The solubility coefficient
S, does not exhibit a significant variation with solubility parameter (Fig.
On the other hand, the solubility coefficient
increases much faster in the organomodified cases than for untreated MMT (Figs.
In the polymer industry, many research and development applications involve the study of diffusion and solubility coefficients
. These, in addition to standard permeability evaluations, allow researchers to better understand the permeant-polymer relationship as well as the intrinsic properties of the polymer itself.
It is now generally accepted among ozone researchers that the average solubility coefficient
of ozone [[alpha].sub.W] ([[alpha].sub.W] = [C.sub.L] */[C.sub.G]) in water at 20[degrees]C is 0.24 .
The decrease in the solubility coefficient
is more pronounced, possibly because of reduction the number of sites in the polymer matrix for physical interaction with oxygen .
where S is the solubility coefficient
of a gas in the polymer ([cm.sup.3] of gas (STP)/[cm.sup.3] of polymer cmHg), [S.sub.0] is a constant, and ([F.sup.ef.sub.g]) is the effective square of a cross sectional-area of a gas penetrant molecule.
where [D.sub.A]/[D.sub.B] is the diffusivity selectivity (the ratio of the diffusion coefficients of Gases A and B) and [S.sub.A]/[S.sub.B] is the solubility selectivity (the ratio of the solubility coefficients
of Gases A and B).
This results in an almost constant solubility coefficient
(ratio of gas concentration in the polymer to its partial pressure) of each component, as shown in Fig.
(1) investigated structure--permeability relationships of the silicone membranes to prove that the effect of temperature on gas permeability coefficient depended on changes in its diffusion coefficient and solubility coefficient
. The diffusion coefficient always increased with increasing temperature, whereas the opposite tendency was generally observed in the solubility coefficient
In glassy rigid polymers, penetrant diffusion coefficient is more important than solubility coefficient
. Therefore, the smaller noncondensable gases such as [H.sub.2] and C[H.sub.4] preferably diffuse through these polymers compared with the larger condensable gases such as [C.sub.3][H.sub.8] and [CO.sub.2].
However, the thermal history does not affect the Henry's solubility coefficient
, [k.sub.d], which is believed to be determined mainly by the interaction between the chemical structures of the polymer and gas .
According to the simple two-phase model, the solubility coefficient
of a gas in a semicrystalline polymer should be given by
where D is the diffusion coefficient and S is the effective solubility coefficient
. In order to measure P, D, and S by a single experiment, the time-lag method (13) was used (11).
Here, the solubility coefficient
[K.sub.H] is a complex function of temperature and pressure for a given polymer melt with dissolved gas system (16).
In the diffusion controlled regime the time scale is [t.sub.D] [varies] 1 / D, where D is the diffusion coefficient, and in the hydrodynamically controlled regime the respective time scale is [t.sub.[mu]] [varies] [K.sub.[mu]], where K is the solubility coefficient
and [mu] is the viscosity of the polymer matrix.