Permeation of simple gases

It illustrates that the permeability P is equal to the flux Q of permeant that is transported through a membrane of thickness L under the influence of a difference Ay in potential. As shown in Table 18.1 the potential y may be a pressure (N/m2), a mass concentration (kg/m3) or a molar concentration (mol/m3). This, of course, influences the dimensions of flux and permeability. 

Other important properties are the barrier performance, which is defined as the resistance to the transport of permeant molecules and thus is the inverse of permeability, and the selectivity of a polymer between two types of molecules, which is the ratio of its permeabilities to those molecules, e.g. Po2/Pn2 is the selectivity between oxygen and nitrogen. 

For simple gases a general relationship between the three main permeation properties P (permeability), S (solubility) and D (diffusivity) is almost exactly valid  

This means that permeation is a sequential process, starting with solution of the gas on the outer surface of the polymer (where equilibrium nearly exists), followed by slow inward diffusion ( reaction with pre-established equilibrium ). For all three physical quantities P, S and D, the temperature dependence can be described by a Van t Hoff-Arrhenius equation  

We shall first of all consider the main characteristic physical data of simple gases then solubility, diffusivity and permeability will be separately discussed finally some useful inter-conversion ratios will be given. 

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The permeation of simple gases in glassy polymers is more complex than in rubbery polymers. An extension of the dual sorption model of permeation leads to a relation, when the downstream pressure is small, of the following form... 

The permeation of simple gases in polar polymers is also dependent on relative humidity because of the water s strong interaction with the polymer. Particularly large is the effect of humidity on the oxygen permeability of barrier layers made from EVOH. At 20 °C and 100 % relative humidity the permeability is 300 times higher than at 0 % relative humidity at the same temperature. By orientation and thermal treatments the barrier properties at high relative humidity can be significantly improved (up to a factor of 10). 

The relevance of the second approach stems from the possibility to use the same pore-structure model as used in description of the process in question (counter-current (isobaric) diffusion of simple gases, permeation of simple gases under steady-state or dynamic conditions, combined diffusion and permeation of gases under dynamic conditions, etc.). 

The experimentally performed transport processes used for evaluation of transport parameters include counter current binary or multicomponent gas diffusion under steady-state or chromatographic conditions, steady permeation of simple gases, dynamics of combined transport of binary or multicomponent gas mixtures, etc. Of significance, however, is that no automatic commercial instrument is available for these processes. Thus, the necessary apparatuses must be homemade. To obtain the transport parameters with acceptable confidence large numbers of experiments is required. It would be, therefore, of significant importance if at least part of the transport parameters could be obtained from standard textural analysis. 

The aim of this study is to compare pore structure characteristics of two porous catalysts determined by standard methods of textural analysis (physical adsorption of nitrogen and mercury porosimetry) and selected methods for obtaining parameters relevant to transport processes (multicomponent gas diffusion and permeation of simple gases). MTPM was used for description of these processes. 

Two non-standard transport processes (counter-current isobaric ternary diffusion and permeation of simple gases were chosen for obtaining pore-structure transport characteristics. MTPM was used for evaluation of transport parameters. 

A polymeric system is, thus, characterized by three transport coefficients, which are the permeability, the solubility, and the diffusion coefficients. The permeability coefficient, P, indicates the rate at which a permeant traverses polymer film. The solubility coefficient, S, is a measure of the amount of permeant sorbed by the polymer when equilibrated with a given pressure of gas or vapour at a particular temperature. Finally, the diffusion coefficient, D, indicates how fast a penetrant is transported through the polymer system. For steady state permeation of simple gases into a homogeneous film, the permeability coefficient, P, can be written as the product of diffusion coefficient D and solubility S (Equation 11.2) ... 

While reasonably accurate for the permeation of simple nonpolar gases, this equation is less suit-able for water vapor, so the permeability data quoted for this substance are of qualitative. significance only. 

For a first approximation, the simple expressions in Eqs. (9-1), (9-2) and (9-5) can be used for calculating the permeation of a given organic substance. However, the applicability is to some degree considerably reduced, depending on the molecular structures and their related properties. Various deviations from the behavior of simple gases complicate the calculated estimation of an organic substance s permeability. 

