Engineering Chemistry, ISSN: 2813-6535, Vol. 13, pp 7-14

doi: 10.4028/p-RvQ1bZ

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2024-11-29

Accepted:
2025-10-10

Microkinetic Comparison of Hydrogenation to Methanol over Unsupported and Supported Subnanometer Pdx Clusters

The original version of this paper is available on https://www.scientific.net/EC.13.7.pdf

Dzaki Ahmad Syaifullah , Muhammad Arkan Nuruzzahran , Abel Pradipta Wijaya , Azhar Ikhtiarudin , Reva Budiantono , Muhammad Haris Mahyuddin and Adhitya Gandaryus Saputro

Quantum and Nano Technology Research Group, Faculty of Industrial Technology, Institut Teknologi Bandung, Bandung, West Java 40132, Indonesia

Research Centre for Nanoscience and Nanotechnology, Institut Teknologi Bandung, Bandung, West Java 40132, Indonesia

dzakiahmad2002@gmail.com, arkannuruzzahran@gmail.com, azharikhtiarudin@gmail.com, budiantonoreva@gmail.com, mahyuddin133@itb.ac.id, gandaryus@itb.ac.id

Abstract

A promising approach to meet rising energy demands while mitigating environmental risks from greenhouse gases is the conversion of carbon dioxide into methanol through hydrogenation. Previous studies have demonstrated that unsupported subnanometer clusters exhibit excellent performance in this conversion. However, the influence of support materials on the activity of Pd clusters remains poorly understood. In this study, we compare the kinetics of hydrogenation to methanol using unsupported clusters and those supported by metal oxides, specifically and . Microkinetic simulations, based on available energetic data from the literatures, reveal that delivers superior kinetic performance, followed by and . These findings demonstrate that the choice of support material plays a critical role in dictating the reaction pathway and rate for supported Pd cluster catalysts.

Introduction

The original version of this paper is available on https://www.scientific.net/EC.13.7.pdf

The increasing concentration of carbon dioxide ( ) in the atmosphare is one of the main causes of global warming and climate change [1-3]. The conversion of into methanol through a hydrogenation process ( ), using hydrogen produced by electrolysis of water, is an alternative solution to reduce excess emissions while producing valuable chemicals [4-6]. Methanol can be used as a liquid fuel in direct methanol fuel cells and as liquid hydrogen storage to reduce our dependence on fossil fuel [7,8]. The hydrogenation process to produce methanol is conventionally carried out using catalyst at high temperature and high pressure . These operating conditions are necessary because is a stable and inert molecule that interacts weakly with catalysts at ambient conditions [11-13]. This certainly makes the process of converting to methanol economically expensive. For this reason, it is important to find catalysts which can operate at lower temperature and pressure.

Recent reports suggest that small size Pd cluster catalyst exhibit higher activity for hydrogenation to methanol compared to conventional catalyst [14]. The high activity is due to the good ability of Pd to adsorb and dissociate to provide hydrogen atoms required in the hydrogenation process of [15]. Previous research by Saputro et al. has shown that subnanometer cluster exhibit good performance in the conversion of to methanol [4,5]. The catalytic activity of Pd catalysts has also been reported to be enhanced by the addition of metal oxide support [15]. Metal oxide plays a role in stabilizing Pd clusters as it is able to interact strongly with Pd. In addition, metal oxide has a higher affinity toward , so it plays an important role in adsorption [16]. Pd clusters that play a role in dissociation and metal oxide support on which is adsorbed provide a synergistic effect, so that hydrogenation can occur either on the metal oxide or at the

Pd-metal oxide interface [14,16]. Therefore, supported Pd clusters have a good potential to be used as catalysts for hydrogenation.

Previous work by Ye et al. demonstrate that cluster supported on is a promising catalyst for methanol synthesis from [16]. Another study by Ou et al. investigated the reaction mechanism of hydrogenation to on catalyst and found that the interface between Pd and support has a significant influence on the catalytic activity [14]. However, the mechanism study was only carried out thermodynamically by comparing the activation barrier and reaction energy between pathways to find the minimum energy reaction path. The kinetic performance of the catalyst has not been further investigated. Kinetic studies are necessary to gain knowledge about reaction rate and the effect of operating variables such as temperature on the reaction rate which can be used as a guide in conducting experiments. Herein, we compare the kinetics of hydrogenation to methanol using unsupported cluster and those supported by metal oxides, specifically and . We perform microkinetic simulations based on energetic data from previous studies to observe the effect of metal oxide support on the reaction rate and the dominant reaction pathway in hydrogenation process.

