Integral sorption kinetics

Roussis, P.P., Diffusion of water vapor in cellulose acetate 2. Permeation and integral sorption kinetics. Polymer, 22 1058-1063, 1981. 

Figure 5.13 — Irreversible-reusable flow-through sensor for the kinetic multidetermination of phosphate and silicate based on integrated sorption of a reaction product, reaction (/ situ reduction) and photometric detection. (A) Microsensor block (1) and components (2). (B) Continuous-flow configuration coupled on-line to the sensor. P peristaltic pumps SV switching valve W waste. For details, see text. (Reproduced from [39] with permission of the American Chemical Society).

The integral permeability coefficient P may be determined directly from permeation steady-state flux measurements or indirectly from sorption kinetic measurements 27 521 activity is usually replaced by gas concentration or pressure (unless the gas deviates substantially from ideal behaviour and it is desired to allow for this) and a<>, ax (p0, Pi) are the boundary high and low activities (pressures) respectively in a permeation experiment, or the final (initial) and initial (final) activities (pressures) respectively in an absorption (desorption) experiment. 

The majority of sorption kinetic stndies have ntilized either batch or flow-through methods coupled with aqueous measurements for determination of the concentrations of species of interest. More recent work has focused on molecular-scale approaches, including spectroscopic and microscopic techniques that allow for observations at increased spatial and temporal resolution to be made, often in situ and in real time. Complementary to both macroscopic and molecular-scale observations has been the utilization of theoretical techniques, such as molecular mechanics and quantum mechanics, to model surface complexes computationally. It has been through the integration of macroscopic, molecular-scale, and theoretical approaches that some of the most profound observations of sorption-desorption phenomena over the past decades have been made. 

It is the first time in the present paper that the uptake curves from a piezometric apparatus have been simulated by the solution of the Volterra integral equation [9,10] which reflects in detail the interaction of the sorption kinetics with the apparatus. This approach enabled us to get kinetic data with a high accuracy. 

Micke, A., and Bulow, M., Application of Volterra integral equations to the modelling of the sorption kinetics of multicomponent mixtures in porous media Fundamentals and elimination of apparatus effects. Gas Sep. Purif.,4(3), 158-170(1990). 

Beside the appropriate design of their chemical composition, the control of morphology and size of PCP crystals at the nanoscale provides an additional mean to modulate their physicochemical properties, in particular their sorption capacity. Recent studies showed that when PCP crystals are downsized to the nanometer scale and for peculiar morphologies, the external surface of the crystal starts to influence the sorption kinetics and sorption type. This phenomenon was explained by the decrease of the diffusion length toward the adsorption sites and by the enhanced accessibility of speciflc pore entrances. Contribution of the size and shape of the crystals upon the sorption properties is an inherent feature of porous materials, which was exploited for facilitating their integration into catalysis, separation, or sensing systems. 

It is also apparent that the dynamics of the sorption processes cannot be studied in isolation. Mechanism postulation and confirmation requires both an integrated experimental approach and investigation of sorption on a variety of sorbents. It has been demonstrated, for example, that interpretation of kinetic processes under static conditions requires consideration of associated sorption isotherms, and that insight to processes can be gained by comparison of different sorbents. While it may never be possible to unequivocally prove a particular sorption mechanism(s), it is possible to build up a body of information from which reliable predictions can be made. 

The unique properties of zeohtes for application in ion exchange, sorption, and catalysis are related to the fact that (1) the diameters of the micropores are in the range of the kinetic diameters of potential reactants (see Fig. 1) and (2) the surface functional groups having acid-base or redox properties are an integral part of the crystal structure. Thus, the nonspecific interactions between these materials and the reactant molecules are typically very strong and, therefore, the sorption properties markedly influence the catalytic activity. 

The complete kinetic expression for the metal-promoted hydrolysis of PVA-QA in the solid state requires the inclusion of terms for the rates of diffusion of the metal ion into the film and diffusion of the cleaved metal chelate out of the film into external buffer. The limited case of metal influx coupled to hydrolysis may be solved by assuming the diffusion is Fickian and the reaction rate is proportional to the average concentration of the metal in the film. Then, combining the kinetic expression for sorption from a fixed volume by a film with that of metal promoted hydrolysis, and integrating, leads to Equation 1, which is only valid if the rate of egress of the metal-chelate is rapid relative to its formation. ... 

The water-holding capacity (WHC) or water-retention capacity of stratum comeum enables not only the state of skin hydration to be characterized, but more importantly, the integrity degree of barrier function. It can be determined by means of a sorption-desorption test based on studying the kinetic of water evaporation (Black et al, 2000, 2002 del Pozo et al, 2000, 2003). 

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