Similar variations can be seen in the ratio of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], indicating the role of variation of the chemical structure on the solubility coefficient
, which also reflects the ability of the gas molecules to interact with the polymer matrix.
The corresponding experiments showed that the solubility coefficients
of both phases were close to each other, and for the whole range of the inlet ozone concentration in gas the coefficients were 0.25 [+ or -] 0.11 for water ([[alpha].sub.W]) and 0.20 [+ or -] 0.10 for octane ([[alpha].sub.OCT]) (Fig.
Consequently, the gas solubility coefficient
increases as the effective diameter increases according to (5).
Figure 9 presents the pure gas permeability, diffusion, and solubility coefficients
of the membranes at 35[degrees]C as a function of UV irradiation time.
At rubbery polymer of PDMS in comparison with glassy polymer of PES, penetrant solubility coefficient
is more important than diffusion coefficient.
where [S.sub.a] is the solubility coefficient
of the purely amorphous material and [alpha] is the amorphous fraction.
From the two relationships we estimate the He solubility coefficient
in PEANi to be about 7.6 x [10.sup.-5] ([cm.sup.3] (S.T.P.)/[cm.sup.3] cm-Hg).
It is related to the gas pressure in the bubble through the solubility coefficient
where S is the cell radius, R is the bubble radius, c is the gas concentration, [p.sub.g] is the gas pressure inside the bubble, [P.sub.[infinity]], is the pressure in the cell after supersaturation, [sigma] is the polymer surface tension, K is the Henry's law constant (solubility coefficient
), and the subscript eq notes the equilibrium conditions.
For the simplest practical cases of m = 2 and m = 3, we present the diffusion behaviors assuming stepwise distribution of both diffusion and solubility coefficients
at the interfacial boundary, changing the penetrant concentration distributions with time in each layer while varying the ratio of the diffusion coefficient and/or the solubility coefficient
, and simulating the sorption curves after exposing the film to the atmosphere of fixed penetrant vapor pressure [p.sub.o] under varying ratios of diffusion coefficients in respectively layers.
In fact, permeability (P) can be defined as [Mathematical Expression Omitted] where [Mathematical Expression Omitted] is an average diffusion coefficient, while [Mathematical Expression Omitted] is an average solubility coefficient
. As a consequence, low permeability values can be attained if gas solubility or gas diffusivity or both display very low values.
Chapter titles: Interactions in Packaging Systems covering the laws of diffusion and solubility; Permeation Methods covering pressure-variable, volume-variable, isotatic or isobaric and standard methods; Sorption and Migration including headspace and gravimetric analysis, inverse gas chromotogarphy, thermal desorption, supercritical fluid extraction, gel permeation chromotography/HPLC, optical methods and diffusion and solubility coefficients
; Packaging Migration including global and specific migration, simulants, theory of migration and recycled materials.