Polyimides correlation between diffusion coefficient

Figures 3 and 4 present correlations between diffusion coefficients, log(D), and calculated CED. For all polyimides examined, including the polyimides in this study, good correlations between log(D) and CED were observed for each gas in spite of differences in measurement temperature.

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

Figure 3. Methane diffusivity and permeability in a series of glassy, aromatic polyimides at 35°C (78), (a) Methane diffusion coefficients as a function of reciprocal free volume, (b) Correlation between methane diffusivity and methane permeability.

We have investigated relations between apparent gas diffusion coefficients in glassy polymers and both calculated and measured physical parameters. Cohesive forces and polymer mobility influence gas diffusivities in our glassy polyimides. The correlation between D and common parameters (i.e. Vf, CED, E ) of polyimides having side chain substituted polar groups differs from those of nonpolar polymers and weakly polar polymers. Gas diffusivity values were not well-correlated with free volume. Relative to free volume, CED and E are more sensitive to polymer mobility. Estimation of gas diffusivities based on group contribution methods is possible by using factors, such as CED, which can be calculated without any measurements. 

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