Free volume polyimides

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. 

It has been reported13 that in the preparation of polyimides the more flexible meta-linked diamine systematically gave lower DE values than the corresponding /mro-linked system and that this may be related to free volume in the polymer since the meta-substituted systems should have a higher degree of entropy. Therefore, the symmetrical meta-substitution in our aromatic structure may result in a reduction of DE. 

Hougham et al. reported that, on average, the decrease in dielectric constant in a polyimide series that was attributable to the change in fractional free volume that accompanied fluorine substitution was greater than 50% Recently, these authors have further refined these estimates. ... 

This is shown semiquantitatively for a series of polyimides, where hydrogen/ fluorine, and symmetric/asyirunetric analogues were synthesized and measured. The free-volume contribution is estimated by a free-volume normalization method developed for this purpose.In these materials, the contribution of changes in free volume to the observed change in dielectric constant ranged from 25 to 95% in moisture-free materials. ... 

Recently, the same series of six polyimides was studied by positron annihilation spectroscopy to determine die fractional free volume directly. In all three H/F analogue pairs, the increased free volume of the fluorinated polymer accounted for around 50% of the observed decrease in refractive index and dielectric constant. This result confims an astonishingly large free volume contribution predicted by our earlier estimates.Future work will investigate the generality of this result to other polymer systems. 

Mercer et al. have studied the effect of moisture in fluorinated polyimides extensively. Beuhler et al. have also studied moisture absorption in fluorinated polyimides and have shown that moisture absorption decreases with fluorine incorporation, even as free volume increases (see Table 13.6). 

In comparing simulated and experimentally measured transport parameters one has to be aware that experimental data in the literature depending, for example, on sample preparation conditions and the chosen measurement methodology can show a considerable scatter, often reaching a factor of two or even more. It is, for example well-known that polyimides often contain residual solvent filling a part of the free volume and thus leading to systematically lower S and D values from experiments than from simulations [34]. 

In a rubbery polymer with flexible macromolecular chains (PDMS for example) the cavities forming the free-volume are clearly separated from each other. The detailed evaluation of the movement of a penetrant particle from cavity (1) to the neighboring (2), did not show any immediate back jumps (2) — (1). This is mainly do to the fact that the channel between (1) and (2) closes quiet quickly. In a polymer with stiff chains (glassy polyimide (PI) for example) the individual cavities are closer to each other and a rather large number of immediate back jumps ocurred during the time interval simulated (120). This indicates that once a channel between two adjacent cavities in a stiff chain polymer is formed it will stay open for some 100 ps. This makes the back jump (2) - (1) of the penetrant more probable than a jump to any other adjacent hole (3). This process seems to be one cause for the general tendency that the diffusion coefficient of small penetrants in stiff chain glassy polymers is smaller than in flexible chain rubbery polymers. 

In PI-3a, PAP produces a relatively small polar order as opposed to the efficient poling achieved by PAP in true side-chain NLO polymers, such as PMMA or polyimides with Tgs in the 120-265°C range, which are flexibly tethered by DR 1-type chromophores. The molecular size of the diaryiiSne azo chromophore of PI-3a is substantially larger than that of the DRl-type mokcules in the polymers studied previously (see PI-3b in Figure 8.4), a feature that requires more free volume for chromophore movement thereby decreasing... 

Dlubek, G., Buchhold, R., Hiibner, Ch., and Naklada, A., Water in local free volumes of polyimides a positron lifetime study. Macromolecules, 32, 2348-2355 (1999c). 

Heuchel, M., Hofmann, D., and Pullumbi, P, Molecular modeling of small-molecule permeation in polyimides and its correlation to free-volume distributions. Macromolecules, 37, 201-214 (2004). 

Brownian motions. As a result of the broadened free volume distribution it becomes possible for o-Ps to find more and larger vacancies. The delayed rise of t 3 and I3 in polyimide indicates that the Henry-type sorption is also taking place after the Langmuir-type sorption process is almost terminated. It is important to note that, unlike all the other conventional methods of sorption studies, the o-Ps method can discriminate the Langmuir-type and the Henry-type sorption processes as contrastingly different effects. 

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