7.2 Dependence of the H 2 Binding Energies Strength on the Transition Metal and Organic
7.2.1 Introduction
A current major obstacle to molecular hydrogen (H2) as an alternative source of energy is the difficulty of storage at opera tional temperatures. The U.S. Department of Energy (DOE) has set the 2015 targets of 5.5 wt % and 40 g/L at 233-358 K and 3-100 bar (and ultimate 7.5 wt % and 70 g/L).[117, 118, 134] Among the most promising routes to obtain this goal is physisorption because is fully reversible and has fast kinetics at desired condi tions. However, current materials have been able to attain<10 kJ/mol at ambient conditions and this decays as the sorption sites get saturated.[121, 135] Thus, sorption sites that are able to ac commodate more H2molecules and have a stronger affinity for H2are needed. We and others have found that this necessary to keep a constant heat of adsorption (Qst) as the loading increase and to be efficient for the loading/unloading cycle, which are requirements for materials to attain the DOE targets.[135, 58] There have been several theoretical studies that try to put stronger interactions between H2 and the material host, however they still have to be synthesized.[120, 115, 136, 137]
We have speculated that using transition metal sites in the structures of porous materials can reach this goal.[138, 139] Our trials have been focusing in using precious late transition metals (TM) such as Pd. In this paper we show that it is not necessary to use such precious and heavy TM to obtain good binding energies with H2. We report the binding energy of 4 H2 interacting with 60 compounds (6 linkers with 12 different transition metals). We found that early TM (Sc to Cu) can attain the same strength of interactions as precious late transition metals (Pd and Pt). We also report that the square planar coordination geometry is not necessary to obtain many strong interactions because the tetrahedral geometry gives similar affinity. This is maybe because we are dealing with mainly long range interactions and the local geometrical environments is not determinant as in the covalent bond formation. We focus on the ligands (building blocks) used for synthesizing porous materials since it is easier to calculate the binding energy to these smaller species and at the fundamental level, there is not a significant difference with the extended structure.
7.2.1.1 Types of Interactions for H2
There are several interactions that H2 can have with other atoms, molecules or solids, which are dispersion, electrostatics and orbital interactions.[140, 2] The nature and magnitude of these inter- actions are shown in Table 7.5 and Figure 7.11. The existence of each of these interactions can allow
us to tune the ∆H◦bind to obtain the optimal value.
Table 7.5: Different interactions H2 can have with other entities that can be used to tune the ∆H◦ads
Interaction Energy dependence Typical values (kJ/mol)
Charge - quadropole 1/r3 ∼3.5 [140]
Charge - induced dipolea 1/r4 ∼6.8 [140]
Dipole - induced dipolea 1/r5 ∼0.6 [140, 141]
Dispersion 1/r6 ∼5-6 [58]
Orbital interaction <vdW radii ∼20-160 [2, 142, 143, 144]
aIf a strong external field is present; a dipole can be induced in H2if a strong external field is present.
H
H δ−
δ−
δ+
δ+
H H δ−
δ+
O H
H δ−
H H δ+
δ−
δ+ δ+
δ+
δ−
δ+
δ+δ−
δ−
H
H δ−
δ−
δ+
δ+
H
H δ−
δ−
δ+
δ+ δ+
δ−
dZ2
dxz
[M] [M]---H2 H2
M L L
L L L
σ σ∗
H H -11.7 eV
+2 eV Charge -
Quadropole
Non covalent interaction Orbital interaction
H-H bond distance Charge -
Induce dipole*
Dipole - Induce dipole*
Dispersion
H
H M
0.75 Å
H H 0.8-1.0 Å
M H
H 1.0-1.3 Å
M H
H 1.3-1.6 Å
M H
H
>1.6 Å True H2
complex
Elongated H2 complex
compressed dihydride
dihydride
reversibility of H2 binding M
+
+
Figure 7.11: Interactions H2can have; noncovalent interactions and orbital interactions. The molec- ular orbital diagram and the H-H bond distances (from crystallography and NMR) are adapted from reference [2]. (*) A strong external field is needed to create a dipole in H2.
Non covalent interactions (electrostatic and dispersion) have a typical ∆H◦ads value of less than 10 kJ/mol while orbital interac tion have values larger than 20 kJ/mol.
The first non-zero multipole moment for H2is the quadrupole moment due to their non-spherical nature and this interaction is responsible for most interactions in bulk H2. However if other species interact with H2, other electrostatic interactions can appear such as charge - quadrupole. If a strong external field is applied, then a dipole can be induced in H2 and generate other interactions such as charge - induced dipole and dipole - induced dipole.[140, 141] The charge - H2 interactions are difficult to appear because we need unscreened coulombic interactions which are rarely present in
many systems, although some examples have been discovered in the so called open metal sites.[145]
The other ubiquitous non covalent interaction is dispersion, and this is responsible for the interaction of H2 with carbonaceous materials such a graphite and carbon nanotubes.[58]
Orbital interactions require either a very high pressure of 490 GPa[146] or d-orbitals of transitions metals (TM) to appear.[2, 142, 143, 144] The use of the d-orbital of TM is the most obvious choice because of the constraint of using up to 100 bar of pressure. The orbital interactions have different magnitude depending on the TM and the ligands used, and ultimately affect the H-H bond. The more the H-H bond elongates the higher the interaction and the less reversible the binding is (Figure 7.11 and Table 7.5).
