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Commercial polymeric gas separation membranes exhibit a trade-off between productivity and selectivity. However, on this same trade-off curve molecular sieving materials like zeolites and carbon molecular sieves (CMS) lie above the upper bound for polymers. A comparison of the gas transport properties of these three different classes of materials highlights the importance of "entropic selectivity" which has hitherto not been focused on for membrane-based separation of gases. A whole new generation of polymeric membrane materials may result from enhancement of entropic selectivity of polymeric membrane materials.

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We have investigated the spin dynamics of YMnO 3 by inelastic neutron scattering and determined the spin-wave dispersion at low temperature. The spin-wave dispersions at low temperature have been analyzed with a simple nearest-neighbor anisotropic Heisenberg model and also by an anisotropic Hubbard model. Best fits are obtained only in the strong-coupling limit ͑U / t Ͼ ϳ 15͒, with planar exchange energy J =4t 2 / U Ӎ 2.4 meV, and anisotropy terms D z = U x Ј − U z Ј Ӎ 0.32 meV and D y = U x Ј − U y Ј Ӎ 0.033 meV. We have shown that in the strong-coupling limit, the anisotropic Hubbard model maps into the anisotropic Heisenberg model.

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