Sorption and diffusion

Sorption thermodynamics were studied using the IGC method for a number of solutes (n-aUcanes C3-C16, cyclohexane, methylcyclohexane) in the range 50-250 °C. For all the solutes, the linear dependencies of log S versus I IT enabled an estimation of the enthalpies of sorption AH. It was shown that when the size of the solutes (e.g. their critical volume Vc) increases the negative enthalpies of sorption also increase. This dependence can be presented by the equation  

A description of high permeability polymers is not complete if the free volume of the material is not considered. In this work, several methods for evaluation of free volume 

The first value of ds in PTMSN can be attributed to intersegmental spacing and is indicative of looser chain packing as compared with other presented norbomene polymers. 

It is worthwhile to note that the conventional glassy polymers like polycarbonates and polysulfones are characterized by much smaller values of d spacing (4-6 A) that is, they have more densely packed chains. 

The generally recognized and the most reliable method for investigation of free volume in polymers is positron annihilation lifetime spectroscopy (PALS). It was applied for investigation of PTMSN and related polymers. This method is based on the measurement of lifetime spectra of positrons in polymers - lifetimes (ns) and corresponding intensities li (%). Longer lifetimes (or T3 and T4) (so-called o-orthopositronium lifetimes) can be related to the mean size of free volume R. 

The amount of supercritical or subcritical (liquid or gaseous) fluid absorbed in the PA-6 granules is usually determined gravimetricaUy, e.g., by using a magnetic suspension balance [75]. In contrast to the conventional gravimetric equipment ]46], where the balance is in direct contact with the sample, this balance 

A mathematical model to describe the diffusion in a cylinder, as presented by Crank [77], is used in this work to calculate diffusion coefficients. The model is based on the assumption that the direction of the diffusion is only radial. In the case of Fickian diffusion the following equation can be applied  

In this equation, Mj is the mass of absorbed gas or fluid, M othe equilibrium amount absorbed, D the diffusion coefficient, r the radius of the initially non-swollen polymer particle, and t the sorption time. For short sorption times, Eq. (1) can be replaced by Eq. (2) [78]. 

For Fickian diffusion, a plot of MfMao versus the square root of sorption time t, according to Eq. (2), should be initially linear. The diffusion coefficient can be readily evaluated from the slope of this graph and the initial radius of the sample. 

For longer sorption times and over 50% saturation, Eq. (1) can be approximated by Eq. (3). A plot of Infl-Mt/Moo) vs time t results in a linear graph, from which the diffusion coefficient can be calculated. 

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Fig. 38. Permeability as a function of molar volume for a mbbery and glassy polymer, illustrating the different balance between sorption and diffusion in these polymer types. The mbbery membrane is highly permeable the permeability increases rapidly with increasing permeant size because sorption dominates. The glassy membrane is much less permeable the permeability decreases with increasing permeant size because diffusion dominates (84).

However, it has been concluded from sorption and diffusion experiments that plutonium exists largely in the tetravalent state (53) and clearly not as Pu(V), in the intermediate pH-range under oxic conditions and at low carbonate concentration. This would be representative of many groundwaters and also in agreement with the calculated curves of Figure 2. 

For gas and vapor systems, by combining the laws of sorption and diffusion in the sequence (l)-(3), general permeation equations are obtained. For sheet membrane samples of polymers above Tg, if the definition is made that permeation coefficient Q = Ds,... 

WA Strickland, Jr., M Moss. Water vapor sorption and diffusion through hard gelatin capsules. J Pharm Sci 51 1002-1005, 1962. 

The influence of the CD content in the membrane and the n-PrOH respectively p-xylene content in the feed mixture on the separation factors and sorption and diffusion selectivities of the CD/PVA membranes for the n-PrOH/I-PrOH and p-xylene and o-xylene mixtures by evapomeation are presented in tables 12 and 13. 

The main emphasis in this chapter is on the use of membranes for separations in liquid systems. As discussed by Koros and Chern(30) and Kesting and Fritzsche(31), gas mixtures may also be separated by membranes and both porous and non-porous membranes may be used. In the former case, Knudsen flow can result in separation, though the effect is relatively small. Much better separation is achieved with non-porous polymer membranes where the transport mechanism is based on sorption and diffusion. As for reverse osmosis and pervaporation, the transport equations for gas permeation through dense polymer membranes are based on Fick s Law, material transport being a function of the partial pressure difference across the membrane. 

Whereas batch equilibrium tests are designed to study equilibrium sorption of solid phase particles with various pollutants, singly or in combination with other pollutants, solid phase column-leaching tests study both sorption and diffusion of organic pollutants through the subsurface environment [10,11,127, 141,142]. 

Hietala, S., Maunu, S. L. and Sundholm, E. 2000. Sorption and diffusion of methanol and water in PVDE-y-PSSA and Nafion 117 polymer electrolyte membranes. Journal of Polymer Science Part B Polymer Physics 38 3277-3284. 

Peterson MS, Lion LW, Shoemaker CA (1988) Influence of vapor phase sorption and diffusion on the fate of trichloroethylene in an unsaturated aquifer system. Environ Sci Technol 22 571-578 Petersen LW, Moldrup P, El-Farhan YH, Jacobsen OH, Yamaguchi Y, Rolston DE (1995) The effect of moisture and soil texture on the adsorption of organic vapors. J Environ Qual 24 752-759 Pignatello JJ (1989) Sorption dynamics of organic compounds in soils and sediments. In Sawhney BL, Brown K (eds) Reactions and movement of organic chemicals in soils. Soil Sci Soc Amer Spec Publ 22 45- 81... 

