Diffusivities, glassy polymers

Fig. 38. Permeability as a function of molar volume for a mbbery and glassy polymer, illustrating the different balance between sorption and diffusion in these polymer types. The mbbery membrane is highly permeable the permeability increases rapidly with increasing permeant size because sorption dominates. The glassy membrane is much less permeable the permeability decreases with increasing permeant size because diffusion dominates (84).

Table 10 contains some selected permeabiUty data including diffusion and solubiUty coefficients for flavors in polymers used in food packaging. Generally, vinyUdene chloride copolymers and glassy polymers such as polyamides and EVOH are good barriers to flavor and aroma permeation whereas the polyolefins are poor barriers. Comparison to Table 5 shows that the large molecule diffusion coefficients are 1000 or more times lower than the small molecule coefficients. The solubiUty coefficients are as much as one million times higher. Equation 7 shows how to estimate the time to reach steady-state permeation t if the diffusion coefficient and thickness of a film are known. 

Crystalline structures have a much greater degree of molecular packing and the individual lamellae can be considered as almost impermeable so that diffusion can occur only in amorphous zones or through zones of imperfection. Hence crystalline polymers will tend to resist diffusion more than either rubbers or glassy polymers. 

Water molecules combine the tendency to cluster, craze and plasticize the epoxy matrices with the characteristic of easily diffusion in the polymer1 10). The morphology of the thermoset may be adversaly influenced by the presence of the sorbed moisture. The diffusion of the water in glassy polymers able to link the penetrant molecules is, therefore, characterized by various mechanisms of sorption which may be isolated giving useful information on the polymer fine structure. 

HB Hopfenberg, V Stannett. Diffusion and sorption of gases and vapors in glassy polymers. In RN Haward, ed. The Physics of Glassy Polymers. New York Wiley, 1973, pp 504-547. 

T Alfrey, EF Gurnee, WG Lloyd. Diffusion in glassy polymers. J Polym Sci Part C 12 249-261, 1966. 

A moving front is usually observed in swelling glassy polymers. A diffusion-controlled front will advance with the square root of time, and a case II front will advance linearly with time. Deviations from this simple time dependence of the fronts may be seen in non-slab geometries due to the decrease in the area of the fronts as they advance toward the center [135,140], Similarly, the values of the transport exponents described above for sheets will be slightly different for spherical and cylindrical geometries [141],... 

JC Wu, NA Peppas. Modeling of penetrant diffusion in glassy polymers with an integral sorption Deborah number. J Polym Sci Polym Phys Ed 31 1503-1518,... 

FA Long, D Richman. Concentration gradients for diffusion of vapors in glassy polymers and their relation to time dependent diffusion phenomena. J Am Chem Soc 82 513-522, 1960. 

THE BERENS-HQPFENBERG MODEL. The Berens and Hopfenberg model considers the sorption process in glassy polymers as a linear superposition of independent contributions of a rapid Fickian diffusion into pre-existing holes or vacancies (adsorption) and a slower relaxation of the polymeric network (swelling).(lS) The total amount of sorption per unit weight of polymer may be expressed as... 

In this contribution we present results obtained with tetra-ethyleneglycol diacrylate (TEGDA). This compound was chosen since its polymer shows an easily discernible maximum in the mechanical losses as represented by tan 5 or loss modulus E" versus temperature when it is prepared as a thin film on a metallic substrate. When photopolymerized at room temperature it forms a densely crosslinked, glassy polymer, just as required in several applications. Isothermal vitrification implies that the ultimate conversion of the reactive double bonds is restricted by the diffusion-limited character of the polymerization in the final stage of the reaction. Therefore, the ultimate conversion depends strongly on the temperature of the reaction and so does the glass transition. 

This was originally a very slow batch process, because of the need to dissolve gaseous CO2 in solid glassy polymers such as polycarbonate and polystyrene. The low diffusivity meant that the time taken was many hours. The foam was formed when there was a phase change from the glassy to the melt state. In recent developments of the process, supercritical CO2 (for temperatures >31 °C, and pressures >7.2 MPa) is... 

The results of the delayed stress on radiation studies presented above (Figure 7) are also consistent with the mechanism of gas buildup within the polymer specimens as the cause of the accelerated creep. An additional interesting conclusion is that applied stress should increase the rate at which gases diffuse out of a polymer specimen. This is not unreasonable in view of the fact that this conclusion is reached for stress application during irradiation, when expansion of the polymer matrix by the internally generated gas would be expected to facilitate gas diffusion. (Actually, one would expect increased gas diffusion in stressed glassy polymers, even in the absence of radiation, owing to the low Poisson ratio in such materials.)... 

The reaction of curing the epoxy-amine system occurring in the diffusion-controlled mode has little or no effect on the topological structure of the polymer 74> and on its properties in the rubbery state. However, the diffusion control has an effect on the properties of glassy polymers 76 78). 

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