3.1. Molecular adsorption of the hydrogen
For evaluation of the adsorption of hydrogen molecules, molecular and atomic adsorption energies of this molecule have been calculated by the DFT model. In the first step, the molecular adsorption of hydrogen was considered. Figure 2 shows the adsorbed hydrogen molecules at 0.25 ML using a p (2 ×2) unit cell for on-top, hollow, and bridge positions on the FCC (100) surface of platinum. Table 1 listed the adsorption energies of the hydrogen molecule (Eads), the distance between the hydrogen atoms in the adsorbed hydrogen molecule on the surface (dH2), the difference between the lengths of the bonds in the hydrogen molecule in the gas phase, and the adsorbed phase (∆dH2) and the distance between the hydrogen molecule and surface of platinum (ZH2) on the (100) and (111) surfaces at the 0.25 ML coverage in three different positions.
Table 1
Adsorption of hydrogen molecule on FCC (100) and FCC (111) of Pt for 0.25 ML.
FCC surface
|
Position
|
Eads
(kJ.mol− 1)
|
dH2a (Å)
|
ΔdH2b (Å)
|
ZH2c (Å)
|
(100)
|
On top
|
-22.2
|
0.752
|
0.010
|
2.533
|
Bridge
|
-25.3
|
0.755
|
0.015
|
2.531
|
Hollow
|
-28.7
|
0.757
|
0.017
|
2.530
|
(111)
|
On top
|
-12.7
|
0.747
|
0.005
|
2.536
|
Bridge
|
-15.2
|
0.749
|
0.007
|
2.534
|
Hollow
|
-19.4
|
0.751
|
0.009
|
2.532
|
a The distance between the hydrogen atoms in the molecule adsorbed on the surface. |
b The difference in the bond length in the adsorbed molecule relative to the gaseous state. |
c The distance between the hydrogen molecule and the surface. |
<<Fig. 2>>
Table 1 shows that the adsorption energies of the hydrogen molecule in the on-top, bridge and hollow positions on the surface of FCC(100) of the Pt are equal to -22.2 kJ.mol− 1, -25.3 kJ.mol− 1, and − 28.7 kJ.mol− 1, respectively. Also, the adsorption energies of the hydrogen molecule in the on-top, bridge and hollow positions on the surface of FCC (111) of the Pt are equal to -12.7 kJ.mol− 1, -15.2 kJ.mol− 1, and − 19.4 kJ.mol− 1, respectively, which is lower than the surface of FCC(100). These results are comparable to the results reported by others [7, 8, 21]. These calculated adsorption energies are used as ε in Eq. (2) for the calculation of potential energies of molecular adsorption in this work. The higher adsorption energies for FCC (100) than FCC (111) are related to the higher surface free energy of the FCC (100), as reported in previous works [3, 21–23]. In addition, the adsorption energy for the hollow position in both the FCC surfaces is higher than in other considered positions. It should be noted that the number of coordinates in the on-top position is one, for the bridge position is two, and for the hollow position is three. Therefore, we expect that the adsorption of hydrogen molecules has higher adsorption energy in the hollow position.
<<Table 1>>
Table 1 shows that the distance between the hydrogen atoms in the molecule adsorbed on the surface (dH2 (Å)) for the on-top, bridge and hollow positions on the surface of FCC (100) surface of the Pt is equal to 0.752 Å, 0.755Å, and 0.757 Å, respectively. Also, the calculated dH2 (Å) for the on-top, bridge and hollow positions on the surface of FCC (111) surface of the Pt is equal to 0.747 Å, 0.749Å, and 0.751 Å, respectively. If these distances are compared with the distance between the hydrogen atoms in the gas phase (0.742 Å), the difference in bond length in the adsorbed molecule and the gas phase molecule (∆dH2 (Å)) for the on-top, bridge, and hollow positions on the surface of the FCC (100) of the Pt is equal to 0.010 Å, 0.015Å, and 0.017 Å, respectively. The calculated ∆dH2 results for the on-top, bridge, and hollow positions on the surface of the FCC (111) surface of the Pt are equal to 0.005 Å, 0.007Å, and 0.009 Å, respectively. Higher surface free energy of the FCC (100) causes the hydrogen atoms to be more drawn to the platinum surface, resulting in a higher distance from the adjacent atom in the hydrogen molecule.
