Beyond the H2/CO2 upper bound: one-step crystallization and separation of nano-sized ZIF-11 by centrifugation and its application in mixed matrix membranes

The synthesis of nano-sized ZIF-11 with an average size of 36 ± 6 nm is reported. This material has been named nano-zeolitic imidazolate framework-11 (nZIF-11). It has the same chemical composition and thermal stability and analogous H2 and CO2 adsorption properties to the conventional microcrystalline ZIF-11 (i.e. 1.9 ± 0.9 μm). nZIF-11 has been obtained following the centrifugation route, typically used for solid separation, as a fast new technique (pioneering for MOFs) for obtaining nanomaterials where the temperature, time and rotation speed can easily be controlled. Compared to the traditional synthesis consisting of stirring + separation, the reaction time was lowered from several hours to a few minutes when using this centrifugation synthesis technique. Employing the same reaction time (2, 5 or 10 min), micro-sized ZIF-11 was obtained using the traditional synthesis while nano-scale ZIF-11 was achieved only by using centrifugation synthesis. The small particle size obtained for nZIF-11 allowed the use of the wet MOF sample as a colloidal suspension stable in chloroform. This helped to prepare mixed matrix membranes (MMMs) by direct addition of the membrane polymer (polyimide Matrimid®) to the colloidal suspension, avoiding particle agglomeration resulting from drying. The MMMs were tested for H2/CO2 separation, improving the pure polymer membrane performance, with permeation values of 95.9 Barrer of H2 and a H2/CO2 separation selectivity of 4.4 at 35 °C. When measured at 200 °C, these values increased to 535 Barrer and 9.1.

Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.