Diffusion desorption kinetics

In one dimension the truncation of the equations of motion has been worked out in detail [59]. This has allowed an accurate examination of the role of diffusion in desorption, and implications for the Arrhenius analysis in nonequilibrium situations. The largest deviations from the desorption kinetics of a mobile adsorbate obviously occur for an immobile adsorbate... 

Its main features are given by the use of a stream of inert carrier gas which percolates through a bed of an adsorbent covered with adsorbate and heated in a defined way. The desorbed gas is carried off to a detector under conditions of no appreciable back-diffusion. This means that the actual concentration of the desorbed species in the bed is reproduced in the detector after a time lag which depends on the flow velocity and the distance. The theory of this method has been developed for a linear heating schedule, first-order desorption kinetics, no adsorbable component in the entering carrier gas (Pa = 0), and the Langmuir concept, and has already been reviewed (48, 49) so that it will not be dealt with here. An analysis of how closely the actual experimental conditions meet the idealized model is not available. 

If the supply of surfactant to and from the interface is very fast compared to surface convection, then adsorption equilibrium is attained along the entire bubble. In this case the bubble achieves a constant surface tension, and the formal results of Bretherton apply, only now for a bubble with an equilibrium surface excess concentration of surfactant. The net mass-transfer rate of surfactant to the interface is controlled by the slower of the adsorption-desorption kinetics and the diffusion of surfactant from the bulk solution. The characteris-... 

Wu and Gschwend (78) successfully employed a radial diffusion model to describe laboratory observed sorption and desorption kinetics. Their data show that sorption and desorption rates were slower for more hydrophobic compounds and sorbents with a larger grain size in a manner consistent with the radial diffusion model. 

Reaction 5.45 is at least partly hypothetical. Evidence that the Cl does react with the Na component of the alanate to form NaCl was found by means of X-ray diffraction (XRD), but the final form of the Ti catalyst is not clear [68]. Ti is probably metallic in the form of an alloy or intermetallic compound (e.g. with Al) rather than elemental. Another possibility is that the transition metal dopant (e.g. Ti) actually does not act as a classic surface catalyst on NaAlH4, but rather enters the entire Na sublattice as a variable valence species to produce vacancies and lattice distortions, thus aiding the necessary short-range diffusion of Na and Al atoms [69]. Ti, derived from the decomposition of TiCU during ball-milling, seems to also promote the decomposition of LiAlH4 and the release of H2 [70]. In order to understand the role of the catalyst, Sandrock et al. performed detailed desorption kinetics studies (forward reactions, both steps, of the reaction) as a function of temperature and catalyst level [71] (Figure 5.39). 

The first attempt to account for surface contamination in creeping flow of bubbles and drops was made by Frumkin and Levich (FI, L3) who assumed that the contaminant was soluble in the continuous phase and distributed over the interface. The form of the concentration distribution was controlled by one of three rate limiting steps (a) adsorption-desorption kinetics, (b) diffusion in the continuous phase, (c) surface diffusion in the interface. In all cases the terminal velocity was given by an equation identical to Eq. (3-20) where C, now called the retardation coefficient , is different for the three cases. The analysis has been extended by others (D6, D7, N2). 

The study of adsorption or desorption kinetics in the first minute or so must take full account of convection-diffusion processes. Fortunately this has been well-modeled by Lok, et al.40) and by Watkins and Robertson 39,42). 

The adsorption and desorption kinetics of surfactants, such as food emulsifiers, can be measured by the stress relaxation method [4]. In this, a "clean" interface, devoid of surfactants, is first formed by rapidly expanding a new drop to the desired size and, then, this size is maintained and the capillary pressure is monitored. Figure 2 shows experimental relaxation data for a dodecane/ aq. Brij 58 surfactant solution interface, at a concentration below the CMC. An initial rapid relaxation process is followed by a slower relaxation prior to achieving the equilibrium IFT. Initially, the IFT is high, - close to the IFT between the pure solvents. Then, the tension decreases because surfactants diffuse to the interface and adsorb, eventually reaching the equilibrium value. The data provide key information about the diffusion and adsorption kinetics of the surfactants, such as emulsifiers or proteins. 