Table 1 shows that the distance of the hydrogen molecule to the surface (ZH2 (Å)) for the on-top, bridge and hollow positions on the surface of FCC (100) surface of the Pt are equal to 2.533 Å, 2.531Å, and 2.530 Å, respectively. Also, the calculated ZH2 (Å) for the on-top, bridge and hollow positions on the surface of FCC (111) surface of the Pt is equal to 2.536 Å, 2.534 Å, and 2.532 Å, respectively, which is higher than FCC (100) surface due to the higher surface free energy of the FCC (100) than FCC (111). These calculated distances are used as rm in Eq. (2) for the calculation of potential energies of molecular adsorption in this work.
3.2. Atomic adsorption of the hydrogen
In this step, a single-layer of hydrogen atoms was located on the surface in the on-top, bridge and hollow positions of FCC (100) and (111) surfaces of the platinum crystal at 0.25 ML using a p(2 ×2) unit cell and calculated results are listed in Table 2.
Table 2
Adsorption of hydrogen atom on FCC (100) and FCC (111) of Pt for 0.25 ML.
FCC surface
|
Position
|
Eads
(kJ.mol− 1)
|
ZHa
(Å)
|
ΔHads (kJ.mol− 1)
|
ΔEads
(kJ.mol− 1)
|
ΔHadstotal (kJ.mol− 1)
|
(100)
|
On top
|
-302
|
1.86
|
-168
|
38.3
|
-152
|
Bridge
|
-351
|
1.84
|
-266
|
25.1
|
-266
|
Hollow
|
-373
|
1.81
|
-310
|
29.7
|
-309
|
(111)
|
On top
|
-265
|
1.91
|
-94
|
29.9
|
-77
|
Bridge
|
-336
|
1.88
|
-236
|
12.5
|
-239
|
Hollow
|
-349
|
1.87
|
-262
|
13.1
|
-268
|
a The distance between the hydrogen atom and the surface. |
<<Table 2>>
The adsorption energies of the hydrogen atoms (Eads) for the on-top, bridge and hollow positions on the surface of FCC (100) of the Pt are equal to -302 kJ.mol− 1, -351 kJ.mol− 1, and − 373 kJ.mol− 1, respectively. Also, the calculated atomic Eads in the on-top, bridge, and hollow positions on the surface of FCC (111) is equal to -265 kJ.mol− 1, -336 kJ.mol− 1, and − 349 kJ.mol− 1, respectively, which is lower than the surface of FCC(100). These results are consistent with the data from the previous results [9, 24, 25].
These calculated adsorption energies are used as ε in Eq. (2) for the calculation of potential energies of chemical adsorption of hydrogen atoms in this work. The calculated distance of hydrogen atoms from the surface (ZH), for the on-top, bridge, and hollow positions on the surface of FCC (100) is equal to 1.86 Å, 1.84Å, and 1.84 Å, respectively and for the on-top, bridge and hollow positions on the surface of FCC (111) is equal to 1.91 Å, 1.88 Å, and 1.87 Å, respectively, which is higher than the surface of FCC (100). These calculated distances are used as rm in Eq. (2) for the calculation of potential energies of chemical adsorption of hydrogen in this work.
