Dual mode model permeability pressure

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). 

Comparing the curves in Fig. 2 shows that representing the permeability versus pressure data by either model provides a satisfactory fit to the data over the pressure range of 1 to 20 atm. However, at pressures less than 1 atm. the two models differ in their prediction regarding the behavior of the permeability-pressure curve [Fig. 2]. While the matrix model predicts a strong apparent pressure dependence of the permeability in this range (solid line), the dual-mode model predicts only a weak dependence (broken line). 

The dual-mode model proved rather successful to describe the isotherms and permeabilities at higher pressures. 

One can easily show that the appropriate equation derived from the dual mode sorption and transport models for the steady state permeability of a pure component in a glassy polymer is given by Eq (7) (18) when the downstream receiving pressure is effectively zero and the upstream driving pressure is p ... 

Permeability and diffusion coefficients of hydrocarbons in polyphenylene oxides are also essentially dependent on pressure (see Figure 9.23). It can be seen that in the case of ethylene, with the increase in pressure, the permeability coefficients first decrease, and then begin to rise. Ref. [18] quotes constants of the dual-mode sorption model for a number of hydrocarbons permeation through polyphenylene oxide. 

Based on the dual-mode transport model, calculate the pure component and mixtures permeability of CO2 and CH4 using a polysulfone membrane. The gas pressure is 10 atm for each component. 

A phenomenological theory known as the "dual-mode sorption" model offers a satisfactory description of the dependence of diffusion coefficients, as well as of solubility and permeability coefficients, on penetrant concentration (or pressure) in glassy polymers (4-6,40-44). This model postulates that a gas dissolved in a glassy polymer consists of two distinct molecular populations ... 

Snch shape of the Pip) curves is typical for glassy polymers. The left, low pressure branch of the curve is explained by sani-empirical dual-mode sorption and mobility model. The right branch that shows increases in permeability with increasing pressure is usually explained by the plasticization effects (see Ref. 19, p. 24). There is, however, one interesting peculiarity of PTMSN in conventional glassy polymers such as polyimides, polycarbonates, etc. the pressure p a where the curve passes through a minimum amount... 

Simple Dual-Mode Transport Models. As a direct extension of the dualmode sorption model, it is convenient to treat pure-gas permeability as the siun of two terms, which are characteristic of the two sorbed penetrant populations. Petropoulos first developed such an expression in terms of the chemical potential gradient of the sorbed gas (100). For the case where there is a vacuum downstream and a pressure pa2 of component A upstream, the following expression results ... 

It is most likely that the prediction of the permeability of gas mixtures containing CO2 could be improved by accoimting for the effects of C02-induced plasticization on transport parameters. This could be tested best at higher CO2 pressures where such effects should be significant and, in fact, would correspond to conditions of practical importance in enhanced oil recovery operations where CO2 and CH4 must be separated at pressures as high as 6.9 MPa (1000 psia) and with CO2 contents above 50%. The dual-mode transport model of Petropoulos has recently been extended to accoimt for the effects of plasticization in both pure- and mixed-gas environments (110). 

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