Sorption coefficient overall

Compound Sorption coefficient S (mg-mg ) Diffusion coefficient D (m -s ) Sorption selectivity Diffusion selectivity Overall permselectivity... 

The selectivity (amcm) of pervaporation membranes critically affects the overall separation obtained and depends on the membrane material. Therefore, membrane materials are tailored for particular separation problems. As with other solution-diffusion membranes, the permeability of a component is the product of the membrane sorption coefficient and the diffusion coefficient (mobility). The membrane selectivity term amem in Equation (9.11) can be written as... 

Sousa et al [5.76, 5.77] modeled a CMR utilizing a dense catalytic polymeric membrane for an equilibrium limited elementary gas phase reaction of the type ttaA +abB acC +adD. The model considers well-stirred retentate and permeate sides, isothermal operation, Fickian transport across the membrane with constant diffusivities, and a linear sorption equilibrium between the bulk and membrane phases. The conversion enhancement over the thermodynamic equilibrium value corresponding to equimolar feed conditions is studied for three different cases An > 0, An = 0, and An < 0, where An = (ac + ad) -(aa + ab). Souza et al [5.76, 5.77] conclude that the conversion can be significantly enhanced, when the diffusion coefficients of the products are higher than those of the reactants and/or the sorption coefficients are lower, the degree of enhancement affected strongly by An and the Thiele modulus. They report that performance of a dense polymeric membrane CMR depends on both the sorption and diffusion coefficients but in a different way, so the study of such a reactor should not be based on overall component permeabilities. 

The overall selectivity in PV is a combination of (1) sorption and (2) diffusion selectivities. Sorption selectivity as is defined as the ratio of the sorption coefficient of solutes A and B in a binary mixture ... 

The second factor affecting the overall membrane selectivity is the sorption or solubility selectivity. The sorption coefficient of gases and vapors, which is a measure of the energy required for the permeant to be sorbed by the polymer, increases with increasing condensability of the permeant. This dependence on condensability means that the sorption coefficient also increases with molecular... 

As a consequence, the overall penetrant uptake cannot be used to get direct informations on the degree of plasticization, due to the multiplicity of the polymer-diluent interactions. The same amount of sorbed water may differently depress the glass transition temperature of systems having different thermal expansion coefficients, hydrogen bond capacity or characterized by a nodular structure that can be easily crazed in presence of sorbed water. The sorption modes, the models used to describe them and the mechanisms of plasticization are presented in the following discussion. 

Equation (9.15) was written for macro-pore diffusion. Recognize that the diffusion of sorbates in the zeoHte crystals has a similar or even identical form. The substitution of an appropriate diffusion model can be made at either the macropore, the micro-pore or at both scales. The analytical solutions that can be derived can become so complex that they yield Httle understanding of the underlying phenomena. In a seminal work that sought to bridge the gap between tractabUity and clarity, the work of Haynes and Sarma [10] stands out They took the approach of formulating the equations of continuity for the column, the macro-pores of the sorbent and the specific sorption sites in the sorbent. Each formulation was a pde with its appropriate initial and boundary conditions. They used the method of moments to derive the contributions of the three distinct mass transfer mechanisms to the overall mass transfer coefficient. The method of moments employs the solutions to all relevant pde s by use of a Laplace transform. While the solutions in Laplace domain are actually easy to obtain, those same solutions cannot be readily inverted to obtain a complete description of the system. The moments of the solutions in the Laplace domain can however be derived with relative ease. 

In all of these cases, the structure of the organic sorbate, the composition of the surface, and the conditions of the vapor or solution exchanging with the solid must be considered. However, it is important to note that with some experience in thinking about the organic chemicals and environmental situation involved, we can usually anticipate which one or two sorption mechanisms will predominate. For example, in Chapter 9 we wrote an expression reflecting several simultaneously active sorption mechanisms, each with their own equilibrium descriptor, to estimate an overall solid-water distribution coefficient for cases of interest (Eq. 9-16) ... 

The sorption of a penetrant by a class (a) membrane can be treated most simply, if the processes of sorption in the polymer matrix and into each kind of specific sorption site within it can be treated as mutually independent and hence additive. Under these conditions, each sorbed species may similarly be expected to contribute additively to the total diffusion flux. Hence, if there are N — 1 kinds of specific sorption sites, the overall sorption and permeability or diffusion coefficients can be written as... 

The sorption of a weak electrolyte by a charged polymer membrane is another case where Nernst + Langmuir-like dual mode sorption, involving the undissociated and dissociated species respectively, may be expected. The concentration of each species in solution follows, of course, from the dissociation constant of the electrolyte. The sorption isotherms of acetic acid and its fluoroderivatives have been analysed in this manner, and the concentration dependence of the diffusion coefficient of acetic acid interpreted resonably successfully, using Nylon 6 as the polymer substrate 87). In this case the major contribution to the overall diffusion coefficient is that of the Nernst species consequently DT2 could not be determined with any precision. By contrast, in the case of HC1, which was also investigated 87 no Nernst sorption or diffusion component could be discerned down to pH = 2 and the overall diffusion coefficient obeyed the relation D = DT2/( 1 — >1D), which is the limiting form of Eq. (25) when p — 00. 

If the component phases denoted by A and B are of sufficient, but still microscopic, size (cf. introductory section) and do not interact appreciably, their individual sorption and diffusion properties may be deduced from measurements on the pure bulk phases. Then, the overall solubility coefficient is given by an additive relation analogous to Eq. (5), except that the volume fractions vA, vB( = 1 — vA) of the respective components in the membranes must be taken into account ... 

Selectivity and productivity depend on sorption and diffusion. Sorption is dictated by thermodynamic properties, namely, the solubility parameter of the solute(s)/membrane material system. On the other hand, the size, shape, molecular weight of the solute, and the availability of inter/intra molecular free space of the polymer largely govern the second property, the diffusion coefficient. For an ideal membrane, both the sorption and diffusion processes should favor the chosen solute. If one step becomes unfavorable for a given solute the overall selectivity will be poor [28]. 

The selection of adsorbents is critical for determining the overall separation performance of the above-described PSA processes for hydrogen purification. The separation of the impurities from hydrogen by the adsorbents used in these processes is generally based on their thermodynamic selectivities of adsorption over H2. Thus, the multicomponent adsorption equilibrium capacities and selectivities, the multi-component isosteric heats of adsorption, and the multicomponent equilibrium-controlled desorption characteristics of the feed gas impurities under the conditions of operation of the ad(de)sorption steps of the PSA processes are the key properties for the selection of the adsorbents. The adsorbents are generally chosen to have fast kinetics of adsorption. Nonetheless, the impact of improved mass transfer coefficients for adsorption cannot be ignored, especially for rapid PSA (RPSA) cycles. 

In order to interpret the Na" " and Cs" " diffusional results in terms of this model, it is assumed that both cations would be able to diffuse readily in both the ionic clusters and interfacial regions. Cesium ion would experience a more tortuous diffusion path compared to sodium ion, and thus would have a smaller measured self-diffusion coefficient. The insensitivity of this diffusion coefficient to increasing water sorption may then be because most of this water serves to increase the size of ionic clusters, which would have a relatively minor overall effect on the diffusion path length. 

The first condition applies to sorption, the second to desorption. Otherwise the evaluation of rate measurements on the basis of the equilibrium assumption can lead to meaningless results e.g., diffusion coefficients measured in sorption and desorption may appear different, because the overall rates are not controlled by diffusion alone, and the rates of transfer through the phase boundary are different in sorption and desorption. 

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