Tachi, Y., Shibutani, T., Sato, H. Yui, M. 2001. Experimental and modeling studies on sorption and diffusion of radium in bentonite. Journal of Contaminant Hydrology, 47, 171 -186. 

From Fig. 19.3a-c, and as opposed to purely sorption controlled processes, it can be seen that during pervaporation both sorption and diffusion control the process performance because the membrane is a transport barrier. As a consequence, the flux 7i of solute i across the membrane is expressed as the product of both the sorption (partition) coefficient S, and the membrane diffusion coefficient Di, the so-called membrane permeability U, divided by the membrane thickness f and times the driving force, which maybe expressed as a gradient of partial pressures in place of chemical potentials [6] ... 

In comparison with adsorptive/absorptive techniques for aroma recovery from bioconversions, the disadvantage of pervaporation is the fact that both sorption and diffusion determine the overall selectivity. While the sorption selectivity is very high (equal to that of adsorptive/absorption), the diffusion selectivity favours water owing to the simple fact that water is a smaller molecule than aroma compounds and thus sterically less hindered during diffusion (Table 19.1). The overall (perm)selectivity P=SD) is therefore lower than in strictly sorption controlled processes, although it is still favourable compared with that for evaporation. This shortcoming compares, however, with operational advantages of pervaporation as outlined before. 

In this review, we focus on the information at an atomic/molecular level that is obtainable via the different techniques. The precise methods and techniques used are not extensively discussed instead we summarize the relevant details and direct the reader toward key references. Nor do we review the potentials that are used in the classical simulations of sorption and diffusion. Derivation and evaluation of these parameters require extensive comparison with detailed spectroscopic data and are beyond the scope of this work. Similarly, the volume of experimental results that may be used in comparison to the calculations is vast. We use representative data taken largely from reviews or books. 

In an MD study of methane sorption and diffusion in silicalite, Nicholas et al. (67) identified favorable sites for sorption. From the MD calculations, the time-averaged position of the center of mass of the methane molecule was plotted. Energy minimization calculations were then performed, locating the methane molecule at positions where the MD calculations predicted they spent the most time. Each channel intersection region was found to contain two sites that are minima for methane-zeolite interactions. These two sites are separated by a translation parallel to the straight channel... 

Sorption capacity is one of the major properties used for industrial applications of zeolites. H. Lee reviews the aspects of zeolites used as adsorbents. The other papers in the section deal with the theory of sorption and diffusion in porous systems, the variation of sorption behavior upon modification, and the variation of crystal parameters upon adsorption. NMR and ESR studies of sorption complexes are reported. H. Resing reviews the mobility of adsorbed species in zeolites studied by NMR. 

In the case of sorption and diffusion, the two-dimensional channel systems of the Cmmm and Immm structures should provide higher rates of diffusion than would the one-dimensional channel systems of the Cmcm and Imcm structures. This should be true also for mixtures containing the Cmmm and Immm structures as separate crystals or as intergrown regions or stacking faults in the Cmcm structure. This effect of such stacking faults was first noted by Gard (18). 

Sorption and Diffusion of Light Hydrocarbons and Other Simple Nonpolar Molecules in Type A Zeolites... 

The results of experimental studies of the sorption and diffusion of light hydrocarbons and some other simple nonpolar molecules in type-A zeolites are summarized and compared with reported data for similar molecules in H-chabazite. Henry s law constants and equilibrium isotherms for both zeolites are interpreted in terms of a simple theoretical model. Zeolitic diffusivitiesy measured over small differential concentration steps, show a pronounced increase with sorbate concentration. This effect can be accounted for by the nonlinearity of the isotherms and the intrinsic mobilities are essentially independent of concentration. Activation energies for diffusion, calculated from the temperature dependence of the intrinsic mobilitieSy show a clear correlation with critical diameter. For the simpler moleculeSy transition state theory gives a quantitative prediction of the experimental diffusivity. 

Although the theoretical models presented in this paper are simple idealizations of complex systems, the theory provides a useful understanding of many aspects of the sorption and diffusion of simple nonpolar molecules in type-A zeolites and in H-chabazite. The extent to which such theories are applicable to other systems has not yet been investigated. 

The discussion above explains why basic information on sorption and diffusion under the reaction conditions, especially at elevated pressures, is required for kinetic and mass- and heat- transfer modelling of catalytic polymerization reactors. If such information is sufficiently available, one should be able, for example, to compare the kinetics of gas-phase and slurry-processes directly by taking into account both gas solubilities in swollen polymers and the hydrocarbons used in slurry processes. 

Membranes Exhibiting Multiple Sorption and Diffusion Modes.96... 

Dual-Mode Gas Sorption and Diffusion in Glassy Polymer Membranes. 97... 

Dual-Mode Ionic Sorption and Diffusion in Charged Polymer Membranes.. 109... 

Sorption and diffusion of a given penetrant in a homogeneous membrane may, in general, be described by l)... 

Membrane-penetrant systems, whose sorption and diffusion properties can be described by Eqs. (5)-(7) with N = 2 ( dual mode sorption and diffusion models ) have attracted much interest. The most important examples of such systems are considered in the next two sections. 

Earlier work on the application of the concept of dual mode sorption and diffusion to glassy polymer-gas systems has been reviewed in detail 6) and important aspects of more recent work have been dealt with in more recent reviews 7 10). Eq. (5) was first applied by Michaels et al U). Sorption in the polymer matrix and in the specific sorption sites was represented by linear (Henry s law) and Langmuir isotherms respectively so that Sj in Eq. (5) is given by... 

Application of the dual mode sorption and diffusion models to homogeneous polymer blend-gas systems 26,65) and filled polymers 66) has also been reported. 

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