The enthalpy of chemical adsorption of hydrogen (ΔHads) on the platinum surface in Table 2 is obtained by Eq. 3 [2]:
where Echem, is the energy of adsorption of hydrogen atoms on the surface and Ediss, is the dissociation energy of the hydrogen molecule (-436 kJ.mol− 1). The experimental result for ΔHads of hydrogen on platinum at 0.25 ML is less than the result in this study because, in Eq. 3, the activation energy (ΔEads) is not considered [26, 27]. Thus the actual ΔHads of hydrogen on the metallic platinum surface must be calculated by consideration of the activation energy (ΔEads) and physical adsorption energy according to Eq. 4 [3]:
The activated energy (ΔEads) can be calculated from the intersection of Lennard-Jones potential energy curves (Eq. 2) for physical and chemical adsorption. The Lennard-Jones potential energy curves for physical and chemical adsorption of hydrogen on the FCC (100) and FCC (111) surfaces for the on-top, bridge, and hollow positions are shown in Figs. 3 and 4.
<<Fig. 3>>
<<Fig. 4>>
The physical adsorption rm is the distance between the physically adsorbed hydrogen molecule to the surface (ZH2) and the chemical adsorption rm is the distance between the chemically adsorbed hydrogen atoms to the surface (ZH). The weakly adsorbed hydrogen molecule can be desorbed or dissociated into chemisorption hydrogen atoms if the physical adsorption overcomes the activation barrier energy (ΔEads). Activation barrier energy (ΔEads) is determined by the intersection of the molecular and atomic adsorption Lennard-Jone's potential energy curves [28]. The calculated activation barrier energies (ΔEads) on the FCC (100) and FCC (111) surfaces for the on-top, bridge and hollow positions are listed in Table 2. The activation barrier energy (ΔEads) of hydrogen adsorption, for the on-top, bridge, and hollow positions on the surface of FCC (100) is 38.3 kJmol− 1, 25.1 kJmol− 1and 29.7 kJmol− 1, respectively and for the on-top, bridge and hollow positions on the surface of FCC (111) are 29.9 kJmol− 1, 12.5 kJmol− 1and 13.1 kJmol− 1, respectively, which is lower than the surface of the FCC (100). The actual ΔHads of hydrogen on the metallic platinum surface which is calculated using the activation energy (ΔEads) and physical adsorption energy according to Eq. 4, for different positions of FCC(100) and FCC(111) surfaces is listed in Table 2. These data for some cases are still higher than the experimental results, due to DFT calculation errors and deference between the FCC (100), and (111) surfaces and real metallic platinum surfaces.
3.3. Hydrogen adsorption on metallic Pt: dissociation or association
The experimental studies of surface adsorption of hydrogen show two different types of hydrogen on the metallic platinum surface, including both molecular and atomic hydrogen adsorption [7, 8]. The reason for the simultaneous presence of atomic and molecular species on the surface of metal platinum is not well known, but various reasons have been reported, such as spatial constraints on the surface of metal platinum for hydrogen dissociation.
The total density of states (DOS) of the FCC (100) and FCC (111) surfaces of metallic platinum and molecular hydrogen adsorption at the on-top, bridge, and hollow positions on these surfaces are shown in Fig. 5.
<<Fig. 5>>
Figure 5 shows that the electron density of FCC (100) of metallic platinum is higher than FCC (111) surface, which corresponds to the molecular hydrogen adsorption energy results in Table 1. The interactions between the adsorbed hydrogen molecule and FCC (100) and FCC (111) surfaces are shown in Fig. 5. The DOS of hydrogen molecules shows a sharp peak which corresponds to the σ bonding state between the two hydrogen atoms [8, 23, 29]. The interaction of adsorbed molecular hydrogen electrons with the electrons of the Pt surface gives rise to bonding and anti-bonding states. Firstly, σ bonding interaction due to the overlap of filled σ orbitals on the hydrogen with the metal orbitals at -15.2 eV (Fig. 5), which leads to electron density transfer from the hydrogen molecule to the metal center [8, 23]. Secondly, the anti-bonding orbital (σ*), which is reduced the hydrogen bond strength at -13.1 eV (Fig. 5) [8].