Methods

The original version of this paper is available on https://www.scientific.net/EC.13.7.pdf

To investigate the kinetics of hydrogenation to methanol, we performed detailed microkinetic simulations based on energies obtained from previous studies. The microkinetic model employed in this study follows a mean-field approach grounded in transition state theory (TST) [17]. Using this framework, we were able to simulate the reaction pathways and rates by numerically solving a set of ordinary differential equations (ODEs) that govern the coverage of a single surface species over time.

For the adsorption and desorption of species, we used the Hertz-Knudsen model, which provides rate expressions for these elementary steps. The adsorption rate constant was calculated as follows:

where is the partial pressure of the molecule in the gas phase, is the surface area available for adsorption, is the molecular mass of the species (in kg ), is the Boltzmann constant, is the temperature (in K ), and is the adsorption energy. For desorption, the rate constant was modeled as:

where refers to the desorption energy in eV , which is crucial in determining how strongly the molecule interacts with the catalytic surface.

For surface reactions, the rate constants were expressed using the Arrhenius equation:

where represents the activation barrier of the reaction in eV . Surface entropy changes were deemed negligible, and hence we omitted partition function ratios in these calculations. The microkinetic model captures the evolution of each species involved in the reaction by solving the following rate equation for fractional surface coverage :

where represents the fractional coverage of species denotes the stoichiometric coefficient of the adsorbate in reaction step , and is the rate of reaction for that step.

This study presents a microkinetic model for the hydrogenation of within the unsupported , and catalysts, focusing on formate and reverse water gas shift followed by CO hydrogenation (RWGS+CO) pathways. In the formate pathway, reacts with hydrogen (H) to form intermediate formate (HCOO). The HCOO undergoes further hydrogenation to yield , which subsequently transforms into intermediate and OH . The can then proceed to generate methanol , while the OH is converted into water . This mechanism differs significantly from the RWGS+CO hydrogenation pathway. In the RWGS pathway, the process begins with the formation of intermediates such as HOCO or COOH , which then dissociate early into CO and OH . The CO undergoes hydrogenation to produce and the OH again being converted into .

Each catalyst exhibits distinct hydrogenation processes. As indicated by the data in Table 1, the formate pathway for the catalyst involves the following elementary reactions: RA0 → RA1 RA2a → RA3a → RA4a → RA5a → RA6 → RA7 → RA8 → RA9 → RA10. Meanwhile, the RWGS+CO hydrogenation pathway for catalyst follows these elementary reactions: RA0 → RA1 → RA2b → RA3b → RA4b → RA6 → RA5b → RA7 → RA8 → RA9 → RA10. The table below summarizes the reaction pathways, activation barriers, reaction energies, and reaction rate equations of each elementary step for the unsupported catalyst [4].

Table 1. hydrogenation step, energies, and reaction rates equation for [4].

