3.2 Results and Discussion
3.2.1 Experimental Results
The chemical potential of hydrogen gas was calculated from the partition function for the hy- drogen molecule obtained from GAMESS, through the relationship:
µgas(T, P) =−kTln (qtot(T, P◦)) + ln P
P◦
(3.1)
where k is Boltzmann’s constant, T is the temperature in Kelvin,P is the pressure of the system, and P◦ is the standard pressure of the system, taken to be 1 atm. Rotational degeneracy for the hydrogen molecule is included in the calculated partition function from the GAMESS software.
The corrected energy,E, for each fragment was obtained as the sum of the ground-state energy, 0, and the thermal correction to the energy obtained from vibrational analysis, corr(T), which contains contributions from translational, vibrational, and rotational motions of the molecule. The binding energy of the hydrogen molecule to the organometallic site was calculated from the corrected energies as:
∆E(T) =EM−H2(T)−EH2(T)−EM(T) (3.2)
where the subscripts M-H2, H2, and M represent the organometallic adduct fragment, hydrogen gas, and the bare organometallic fragment, respectively.
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
0 100 200 300 400 500 600 700
x, molecules H2 per manganese
Pressure, torr
T=313K T=333K T=343K T=353K T=363K T=373K
Figure 3.2: Absorption isotherms for hydrogen gas onto [Mn(CO)dppe2][BArF24]. Solid lines are Langmuir isotherm fits to the data.
dihydrogen materials.125
Initial rate kinetics measurements were performed at 298K and 318K to determine the dependence of the absorption rate on pressure and quantity absorbed. The results for 318K appear in 3.3. The rate of change of the pressure was determined to be linearly dependent on the pressure and the remaining capacity, such that:
∂P
∂t =−kP(1−θ)
where θ is the fraction of the reversible absorption capacity absorbed, and k is the rate constant.
Rate constants for 298K and 318K were 0.3090 s−1 and 0.3116 s−1, respectively. The Arrhenius activation energy obtained from these values is Ea = 330 J/mol, indicating a very low activation barrier to absorption.
The isotherms presented in 3.2 do not demonstrate a maximum like with physisorptive materials,
-1.00 -0.80 -0.60 -0.40 -0.20 0.00
0.00 0.50 1.00 1.50 2.00 2.50 3.00
dP/dt, psia s-1
P*(1-θ), psia
Figure 3.3: Initial rate measurements for hydrogen absorption onto [Mn(CO)dppe2][BArF24] at 318K. Absorption kinetics were found to be linearly dependent on pressure and capacity. Linear regression gives a rate constant of k = 0.3661, R2 = 0.9545.
but rather achieve a stable plateau at 0.35 H2molecules per manganese. This behavior is particularly evident in the isotherm at 313K. The existence of the stable plateau in the experimental isotherms is consistent with total absorption144 and indicates that hydrogen absorbs into the bulk material instead of adsorbing onto the surface. However, the absorption rate is comparable to physisorption materials, despite no additional processing used to increase the surface area of the solid or the exposure of manganese centers to the gas. This rapid absorption is likely due to the loose packing of the bulky organic ligands in the solid, which allows the small hydrogen molecule to diffuse rapidly through the structure.100
The rapid kinetics and high reversibility observed in the absorption process suggest a site-binding mechanism for the binding interaction of H2 with solid [Mn(CO)dppe2][BArF24] that is similar to physisorptive materials. In organometallic dihydrogen complexes, the binding orientation of the ligands is considered fixed by the atomic orbitals of the metal center, producing distinct binding sites
for each ligand at the metal center. The isolation of the metal centers by the organic constituents ensures both non-interacting sites and chemical uniformity, suggesting the binding interaction at each site is isoenergetic. With this interpretation of the coordination site, we investigated the binding behavior by fitting the experimental isotherms to the Langmuir model. The Langmuir isotherm model assumes an established equilibrium between a mobile phase of guest molecules and fixed sites capable of binding a single molecule, with homogeneous, non-interacting, and isoenergetic interactions, representing an appropriate description of the organometallic coordination site if the behavior is similar to other site-binding mechanisms.
