Gas Permeation
in a Molecular Crystal and Space Expansion
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Abstract
A novel
single-crystal membrane [Cu(II)<sub>2</sub>(4-F-bza)<sub>4</sub>(2-mpyz)]<sub><i>n</i></sub> (4-F-bza = 4-fluorobenzoate;
2-mpyz = 2-methylpyrazine) was synthesized and its identical permeability
in any crystal direction in the correction for tortuosity proved that
gas diffuses inside the channels without detour. H<sub>2</sub> permeated
by 1.18 × 10<sup>–12</sup> mol m m<sup>–2</sup> s<sup>–1</sup> Pa<sup>–1</sup> with a high selectivity
(<i>F</i>α: 23.5 for H<sub>2</sub>/CO and 48.0 for
H<sub>2</sub>/CH<sub>4</sub>) through its 2D-channels having a minimum
diameter of 2.6 Å, which is narrower than the Lennard-Jones diameter
of H<sub>2</sub> (2.827 Å), CO (3.690 Å), and CH<sub>4</sub> (3.758 Å). The high rate of permeation was well explained by
a modified Knudsen diffusion model based on the space expansion effect,
which agrees with the observed permselectivity enhanced for smaller
gases in considering the expansion of a channel resulting from the
collision of gas molecules or atoms onto the channel wall. An analysis
of single-crystal X-ray data showed the expansion order to be H<sub>2</sub> > Ar > CH<sub>4</sub>, which was expected from the
permeation
analysis. The permselectivity of a porous solid depends on the elasticity
of the pores as well as on the diameter of the vacant channel and
the size of the target gas
