Euromembrane-2006, Giardian Naxos-Taormina (Messina) – Italy, 24-28 September 2006.

^{1}A. V. Topchiev Institute of Petrochemical Synthesis (TIPS), Russian Academy of Sciences,
119991, Leninsky pr., 29, Moscow, Russia

^{2}M. V. Lomonosov Moscow State University (MSU), 119992, Leninskie Gory, 1, Moscow, Russia

**Introduction**

The amount of gas permeability data for polymers drastically increased during last decade. Thus, there is opportunity to check the more general hypothesis based on representative selection of the parameters choice including different polymeric materials such as homopolymers (polyimides, polyamides, polysulfones, polycarbonates, silicon-containing polymers, polyolefins, polyphosphasenes, etc.), copolymers, composite membrane materials and surface-modified membranes. In the present work the statistical analysis for permeability parameters of 9 permanent gases through ~300 polymeric materials was carried out by using of General Regression Models (GRM).

**Results and Discussion**

The correlations of the gas permeability parameters of polymers with physical properties of gases (the kinetic cross-section of diffusing molecule and effective Lennard-Jones force constant), and polymers (Free volume and Group contribution models) are known [1,2]. As a result of GRM analysis it is shown by us that permeability of gas
*P _{i}* through different polymers can be described by the Multiple Regression Model, represented by general equation (in decimal logarithms):

where *a* and *b _{n}* parameters are determined by gas nature, and polymer is responsible for permeabilities.

The equation (1) holds for all of amount of experimental data with accuracy, which is normal for existing measurement techniques (Fig.1).

**Fig. 1.** The histogram for differential function of the distribution of standard deviations from experimental data (eqn. (1)) for different polymeric materials. The average error for all amounts of data is 15% of P value.

So, it was suggested that the log-scale of the gas permeability of polymers can be described by linear model with two parameters depending on physical properties of polymer, and by three coefficients (free member included) determining by gas (Fig.2).Experimental data combine into very dense cloud (galaxy).

**Fig. 2.**
N_{2}* permeability coefficient as a function of permeability of
CO*_{2}* and O*_{2}*. *

The result of the GRM technique is an equation (2) where both a and bn empirical gas parameters are represented, so that this definite coefficients are suitable for the calculation of permeability of desired gas through almost any known polymer membrane.

**Conclusions**

The statistical analysis for the permeability parameters of 9 permanent gases through ~300 polymeric materials was carried out by using of Multiple Regression Model. It is shown that permeability of desired gas Pi through different polymers can be described by general equation with three parameters, which are determined by the gas nature, and polymer is responsible for permeability in relation to selected gases. Thus, the suggested approach and developed regularities providing by prediction power give us the chance for new estimation of structure/properties relations for polymeric materials including copolymers as a gas separation membranes.

In advance, we plan to apply this technique to predict permeability parameters of lower hydrocarbons and aggressive gases, and to continually expand the database by including new polymer membranes.

References

[1] V.V. Teplyakov, P. Meares, Correlation aspects of the selective gas permeabilities of polymeric materials and membranes, Gas Separation and Purification 4 (1990) 66-74.

[2] A.Y. Alentiev, Y.P.Yampolskii, Free volume model and tradeoff relations of gas permeability and selectivity in glassy polymers, Journal of Membrane Science 165 (2000) 201-216.