Kinetics, nonequilibrium adsorption

Whitley, R. D., Van Cott, K. E., Wang, N.-H. Analysis of nonequilibrium adsorption/ desorption kinetics and implications for analytical and preparative chromatography, Ind. 

In the equilibrium-dispersive model, we assume that the mobile and the stationary phases are constantly in equilibrium. We recognize, however, that band dispersion takes place in the column through axial dispersion and nonequilibrium effects e.g., mass transfer resistances, finite kinetics of adsorption-desorption). We assume that their contributions can be lumped together in an apparent dispersion coefficient. This coefficient is related to the experimental parameters by... 

Disequilibrium due to chemical kinetic limitations on heterogeneous soil surfaces have been modeled by Selim et al. (1976a) and Cameron and Klute (1977). These transport models are commonly known as two-site nonequilibrium models, which assume solute adsorption on the two types of sites occur at different rates. Generally, empirical first-order and second-order expressions are utilized to dc.scribe the nonequilibrium adsorption process. 

Since this book is dedicated to the dynamic properties of surfactant adsorption layers it would be useful to give a overview of their typical properties. Subsequent chapters will give a more detailed description of the structure of a surfactant adsorption layer and its formation, models and experiments of adsorption kinetics, the composition of the electrical double layer, and the effect of dynamic adsorption layers on different flow processes. We will show that the kinetics of adsorption/desorption is not only determined by the diffusion law, but in selected cases also by other mechanisms, electrostatic repulsion for example. This mechanism has been studied intensively by Dukhin (1980). Moreover, electrostatic retardation can effect hydrodynamic retardation of systems with moving bubbles and droplets carrying adsorption layers (Dukhin 1993). Before starting with the theoretical foundation of the complicated relationships of nonequilibrium adsorption layers, this introduction presents only the basic principles of the chemistry of surfactants and their actions on the properties of adsorption layers. 

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. 

In this picture, the kinetic barriers hindering the exchange between the two adlayers are related to the presence of metastable, but rather strongly bound, adsorbed species (Hupd and OHad), which cannot be removed easily, and which block the surface for adsorption of the respective other species. The nonequilibrium situation is also reflected in the shape of the corresponding peaks A and A, where the anodic one (A) is less sharp and extends over a larger potential range. 

On the other hand, equilibrium constant for this reaction at the temperatures of study is rather small. But it is suspected that with the fixed-bed operation and with the possibility of some sulfur vapor adsorption on the solid, nonequilibrium conditions may be prevailing in the system. As a result, high sulfur yields could be obtained. This plausible explanation is only speculative, and more studies are necessary before a definite conclusion can be drawn. At WVU studies are in progress to obtain the kinetics of the reactions involved in this scheme. 

Jardine et al. (1985b) employed a two-site nonequilibrium transport model to study Al sorption kinetics on kaolinite. They used the transport model of Selim et al. (1976b) and Cameron and Klute (1977). Based on the above model, Jardine et al. (1985a) concluded that there were at least two mechanisms for Al adsorption on Ca-kaolinite. It appeared that there were equilibrium (type-1) reactions on kaolinite that involved instantaneous Ca-Al exchange and rate-limited reaction sites (type-2) involving Al polymerization on kaolinite. The experimental breakthrough curves (BTC) conformed well to the two-site model. 

Jardine, P. M., Parker, J. C., and Zelazny, L. W. (1985b). Kinetics and mechanisms of aluminum adsorption on kaolinite using a two-site nonequilibrium transport model. Soil Sci. Soc. Am. J. 49, 867-873. 

When a surfactant-water or surfactant-brine mixture is carefully contacted with oil in the absence of flow, bulk diffusion and, in some cases, adsorption-desorption or phase transformation kinetics dictate the way in which the equilibrium state is approached and the time required to reach it. Nonequilibrium behavior in such systems is of interest in connection with certain enhanced oil recovery processes where surfactant-brine mixtures are injected into underground formations to diplace globules of oil trapped in the porous rock structure. Indications exist that recovery efficiency can be affected by the extent of equilibration between phases and by the type of nonequilibrium phenomena which occur (J ). In detergency also, the rate and manner of oily soil removal by solubilization and "complexing" or "emulsification" mechanisms are controlled by diffusion and phase transformation kinetics (2-2). 

