Adsorption non-uniform

Adsorption studies with Cd2+, Zn2+, Cu2+, and Pb2+ on y-FeOOH, y-Al203, Fe203. H20 and a-Si02182) indicate that the solid surface is composed of non-uniform adsorptive binding sites. At extremely low adsorption densities, all sites are available in excess and... 

The sulfur and carbon contents of selected spent catalyst beds (900°C, 20 bar) were analyzed as a function of bed length (Table 1). The content of these components of the bed proved to be higher at the inlet than in the middle and bottom of the bed. Due to endothermic reactions, i.e., steam reforming of hydrocarbons and atmnonia decomposition, the bed temperature decreased considerably (max. about 100°C at 20 bar) at the top of the catalyst bed, but after poisoning the temperature increased again [6]. This demonstrates, in addition to a strong non-uniform adsorption of sulfur on metals, higher sulfur and carbon contents at the inlet of the bed compared with those of the other parts of the bed. 

From the point of view of microporous structure, adsorbents (i.e., nanoporous carbons) are classified as homogeneous (uniform) and heterogeneous (non-uniform). Adsorption on uniformly microporous carbons is often described by the Dubinin-Radushkevich (DR) or the Dubinin-AstaJdiov (DA) equations however, it should be mentioned that there is no a rigorous analytical equation for gas adsorption in carbons with uniform micropores. 

Several mechanisms may be proposed to explain the process of spontaneous emulsification, all of which are related to the properties of the interfacial film. The first mechanism is due to interfacial turbulence that may occur as a result of mass transfer or by non-uniform adsorption of the surfactant molecules at the OAV interface. The interface shows unsteady motions - streams of one phase are ejected and penetrate into the second phase. This is illustrated in Figure 4.1(a) which shows the localized reduction in interfacial tension caused by non-uniform adsorption of surfactants or mass transfer of surfactants across the interface (5-7). When the two phases are not in chemical equilibrium, convection currents may be formed which transfers the liquid rich in surfactants towards the areas deficient in surfactants. These convection currents may give rise to... 

It should be emphasized that the value of tf resulting from use of (1.49) or (1.50) applies to a particular value of n,. Because of the joint effects of the energetic non-uniformity of the adsorbent surface and the interaction of adsorbate molecules in the adsorbed film itself, the heat of adsorption in general varies significantly with the amount adsorbed. It is therefore essential to repeat the calculation of (f for a succession of values of n, and thereby obtain the curve of against n,. 

Numerous materials have been used to fabricate open tubular columns. Most early studies were conducted using stainless steel tubing and later nickel tubing of capillary dimensions [147-149]. These materials had rough inner surfaces (leading to non-uniform stationary phase films), metal and oxide impurities at their surface which were a cause of adsorption, tailing, and/or decomposition of polar solutes and because their walls were thick, thermal Inertia that prevented the use of fast temperature programming. None of these materials are widely used today. 

While adsorption equiUbrium considerations do justify the possibility to regenerate an adsorbent bed completely and to uniform levels, this is rarely achieved in practice in either thermal swing adsorption and is almost never the case in pressure swing adsorption. Some residual sorbate is always left on the sorbent and in general, except for TSA with only one or two sorbates, the residual loadings are almost always found as a non-uniformly distributed profile across the length of the bed. 

Because polymer adsorption tends to be irreversible, inadequate mixing, with non-uniform distribution of polymer in the particle suspension, cannot be rectified by subsequent rearrangement. Locally high concentrations can lead to rapid floe growth, but with corresponding regions of starvation elsewhere in the... 

Ni(lOO) reduces the degree of backdonation and results in a blue-shift in the v(CO) frequency. We have carried out a detailed FTIR investigation of the complex effect of potassium and chemisorbed oxygen on the adsorption of CO on Ni(KX)) [32]. In brief, the 2090,2013 and 1898 cm-i features in Figure 7b are related to the adsorption of CO on Ni sites which are non-uniformly modified by the coadsorbed potassium and atomic oxygen [32]. In addition, the 2134 cm-i feature in Figure 7b can be assigned to the adsorption of CO on the Ni2-n sites of NiO clusters that are not modified by the presence of potassium. 

Let the gas pressure that corresponds to adsorption equilibrium be denoted as p. The value of p for the standard state of a site is denoted as b and is called desorption pressure of the site (Section IV). Each site of a non-uniform surface is characterized by a certain b value or by an adsorption coefficient, a = l/b (for a given temperature). At adsorption equilibrium, the probability that a site is occupied... 

Non-uniformity of catalytic sites A characteristic of a catalytic surface is that its sites may differ in their thermodynamic and kinetic properties. In the kinetic description of catalytic reactions on non-uniform surfaces, a parameter a is frequently used to connect changes in the activation energy of activated adsorption with the enthalpy of the adsorption... 

