Ionic bonds heat capacity

The sp-valent metals such as sodium, magnesium and aluminium constitute the simplest form of condensed matter. They are archetypal of the textbook metallic bond in which the outer shell of electrons form a gas of free particles that are only very weakly perturbed by the underlying ionic lattice. The classical free-electron gas model of Drude accounted very well for the electrical and thermal conductivities of metals, linking their ratio in the very simple form of the Wiedemann-Franz law. However, we shall now see that a proper quantum mechanical treatment is required in order to explain not only the binding properties of a free-electron gas at zero temperature but also the observed linear temperature dependence of its heat capacity. According to classical mechanics the heat capacity should be temperature-independent, taking the constant value of kB per free particle. 

From the heat capacities of EiPis and KP15, it was derived that the soft vibrational modes at low temperatme are only affected by interaction between the metal cation and the six nearest neighbors. Therefore, the covalently bonded Pi5 tubes and the ionic interaction between the cation and the polyanion produce two distinctly separate sets of vibrational excitations (see below). At low temperatures, interchain vibrations occur, partially transmitted through the cations. At higher temperatures, intrachain vibrations, propagated through the covalently bonded tubes, are the dominant vibrational modes. 

Instead of the surface area or the free volume, the authors found that MOFs such as Mg/DOBDC and Ni/DOBDC with a high density of open metal sites are promising candidates for CO capture from flue gas in, which CO partial pressure is about 0.1 atm. Caskey et al. [43] found that metal substitution in the DOBDC series can significantly impact their CO capacities in the low-pressure region. The metal substitution effect m be caused by the differences in the ionic character of the metal-oxygen bonds in the DOBDC-series MOFs. Liu et al. found that Ni/DOBDC has a higher CO capacity than NaX and 5A zeolites at 0.1 atm, and 25° C. In addition, water does not affect CO adsorption in the Ni/DOBDC as much as in NaX and 5A zeolites, and it is much easier to remove water from Ni/DOBDC by heat regeneration [44]. Therefore, the Ni/DOBDC can adsorb more CO than traditional zeolites under the same moist conditions. 

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