# Highly Porous Organic Polymers for Hydrogen Fuel Storage
## 2 Theoretical Considerations
However, when charged sites are present, additional charge-induced forces, such as dipole-induced dipole interactions, are generated, as shown in the schematic diagram Figure 3. The dependence of interactions with the distance of H\({}_{2}\) from a host site, as well as the magnitude of interactions is shown in Table 2. The sum of the interactions determines the overall adsorption enthalpy \(\Delta H^{\circ}\) of H\({}_{2}\) molecules. Figure 1: Theoretical simulation of adsorption potential for H\({}_{2}\) ultra micropores with a few Å in radius: (**a**) schematic diagram of quantum sieving effect, (**b**) behavior of interaction potential, (**c**) adsorption potential versus pore size (Reproduced with permission from Ref. [32]. Copyright © 2016 John Wiley and Sons). Figure 2: H\({}_{2}\) adsorption in pores with different sizes studied via in-situ neutron scattering (Reproduced with permission from [33]. Copyright © 2011 ACS publications). A third approach to increase absorption enthalpy is to create orbital interactions between an H\({}_{2}\) molecule and \(d\)-orbitals of a transition metal intercalated in the highly porous materials [36]. The typical adsorption enthalpy from orbital interactions is 20-160 kJ/mol and therefore exceeds the optimal value for the maximum delivery of H\({}_{2}\). This adsorption of H\({}_{2}\) is on the order of a chemical adsorption mechanism. Such metals are typically intercalated in covalent organic frameworks (COFs), which are technically classified as molecular crystals rather than polymeric materials, and hence are beyond the scope of this review. Although the adsorption enthalpy is the key parameter needed to retain H\({}_{2}\) molecules at room temperature, the internal surface area of micropores is another essential parameter in storing needed quantities of H\({}_{2}\). Internal surface area is paramount, as the critical temperature of H\({}_{2}\) (22 K) is well below the most practical cryogenic temperature afforded by liquid nitrogen temperature (77 K). Consequently, even at liquid nitrogen temperature, only a single layer of H\({}_{2}\) molecules is adsorbed on the internal surface of micropores in highly porous materials, including polymers. This is why the Langmuir model, which is based on the single layer adsorption, can be used to obtain the optimal adsorption enthalpy \(\Delta H^{\circ}\). The presumption of the Langmuir model is that adsorption ability is proportional to the number of active adsorbing sites, which are in turn proportional to the total surface area of the internal wall of micropores. Therefore, most published reports for H\({}_{2}\) storage polymers optimize high internal surface area through synthetic strategies and/or physical methods. The corresponding H\({}_{2}\) adsorption ability is measured at liquid nitrogen temperature (77 K), not ambient temperatures needed for practical use. In the following section, we review different classes of highly porous polymers with large internal surface areas, achieved by employing different synthetic methods and by adding different functional groups.