Adsorption kinetics transport control

Two general models can describe the kinetics of adsorption. The first involves fast adsorption with mass transport control, while the other involves kinetic control of die system. Under the latter (and Langmuirian) conditions, the surface coverage of tlie adsorbate at time t, Tt, is given by. 

Zogorski et al. [125] indicate that external transport is the rate-limiting step in systems having poor mixing, dilute concentration of adsorbate, small particle sizes of adsorbent, and a high affinity of adsorbate for adsorbent. Some experiments conducted at low concentrations have shown that film diffusion solely controls the adsorption kinetics of low molecular weight substances [81,85]. 

Understanding the kinetics of contaminant adsorption on the subsurface solid phase requires knowledge of both the differential rate law, explaining the reaction system, and the apparent rate law, which includes both chemical kinetics and transport-controlled processes. By studying the rates of chemical processes in the subsurface, we can predict the time necessary to reach equilibrium or quasi-state equilibrium and understand the reaction mechanism. The interested reader can find detailed explanations of subsurface kinetic processes in Sparks (1989) and Pignatello (1989). 

Any surface reaction that involves chemical species in aqueous solution must also involve a precursory step in which these species move toward a reactive site in the interfacial region. For example, the aqueous metal, ligand, proton, or hydroxide species that appear in the overall adsorption-desorption reaction in Eq. 4.3 cannot react with the surface moiety, SR, until they leave the bulk aqueous solution phase to come into contact with SR. The same can be said for the aqueous selenite and proton species in the surface redox reaction in Eq. 4.50, as another example. The kinetics of surface reactions such as these cannot be described wholly in terms of chemically based rate laws, like those in Eq. 4.17 or 4.52, unless the transport steps that precede them are innocuous by virtue of their rapidity. If, on the contrary, the time scale for the transport step is either comparable to or much longer than that for chemical reaction, the kinetics of adsorption will reflect transport control, not reaction control (cf. Section 3.1). Rate laws must then be formulated whose parameters represent physical, not chemical, processes. 

This point can be appreciated more quantitatively after consideration of an important (but simple) model of transport-controlled adsorption kinetics, the film diffusion process.34 35 This process involves the movement of an adsorptive species from a bulk aqueous-solution phase through a quiescent boundary layer ( Nemst film ) to an adsorbent surface. The thickness of the boundary layer, 5, will be largest for adsorbents that adsorb water strongly and smallest for aqueous solution phases that are well stirred. If j is the rate at which an... 

In this limiting case the adsorption reaction produces the steady-state value of [i]surf and the adsorption kinetics are wholly transport-controlled. Measurement of the rate of adsorption accordingly provides little or no chemical information about the adsorption process.35,37... 

Flocculation processes are complicated phenomena because of the varieties of both particle morphology and chemical reactions they encompass.34 A few concepts of a general nature have emerged, however, and they will be the focus of this chapter. From the perspective of kinetics, perhaps the most important of these broad generalizations is the distinction that can be made between transport-controlled and reaction-controlled flocculation, parallel to the classification of adsorption processes described in Section 4.5. Flocculation kinetics are said to exhibit transport control if the rate-limiting step is the movement of two (or more) particles toward one another prior to their close encounter and subsequent combination into a larger particle. Reaction control occurs if it is particle combination instead of particle movement (toward collision) that limits the rate of flocculation. 

Factors which cause deviations from standard transport-controlled kinetics are discussed. Some of these are Surface roughness of the metal samples adsorption of reaction products a slow intermediate stage in the dissolution and conditions which cause the metal to assume a passive potential. 

In order to undergo a redox process, the reactant must be present within the electrode-reaction layer, in an amount limited by the rate of mass transport of Yg, to the electrode surface. In electrolyte media, four types of mass-transport control, namely convection, diffusion, adsorption and chemical-reaction kinetics, must be considered. The details of the voltammetric procedure, e.g., whether the solution is stirred or quiet, tell whether convection is possible. In a quiet solution, the maximum currents of simple electrode processes may be governed by diffusion. Adsorption of either reactant or product on the electrode may complicate the electrode process and, unless adsorption, crystallization or related surface effects are being studied, it is to be avoided, typically... 

The first physically sound model for adsorption kinetics, which was derived by Ward and Tordai [18], is based on the assumption that the time dependence of a surface or interfacial tension (which is directly proportional to the surface excess F, in mol m ) is caused by diffusion and transport of surfactant molecules to the interface. This is referred to as diffusion-controlled adsorption kinetics model . The interfacial surfactant concentration at any time t, T(t), is given by the following expression,... 

To appreciate the impact of SECM on the study of phase transfer kinetics, it is useful to briefly review the basic steps in reactions at solid/liquid interfaces. Processes of dissolution (growth) or desorption (adsorption), which are of interest herein, may be described in terms of some, or all, of the series of events shown in Figure 1. Although somewhat simplistic, this schematic identifies the essential elements in addressing the kinetics of interfacial processes. In one limit, when any of the surface processes in Figure 1 (e.g., the detachment of ions or molecules from an active site, surface diffusion of a species across the surface, or desorption) are slow compared to the mass transport step between the bulk solution and the interface, the reaction is kinetically surface-controlled. In the other limit, if the surface events are fast compared to mass transport, the overall process is in a mass transport-controlled regime. 

Although many books have described the mechanisms of moisture adsorption and adsorption isotherms for drug substances, few reports have dealt with the kinetics of moisture adsorption. Zografi and co-workers reported that the moisture adsorption rate, IV, for water-soluble substances can be represented by the following equations, based on a heat-transport control model5 -601 ... 