The detail of the molecular orbital picture of H adsorbed on the FCC (111) and FCC (110) of the Pt surface is analyzed with the help of the Crystal Orbital Hamilton Population (COHP) method in Fig. 6. The COHP results enable one to localize the total energy change to the immediate vicinity of the perturbation. Since the COHP analysis is carried out on the energy scale, negative energies (COHP contributions) indicate bonding interactions and positive energies (COHP contributions) indicate antibonding interactions. Figure 6 shows that the bonding region near the H band at -15.2 eV is stabilized and the antibonding region near the H band at -13.1 eV is destabilized. As shown in Figs. 5 and 6, by increasing the interaction between the hydrogen molecule and the metal surface, the intensity of the bonding peak decreases, and the intensity of the anti-bond peak increases. Finally, if sufficient electron density is transferred from the bonding to anti-bonding orbitals, the hydrogen molecule decomposes into its atoms. As shown in Fig. 5, the intensity of the molecular hydrogen orbitals on the FCC (111) surface has increased, which indicates a higher interaction between hydrogen molecules and the metallic surface. As seen in Fig. 5, the intensity of the anti-bonding orbital (σ*) for the bridge position is higher than two other positions on the FCC (100) surface, which shows the hydrogen molecule in this position is ready to be dissociated into hydrogen atoms. In addition, Fig. 5 shows that the intensity of anti-bonding orbital (σ*) for hollow and bridge positions are higher than the on-top position on the FCC (111) surface, which indicates the hydrogen molecule in these positions are dissociated into hydrogen atoms, but the hydrogen adsorbed on the on-top position may be molecularly adsorbed. Also, the intensity of the anti-bonding orbital for the bridge position is higher than two other positions on the FCC (100) surface, which shows that the hydrogen molecule in this position is ready to be dissociated into hydrogen atoms. In addition, the intensity of the anti-bonding orbital for hollow and bridge positions are higher than the on-top position on FCC (111) surface, which shows the hydrogen molecule in these positions are dissociated into hydrogen atoms.
As shown in Figs. 3 and 4 and Table 2, the activation barrier energy (ΔEads) for hydrogen adsorption on the metallic platinum surface depends on the position and FCC surface. The results show that the comparison between the activation barrier energy (ΔEads) calculated from Lennard-Jones potential curves, and molecular adsorption energy determines whether the hydrogen molecule is dissociated on the surface. If the activation barrier energy (ΔEads) is higher than molecular adsorption energy, the probability that the hydrogen molecule will dissociate on the surface is very low. If the activation barrier energy (ΔEads) is high, the probability that the hydrogen molecule will dissociate on the surface is very low. The results show that the value of the activation barrier energy (ΔEads) for hydrogen adsorption on the on-top, bridge and hollow positions on the surface of FCC (100) is 38.3 kJmol− 1, 25.1 kJmol− 1and 29.7 kJmol− 1, respectively. If these values are compared with the physical adsorption heat data for these situations (Table 1), it is clear that only in the bridge position, the physical adsorption heat is higher than the activation barrier energy. Thus for this position, the physical adsorption provides the energy needed to overcome this activation barrier energy (ΔEads). Therefore, we expected that the hydrogen molecule dissociated on the bridge position on the FCC (100) surface of platinum but for the other two positions, the hydrogen adsorbed in molecular form. In addition, the activation barrier energy of hydrogen adsorption, for the on-top, bridge, and hollow positions on the surface of FCC (111) is 29.9 kJmol− 1, 12.5 kJmol− 1, and 13.1 kJmol− 1, respectively. If these activation barrier energies are compared with the released energy due to physical adsorption for these positions on the FCC (111) of platinum surface, it is clear that only in the on-top position, the physical adsorption heat is lower than the activation barrier energy. Therefore, we expect the hydrogen molecule to be dissociated on the other two positions for FCC (111) surface. These results are fully consistent with the DOS results and could be a justification for the physical and chemical adsorption on the platinum surface.