Adsorption and Desorption Kinetics

So far we have considered the dynamics of an adsorbate, including a description of the adsorption potential for different adsorption sites and vibrations of adsorbed species in the electronic potential wells. To this picture one should add the kinetic description, i.e., the time evolution of the population of adsorption sites. This involves evaluation of the rates of different processes which influence the coverage of the surface with adsorbates. 

We shall begin with the consideration of the adsorption rate, i.e., the sticking rate of atoms or molecules approaching the surface from the gas phase. We assume that the gas is in thermodynamical equilibrium. Then the flux density / of gas particles towards the surface is determined by the gas pressure, P, and the gas temperature, T, and is given by 

The sticking probability depends on various factors determining the dynamics of adsorption. The adsorption site must be empty to be available for adsorption and therefore the sticking probability is proportional to the fraction of free adsorption sites. For example, in the case of nondissociative adsorption S(0) = a l — 9) with a a proportionality coefficient. In general, S depends on the kinetic energy of the particles arriving at the surface. To be 

The reverse process to adsorption, i.e., the breaking of the adsorbate-surface bonding and departing of a particle towards the gas phase, is called desorption. It is characterized by the desorption rate w which can be represented as 

In equilibrium, the number of particles stuck on the surface per unit time is equal to that desorbed from it. Taking into account Eqs (2.143) and (2.145) we obtain, in the case of nondissociative adsorption, the equation 

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Additional applications of the transfer matrix method to adsorption and desorption kinetics deal with other molecules on low index metal surfaces [40-46], multilayers [47-49], multi-site stepped surfaces [50], and co-adsorbates [51-55]. A similar approach has been used to study electrochemical systems. 

CONDER, J. R. and Hayek, B. O. Biochem. Eng. J. 6 (2000) 225. Adsorption and desorption kinetics of bovine semm albumin in ion-exchange and hydrophobic interaction chromatography on silica matrices. 

The diversity of possibilities of the general picture of a nonuniform surface makes it indefinite and hence scarcely suitable for concrete applications. On the basis of experimental data on heat of adsorption, adsorption equilibria, adsorption and desorption kinetics, the kinetics of reactions and electrode processes, a special model of a nonuniform surface has been formulated (41) that describes the experiments satisfactorily and without excessive mathematical complexity. 

The adsorption and desorption kinetics of surfactants, such as food emulsifiers, can be measured by the stress relaxation method [4]. In this, a "clean" interface, devoid of surfactants, is first formed by rapidly expanding a new drop to the desired size and, then, this size is maintained and the capillary pressure is monitored. Figure 2 shows experimental relaxation data for a dodecane/ aq. Brij 58 surfactant solution interface, at a concentration below the CMC. An initial rapid relaxation process is followed by a slower relaxation prior to achieving the equilibrium IFT. Initially, the IFT is high, - close to the IFT between the pure solvents. Then, the tension decreases because surfactants diffuse to the interface and adsorb, eventually reaching the equilibrium value. The data provide key information about the diffusion and adsorption kinetics of the surfactants, such as emulsifiers or proteins. 

Cornelissen, G., van Noott, P.C.M., Parsons, J.R., and Covers, H.A.J. 1997. Temperature dependence of slow adsorption and desorption kinetics of organic compounds in sediments. Environmental Science and Technology, 31 454-60. 

This equation is a result of considering the adsorption and desorption kinetics described in the equilibrium which establishes the Langmuir equation 9.31. Chen, et al. [68] have studied the adsorption kinetics of poly(acrylic add) onto BaTiOs from aqueous solution. Their results are given in Table 9.13. The adsorption kinetics are faster in the case of pH 10.5 because the n ative charge on the polymer attracts the positive charge on the BaTiOg surface. At pH 1.5 there is no charge on the polymer, thus diffusion to the surface is not enhanced. 

Fig. 4. Adsorption and desorption kinetics of ethane at different bulk gas concentrations in Norit activated carbon of 4.41 mm half-length slab at 30 °C. I atm. — MPSD model-------------Energy distribution model...

Alnot P, Cassuto A, King DA (1989) Adsorption and desorption kinetics with no precursor trapping hydrogen and deuterium on W 100. Surf Sci 215 29... 

In some chapters of Sections 2 and 3 the adsorption and desorption kinetics is discussed in terms of the phenomena including inorganic sorbents. 

During the last few years many studies of the behaviour of sulfur on and with metallic surfaces have been published and have provided a more complete understanding of the interaction processes. They have included gas adsorption and desorption kinetics, surface and grain boundary segregation, embrittlement, sulfidation, corrosion, passivation, catalyst poisoning, among others. 

RudziAski and Panczyk [33] have recently reviewed the classical theories of adsorption and desorption kinetics and concluded that models based on the absolute rate theory were challenged by new theories linking the rate of adsorption-desorption with the chemical potentials of bulk and adsorbed molecules. Of the... 

However, there is evidence that this reduction involves at least a charge-transfer step, creating an adsorbed silver atom adatom), and a crystallization step, in which the adatom migrates across the surface until it finds a vacant lattice site. Electrode processes may also involve adsorption and desorption kinetics of primary reactants, intermediates, and products. 

The available data concerning the adsorption and desorption kinetics and reversibility of the process for fluid interfaces are rather contradictory. 

Two schematic combined potential energy wells for the interaction of a gaseous species with a surface are shown in Fig. 2, illustrating the importance of the crossover point of the chemisorption and physisorption wells for adsorption and desorption kinetics. In the first case, adsorption is activated in the second, it is non-activated. (There are, in fact, only a few well-documented cases of activated chemisorption.) Recently, Lundqvist et al. [43] have made detailed calculations of the potential interaction between H2 and a magnesium surface which substantiate the presence of two minima. Their work is reviewed elsewhere [44]. It must be borne in mind that diagrams such as Fig. 2 grossly oversimplify the... 

Volume 19 is devoted to considering simple processes occurring at the gas-solid interface. Chapter 1 serves as an introduction and deals with the methodology of experimental surface science. Experimental results for metal surfaces on both adsorption and desorption kinetics and surface diffusion are discussed in terms of the current theories of these processes. Chapter 2 deals in the same way with these processes on semi-conductor surfaces. Finally, Chapter 3 is concerned with radiation and photoeffects at gas—solid interfaces. 

A. Cassuto and D.A. King. Rate Expressions for Adsorption and Desorption Kinetics with Precursor States and Lateral Interactions. Surf. Sci. 102 388 (1981). 

K. Schdnhammer. On the Kisliuk Model for Adsorption and Desorption Kinetics. Surf Sci. 83-.L633 (1979). 

Since chemisorption occurs on the first layer and physisorption occurs on all subsequent layers, one assumes that the adsorption and desorption kinetic rate constants, as well as /c , are not strongly dependent on the physisorbed layer under consideration. Hence, /c is independent of n, for n > 0. If this is valid, then... 

This matches the functional form of the BET isotherm when the parameter k is given by the ratio of adsorbate partial pressure pa to its saturation vapor pressure at the experimental temperature T, PA,saturation(P)- Let s consider the parameter f), which was defined above as the ratio of kq to k. If the adsorption and desorption kinetic rate constants for chemisorption follow Arrhenius temperature dependence, then kq for chemisorption on the bare surface is expressed as... 

Adsorption and Desorption Kinetics of Single-Component Adsorbates. . 156... 

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