Adsorption-desorption kinetics methods

In this review we put less emphasis on the physics and chemistry of surface processes, for which we refer the reader to recent reviews of adsorption-desorption kinetics which are contained in two books [2,3] with chapters by the present authors where further references to earher work can be found. These articles also discuss relevant experimental techniques employed in the study of surface kinetics and appropriate methods of data analysis. Here we give details of how to set up models under basically two different kinetic conditions, namely (/) when the adsorbate remains in quasi-equihbrium during the relevant processes, in which case nonequilibrium thermodynamics provides the needed framework, and (n) when surface nonequilibrium effects become important and nonequilibrium statistical mechanics becomes the appropriate vehicle. For both approaches we will restrict ourselves to systems for which appropriate lattice gas models can be set up. Further associated theoretical reviews are by Lombardo and Bell [4] with emphasis on Monte Carlo simulations, by Brivio and Grimley [5] on dynamics, and by Persson [6] on the lattice gas model. 

Adsorption-Desorption Kinetics at the Metal-Oxide-Solution Interface Studied by Relaxation Methods... 

Chemical relaxation methods can be used to determine mechanisms of reactions of ions at the mineral/water interface. In this paper, a review of chemical relaxation studies of adsorption/desorption kinetics of inorganic ions at the metal oxide/aqueous interface is presented. Plausible mechanisms based on the triple layer surface complexation model are discussed. Relaxation kinetic studies of the intercalation/ deintercalation of organic and inorganic ions in layered, cage-structured, and channel-structured minerals are also reviewed. In the intercalation studies, plausible mechanisms based on ion-exchange and adsorption/desorption reactions are presented steric and chemical properties of the solute and interlayered compounds are shown to influence the reaction rates. We also discuss the elementary reaction steps which are important in the stereoselective and reactive properties of interlayered compounds. 

Astumian, R.D. Sasaki, M. Yasunga,T. Schelly, Z.A. (1981) Proton adsorption-desorption kinetics on iron oxides in aqueous suspensions, using the pressure jump method. J. Phys. Chem. 85 3832—3835 Atkins, P.W. (1990) Physical chemistry. 4 Ed. 

Yasunaga, T., and Ikeda, T. (1986). Adsorption-desorption kinetics at the metal-oxide-solution interface studied by relaxation methods. ACS Symp. Ser. 323, 230-253. 

Ikeda, T., Sasaki, M., Hachiya, K., Astumian, R, D., Yasunaga, T., and Schelly, Z. A. (1982b). Adsorption-desorption kinetics of acetic acid on silica-aluminum particles in aqueous suspensions, using p-jump relaxation method. J. Phys. Chem. 86, 3861-3866. 

See especially Chaps. 2 and 3 in D. L. Sparks and D. L. Suarez, op. cit.10 A summary review of chemical relaxation methods is given by T. Yasunaga and T. Ikeda, Adsorption-desorption kinetics at the metal-oxide-solution interface studied by relaxation methods, Chap. 12 in J. A. Davis and K. F. Hays, op. cit.2... 

Long ago, Langmuir suggested that the rate of deposition of particles on a surface is proportional to the density of particles in the vicinity of the surface and to the available area on the surface [1], However, the calculation of the available area is still an open problem. In a first approximation, one can assume that the available area is the total area of the surface minus the area already occupied by the adsorbed particles [1]. A better approximation can be obtained if the adsorbed particles, assumed to have the shape of a disk, are in thermal equilibrium on the surface, either because of surface diffusion and/or of adsorption/desorption kinetics. In this case, one can use one of the empirical equations available for the compressibility of a 2D gas of hard disks, calculate the chemical potential in excess to that of an ideal gas [2] and then use the Widom relation between the area available to one particle and its excess chemical potential on the surface (the particle insertion method) [3], The method is accurate at low densities of adsorbed particles, where the equations of state are accurate, but, in general, poor at high concentrations. The equations of state for hard disks are based on the virial expansion and only the first few coefficients of this... 

Abstract Investigations of alternate adsorption regularities of cationic polyelectrolytes a) copolymer of styrene and dimethylaminopropyl-maleimide (CSDAPM) and b) poly(diallyldimethylammonium chloride) (PDADMAC) and anionic surfactant - sodium dodecyl sulfate (SDS) on fused quartz surface were carried out by capillary electrokinetic method. The adsorption/desorption kinetics, structure and properties of adsorbed layers for both polyelectrolytes and also for the second adsorbed layer were studied in dependence on different conditions molecular weight of polyelectrolyte, surfactant and polyelectrolyte concentration, the solution flow rate through the capillary during the adsorption, adsorbed layer formation... 

Rather than trying to describe the sparse and occasional results hitherto reported, this work is devoted to the foundation of a general and comprehensive theory of adsorption-desorption kinetics. The emphasis, however, will not be concentrated on the formal mathematical aspects of the theory, but rather on its physical bases in particular, the validity of the methods developed will be checked by verifying how they are able to explain the observed experimental behaviours. Among them one plays a special role — the time-logarithm law known as Elovich equation. 

A theory as rigorous and comprehensive as the theory of adsorption equilibrium on heterogeneous surfaces has not been developed yet for the description of adsorption [desorption] kinetics on [from] heterogeneous surfaces. This work aims to fill, at least partially, this gap and new methods are developed for kinetics in strict analogy to what was done... 

Yasunaga, T., and T. Ikeda. 1986. Adsorption-desorption kinetics of the metal-oxide-solution interface studied by relaxation methods, p. 230-253. In J.A. Davis and K.F. Hayes (ed.) Geochemical processes at mineral surfaces. Proc. Am. Chem. Soc. Symp. Ser. 323, Chicago, IL. 8-13 Sept. 1985. ACS, Washington, DC. 

