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.

新型单晶膜[Cu(II)₂(4-F-bza)₄(2-mpyz)]ₙ（其中4-F-bza为4-氟苯甲酸根；2-mpyz为2-甲基吡嗪）经合成后，通过迂曲度校正测得其在任意晶向上的渗透性能均一致，证明气体在孔道内无迂回地扩散。该膜的二维孔道最小孔径为2.6 Å，小于氢气（H₂，2.827 Å）、一氧化碳（CO，3.690 Å）与甲烷（CH₄，3.758 Å）的伦纳德-琼斯（Lennard-Jones）直径，氢气以1.18×10⁻¹² mol·m⁻²·s⁻¹·Pa⁻¹的渗透通量透过膜，且对H₂/CO与H₂/CH₄的选择性分别高达23.5和48.0。基于空间膨胀效应的修正克努森（Knudsen）扩散模型可很好地解释该高渗透速率：当气体分子或原子与孔道壁碰撞时会引发孔道膨胀，较小气体的渗透选择性会因此提升，这与实验观测结果一致。单晶X射线衍射数据分析表明，孔道膨胀程度排序为H₂ > 氩气（Ar） > CH₄，这与渗透分析的预期结果相符。多孔固体的渗透选择性不仅取决于有效孔道直径与目标气体的尺寸，还与孔道的弹性密切相关。