For the assumed ideal gas reaction:
[M(CO)dppe2][BArF24] +H2−−−)−−−*[M(η2-H2)(CO)dppe2][BArF24] (3.3)
in which a single hydrogen molecule binds to the open coordination site on the metal, represented byM, the Langmuir isotherm is given by:
n
N = αP
1 +αP , α= Keq
RT (3.4)
wherenis the number of bound hydrogen molecules,N is the total number of active binding sites,P is the pressure of the gas in atmospheres,Ris the universal gas constant,Tis the system temperature in Kelvin, and Keqis the equilibrium constant for Equation 3.3.
Langmuir fits to the experimental data are shown as the solid lines in 3.2. The fit for 313K was obtained by varying both the total number of active binding sites,N, andαas fitting parameters.
A value of 0.344 H2 per manganese center was found forN at 313K, and was held constant for the fits at all other temperatures. The values for Keq derived from the fitted values forαand the R2 values of the fits appear in 3.1. As can be seen from the figure and the R2 values, the Langmuir model very accurately describes hydrogen absorption by the manganese complex, indicating that the open coordination sites within [Mn(CO)dppe2][BArF24] interact with hydrogen gas through a site-binding mechanism.
The standard enthalpy and entropy of the absorption interaction are readily obtained from the values of the equilibrium constant in Equation 3.4 through the general form of the van’t Hoff equation:
lnKeq=−∆H◦
RT +∆S◦
R (3.5)
where ∆S◦and ∆H◦are the entropy and enthalpy of the absorption reaction, as defined by Equation 3.3, at standard conditions of one atmosphere pressure and 298K. A van’t Hoff plot of the equilibrium constants from the Langmuir fits appears in 3.4. Linear regression gives values of ∆H◦ = -52.2 kJ/mol and ∆S◦ = -99.6 J/mol-K for hydrogen absorption over [Mn(CO)dppe2][BArF24]. This enthalpy is similar to experimental values found by Gonzalez and Hoff95 for hydrogen binding to the group 6 complexes M(CO)3(PCy3)2 (M = Cr, Mo, W) by solution calorimetry, and represents an interaction of comparable strength to chemisorption seen in the formation of metal hydrides.
In addition, a significant increase in the absorption entropy from the standard145 -131 J/mol-K typical for hydrogen storage materials is observed. The higher enthalpy and entropy values allow [Mn(CO)dppe2][BArF24] to bind hydrogen effectively near room temperature while exhibiting the rapid absorption kinetics and long cycle life characteristic of physisorption materials, a combination of properties that are highly favorable for hydrogen storage applications.
The kinetic absorption behavior is consistent with observations made by Gonzalez, et al.123 that the kinetics of absorption and dissociation of H2 with W(CO)3(PCy3)2 in solution were several times faster than oxidative (dissociative) addition, which also supports the site-binding model. The Table 3.1: Equilibrium constants and R2 values from experimental Langmuir fits and simulated Langmuir isotherms for H2 absorption onto [Mn(CO)dppe2]+
Temperature Keq,exp, atm−1 Keq,sim, atm−1 R2exp R2sim
313K 3241.74 3117.22 0.9702 0.9692
333K 1013.12 926.34 0.9882 0.9902
343K 581.82 528.31 0.9919 0.9892
353K 371.65 309.63 0.9937 0.9766
363K 214.78 186.08 0.9962 0.9800
373K 124.19 114.37 0.9914 0.9808
4.00 5.00 6.00 7.00 8.00 9.00
2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30
ln Keq
1000/T, K-1
Figure 3.4: Van’t Hoff plot of the equilibrium constants derived from the Langmuir model. Linear regression gives lnKeq= 6280.6/T - 11.986, R2= 0.9985, giving thermodynamic properties ∆H◦= -52.2 kJ/mol and ∆S◦ = -99.6 J/mol-K.
solution results also imply that the site-binding mechanism is not limited to the solid state. Quali- tative assessments of affinities based on competitive ligand binding would thus require control of the local hydrogen concentration, particularly in solution state measurements where the concentration of dissolved hydrogen depends on the solvent used. This additional aspect needs to be considered before using such assessments to disqualify materials as potential candidates.