# Highly Porous Organic Polymers for Hydrogen Fuel Storage
## 2 Theoretical Considerations
Unfortunately, for most physical adsorbents, the heat of adsorption is much less that this value. For instance, for activated carbons or hydrocarbons, the adsorption enthalpy is only about -5.6 kJ/mol [24], so that adsorption of hydrogen on carbon-related materials is too weak for storing large amount of hydrogen at ambient temperature. Similar values and conclusions have also been applied to other porous materials such as zeolites [25] and metal organic frameworks (MOFs) [26]. On the other hand, if \(\Delta H^{\circ}=-5.6\) kJ/mol for hydrocarbons, including polymers, is used in Equation (6), the calculated optimal temperature for highest delivery \(T_{opt}=\) 114.4 K, which is much lower than the ambient temperature needed to meet the DOE specifications. This analysis explains why most highly porous materials, including polymers, can adsorb a relatively large amount of H\({}_{2}\) at liquid nitrogen temperature (77K), some of them up to 8.0 wt %, but the capacity drops to \(<\)1.0 wt % under ambient conditions. Therefore, to increase H\({}_{2}\) adsorption ability at room temperature via physisorption, we must increase the adsorption enthalpy \(\Delta H^{\circ}\). To achieve this, several methods from the theoretical perspective have been proposed. A first approach is to create as many ultra micropores (\(<\)1 nm) at the atomic scale as possible. Theoretical simulations show that at low pressure and high temperature (desired conditions of the DOE), graphite with an inter-layer distance of 6 A (0.6 nm) has the highest adsorption capability, of above 10 kJ/mol, achieved through the overlap of adsorption potentials from the opposite walls [27]. In addition to such 1D slit pores, 2D cylindrical, and 3D spherical pores exhibit the same principle: cylindrical pores with \(r\approx\) 2.0 A and spherical pores with \(r\approx\) 3.8 A have maximum adsorption abilities [28; 29]. Furthermore, although the free H\({}_{2}\) molecules at room temperature behavior classically, when localized in ultra micropores, H\({}_{2}\) molecules manifest quantum confinement behavior via the quantum sieving effect [30; 31], which persists up to 300 K [26]. The quantum sieving effect versus the pore size is illustrated in Figure 1, in which the optimal pore diameter, on the order of the de Broglie wavelength for H\({}_{2}\), corresponds to the point in which both sides of the pore interact with the absorbed molecule (corresponding to Figure 1a, blue band \(\lambda_{\rm H2}\); Figure 1b, region A; and point 2 on Figure 1c) [32]. The theoretical predictions for enhancement of H\({}_{2}\) adsorption due to ultra micropores have been demonstrated by the experiment. For example, [PERSON] et al., employed in-situ small-angle neutron scattering to study H\({}_{2}\) adsorption in activated carbons with different pore sizes, and concluded that the smaller the pore size, the larger the absorbed H\({}_{2}\) density, as shown in Figure 2[33]. More recently, [PERSON] and coworkers reported that hard carbon materials with the largest micropore (<1.05 nm) volume showed the greatest H\({}_{2}\) uptake at ambient temperature and high pressure[34]. It is of particular interest to find from the figure that the density of adsorbed H\({}_{2}\) inside pores with 9 A is almost same as the liquid H\({}_{2}\) density at 298 K and 200 bar. A second approach to improve adsorption enthalpy is to introduce charge sites in porous materials, creating charge-induced interaction between H\({}_{2}\) and adsorbent[35]. At the molecular level, H\({}_{2}\) molecules interact with each other or with other non-polar molecules such as hydrocarbon polymers via quadropole-quadropole interaction due to the London dispersion effect and generate a very weak van der Waals attractive force.