The electrostatic retardation of the adsorption kinetics of ionic siufactants is one of these nonequilibrium surface phenomena to be described on the basis of this physical model, consisting of the electrochemical macro-kinetic equations used in theoretical and colloid electrochemistry. This approach describes the flux of ions in terms of their spatial distribution. The equations were first developed by Overbeek (1943) and later proved to be valid for the theory of different... 

At first glance, when taking into account Eq. (7.19), it seems to be ill-defined to set Co Cg. However, this condition does not effect the given estimate. Although the relation for k becomes more complex, its value does not change so much. A more exact analysis of the nonequilibrium DL and its influence on adsorption kinetics is given in Appendix 7A. 

Most of the traditional adsorption studies of surfactants correspond to dilute systems without aggregation in the bulk phase. At the same time micellar solutions are much more important from a practical point of view. To estimate the equilibrium adsorption, neglecting the effect of micelles can usually lead to reasonable results. However, the situation changes for nonequilibrium systems when the adsorption rate can increase by orders of magnitude when the of surfactant concentration is increased beyond the CMC. Current interest in the adsorption from micellar solutions is mainly caused by recent observations that the stability of foams and emulsions depends strongly on the concentration in the micellar region [1]. This effect can be explained by the influence of the micellisation rate on the adsorption kinetics. 

Two-phase mixtures of polymers differ from classic ll colloid systems mainly by a transition layer that exists between the system components and is of special significance. The formation of such a layer in mixtures of linear polymers is governed by the kinetic factors of the retarded process of phase sep u ation, by the collid-chemic ll mechanism of formation, or by the adsorption interaction as well as by the segmental solubility [103,104], In mixtures of crosslinked polymers its formation is governed also by the conditions of synthesis. Note also that in the thermodynamic llly nonequilibrium mixtures of polymers in the two-phase systems, the processes of segmental solubility usually have time to reach completion while the macromolecules do not move inside the high-viscosity medium, which ensures the stability of the structure and its mechanical properties [103]. 

Because the measurement of a contact angle must involve some movement of the wetting line, it is possible, or even probable, that the act of spreading of the hquid will displace certain surface equilibria that will not be reestablished over the time frame of the experiment. For example, the displacement of a second fluid may result in the estabhshment of a nonequilibrium situation in terms of the adsorption of the various components at the solid-liquid, solid-fluid 2, and liquid-fluid 2 interfaces. Time will be required for adsorption equilibrium to be attained, and it may not be attained during the time of the contact angle measurement if the transport and adsorption-desorption phenomena involved are slow. The kinetic effect may be especially significant for solutions containing surfactants, polymers, or other dissolved adsorbates. 

Eq.3 explains the observed independence of the reaction rate from partial pressure of CO (Fig.3(b)) and the tendency of the NO conversion rate to stabilize at high partial pressure of NO (Fig.3(a)). The fitting of Eq.3 on the experimental results is satisfactory as shown by the RSQ values of Table 3. In Table 3 the calculated from the mathematical simulation procedure values of ks and Knonio are shown. The problem of the above kinetic analysis is that the calculated values of the adsorption equilibrium constant Knoni seems to be unvariant with temperature. To avoid this problem a new approach was applied according to which both NO adsorption and reaction 3 are in nonequilibrium conditions [8]. According to this approach the conversion rate of NO is given by ... 

Adsorption may also be modeled as a nonequilibrium process using nonequilibrium kinetic equations. In a kinetic model, the solute transport equation is linked to an appropriate equation to describe the rate that the solute is sorbed onto the solid surface and desorbed from the surface (Fetter, 1999). Depending on the nonequilibrium condition, the rate of sorption may he modeled using an irreversible first-order kinetic sorption model, a reversible linear kinetic sorption model, a reversible nonlinear kinetic sorption model, or a bilinear adsorption model (Fetter, 1999). 

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