In contrast to the sorption of simple gases in glassy polymers, sorption of water often results in the swelling of the polymer matrix. It was observed that the presence of water vapour in some instances accelerate the permeation rate of some gaseous species, while in other cases it could reduce the permeation rate of the gases. The first effect is attributed to the matrix plasticization while the second effect is due to the exclusion of gas from the micro void content of the polymer network, which reduces the available diffusive paths for the gas [41]. 

Plasticization and Other Time Effects Most data from the literature, including those presented above are taken from experiments where one gas at a time is tested, with Ot calculated as a ratio of the two permeabihties. If either gas permeates because of a high-sorption coefficient rather than a high diffusivity, there may be an increase in the permeabihty of all gases in contact with the membrane. Thus, the Ot actually found in a real separation may be much lower than that calculated by the simple ratio of permeabilities. The data in the hterature do not rehably include the plasticization effect. If present, it results in the sometimes slow relaxation of polymer structure giving a rise in permeabihty and a dramatic dechne in selectivity. 

If D only depends on temperature (and thus not on concentration or time), the diffusion process is called Fickian. Simple gases show Fickian diffusion and so do many dilute solutions (even in polymers).The diffusivity can be determined directly either from sorption or from permeation experiments. In the first case the reduced sorption, c(t) / (cfX, cG), is plotted versus the square root of the sorption time and D is calculated from the equation ... 

Gas permeation through non-porous polymeric membranes is generally described by the solution-diffusion mechanism [2], This is based on the solubility of specific gases within the membrane and their diffusion through the dense membrane matrix. In turn, the solubility of a specific gas component within a membrane is a function of its critical temperature, as this is a measure of the gas condensability. Critical temperatures for a range of gas components are provided in Table 11.2. Conversely, the diffusivity depends upon the molecular size, as generally indicated by the kinetic diameter. Indeed, Robeson et al. [9] have recently postulated that the relationship between the ideal permeability of one species P, and that of another Pj are related by a simple function ... 

The permeation of gases in such a complex structure is very difficult to model due to the lack of information on the phase structures and properties, as well as the complexity of such modelling. Qualitatively, the reduced mobility and the chain orientation in semi-ordered interphases due to the stiff and ordered crystallites would make the permeability smaller. For the Pebax grades with shorter polyether blocks and longer polyamide blocks, the tortuosity of the diffusion path will increase sharply when the polyether and amorphous PA phases become finely divided by the crystalhne phase. Nevertheless, we tried to use the PA phase crystallinity to simulate the CO2 and nitrogen permeabilities in Pebax films with the simple resistance model [35] to estimate the influence of the Pebax structure on the permeability. 

The permeation method works well for simple gases diffusing through polymers above the glass transition temperature because in this situation, the solubility and diffusivity are both constant, independent of concentration, at a given temperature. With increasing temperature, the diffusion coefficient... 

The gas-polymer-matrix model for sorption and transport of gases in polymers is consistent with the physical evidence that 1) there is only one population of sorbed gas molecules in polymers at any pressure, 2) the physical properties of polymers are perturbed by the presence of sorbed gas, and 3) the perturbation of the polymer matrix arises from gas-polymer interactions. Rather than treating the gas and polymer separately, as in previous theories, the present model treats sorption and transport as occurring through a gas-polymer matrix whose properties change with composition. Simple expressions for sorption, diffusion, permeation and time lag are developed and used to analyze carbon dioxide sorption and transport in polycarbonate. 

RH requirement of the membrane means that a low-pressure system is restricted to temperatures below 100°C since the saturation partial pressure of water increases exponentially with temperature. In addition, it would be highly desirable to have a water-neutral situation in order to obtain a compact and simple system where the water produced at the cathode of the fuel cell as well as the permeated water is collected completely (a condenser would be necessary) to humidify the gases. In this respect, it would be an ideal situation to operate the fuel cell at the intersections of solid and dashed lines, which are the water-neutral operating conditions. The only... 

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