The role of adsorption kinetics and the diffusion of surfactants is especially important in controlling capillary impregnation. According to studies by N.N. Churaev, the solution impregnating the capillary quickly loses its dissolved surfactant due to adsorption of the latter on capillary walls, so the rate of impregnation may be limited by the diffusional transport of surfactant from the bulk of the solution to the menisci in the pores. 

The adsorption kinetics of interfacial active molecules at liquid interfaces, for example surfactants at the aqueous solution/air or solution/organic solvent interface, can be described by quantitative models. The first physically founded model for interfaces with time invariant area was derived by Ward Tordai (1946). It is based on the assumption that the time dependence of interfacial tension, which is directly correlated to the interfacial concentration T of the adsorbing molecules, is caused by a transport of molecules to the interface. In the absence of any external influences this transport is controlled by diffusion and the result, the so-called diffusion controlled adsorption kinetics model, has the following form... 

The adsorption kinetics of surfactant molecules to a liquid interface is controlled by transport processes in the bulk and the transfer of molecules from a solution state into an adsorbed state or vice versa. In this paragraph qualitative and quantitative models are discussed. 

Further models of adsorption kinetics were discussed in the literature by many authors. These models consider a specific mechanism of molecule transfer from the subsurface to the interface, and in the case of desorption in the opposite direction ((Doss 1939, Ross 1945, Blair 1948, Hansen Wallace 1959, Baret 1968a, b, 1969, Miller Kretzschmar 1980, Adamczyk 1987, Ravera et al. 1994). If only the transfer mechanism is assumed to be the rate limiting process these models are called kinetic-controlled. More advanced models consider the transport by diffusion in the bulk and the transfer of molecules from the solute to the adsorbed state and vice versa. Such mixed adsorption models are ceilled diffusion-kinetic-controlled The mostly advanced transfer models, combined with a diffusional transport in the bulk, were derived by Baret (1969). These dififiision-kinetic controlled adsorption models combine Eq. (4.1) with a transfer mechanism of any kind. Probably the most frequently used transfer mechanism is the rate equation of the Langmuir mechanism, which reads in its general form (cf. Section 2.5.),... 

The equation derived for the transport of surfactant ions through the DL describes the adsorption kinetics as a reversible process. The qualitatively new result in the theory of ionic adsorption kinetics is the incorporation of electrostatic retardation for both the adsorption and desorption process, which is of essential importance for processes close to equilibrium. Such a situation exists at harmonically disturbed surfaces, used in investigations of adsorption dynamics like the damping of capillary waves or oscillating bubbles. At sufficiently high frequencies the diffusion layer becomes very thin and the adsorption-desorption exchange is controlled only by the ion transport through the DL, i.e. by the electrostatic retardation. At... 

The adsorption kinetics of a surfactant to a freshly formed surface as well as the viscoelastic behaviour of surface layers have strong impact on foam formation, emulsification, detergency, painting, and other practical applications. The key factor that controls the adsorption kinetics is the diffusion transport of surfactant molecules from the bulk to the surface [184] whereas relaxation or repulsive interactions contribute particularly in the case of adsorption of proteins, ionic surfactants and surfactant mixtures [185-188], At liquid/liquid interface the adsorption kinetics is affected by surfactant transfer across the interface if the surfactant, such as dodecyl dimethyl phosphine oxide [189], is comparably soluble in both liquids. In addition, two-dimensional aggregation in an adsorption layer can happen when the molecular interaction between the adsorbed molecules is sufficiently large. This particular behaviour is intrinsic for synergistic mixtures, such as SDS and dodecanol (cf the theoretical treatment of this system in Chapters 2 and 3). The huge variety of models developed to describe the adsorption kinetics of surfactants and their mixtures, of relaxation processes induced by various types of perturbations, and a number of representative experimental examples is the subject of Chapter 4. 

Adsorption control The kinetics of the adsorption step in the absence of mass transport control was treated by Lorenz [87] and Delahay[89, 90] assuming either a Langmuir- or a Temkin-type formalism. 

The present state of research allows describing the adsorption kinetics for most surfactants at liquid interfaces quantitatively. The first model derived by Ward Tordai (1946) was based on the assumption that the time dependence of interfacial tension, which is directly related to the interfacial concentration T of adsorbed molecules via an equation of state, is mainly caused by the diftusional transport of surfactant molecules to the interface. A schematic picture of this model is shown in Fig. 1. Transport in the solution bulk is controlled by surfactant diffusion. The transfer of molecules from the so-called subsurface, the liquid layer adjacent to the interface, to the interface itself is assumed to happen without transport. 

Adsorptive accumulation can also be used in chronopotentiometric stripping as the preconcentration step allowing a large number of organic compoimds to be determined. It is assumed that the adsorption kinetics is sufficiently rapid for the process to be mass transport controlled. During the preconcentration step, the solution is normally stirred in order to enhance the mass transport of the analyte to the electrode smface, thereby reducing the time required for preconcentration. For nonelectrolytic or adsorptive accumulation, tacc has an upper limit governed by the time required for the electrode to be saturated with a monolayer of adsorbate. This is determined experimentally and will depend on the mass transport conditions that exist in the electrochemical cell. For example, the amount of adsorbed metal ion complex would be... 

The multiphasic nature of the intra-particle diffusion plot confirms the presence of both surface and pore diffusion. In order to predict the actual slow step involved, the kinetic data were further analysed using Boyd kinetic expression. Equation A.22 was used to calculate B( values at different time t. The linearity of the plot of B( versus time was used to distinguish whether surface and intra-particle transport controls the adsorption rate. It... 

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