Sorption-diffusion mechanism

The sorption-diffusion mechanism considers that some thermally agitated motions (either in the matrix or by the penetrant) provide opportunities for sorbed penetrants to... 

Separations Controlled by Sorption-Diffusion Mechanisms When Size Exclusion Occurs.284... 

Sorption-Diffusion Mechanisms when Size Exclusion Occurs... 

Gas transport in zeolites, some molecular sieve carbons, and polymers is described by a sorption-diffusion mechanism. In these cases, the permeability coefficient, P, of penetrant A is the product of a kinetic parameter, the average diffusion coefficient and a thermodynamic parameter, S, the solubility coefficient (2). 

Porous solids of various origins are of various and complex morphology (ref. 1). Their structure is corpuscular (ensembles of particles) or spongy (labyrinth of shannels and cavities). Modelling of these complex systems is necessary for theoretical description and Interpretation of their geometrical, sorption, diffusion, mechanical, thermal and electrical properties (ref. 2). 

Mass transfer through dense polymeric membranes is nowadays accepted to be described by the sorption-diffusion mechanism. According to this, the species being transported dissolve (sorb) in the polymer membrane surface on the higher chemical potential side, diffuse through the polymer free volume in a sorbed phase, and pass into the fluid phase downstream of the membrane (lower chemical potential side). In the case of dense polymeric membranes the polymer is an active participant in both the solution and diffusion processes. However, since in many porous membranes the mass transfer takes place mainly in the pores, the membrane material is not an active participant and only its pore structure is important. ... 

We may also postulate that the rate of sorption or desorption can be described by a diffusive mechanism. The application of diffusion equations to describe the uptake of a sorbing solute can be... 

Kinetic models proposed for sorption/desorption mechanisms including first-order, multiple first-order, Langmuir-type second-order, and various diffusion rate laws are shown in Sects. 3.2 and 3.4. All except the diffusion models conceptualize specific sites to or from which molecules may sorb or desorb in a first-order fashion. The following points should be taken into consideration [ 181,198] ... 

The moments of the solutions thus obtained are then related to the individual mass transport diffusion mechanisms, dispersion mechanisms and the capacity of the adsorbent. The equation that results from this process is the model widely referred to as the three resistance model. It is written specifically for a gas phase driving force. Haynes and Sarma included axial diffusion, hence they were solving the equivalent of Eq. (9.10) with an axial diffusion term. Their results cast in the consistent nomenclature of Ruthven first for the actual coefficient responsible for sorption kinetics as ... 

Most polymers that have been of interest as membrane materials for gas or vapor separations are amorphous and have a single phase structure. Such polymers are converted into membranes that have a very thin dense layer or skin since pores or defects severely compromise selectivity. Permeation through this dense layer, which ideally is defect free, occurs by a solution-diffusion mechanism, which can lead to useful levels of selectivity. Each component in the gas or vapor feed dissolves in the membrane polymer at its upstream surface, much like gases dissolve in liquids, then diffuse through the polymer layer along a concentration gradient to the opposite surface where they evaporate into the downstream gas phase. In ideal cases, the sorption and diffusion process of one gas component does not alter that of another component, that is, the species permeate independently. 

Besides Knudsen diffusion, permselective transport of gases can occur by various mechanisms involving molecular scale interactions of the sorption-diffusion type. These can be broadly classified into three groups as described below and pictured in Fig. 7. 

Many computational studies of the permeation of small gas molecules through polymers have appeared, which were designed to analyze, on an atomic scale, diffusion mechanisms or to calculate the diffusion coefficient and the solubility parameters. Most of these studies have dealt with flexible polymer chains of relatively simple structure such as polyethylene, polypropylene, and poly-(isobutylene) [49,50,51,52,53], There are, however, a few reports on polymers consisting of stiff chains. For example, Mooney and MacElroy [54] studied the diffusion of small molecules in semicrystalline aromatic polymers and Cuthbert et al. [55] have calculated the Henry s law constant for a number of small molecules in polystyrene and studied the effect of box size on the calculated Henry s law constants. Most of these reports are limited to the calculation of solubility coefficients at a single temperature and in the zero-pressure limit. However, there are few reports on the calculation of solubilities at higher pressures, for example the reports by de Pablo et al. [56] on the calculation of solubilities of alkanes in polyethylene, by Abu-Shargh [53] on the calculation of solubility of propene in polypropylene, and by Lim et al. [47] on the sorption of methane and carbon dioxide in amorphous polyetherimide. In the former two cases, the authors have used Gibbs ensemble Monte Carlo method [41,57] to do the calculations, and in the latter case, the authors have used an equation-of-state method to describe the gas phase. 