Karickhoff (1980) and Karickhoff et al. (1979) have studied sorption and desorption kinetics of hydrophobic pollutants on sediments. Sorption kinetics of pyrene, phenanthrene, and naphthalene on sediments showed an initial rapid increase in sorption with time (5-15 min) followed by a slow approach to equilibrium (Fig. 6.7). This same type of behavior was observed for pesticide sorption on soils and soil constituents and suggests rapid sorption on readily available sites followed by tortuous diffusion-controlled reactions. Karickhoff et al. (1979) modeled sorption of the hydrophobic aromatic hydrocarbons on the sediments using a two-stage kinetic process. The chemicals were fractionated into a labile state (equilibrium occurring in 1 h) and a nonlabile state. 

Polymer Adsorption. A review of the theory and measurement of polymer adsorption points out succinctly the distinquishing features of the behavior of macromolecules at solid - liquid interfaces (118). Polymer adsoiption and desorption kinetics are more complex than those of small molecules, mainly because of the lower diffusion rates of polymer chains in solution and the "rearrangement" of adsorbed chains on a solid surface, characterized by slowly formed, multi-point attachments. The latter point is one which is of special interest in protein adsoiption from aqueous solutions. In the case of proteins, initial adsoiption kinetics may be quite rapid. However, the slow rearrangement step may be much more important in terms of the function of the adsorbed layer in natural processes, such as thrombogenesis or biocorrosion / biofouling caused by cell adhesion. 

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... 

The lossy character of the adsorption impedance stems in the finite-rate response of coverages to potential changes T = )( , t). Assuming one adsorption-desorption process, the adsorption-related current at a certain potential contains a dqM/dt = (dqM/dr) dr/ df term which, through the dT/ df term, depends on the (eventually diffusion-controlled) kinetics of the adsorption process. 

Results of efficiency enhancement studies have been controversial. Increasing the temperature lowers eluent viscosity and system back pressure, leading to the nse of (1) higher flow rates (shorter cycle times) [9], (2) longer columns, and (3) smaller particles that enhance efficiency in their own right. However, efficiency is also expected to increase because high column temperatures involve (1) faster adsorption-desorption kinetics, (2) enhanced diffusivity, (3) lower mass transfer resistance (C in the van Deemter Equation 6.4), and (4) flatter van Deemter curves. 

This equation is a result of considering the adsorption and desorption kinetics described in the equilibrium which establishes the Langmuir equation 9.31. Chen, et al. [68] have studied the adsorption kinetics of poly(acrylic add) onto BaTiOs from aqueous solution. Their results are given in Table 9.13. The adsorption kinetics are faster in the case of pH 10.5 because the n ative charge on the polymer attracts the positive charge on the BaTiOg surface. At pH 1.5 there is no charge on the polymer, thus diffusion to the surface is not enhanced. 

Information on the distribution of diffusion obstacles such as coke, modifiers, or regions of framework damage can be derived from combined PFG NMR and TD NMR measurements. Limitations of the overall adsorption/desorption kinetics as followed by TD NMR can be caused by deposits inside the crystals and/or on their outer surfaces. In contrast, in PFG NMR only diffusion obstacles in the volume phase of the zeolite crystal are detected. Conclusions can be drawn from the following considerations ... 

Tt is generally recognized that water plays an important role in main-taining skin in a healthy state with desirable mechanical properties (I). This work describes a technique for generating information on the state of water in the stratum corneum in vitro, with particular emphasis on the mobility of water in the corneum matrix and the eflEect of stratum corneum components on the characteristics of water diffusion. The characteristics of water diffusion in the stratum corneum are derived from sorption and desorption kinetics by using a gravimetric technique which allows determination of the amount of water vapor sorbed or desorbed continuously from an air stream of any given relative humidity. 

Calculation of the Diffusion Coefficient from Sorption and Desorption Kinetics in a Plane Sheet... 

Mth problems concerned with the reduction of residual monomer content desorption kinetics are relevant. Fortunately these are normally Fickian but with concentration dependent diffusion constants. The com cations of so-called Case II, relaxation controlled diffusion often found in glassy polymers at high concentration gradients " are also not normally observed in desorption processes. 

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