Superpermeable Hydrogen Transport Membranes

For a superpermeable membrane, the flux of hydrogen through the membrane cannot exceed the number of gas phase hydrogen molecules incident upon the feed side surface of the membrane. This ultimate limit holds for all types of membrane, whether porous or dense. It is instructive, therefore, to calculate this limit for the hydrogen flux of superpermeable membranes, which, by definition, transport every atom of hydrogen incident upon the feed side surface of the membranes [1-3]. 

From the kinetic theory of gases [5-8], it is found that the number of molecules striking each unit area of surface depends upon the velocity of the molecules in the gas phase and the number of molecules per unit volume in the gas. For a simple estimate, the flux, J, incident upon a surface is given by 

Under true superpermeable hydrogen flux conditions, the large numbers of molecules predicted to impact upon a membrane surface follow, in part, as a consequence of the very high molecular speeds of gas phase hydrogen relative to the size of reactor vessels. For example, the mean velocity of a hydrogen molecule, H2, in the gas phase at 273 K (0 °C) is 1.7 km s [8]. Mean molecular velocity increases in proportion to the square root of the absolute temperature. In a chemical reactor at 673 K (400 °C), for example, the mean velocity of H2 will increase by a factor of (673 K/273 K) / from 1.7 km s at 273 K to 2.7 km s at 673 K. Mean molecular velocity decreases inversely with the square root of the molecular mass. For deuterium molecules, D2, with a molecular mass approximately twice that of H2, the mean molecular velocity is less than that of H2 by a factor of 2 /, approximately 1.2 km s at 273 K (0 °C) [8]. 

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Mundschau, M.V., X. Xie, and C. Evenson, Superpermeable hydrogen transport membranes, Non-porous Inorganic Membranes, Chapter 4, eds. A.F. Sammells and M.V. Mundschau, Wiley VCH Verlag GmBH, Weinheim, 2006. 

Mundschau, Michael V, Xie, Xiaobing, Evenson IV Carl R. Superpermeable hydrogen transport membranes. In SammeUs, A. F, Mundschau, M. V, editors. Nonporous inorganic membranes. Weinheim, Germany WUey-VCH 2006. pp. 107-38, and references therein. 

Although the membranes used to extract hydrogen isotopes from plasmas meet the criterion for the definition of superpermeability, in that every atom of hydrogen incident upon the feed side surface of the membrane is transported through the dense membrane, it must be noted that superpermeability is achieved, in very large part, because of the relatively low flux of hydrogen incident upon the membranes. The plasma density in the quoted experiments was 5 x 10 cm-, and the total gas pressure was relatively low, 0.002-0.004 torr (0.3-0.6 Pa) [2]. 

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