In this connection, it is interesting to consider questions of the heat of adsorption on a non-uniform surface, of the fraction of the specific heat of the adsorbed gas related to redistribution of the gas on the surface for a change in temperature, and so on—both for the general case and for a distribution of the form (17). The elaboration of these problems, however, at present would necessarily be nothing more than a mathematical exercise. We note only that for the distribution equation (17), the smaller the value of q, the sharper is the maximum of the specific heat near T = 7, while the differential heat of absorption at T = 0 obeys the equation... 

In conclusion, I would like to emphasize that the main object of this part of the paper has not been a quantitative theory of adsorption on non-uniform surfaces, but a struggle for the correct qualitative interpretation of a specific set of experimental data. 

An integral equation for adsorpt ion on non-uniform surfaces is derived and an approximate method for its solution T is given. 

This work was carried out independently of and simultaneously with Temkin s work on adsorption on non-uniform surfaces (performed at the L. Ya. Karpov Physico-Chemical Institute). The difference in methods, objectives and, partly, results justifies the separate publication of our articles. 

This paper by Ya.B. was translated and published, with a few changes, in the collection Statistical phenomena in heterogeneous systems, 1 which was devoted especially to the theory of non-uniform surfaces and to statistical phenomena in adsorption and catalysis. In the review article by V. I. Levin in this collection the priority of Ya.B. s article in statistical research on the theory of adsorption and catalysis is emphasized. The article also cites articles by other authors who came to similar conclusions, but later than Ya.B. The significance of Ya.B. s work for the theory of catalysis is elucidated in detail in S. Z. Roginskii s book, Adsorption and Catalysis on a Non-Uniform Surface. 2 After this a summary of this paper by Ya.B. has entered into the majority of monographs and textbooks on catalysis. Thus, in the course of Thomas and Thomas3 the derivation of the adsorption isotherm on a non-uniform surface is given in full and referred to as classical. 

Roginskii S. Z. Adsorbtsiia i kataliz na neodnorodnoi poverkhnosti [Adsorption and Catalysis on a Non-Uniform Surface]. Moscow, Leningrad Izd-vo AN SSSR, 643 p. (1948). 

An unusual dependence for adsorption on a uniform surface arises when it is assumed that the rate of change of the surface is considerably slower than the rate of adsorption (see figure). If adsorption and desorption occur rapidly, the state of the surface remains practically unaltered and we then get an adsorption isotherm corresponding to a non-uniform surface with a distribution p(E, 0) of the heat of adsorption (curve 1) [3]. However, when the time interval is considerable, slow adsorption accompanies changes in the properties of the surface, and the amount of gas adsorbed approaches that given by the Langmuir isotherm (curve 2, point B), which describes a state of complete equilibrium (see above). 

These results are in agreement with those obtained with the thick-layer dsDNA-electrochemical biosensor. The clear separation of the adriamycin and 8-oxoGua peaks can be explained by the non-uniform coverage of the electrode surface by DNA and the adsorption of adriamycin [37] on the uncovered glassy carbon. This peak separation is... 

The adsorbed CO molecules are under strong lateral repulsion, in particular, adsorption of these molecules on the Ru(001) face leads to an appearance of the R( /3 x /3) ordered structures in LEED patterns [153]. This means absence of an uniform occupation of every adsoprtion site by the CO molecules the CO molecules are accommodated in the different sublattices non-uniformly, and this is the typical case when lateral interactions are responsible for a non-uniform adspecies distribution on a homogenous surface. Splitting of the experimental spectra is a signal of the... 

The local partial adsorption isotherms O j( P ) of various adsorption centers, which are needed for Eq. (A.5), are calculated by the system of equations from Refs. [80,89]. These equations take into account energetic non-uniformity of lattice sites and intermolecular interactions at a distance of R c.s.,... 

What functions to describe a distribution of adsorption centers on non-uniform surfaces are needed for calculation of adsorption isotherm, the adsorption and desorption rates of dissociating molecules, for allowing the lateral interaction between the nearest neighbors ... 

The SECM can be used in the feedback mode to probe lateral mass-charge transfer [79-83]. The theory of SECM feedback surveyed in Section IV.A.2 assumes that the substrate surface is uniformly reactive. When lateral mass and/ or charge transfer occurs on the substrate surface, or within a thin film, the surface reactivity of the substrate becomes non-uniform and the SECM feedback theory must be modified. Unwin and Bard [79] developed the theory for adsorption-desorption of a redox species at the substrate that allowed for surface diffusion of the adsorbate. They introduced a new approach, the scanning electrochemical microscope induced desorption (SECMID), as a way to probe surface diffusion. The set of differential equations for the diffusion problem comprise Eqs. (8a,b), and Eq. (26), which relates the redox concentration at the substrate surface and the surface coverage by adsorbed species... 

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