Gas Permeation in a Molecular Crystal and Space Expansion

A novel
single-crystal membrane [Cu­(II)2(4-F-bza)4(2-mpyz)]n (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. H2 permeated
by 1.18 × 10–12 mol m m–2 s–1 Pa–1 with a high selectivity
(Fα: 23.5 for H2/CO and 48.0 for
H2/CH4) through its 2D-channels having a minimum
diameter of 2.6 Å, which is narrower than the Lennard-Jones diameter
of H2 (2.827 Å), CO (3.690 Å), and CH4 (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 H2 > Ar > CH4, 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.