Adsorption Relaxation Kinetics

In analogy with Eqs. 1.50 and 2.5, the overall surface ligand-exchange reactions in Eqs. 3.46, 3.53, 3.56, 3.65, 3.66, and 4.15b can be dissected into steps by applying the concept of the Eigen-Wilkins-Wemer mechanism, discussed in Section 2.1. Following this perspective, one would decompose the overall surface complexation reaction in Eq. 4.15b into a set of coupled reactions (cf. Eq. 1.50)  

A full mathematical description of the time dependence of the concentrations of the species in Eq. 4.29 based on the rate laws in Eqs. 1.54a and 1.54c can be accomplished by computer calculation, but often a good approximation can be obtained without extensive numerical analysis by linearization of the rate laws. This approach assumes that a suitable experimental method exists to detect very small perturbations from equilibrium among species linked by a set of 

The linearization of Eqs. 1.54a and 1.54c proceeds as follows. Let cA = cAq + Aca, cb = eg + Acb, etc., where ceq is an equilibrium species concentration and Ac is a small deviation from an equilibrium value. This decomposition of each species concentration in Eqs. 1.54a and 1.54c produces the following set of equations  

A final simplification of the rate laws can be made by incorporating mole-balance conditions that follow from the stoichiometry of the reactions in Eq. 1.52 (cf. Eq. 1.29)  

Were it not for the coupling terms, kbAcD and k fAcA, Eq. 4.34 would have the same form as Eq. 1.55 (neglecting its constant term on the right side), with an exponential-decay solution typical of first-order reactions (Eqs. 1.56 and 4.19). Because the coupling terms are linear in the Ac, however, it is always possible to find a solution to Eq. 4.34 by postulating that a pair of time constants, r, and r2, exists such that the Ac still show an exponential time dependence ( rel axation ) 19 

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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. 

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. 

Wertz CF, Santore MM (1999) Adsorption and relaxation kinetics of albumin and fibrinogen on hydrophobic surfaces single-species and competitive behavior. Langmuir 15(26) 8884-8894... 

A reaction sequence analogous to that in Eq. 4.40 can also be developed for the specific adsorption of bivalent metal cations (e.g., Cu2+, Mn2 or Pb2+) by metal oxyhydroxides.21 In this application the abstract scenario in the first row of Table 4.3 is realized with A = =Al-OH, B = M2+, C = =Al-OH - - M2+, D = = Al-OM+, and E = H where M is the metal complexed by an OH group on the surface of an aluminum oxyhydroxide. Analysis of pressure-pulse relaxation kinetics data leads to a calculation of the second-order rate coefficient kf, under the assumption that the first step in the sequence in Eq. 4.40 is rate determining. Like k(l, the rate coefficient for the dissolution of a metal-containing solid (Section 3.1 cf. Fig. 3.4), measured values of k, correlate positively in a log log plot with kw,. , the rate coefficient for water exchange on the metal... 

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... 

Grossl, P. R., and Sparks, D. L., 1995, Evaluation of contaminant ion adsorption/desorpton on goethite using pressure-jump relaxation kinetics Geoderma, v. 67, p. 87-101. 

Pressure-jump relaxation was also used by others to study anion adsorption/desorption kinetics on soil constituents. These investigations have included the study of the kinetics and mechanisms of acetic acid adsorption on a silica-alumina surface (Ikeda et al., 1982a) and phosphate (Mikami et al., 1983a) and chromate adsorption (Mikami et al., 1983b), on 7-AI2O3. Double relaxation times on the order of milliseconds were observed in each of these studies. 

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. 

An extensive numerical study on such heterogeneous three-step processes has been given by Stone and Morgan (1987). The adsorption-desorption kinetics of divalent metal ions is fast Yasunaga and Ikeda (1986) report relaxation times in the order of milliseconds to seconds. The pH as a master variable governs the adsorption of Fe(II) in the preceding example. The elucidation of adsorption equilibria and the structure of precursor complexes such as (=Fen,-0-Fen)+ at the mineral surface is therefore a prerequisite for the study of heterogeneous redox kinetics. 