Reaction
Number
Reaction Notation
Eact [eV]
ΔE [eV]
Reaction Rates

RA0
H₂ + 2* → 2H*
0
-0.73
rA0 = kA0PH₂θ*² − k−A0θH²

RA1
CO₂ + * → CO₂*
0
-0.21
rA1 = kA1PCO₂ θ* − k−A1θCO₂

RA2a
CO₂* + H* → HCOO* + *
0.93
-0.21
rA2a = kA2aθCO₂θH − k−A2aθHCOOθ*

RA2b
CO₂* + H* → HOCO* + *
1.90
0.39
rA2b = kA2bθCO₂θH − k−A2bθHOCOθ*

RA3a
HCOO* + H* → HCOOH* + *
1.16
0.94
rA3a = kA3aθHCOOθH − k−A3aθHCOOHθ*

RA3b
HOCO* + H* → CO* + OH*
0.44
-1.05
rA3b = kA3bθHOCOθH − k−A3bθCOθOH

RA4a
HCOOH* + H* → H₂COOH* + *
1.39
0.33
rA4a = kA4aθHCOOHθH − k−A4aθH₂COOHθ*

RA4b
CO* + H → HCO* + *
1.44
1.26
rA4b = kA4bθCOθH − k−A4bθHCOθ*

RA5a
H₂COOH* + * → H₂CO* + OH*
1.00
0.92
rA5a = kA5aθH₂COOHθ* − k−A5aθH₂COθOH

RA5b
HCO* + H* → H₂CO* + *
0.85
0.21
rA5b = kA5bθHCOθH − k−A5bθH₂COθ*

RA6
OH* + H* → H₂O* + *
0a; 1.26b
-1.23a; -0.17b
rA6 = kA6θOHθH − k−A6θH₂Oθ*

RA7
H₂CO* + H* → H₃CO* + *
1.10
0.61
rA7 = kA7θH₂COθH − k−A7θH₃COθ*

RA8
H₃CO* + H* → CH₃OH* + *
1.06
-0.67
rA8 = kA8θH₃COθH − k−A8θCH₃OHθ*

RA9
H₂O* → H₂O + *
0
0.34a; 0.51b
rA9 = kA9θH₂O − k−A9PH₂Oθ*

RA10
CH₃OH* → CH₃OH + *
0
0.55
rA10 = kA10θCH₃OH − k−A10PCH₃OHθ*

Formate pathway
RWGS+CO hydrogenation pathway
Turnover frequency (TOF) is defined as the lowest reaction rate:

The TOF can be calculated by numerically solving a set of differential equations, which represent the rate of change in coverage for each species involved in hydrogenation. Eqs. (6)-(16) show the examples of these differential equations for hydrogenation in catalyst using formate pathway. The differential equation for other catalysts or pathways is only slightly different from these examples.

Similar to the previous catalyst, the hydrogenation of on the catalyst also proceeds through two pathways: formate and RWGS+CO hydrogenation. Each pathway also has its own elementary reactions that are slightly different from those described previously. Table 2 below presents the reaction pathways, energy values, and rate equations for the hydrogenation on the catalyst [14]. Based on the table, it is evident that the formate pathway on this catalyst follows elementary reactions: RB8 → RB9. On the other hand, the RWGS + CO pathways for this catalyst follow these reaction steps: .

Table 2. hydrogenation step, energies, and reaction rates equation for [14].

Reaction
Number
Reaction Notation
Eact [eV]
ΔE [eV]
Reaction Rates

RB0
H₂ + 2* → 2H*
0.34
-1.33
rB0 = kB0PH₂θ*² − k−B0θH²

RB1
CO₂ + * → CO₂*
0
-1.49
rB1 = kB1PCO₂ θ* − k−B1θCO₂

RB2a
CO₂* + H* → HCOO* + *
1.63
0.66
rB2a = kB2aθCO₂θH − k−B2aθHCOOθ*

RB2b
CO₂* + H* → COOH* + *
1.11
0.60
rB2b = kB2bθCO₂θH − k−B2bθCOOHθ*

RB3a
HCOO* + H* → H₂COO* + *
2.43
0.75
rB3a = kB3aθHCOOθH − k−B3aθH₂COOθ*

RB3b
COOH* + H* → CO* + OH*
0.21
-1.20
rB3b = kB3bθCOOHθH − k−B3bθCOθOH

RB4a
H₂COO* + H* → H₂CO* + OH*
1.88
0.23
rB4a = kB4aθH₂COOθH − k−B4aθH₂COθOH

RB4b
CO* + H → HCO* + *
1.50
1.07
rB4b = kB4bθCOθH − k−B4bθHCOθ*

RB5
OH* + H* → H₂O* + *
0.74
-0.04
rB5 = kB5θOHθH − k−B5θH₂Oθ*

RB6a
H₂CO* + * → H₃CO* + *
1.43
1.34
rB6a = kB6aθH₂COθH − k−B6aθH₃COθ*

RB6b
HCO* + H* → H₂CO* + *
0.95
0.43
rB6b = kB6bθHCOθH − k−B6bθH₂COθ*

RB7
H₃CO* + H* → CH₃OH* + *
0.85
0.34
rB7 = kB7θH₃COθH − k−B7θCH₃OHθ*

RB8
H₂O* → H₂O + *
0
1.43
rB8 = kB8θH₂O − k−B8PH₂Oθ*

RB9
CH₃OH* → CH₃OH + *
0
1.51
rB10 = kB10θCH₃OH − k−B10PCH₃OHθ*

Hydrogenation of in also goes through the same pathways which are formate and RWGS+CO. Based on the data presented in Table 3, the formate pathways in this catalyst will follow these elementary steps: . While RWGS+CO hydrogenation pathways in catalyst consists of these steps: .