The region of "Case II sorption (relaxation-controlled transport) is separated from the Fickian diffusion region by a region where both relaxation and diffusion mechanisms are operative, giving rise to diffusion anomalies time-dependent or anomalous diffusion. 

The mechanical behavior of the dry-to-wet and wet-to-dry cycles complement each other. In the first sorption curve, blocking of the network structure was explained by sorption of a small quantity of moisture Into free volume of the near saturated matrix. If this small quantity of moisture Is allowed to escape, the network takes on mechanical behavior of the unblocked plasticized state. This transition occurs rapidly during the Initial stages of drying. The peak tan 6 value Is representative of plasticized state properties. As further desorption takes place, mechanical properties approach the Initial dry state values. A qualitative description of the diffusion-mechanical mechanisms associated with each segment of the sorption-desorption cycle is outlined in Figure 7. 

Selective separation of hquids by pervaporation is a result of selective sorption and diffusion of a component through the membrane. PV process differs from other membrane processes in the fact that there is a phase change of the permeating molecules on the downstream face of the membrane. PV mechanism can be described by the solution-diffusion mechanism proposed by Binning et al. [3]. According to this model, selective sorption of the component of a hquid mixture takes place at the upstream face of the membrane followed by diffusion through the membrane and desorption on the permeate side. 

As the mobile phase moves through the capillary containing the sorbent under the effect of this electro-osmotic flow (EOF), sample components partition between the two phases in sorption and diffusive mechanisms characteristic of liquid chromatography. Ions in the sample move both under the influence of EOF and by their added attraction toward the oppositely charged electrode (electrophoresis). Uncharged components, on the other hand, move only under the influence of EOF. Thus, sample components, in general, separate by chromatographic and, sometimes, electrophoretic processes. 

The theory of transport in microporous solids is complex and involves many aspects and steps. Although many aspects has been treated separately (e.g., sorption, diffusion, simulation studies, mechanisms, etc.) there are no coherent descriptions of permeation and separation in microporous membrcmes covering all the important aspects. In this chapter an attempt is made to introduce such a description. It is useful to give a qualitative picture first (Section 9.4.2.1). 

Whereas the pore-flow mechanism describes transport through porous UF, NF and RO membranes show a transient structure between porous and non-porous, with probably also sorption-diffusion as part of the transport mechanism. Nanofiltration is a relatively new membrane process with a nominal MWCO in the range of 200-1000 Da. Its application in water treatment has been growing rapidly, but the nonaqu-eous application is still an emerging field. All efforts to enlarge catalysts become superfluous when the membranes are capable of retaining off-the-shelf TMCs. 

For the separation of gas mixtures (permanent gases and/or condensable vapors) where the feed and permeate streams are both gas phase, the driving force across the membrane is the partial pressure difference. The membrane is typically a dense film and the transport mechanism is sorption-diffusion. The dual-mode transport model is typically used with polymer materials that are below their glass transition temperature. 

Some tentative conclusions can now be drawn regarding the way in which silica is released from Mattole soils. The linear relation between silica concentration and the square root of time in soil and sediment suspensions, where dissolved silica is less than about 1 mg/liter, suggests that a diffusion mechanism controls the release of silica from mineral particles. Such a mechanism would be in agreement with studies by others (14, 17, 18). Those studies suggest that in the initial release of silica from feldspar only a diffusion mechanism would be apparent, but as the silica concentration increased a subsequent sorption (precipitation ) reaction on the altered solid surface would slow the net release of silica until a relatively steady condition existed. This appears to be a pattern that would explain the silica released from both low and high concentrations of prewashed Mattole soil and sediment in water. 

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