There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Crystalline metal-organic frameworks (MOFs) are formed by reticular synthesis, which creates strong bonds between inorganic and organic units. Careful selection of MOF constituents can yield crystals of ultrahigh porosity and high thermal and chemical stability. These characteristics allow the interior of MOFs to be chemically altered for use in gas separation, gas storage, and catalysis, among other applications. The precision commonly exercised in their chemical modification and the ability to expand their metrics without changing the underlying topology have not been achieved with other solids. MOFs whose chemical composition and shape of building units can be multiply varied within a particular structure already exist and may lead to materials that offer a synergistic combination of properties.

The Chemistry and Applications of Metal-Organic Frameworks

Adsorptive separation is very important in industry. Generally, the process uses porous solid materials such as zeolites, activated carbons, or silica gels as adsorbents. With an ever increasing need for a more efficient, energy-saving, and environmentally benign procedure for gas separation, adsorbents with tailored structures and tunable surface properties must be found. Metal–organic frameworks (MOFs), constructed by metal-containing nodes connected by organic bridges, are such a new type of porous materials. They are promising candidates as adsorbents for gas separations due to their large surface areas, adjustable pore sizes and controllable properties, as well as acceptable thermal stability. This critical review starts with a brief introduction to gas separation and purification based on selective adsorption, followed by a review of gas selective adsorption in rigid and flexible MOFs. Based on possible mechanisms, selective adsorptions observed in MOFs are classified, and primary relationships between adsorption properties and framework features are analyzed. As a specific example of tailor-made MOFs, mesh-adjustable molecular sieves are emphasized and the underlying working mechanism elucidated. In addition to the experimental aspect, theoretical investigations from adsorption equilibrium to diffusion dynamics via molecular simulations are also briefly reviewed. Furthermore, gas separations in MOFs, including the molecular sieving effect, kinetic separation, the quantum sieving effect for H2/D2 separation, and MOF-based membranes are also summarized (227 references).

Selective gas adsorption and separation in metal–organic frameworks

Metal–Organic Frameworks for Separations

Kenji Sumida, David L. Rogow, Jarad A. Mason, Thomas M. McDonald, Eric D. Bloch, Zoey R. Herm, Tae-Hyun Bae, Jeffrey R. Long

Carbon Dioxide Capture in Metal–Organic Frameworks

https://arxiv.org/pdf/cond-mat/0610139.pdf

Pressure–temperature phase diagram of the heavy-electron superconductor URu2Si2

We study the phenomenological implications of the modular symmetry $\Gamma(3) \simeq A_4$ of lepton flavors facing recent experimental data of neutrino oscillations. The mass matrices of neutrinos and charged leptons are essentially given by fixing the expectation value of modulus $\tau$, which is the only source of modular invariance breaking. We introduce no flavons in contrast with the conventional flavor models with $A_4$ symmetry. We classify our neutrino models along with the type I seesaw model, the Weinberg operator model and the Dirac neutrino model. In the normal hierarchy of neutrino masses, the seesaw model is available by taking account of recent experimental data of neutrino oscillations and the cosmological bound of sum of neutrino masses. The predicted $\sin^2\theta_{23}$ is restricted to be larger than $0.54$ and $\delta_{CP}=\pm (50^{\circ}\mbox{--}180^{\circ})$. Since the correlation of $\sin^2\theta_{23}$ and $\delta_{CP}$ is sharp, the prediction is testable in the future. It is remarkable that the effective mass $m_{ee}$ of the neutrinoless double beta decay is around $22$\,meV while the sum of neutrino masses is predicted to be $145$\,meV. On the other hand, for the inverted hierarchy of neutrino masses, only the Dirac neutrino model is consistent with the experimental data.

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Modular $A_4$ invariance and neutrino mixing

An indenter-type high-pressure cell has been developed for electric and magnetic measurements in low-temperature and high-magnetic-field environments. The maximum pressure achieved at low temperatures is more than 4.5GPa, which is higher than that of a conventional piston-cylinder cell. The typical sample space at maximum pressure is 1.6mm in diameter and approximately 0.7mm in depth, and magnetic measurements such as ac-susceptibility and nuclear magnetic resonance can be performed using a miniature coil. All the components of the indenter cell are made of nonmagnetic materials that have enough thermal conductivity for low-temperature experiments using a He3∕He4 dilution refrigerator. Another indenter-type cell designed for a commercial superconducting quantum interference device magnetometer is also reported.

Nonmagnetic indenter-type high-pressure cell for magnetic measurements

Metastable sorption state of a metal-organic porous material determined by in situ synchrotron powder diffraction.

We study a flavor model with $A_4$ symmetry which originates from $S_4$ modular group. In $S_4$ symmetry, $Z_2$ subgroup can be anomalous, and then $S_4$ can be violated to $A_4$. Starting with a $S_4$ symmetric Lagrangian at the tree level, the Lagrangian at the quantum level has only $A_4$ symmetry when $Z_2$ in $S_4$ is anomalous. We obtain modular forms of two singlets and a triplet representations of $A_4$ by decomposing $S_4$ modular forms into $A_4$ representations. We propose a new $A_4$ flavor model of leptons by using those $A_4$ modular forms. We succeed in constructing a viable neutrino mass matrix through the Weinberg operator for both normal hierarchy (NH) and inverted hierarchy (IH) of neutrino masses. Our predictions of the CP violating Dirac phase $\delta_{CP}$ and the mixing $\sin^2\theta_{23}$ depend on the sum of neutrino masses for NH.

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Tatsuo C. Kobayashi

Papers

Pressure–temperature phase diagram of the heavy-electron superconductor URu2Si2

Modular $A_4$ invariance and neutrino mixing

Nonmagnetic indenter-type high-pressure cell for magnetic measurements

Metastable sorption state of a metal-organic porous material determined by in situ synchrotron powder diffraction.

New $A_4$ lepton flavor model from $S_4$ modular symmetry