(594a) The Influence of Coverage on Entropy: Changes in Vibrational Frequencies of CO on Pt (111)

Significance of coverage-awareness in kinetic modeling of heterogeneous catalysis has been well recognized [1]. In fact, with various models ranging from a simple linear model to a rigorous cluster expansion method [2], coverage-dependent binding energy and coverage-dependent barrier energies are being incorporated in the kinetic modeling. On the other hand, the coverage-dependent entropy, specifically due to the coverage dependency of the adsorbate vibrational frequencies, has not been analyzed in detail when there have been experimental evidences illustrating vibrational frequencies could be significantly affected by the surface coverage [3, 4]. The importance of the vibrational entropy in kinetic modeling is getting more addressed [5, 6] in the field but still, the direct effect of coverage on entropy has not been discussed.

We conducted a study on a model system of CO adsorption on Pt (111) to investigate how coverage affects vibrational frequencies and to quantitatively assess the impact on the adsorption thermodynamics. Furthermore, to improve the adsorption thermodynamics estimation through system-specific coverage-dependent binding energy, a comparison between concepts of average binding energy [7] and incremental binding energy [8] was made and the suitability of each model to different situations was discussed.

Materials and Methods

Global minimum optimization as well as vibrational frequency calculations of CO adsorbates were performed using density functional theory (DFT). A periodic slab model of 3×3×4 Pt was used to model the Pt surface by Quantum ESPRESSO suite [9] with plane wave basis sets and PBE exchange-correlation functional. At each CO coverage, ranging from one adsorbate in the unit cell to a full monolayer (ML) with nine adsorbates, the global minimum energy configuration was discovered by the constrained minima hopping algorithm [8]. Then the vibrational frequency calculations were conducted with the optimized configurations. Free energy, enthalpy, and entropy of adsorption were calculated using the coverage-dependent binding energy and vibrational partition function with the harmonic oscillator approximation.

Results and Discussion

Result of coverage-dependent binding energy is shown first. The average binding energy and the incremental binding energies were calculated by referencing the energy of the empty surface [7] and the energy of the global minimum configuration with one less adsorbate [8], respectively. The two binding energies at different coverages are compared in Figure 1. At low coverages , up to 4/9 ML coverage, the difference was insignificant. However, the differences at higher coverages were considerable. Consequently the choice of which binding energy model to deploy could bring dramatically different adsorption thermodynamics, for instance, at the higher coverages in this system.

In order to calculate coverage-dependent vibrational entropy, frequencies of the six vibrational modes of CO adsorbates were first grouped into four distinct motions: tilting, pendulum, desorption, and stretching motions. Then the frequencies of each group was averaged by the number of CO adsorbates and plotted as a function of coverage in Figure 2. Except for the tilting motion, frequencies of all motions showed an monotonically increasing trend with increasing coverage. But the frequency of the tiling motion showed a parabolic trend: initially decreased until 4/9 ML then increased as the coverage increased. Because the tilting motion is the lowest-frequency mode, its changes affected the overall vibrational entropy the most. Therefore the dip in the tilting motion frequency at the low coverages entropically favors additional adsorptions by increasing the overall vibrational entropy, which is the opposite trend observed in the binding energy. Then at higher coverages, increasing frequencies make adsorption entropically unfavorable.

Significance

Our study provides an insight of how often-neglected coverage dependence on adsorbate vibrational frequencies could result in considerable difference in adsorption thermodynamics.

References

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