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. 

We must point out that if the adsorption layer contacts with a sufficiently deep liquid, then the diffusion relaxation time can be comparable with the adsorption relaxation time. In this case, the kinetics of the adsorption layer filling, which is determined by Eqs. (7.3.3) and (7.3.4), can be diffusion-controllable for small volume concentrations of surfactants in the solution or be governed by a diffusion-kinetic mechanism for higher concentrations [274]. A pure kinetic region of the adsorption layer filling is possible only in thin layers of surfactant solutions, for example, in liquid elements of foam structures. 

Siuface rheology has to be taken into account when describing siuface movement and adsorption/desoiption kinetics. Some brief information on surface rheology is given in Section 3.2. The rate of normal and lateral surfactant transport and dynamic surface tension response on external disturbances depends on relaxation properties, into which Section 3.1. introduces. 

The diffusion equations of micelles and monomers obtained in the preceding sections allow us to formulate a mathematical problem of surfactant diffusion to the interface. Investigation of the adsorption kinetics is reduced then to the solution of this problem. It is noteworthy that the diffusion equations (5.210) - (5.211), (5.223), (5.224), (5.226), (5.228) and the results given in the preceding sections on the relaxation kinetics of the concentration perturbations in the... 

ION ADSORPTION-DESORPTION KINETICS relaxation times can be expressed as... 

Syunyaev, 2008). Concentration oscillations in water solutions of dye were also observed by laser refractometry. It is possible to suppose that adsorption is kinetically limited by diffusion. The mechanism of diffusion relaxation suggested by I. Akhatov is realized (Akhatov, 1988, as cited in Syunyaev at al., 2009). The classic Pick s law can be generalized by introduction of additional relaxation item... 

The kinetic of adsorption charging of the surface of semiconductor under relaxation of biographic surfacing charge... 

In case of small density of adsorbed particles if contrasted to the density of charged BSS the adsorption of donors can be accompanied by non-monotonous kinetics change in 4s t) which is caused by fast ASS depletion with subsequent slow BSS recharging (see Fig. 1.10, curve J). The use of typical values of parameters in absorbate-adsorbent systems shows that depletion of donor levels is characterized by the times of the order of seconds whereas the relaxation of charge in BSS takes hours. 

Therefore, the theoretical analysis and numerous experimental data enable one to assume that charging of the surface of adsorbent occurring during adsorption can result in relaxation of the charge state of an a priori existing BSS and influence the kinetics of transition of adsorption particles into the charged form. However, during chemisorption of ac-... 

We used polycrystalline films of ZnO and Sn02 as adsorbents. The films were deposited from the water suspension of respective oxides on quartz substrates. These substrates contained initially sintered contacts made of platinum paste. The gap between contacts was of about lO" cm. All samples were initially heated in air during one hour at T 500 C. We used purified molecular oxygen an acceptor particle gas. H and Zn atoms as well as molecules of CO were used as donor particles. We monitored both the kinetics of the change of ohmic electric conductivity and the tangent of inclination angle of pre-relaxation VAC caused by adsorption of above gases and the dependence of stationary values of characteristics in question as functions of concentrations of active particles. 

All preparations were structurally characterized by means of XRD (Siemens 5005). TEM imaging was performed with a Philips CM200 instrument. 27A1 and 29Si MAS NMR (Broker 500 MFlz and 360 MFlz respectively) was used to study the microporous phase and the kinetic of its formation. The relaxation delays were 0.2s and 200s respectively. Acidity was determined by the adsorption of carbon monoxide after activating the samples in vacuum (10 6 mbar) at 450°C for 1 h. The spectra were recorded on a Equinox 55 Broker spectrometer with a resolution of 2 cm 1 and normalized to 10 mg of sample. 

The Heterogeneous Case. Hachiya et al. (1984) and Hayes and Leckie (1986) used the pressure-jump relaxation method to study the adsorption kinetics of metal ions to oxide minerals. Their results support in essence the same adsorption mechanism as that given for homogeneous complex formation. 

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