Hachiya, K., Takeda, K., and Yasunaga, T, Pressure-jump method to adsorption-desorption kinetics. Adsorption Sci. Technol.. 4. 25, 1987. 

Yasunaga, T. and T. Ikeda (1986), Adsorption-Desorption Kinetics at the Metal-oxide-Solution Interface studied by Relaxation Methods, in J. A. Davies and K. F. Hayes, Eds., Geochemical Processes at Mineral Surfaces, American Chemical Society, Washington, DC, pp. 230-253. 

A related method involves the use of the tip reaction to perturb a reaction at a surface an example of this approach is SECM-induced desorption (SECMID) (22). For example, the adsorption/desorption kinetics of protons on a hydrous metal oxide surface can be studied in an unbuffered solution by bringing the tip near the surface and reducing proton (to hydrogen) at the tip. This causes a local change in pH that results in proton desorption from the surface. The tip current can be used to study the kinetics of proton desorption and diffusion on the surface (Chapter 12). 

Adsorption from liquids onto solid adsorbents is widely utilized in liquid chromatography (HPLC, see Chapter 11,4), described in detail in physical chemistry and instrumental methods textbooks, e.g. in [16]. The separation by HPLC is based on adsorption-desorption kinetics, i.e. on how long various dissolved compounds remain present in the adsorbed state. The average time, ta, during which molecules are present in an adsorption layer is... 

However, adsorption/desorption kinetics are difficult to follow, particularly when simultaneous structural observations are being made. In this chapter we present information pertaining to two different techniques. The first method extends our previous measurements of surface circular dichro-ism, indicating structural changes as a function of contact time between a plane surface and protein solution. The second technique is based on a chromatographic method that allows us direct access to the kinetics of adsorption/desorption with a subsequent assessment of structural damage. 

Acar and coworkers (46] and Shapiro et al. [52] have presented general models based on the first of these two approaches. These models predict that the contaminant and the electrolysis products at inert electrodes will be transported and dispersed by advection, migration, and diffusion. Modelling in this manner provides only a first-order, mathematical framework to examine the flow patterns and chemistry generated in the process adsorption/desorption kinetics, acld/base chemical reactions, complex equilibria, and precipitatlon/solubility factors may heavily influence the model accuracy and outcome of any site remediation. Two approaches for mathematic modelling are the use of analytical solutions or numerical, finite element methods (FEM). Both models require adequate definitions for the boundary conditions (nature of electrolyses, flow behaviour). 

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. 

This is the same case with which in Eqs. (2)-(4) we demonstrated the elimination of the time variable, and it may occur in practice when all the reactions of the system are taking place on the same number of identical active centers. Wei and Prater and their co-workers applied this method with success to the treatment of experimental data on the reversible isomerization reactions of n-butenes and xylenes on alumina or on silica-alumina, proceeding according to a triangular network (28, 31). The problems of more complicated catalytic kinetics were treated by Smith and Prater (32) who demonstrated the difficulties arising in an attempt at a complete solution of the kinetics of the cyclohexane-cyclohexene-benzene interconversion on Pt/Al203 catalyst, including adsorption-desorption steps. 

The Monte Carlo method as described so far is useful to evaluate equilibrium properties but says nothing about the time evolution of the system. However, it is in some cases possible to construct a Monte Carlo algorithm that allows the simulated system to evolve like a physical system. This is the case when the dynamics can be described as thermally activated processes, such as adsorption, desorption, and diffusion. Since these processes are particularly well defined in the case of lattice models, these are particularly well suited for this approach. The foundations of dynamical Monte Carlo (DMC) or kinetic Monte Carlo (KMC) simulations have been discussed by Eichthom and Weinberg (1991) in terms of the theory of Poisson processes. The main idea is that the rate of each process that may eventually occur on the surface can be described by an equation of the Arrhenius type ... 

Due to the fast kinetics of adsorption/desorption reactions of inorganic ions at the oxide/aqueous interface, few mechanistic studies have been completed that allow a description of the elementary processes occurring (half lives < 1 sec). Over the past five years, relaxation techniques have been utilized in studying fast reactions taking place at electrified interfaces (1-7). In this paper we illustrate the type of information that can be obtained by the pressure-jump method, using as an example a study of Pb2+ adsorption/desorption at the goethite/water interface. 

The fast reactions of ions between aqueous and mineral phases have been studied extensively in a variety of fields including colloidal chemistry, geochemistry, environmental engineering, soil science, and catalysis (1-6). Various experimental approaches and techniques have been utilized to address the questions of interest in any given field as this volume exemplifies. Recently, chemical relaxation techniques have been applied to study the kinetics of interaction of ions with minerals in aqueous suspension (2). These methods allow mechanistic information to be obtained for elementary processes which occur rapidly, e.g., for processes which occur within seconds to as fast as nanoseconds (j0. Many important phenomena can be studied including adsorption/desorption reactions of ions at electri fied interfaces and intercalation/deintercalation of ions with minerals having unique interlayer structure. 

Lietti and co-workers studied the kinetics of ammonia adsorption-desorption over V-Ti-O and V-W-Ti-O model catalysts in powder form by transient response methods [37, 52, 53[. Perturbations both in the ammonia concentration at constant temperature in the range 220-400 °C and in the catalyst temperature were imposed. A typical result obtained at 280 °C with a rectangular step feed of ammonia in flowing He over a V2O5-WO3/TiO2 model catalyst followed by its shut off is presented in Figure 13.5. Eventually the catalyst temperature was increased according to a linear schedule in order to complete the desorption of ammonia. 

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