We need all these different kind of interaction in order to obtain strong interactions with H2 but without modifying the H-H bond length significantly in order to obtain reversibility. For example combinations of charge - quadrupole, dispersion as well as orbital interactions can give us the in- teraction ion - H2 and ligands - H2 in a range 0.4-35 kJ/mol by changing the charge on the ligand or the ligand itself.[140] Thus ligands that bind to transition metals can have different binding sites and by designing the counteranion, we can obtain different kinds of strong enough interactions with H2.
7.2.1.2 Langmuir Theory and the Optimal Enthalpy
In this paper we consider the single layer approximation of the Langmuir model to get an estimation of the optimal en thalpy needed for maximum delivery. Previous work done by Bathia et al.,[58] has shown that this approximation is a good estimation for the H2 sorption on porous materials such as graphite and carbon nanotubes. This is an acceptable first order approximation because H2is a small molecule and the H2- H2 interactions are not very important.
With the Langmuir theory we can determine the uptake (n) and we can determined the necessary properties to get the delivery amount (D):[147]
D(K, Pmax, Pmin= KPmaxnm
1 +KPmax − KPminnm
1 +KPmin (7.2)
where K is the equilibrium constant from the Langmuir theory at certain temperature,Pmaxand Pminare the maximum and minimum pressure of the delivery andnmis the adsorption capacity of the material. The maximum delivery amount can be found by finding the optimal K. Thus from
∂D/∂K = 0, the optimal value isKopt=1/(√
PmaxPmin).[58, 147, 148]
Therefore, from Kopt=(e∆S◦/R)(e∆H◦/RT)/P0, where ∆S0 is the entropy change, ∆H0 is the enthalpy change and the reference pressure,P0 = 1 bar, we obtain the optimal binding value;
∆H◦opt =T∆S◦+RT 2 ln
PmaxPmin
P02
(7.3)
Bathia et al. reported that for various porous adsorbents a typical value for the H2 adsorption is ∆S0≈-8R.[58] Assuming this ∆S0 value for the temperatures range of the DOE targets, we can estimate the optimal values for ∆H◦opt for a homogenous material (same type of binding site).
In Table 7.6, we show the optimal values calculated for the 2015 DOE goals. We are going to focus on the Fuel Cell (FC) delivery condition for 3/100 atm delivery limits but the same arguments can be applied to the Internal Combustion Engine (ICE) case. At 233K the optimal enthalpy change (∆H◦opt) is equal to -10.0 kJ/mol. On the other hand at 358K the ∆H◦opt = -15.3 kJ/mol. A second order approximation is undergoing.
Table 7.6: DOE targets for H2 storage system for light-duty vehicle and the estimation of the optimal ∆H◦ads under these conditions using the Langmuir model
Storage parameter Units 2015
System gravimetric capacity kg(H2)/kg(System) 0.055
System volumetric capacity kg/m3 40
Min/Max delivery temperature K 233/358
Min/Max delivery pressure FCa atm 3/100
Min/Max optimal ∆Hopt◦ (This work) FCa kJ/mol -10.0/-15.3
aFC = fuel cell
In order to show how ∆H◦ affects the delivery amount we plot the different uptakes at 298K in Figure 7.12. We can see how the optimal value strength of 12.8 kJ/mol at 298K offers the best enthalpy of adsorption for the delivery amount for the range from 3 to 100 bar. The maximum delivery value calculated with these assumptions is of 0.709 (Table 7.7).
Figure 7.12: We show the normalized uptake (n/nm = uptake/sorption capacity) for three different temperature conditions (left: 233K, center: 298K, right: 358K) using the Langmuir model and ∆S◦
= -8R. We can see that the magnitude ∆Hads have a strong effect on the amount that can be delivered between 3 and 100 bar, i.e., a small value (3 kJ/mol) gives poor uptake and poor delivery, a large value (25 kJ/mol) gives high uptake but poor delivery. The ideal ∆Hads gives both a high uptake and high delivery.
Therefore, using these premises we embark ourselves in finding new ligands that can have a binding energy between 10 and 15.3 kJ/mol in order to get the optimal delivery amount for the DOE targets (233/358 K) by exploiting all the different types of interactions that the H2 can have.
Table 7.7: Delivery amount obtained using ideals
∆H◦ads and different temperatures
Temperature(/K) ∆H◦opt Deliverya (/kJ mol-1) (3 to 100 bar)
233 -10 0.709
298 -12.8 0.709
358 -15.3 0.709
aWe have normalized the Delivery amount us- ingD(K, Pmax, Pmin/nm=1+KPKPmaxmax−1+KPKPminmin, where the maximum delivery is close to 1.