Diffusion and Permeability of Gases

Diffusion is an activated energy process and can be represented by an Arrhenius relationship 

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As the molecular size of most gases is much smaller than any scale of structure expected in polymer blend morphology, diffusion and permeability of gases can be employed to determine the phase behavior of a polymer blend. Therefore, the study of transport phenomena in blends would be motivated not only by the requirements of producing improved barrier materials but also by the continuous interest in the nature and characterization of polymer blend morphology. 

Factors determining the solubility, diffusion and permeability of gases in elastomers, and the influence of high temperatures and pressures on these processes are examined, together with a study of the possibility of increasing the working life of seals under these conditions. 46 refs. (Translated from Kauchuk i Rezina, No.4,2000, p.36)... 

Cellulose materials contain structural defects, pores and capillaries, which affect the physical adsorption of various substances absorption of liquids diffusion and permeability of gases, vapors, and liquids mechanical and some other properties. Investigations have shown that pores between elementary fibrils have diameter about 1.5-2 nm (loelovich et al., 1988]. Diameter of pores and capillaries between microfibrillar bundles can be in the range from 2 to 20 nm (Papkov et al., 1976]. Cell wall of natural cellulose fibers has mesopores with diameter from 40 to 100 nm (Segeeva, 1972]. Samples of paper and paperboard contain also macropores with diameter above 100 nm (loelovich et al., 1988]. 

Ferguson, L. Scovazzo, P. (2007). Solubility, diffusivity, and permeability of gases in phosphonium-based room temperature ionic liquids data and correlations, Ind. Eng. Chem. Res., 46,1369-1374, ISSN 0888-5885. 

The nature of the penetrant and the nature of the polymer are the main factors affecting the diffusivity or permeability of gases. Thus if the operating temperature is lower than or equal to the critical temperature of the penetrant vapour, there appears a strong concentration and... 

Nonlinearity of the dependence on the blend content could be explained, to a certain extent, with structural changes in the polymer melt, as a result of which the intermolecular interaction is weakened, which undoubtedly also influence the relaxation processes in the polymer. The kinetics of the diffusion of low-molecular compounds and permeability of gases depends on the microheterogeneous stracture of the investigated PVC-CPE blends as well as on the amount of the microvoids on the interfacial boundary area, locked there during thermoplastic mixing of PVC and CPE. Different mass transfer mechanisms can govern the diffusion process in various stractural areas of the PVC-CPE blend. 

Nonlinear, pressure-dependent sorption and transport of gases and vapors in glassy polymers have been observed frequently. The effect of pressure on the observable variables, solubility coefficient, permeability coefficient and diffusion timelag, is well documented (1, 2). Previous attempts to explain the pressure-dependent sorption and transport properties in glassy polymers can be classified as concentration-dependent and "dual-mode models. While the former deal mainly with vapor-polymer systems (1) the latter are unique for gas-glassy polymer systems (2). 

In Section I we introduce the gas-polymer-matrix model for gas sorption and transport in polymers (10, LI), which is based on the experimental evidence that even permanent gases interact with the polymeric chains, resulting in changes in the solubility and diffusion coefficients. Just as the dynamic properties of the matrix depend on gas-polymer-matrix composition, the matrix model predicts that the solubility and diffusion coefficients depend on gas concentration in the polymer. We present a mathematical description of the sorption and transport of gases in polymers (10, 11) that is based on the thermodynamic analysis of solubility (12), on the statistical mechanical model of diffusion (13), and on the theory of corresponding states (14). In Section II we use the matrix model to analyze the sorption, permeability and time-lag data for carbon dioxide in polycarbonate, and compare this analysis with the dual-mode model analysis (15). In Section III we comment on the physical implication of the gas-polymer-matrix model. 

The factors affecting the selectivity and permeability of polymer membranes to different gases are best discussed on the basis of Eqs. (12) and (14). As noted in Eq. (12), the permeability coefficient, P, of a penetrant gas in a polymer membrane is the product of a (concentration-averaged) diffusion coefficient, D, and of a solubility coefficient,... 

The measurement of sorption, diffusion and permeability coefficients takes place as a rule using one of three methods sorption of the gases in the polymer, permeation through a membrane (film or sheet) into a sealed container or permeation through a membrane into a gas stream. As far as possible sorption methods should be used together with permeation methods that are specific for the measured gas/polymer system in order to uncover any possible anomalies or errors in the measurements by comparison of results. 

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. 

