Energetics and Kinetics of Hydrogen Electrosorption on a Graphene-Covered Pt(111) Electrode

The Angstrom-scale space between graphene and its substrate provides an attractive playground for scientific exploration and can lead to breakthrough applications. Here, we report the energetics and kinetics of hydrogen electrosorption on a graphene-covered Pt(111) electrode using electrochemical experiments, in situ spectroscopy, and density functional theory calculations. The graphene overlayer influences the hydrogen adsorption on Pt(111) by shielding the ions from the interface and weakening the Pt–H bond energy. Analysis of the proton permeation resistance with controlled graphene defect density proves that the domain boundary defects and point defects are the pathways for proton permeation in the graphene layer, in agreement with density functional theory (DFT) calculations of the lowest energy proton permeation pathways. Although graphene blocks the interaction of anions with the Pt(111) surfaces, anions do adsorb near the defects: the rate constant for hydrogen permeation is sensitively dependent on anion identity and concentration.


Fig. S1.
Hydrogen and graphene binding sites on Pt(111). A) 3×3 Pt(111) surface. Line intersections represent on-top sites, lines represent bridge sites, grey and white triangles represent hcp and fcc sites, respectively. B) Pt(111) with a top-centered graphene overlayer. C) Pt(111) with an hcpcentered graphene overlayer. D) Pt(111) with an fcc-centered graphene overlayer. (111) Similarly, 1 and 9 *H configurations are calculated on individual sites (top, bridge, hcp, and fcc) on the graphene-covered Pt(111) surface. When a graphene carbon atom is centered above a specific site, there are two unique types of adsorption site corresponding to the graphene site as shown in Figure S1: one under a graphene carbon atom, and another under a graphene ring. From the most stable 1 *H site, 2 *H configurations are generated, while for the 7 *H and 8 *H configurations, two or one H atom(s) are removed from all stable 9 *H configurations, respectively.

S.2.1. Definition of thermodynamic methods
Energies of formation for H2(g) and all adsorbed *H configurations on the pristine or graphenecovered Pt(111) surface were calculated, with or without vibrational free-energy corrections, with respect to the ground state at 300 K and standard pressure, using computational parameters described in the main text. For *H on pristine Pt(111), formation energies (excluding *H vibrational free energy corrections) are defined with respect to H2(g)  where ( ) is the DFT energy of the ground state of species , PtH , is the slab with n *H in configuration i, and Pt is the (3×3) Pt (111) where , , is the number of configurations which are symmetry-equivalent to configuration , and , , is the corresponding configurational entropy. For each coverage, we chose the most probable configurations together representing a total probability greater than 50% for that specific coverage and functional. Additional vibrational calculations are performed if the 1 *H calculations for a functional suggest that one specific site is energetically less stable yet vibrationally favored, and the positive internal energy difference at greater coverages may be cancelled out by the vibrational free energy. After calculating the vibrational free energies , , for each mode for a specific coverage, we obtained the weighted , by multiplying the individual , , with their adjusted vibrational contributions The vibrational free energies per *H near these limits for PBE, PBE-D3, and optPBE-vdW amount to 0.15 ± 0.02 eV, 0.15 ± 0.01 eV, and 0.14 ± 0.00 eV, respectively, all based on predominantly fcc-bound configurations. Since the maximum errors in the vibrational free energies are similar to or smaller than 0.01 eV and there is no coverage dependence, the mean vibrational free energies per *H are used for all coverages as vibrational corrections per *H: , . For optPBE-vdW, for top-bound *H is lower than for fcc-bound *H, while , , for top-bound configurations is 0.18 ± 0.02 eV instead. Hence, for configurations calculated with optPBE-vdW for which the vibrational energy is not directly calculated, an additional correction Δ , of 0.04 eV is added to each top-bound *H. For other functionals, Δ , is 0.00 eV. Weighted energies , , which are free energies based on internal energies and configurational entropies, are calculated using the following formula: where is the number of top-bound *H. From these weighted internal energies, the overall free energy for *H coverage is calculated: (S6) Similarly, we calculated the free energy of *H on graphene-covered (3×3) Pt(111) for 1, 2, 7, 8, and 9 *H coverages. For graphene and *H on graphene-covered Pt(111), formation energies (excluding *H vibrational free energy corrections) are defined with respect to H2(g), graphene in vacuum, and the pristine surface: * + 2 H 2 + gr → gr H * (S7) as Δ , , , = (grPtH , , ) − (Pt) − (gr) − 2 (H 2 ( )) (S8) where ( ) is the internal (or DFT) energy of the ground state of species , grPtH , is the slab with n *H in configuration i and graphene adsorbed on site j, Pt is the (3×3) Pt(111) slab, and gr is the graphene overlayer. This time, the graphene orientation yielding the lowest Δ , , , for each coverage and configuration was selected for vibrational analysis. The vibrational mode energies of the adsorbed hydrogen atoms were calculated using 0.02 Å single-atom displacements under the harmonic approximation. Contrary to Pt(111), however, values are calculated for all *H configurations within each coverage. Again, we calculated all *H and graphene adsorption configurations described in Section S.1, and selected the most stable graphene adsorption site for each hydrogen adsorption site (i.e. Δ , , ) for calculating their vibrational free energies, , , . This time, the total free energy of each of these *H configurations is used to calculate a cumulative free energy for its corresponding *H coverage: where , , is the configurational entropy of the *H configuration. From these values, first the formation energy of the *H configuration onto a graphene-covered Pt(111) was calculated: where Δ ,0,0, is the most stable energy for graphene on Pt(111). We used this formation energy with respect to graphene-covered Pt(111) to calculate the change in binding energy for coverage n:

S.2.2. Examples for thermodynamic methods
To illustrate the thermodynamic methods described above, we first consider a fictitious system in which two hydrogen atoms are adsorbed either on Pt(111) or on the interface of Pt(111) and the graphene overlayer. Our goal is to calculate the graphene effect ΔΔ ,2 on Pt-H bonds in systems with 2/9 ML *H coverage. For the sake of clarity, we will first focus on hydrogenated Pt(111). First, we obtain the DFT energies for hydrogenated Pt(111) (PtH 2, ) for various configurations i of *H. Each have an associated number of equivalent configurations as described in S.1.2. Assuming that the free energy of H2(g) formation (H 2 ( )) is -7.00 eV and the DFT energy of the Pt(111) slab (Pt) is -200.00 eV, we obtain their individual formation energies Δ , , as listed in Table S1. Using the number of configurations , and its associated at T = 300 K as defined in S.1.2, we obtain the configurational entropy corrected formation energies Δ , , − , , . One thing emanating from this calculation is that for the Pt calculations, *H configuration i = 2 has a lower corrected formation energy than i = 1, despite its Δ being more positive. The associated single configuration partition functions , , , the total partition function for the set of configurational entropy corrected formation energies , , and the resulting net probabilities , , are calculated as described in Equation S3, and are listed in Table S1. Moreover, the individual partition functions are used as parameters in Equation S5 to obtain a free energy term Δ ,2 for the *H coverage based entirely on energetics and configurational entropy, also listed in Table S1 under Δ − . Table S1. No single configuration accounts for 50% of all possible observed configurations. However, the two most probable configurations combined (i = 1, 2) account for more than 50% of possible observed configurations, so they will be used for vibrational-energy calculations. Vibrational corrections Δ ,2, are added to the previously calculated Δ ,2, − ,2, to obtain new partition functions , cumulative partition function , and probabilities ,2, as described in Equation S4, which are used to obtain a weighted average vibrational correction Δ ,2 . This correction is added to the previously calculated Δ ,2 free-energy term to obtain the net free energy of formation for 2/9 ML *H on Pt (111): Δ ,2 , which in this example is -0.97 eV.
Subsequently, the corresponding graphene calculations are performed. Here, we assume a formation energy (gr) of -23.00 eV for graphene. Both for 0 *H, which is graphene on otherwise pristine Pt(111), and for 2/9 ML *H, we calculate DFT energies (grPtH , , ) for various configurations i = 1, 2 of *H (if applicable) and j = A,B,C of graphene, as listed in Table S3. We use the energies described above to calculate formation energy Δ , , , by means of Equation S8, and, similarly to the Pt(111) *H configurations, correct these by which are also listed in Table S3. In this dataset, each *H configuration i is combined with each graphene configuration j, and only the most stable graphene configurations for each *H configuration are used for vibrational analysis: grPtH2,1,A and grPtH2,2,B. From their energies, configurational entropies and , the total Δ ,2, for both *H configurations is calculated, and are combined into a cumulative free energy for the entire coverage, Δ ,2 , as illustrated in Table S3. For the entire coverage, Δ ,2 is calculated using Equation S9, using grPtH0,0,C as a reference. The resulting binding energy amounts to -0.33 eV. Finally, the difference ΔΔ between the binding energy of *H on Pt(111), Δ ,2 , and the binding energy of *H on the interface of graphene and Pt(111), Δ ,2 , is calculated, which is 0.65 eV in the example considered.    a: Configurations are denoted as described in Figure S1. b: Vibrational energies for this *H coverage are calculated using the average Gvib for 1, 2, 7, 8, and 9 *H atom coverages. c: Probabilities for these configurations are based on Ef -TSconf -Gvib.    a: Configurations are denoted as described in Figure S1.  Hydrogenated graphene energies.

S.4. Hydrogen atom diffusion and permeation
a Configurations illustrated as described in Figure S1, with graphene-binding H represented using a red circle. b Ef as described in Subsection S.1.2.

Fig. S2.
Hydrogen atom energies with respect to the barrier as a function of distance from the graphene layer. Solid squares and open circles represent the hydrogen atom diffusing through graphene onto a bridge site, and onto a top site, respectively. Energies of vacancy passivation.
a Configurations illustrated as described in Figure S1, with C-H bonds pointing towards the surface depicted as empty white triangles and C-H bonds pointing away from the surface depicted as solid red triangles. a Configurations illustrated as described in Figure S1, with C-H bonds pointing towards the surface depicted as empty white triangles and C-H bonds pointing away from the surface depicted as solid red triangles.
b Ef compared to the lowest Ef for 1 *H between graphene and Pt(111).
on the binding energy of graphene, and net binding energies per *H trend closer to those on the non-graphene Pt(111) surface.

Fig. S3.
Differences in the adsorption energies of *H for PBE versus PBE-D3 as a function of the number of atoms adsorbed. Linear fits are included as guides for the eye. Filled: adsorption on bare Pt(111). Empty: adsorption on Pt(111) with a graphene overlayer.