right-hand side of Eq. (5) is based on the strength of the static and hydrophobic interactions and is independent of the degree of adsorption p. The second term is a step function of the degree of adsorption Its slope becomes steep as AF[, increases. Accordingly, the adsorption isotherm curves of linear polymers can be characterized by the critical adsorption concentration in the first term (initiation process) and cooperativity of adsorption in the second term. The critical adsorption concentration depends not only on static interaction but also on the strength of the hydrophobic interaction. In contrast, the cooperativity of adsorption depends only on hydrophobic interaction. If die cooperative interaction of the surfactant and polyelectrol)de is expressed by the inverse slope of the adsorption isotherm curve at = 0.5, die following relationship is obtained for a linear polymer,... 

This equation has the same form of that obtained for solid diffusion control with D,j replaced by the equivalent concentration-dependent diffusivity = pDpj/[ pn]Ki l - /i,//i)) ]. Numerical results for the case of adsorption on an initially clean particle are given in Fig. 16-18 for different values of A = = 1 - R. The upt e curves become... 

Hydrated alumina is one of the most widespread hydrophilic polar sorbents for concentration and separation of different substances. In water Al Oj shows cation or anion exchange properties and its protolytic and adsorption characteristics depend on a way of obtaining. 

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

For many metals and alloys the determination of /p is complex, and its magnitude is governed by many factors such as surface finish, rate of formation, alloying constituents, and the presence of those anions, such as halides, that promote localised breakdown. In many instances the attack on passive films by halide ions shows a temperature and concentration dependence similar to the effect of hydrogen ions, i.e. the rate of film dissolution increases with concentration in accordance with a Freundlich adsorption relationship... 

Figure 6.10b shows a pattern of antagonism often observed in isolated tissue studies but not so often in cell-based assays. Saturation of uptake systems for the agonist or saturation of an adsorption site for the agonist can account for this effect. The linear portion of the regression can be used to estimate the pKB or the pA2. If there is a loss of concentration dependence of antagonism, as seen in... 

The simplest case to be analyzed is the process in which the rate of one of the adsorption or desorption steps is so slow that it becomes itself rate determining in overall transformation. The composition of the reaction mixture in the course of the reaction is then not determined by kinetic, but by thermodynamic factors, i.e. by equilibria of the fast steps, surface chemical reactions, and the other adsorption and desorption processes. Concentration dependencies of several types of consecutive and parallel (branched) catalytic reactions 52, 53) were calculated, corresponding to schemes (Ila) and (lib), assuming that they are controlled by the rate of adsorption of either of the reactants A and X, desorption of any of the products B, C, and Y, or by simultaneous desorption of compounds B and C. 

The most frequent type of interaction between solid and species in solution would be electrostatic adsorption (ion exchange), due to the action of attractive coulomb forces between charged particles in solution and the solid surfaces. This process would also be concentration dependent. 

Studies of the adsorption of surface active electrolytes at the oil-water interface provide a convenient method for testing electrical double layer theory and for determining the state of water and ions in the neighborhood of an interface. The change in the surface amount of the large ions modifies the surface charge density. For instance, the surface ionic area of 100 per ion corresponds to 16, /rC/cm. The measurement of the concentration dependence of the changes of surface potential were also applied to find the critical concentration of formation of the micellar solution [18]. 

Adsorption kinetics of Zn on the untreated soil and the soils with the removal of organic matter and Fe oxides has been studied in detail by Hinz and Selim (1999) using a thin disk flow method. They reported that Zn sorption was highly concentration-dependent. When Zn concentration was... 

Glucose oxidase was first adsorbed onto the platinum surface at a controlled potential. The protein adsorption varied depending on several factors as electrode potential, glucose oxidase concentration, pH and temperature. The effects of these factors on protein adsorption were carefully investigated. 

As seen in equations (32)-(34), the forward adsorptive flux depends upon the concentration of free cell surface carriers. Unfortunately, there is only limited information in the literature on determinations of carrier concentrations for the uptake of trace metals. In principle, graphical and numerical methods can be used to determine carrier numbers and the equilibrium constant, As, corresponding to the formation of M — Rcen following measurement of [M] and (M —Rceii. For example, a (Scatchard) plot of (M — RCeii /[M] versus (M — RCeii should yield a straight line with a slope equal to the reciprocal of the dissociation constant and abscissa-intercept equal to the total carrier numbers (e.g. [186]). 

The electrode roughness factor can be determined by using the capacitance measurements and one of the models of the double layer. In the absence of specific adsorption of ions, the inner layer capacitance is independent of the electrolyte concentration, in contrast to the capacitance of the diffuse layer Q, which is concentration dependent. The real surface area can be obtained by measuring the total capacitance C and plotting C against Cj, calculated at pzc from the Gouy-Chapman theory for different electrolyte concentrations. Such plots, called Parsons-Zobel plots, were found to be linear at several charges of the mercury electrode. ... 

The data for the p-phenylenediamine-silver ion reaction are not accounted for by Bagdasar yan s treatment. On the basis of an adsorption mechanism, the data would suggest that the important phase for the catalyzed reaction is adsorption of the p-phenylenediamine by the silver catalyst. The extent of the adsorption would depend upon the surface conditions of the catalyst, which apparently depend on changes in the protective colloid or in the salt concentration. A catalytic mechanism involving activation of the p-phenylenediamine by the catalyst would be consistent with the observation of Weissberger and Thomas that colloidal silver markedly catalyzes the oxygen oxidation of p-phenylenediamine. 

The common shape observed for Tq as a function of the substrate or catalyst concentration depending on the primary events depicted in Eqs. (la)-(lf) is normally reported of saturative type as if the rate would be determined by adsorption properties of the substrate on the catalyst surface according to a Langmuir isotherm ... 

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