The models most frequently used to describe the concentration dependence of diffusion and permeability coefficients of gases and vapors, including hydrocarbons, are transport model of dual-mode sorption (which is usually used to describe diffusion and permeation in polymer glasses) as well as its various modifications molecular models analyzing the relation of diffusion coefficients to the movement of penetrant molecules and the effect of intermolecular forces on these processes and free volume models describing the relation of diffusion coefficients and fractional free volume of the system. Molecular models and free volume models are commonly used to describe diffusion in rubbery polymers. However, some versions of these models that fall into both classification groups have been used for both mbbery and glassy polymers. These are the models by Pace-Datyner and Duda-Vrentas [7,29,30]. 

Permeability of gases and vapours through plastic involves absorption, followed by diffusion, followed by evaporation and desorption from the other face. Permeability is greatest with amorphous plastics where diffusion occurs via the spaces between the moving mass of molecular chains. Crystalline plastics or those with crystalline regions present a greater barrier to diffusion. With thinner materials where pinholes or micropores occur, diffusion may occur via these small holes. Various other factors influence permeation, including ... 

The fit of these expressions to experimental results is very good. At low pressure regimes, the fit was shown to be even better than that of dual sorption expressions. Except for these regimes, the two models seem to do equally well in describing sorption and permeability data. Concentration dependent diffusivity and permeability have been considered before mainly for vapors. The new aspect of the matrix model is that it broadens these effects to fixed gases. The important difference between the matrix and dual sorption models is in the physical picture they convey of gas transport and interaction with the polymer. Additional experimental evidence will be needed to determine the preference of these different physical representations. 

The permeability of gases and vapors in a flawless polymer matrix is well established by the solution-diffusion principle in which permeability, P, is given by the product of solubility, s, and the diffusivity, D, i.e., P = sD. 

Since the solubility of various gases in ILs varies widely, they may be uniquely suited for use as solvents for gas separations [97]. Since they are non-volatile, they cannot evaporate to cause contamination of the gas stream. This is important when selective solvents are used in conventional absorbers, or when they are used in supported liquid membranes. For conventional absorbers, the ability to separate one gas from another depends entirely on the relative solubilities (ratio of Henry s law constants) of the gases. In addition, ILs are particularly promising for supported liquid membranes because they have the potential to be incredibly stable. Supported liquid membranes that incorporate conventional liquids eventually deteriorate because the liquid slowly evaporates. Moreover, this finite evaporation rate limits how thin one can make the membrane. This means that the net flux through the membrane is decreased. These problems could be eliminated with a non-volatile liquid. In the absence of facilitated transport (e.g., complexation of CO2 with amines to form carbamates), the permeability of gases through supported liquid membranes depends on both their solubility and diffusivity. The flux of one gas relative to the other can be estimated using a simplified solution-diffusion model ... 

For semi-crystalline polymers above Tg, the permeability is proportional to the nth power of the amorphous volume fraction n lies between 1.2 and 2. The gas must diffuse between the lamellar crystals, and the detailed morphology depends on the polymerisation route, thermal history and whether orientation is present. The permeability of gases of molecular weight M is approximately inversely proportional to y/M. However, Table 11.2 shows that the ratio of CO2 to O2 permeability in glassy polymers is higher than in semi-crystalline polymers. 

For the simple gases-such as He, Hj, O2, Nj, and COj, with gas pressures up to 1 or 2 atm, the solubility in solids such as polymers and glasses generally follows Henry s law and Eq. (6.5-5) holds. Also, for these gases the diffusivity and permeability are independent of concentration, and hence pressure. For the effect of temperature T in K, the In Pm is approximately a linear function of 1/T. Also, the diffusion of one gas, say H2, is approximately independent of the other gases present, such as O2 and N2. 

Permeability is an intrinsic property of a gas-polymer membrane system. Correlations that relate diffusion, solubility, and permeability coefficients of diverse gases in polymers are available. Models and group contribution theories have been developed to predict permeability of gases in polymers. However, general rules or universal correlations are usually not as good at predicting permeability as rules for a particular set of polymers. A detailed description of these correlations can be found elsewhere [29], This section presents the main barrier properties of PLA to O2, CO2 and N2. 

In this equation the permeabilities of gases are measured with the gas mixture. The selectivity calculated from the ratio of pure gas permeabilities is sometimes called the ideal gas selectivity and is often higher than the actual selectivity value. Permeability Pi can be expressed as the product of two terms. One, the diffusion coefficient Z), reflects the mobility of the individual molecules in the membrane material the other, the Henry s law sorption coefficient ki, reflects the number of molecules dissolved in the membrane material. Thus, equation (6) can also be written as... 

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