  The gas permeation behavior in the single crystal of syndiotactic polystyrene
(s-PS) S-I form was investigated in detail, in comparison to that in the s-PS
$\varepsilon$ form. The S-I form exhibits high CO$_2$/N$_2$ and CO$_2$/CH$_4$
separation factors while preserving its high CO$_2$ permeability; a trade-off
between selectivity and permeability was broken through.The mechanism of the
effective and efficient transport of CO$_2$ in the S-I form was examined in
relation to the cavity structure in the crystal. Because the CO$_2$ molecule is
only fitted to the cavities in the S-I form, the solubility of CO$_2$ becomes
high. In addition, tri-atomic molecules can more effectively diffuse in the S-I
form compared with di-atomic molecules, as proved by the "long-gas" model. A
novel design criterion for the CO$_2$ separation membranes is proposed based on
the aspect of momentum transfer from polymer matrix to the penetrant.