Table 3. hydrogenation step, energies, and reaction rates equation for [16].

Reaction
Number
Reaction Notation
Eact [eV]
ΔE [eV]
Reaction Rates

RC0
H₂ + 2* → 2H*
0
-1.08
rC0 = kC0PH₂θ*² − k−C0θH²

RC1
CO₂ + * → CO₂*
0
-0.37
rC1 = kC1PCO₂ θ* − k−C1θCO₂

RC2a
CO₂* + H* → mono-HCOO* + *
1.17
0.81
rC2a = kC2aθCO₂θH − k−C2aθmonoHCOOθ*

RC2b
CO₂* + H* → trans-COOH* + *
1.01
0.21
rC2b = kC2bθCO₂θH − k−C2bθtransCOOHθ*

RC3a
mono-HCOO* → bi-HCOO*
0
-0.68
rC3a = kC3aθmonoHCOO − k−C3aθbiHCOO

RC3b
trans-COOH* → cis-COOH*
0.39
0.01
rC3b = kC3bθtransCOOH − k−C3bθcisCOOH

RC4a
bi-HCOO* + H* → H₂COO* + *
1.09
0.75
rC4a = kC4aθbiHCOOθH − k−C4aθH₂COOθ*

RC4b
cis-COOH* + H* → CO* + H₂O*
1.90
0.26
rC4b = kC4bθcisCOOHθH − k−C4bθCOθH₂O

RC5a
H₂COO* + H* → H₂CO* + OH*
0.89
-1.15
rC5a = kC5aθH₂COOθ* − k−C5aθH₂COθOH

RC5b
CO* + H* → HCO* + *
1.36
0.89
rC5b = kC5bθCOθH − k−C5bθHCOθ*

RC6a
H₂CO* + H* → H₂COH* + *
0.84
0.76
rC6a = kC6aθH₂COθH − k−C6aθH₂COHθ*

RC6b
HCO* + H* → H₂CO* + *
0.82
0.21
rC6b = kC6bθHCOθH − k−C6bθH₂COθ*

RC7
OH* + H* → H₂O*
0.98
-0.65
rC7 = kC7θOHθH − k−C7θH₂O

RC8a
H₂COH* + H* → CH₃OH* + *
1.11
0.20
rC8a = kC8aθH₂COHθH − k−C8aθCH₃OHθ*

RC8b
H₂CO* + H* → H₃CO* + *
0.41
0.03
rC8b = kC8bθH₂COθH − k−C8bθH₃COθ*

RC9
H₃CO* + H* → CH₃OH* + *
1.33
0.24
rC9 = kC9θH₃COθH − k−C9θCH₃OHθ*

RC10
H₂O* → H₂O + *
0
0.58
rC10 = kC10θH₂O − k−C10PH₂Oθ*

RC11
CH₃OH* → CH₃OH + *
0
0.78
rC11 = kC11θCH₃OH − k−C11PCH₃OHθ*

The activation barriers and reaction energies summarized in Tables 1, 2, and 3 are used as inputs for microkinetic modeling to calculate the TOF for hydrogenation to methanol on each catalyst.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/EC.13.7.pdf

The TOF as a function of temperature for hydrogenation to methanol on , and has been calculated for both the formate and the RWGS+CO hydrogenation pathways. The results are shown in Fig. 2. The TOF was calculated under typical conditions used for hydrogenation on standard Cu -based catalyst, that is at bar with a pressure ratio of 1:3. These results show that the TOF for the formate pathway on and Pd 7 is higher than that for the RWGS+CO hydrogenation pathway. This means that for both catalysts the hydrogenation tends to be more selective towards the formate pathway. This finding is consistent with the result from previous studies by Ye et al. [16] and Saputro et al. [4]. However, at temperatures below 700 K , the TOF for the RWGS+CO hydrogenation pathway on the is higher than the TOF for the formate pathway. This indicates that is more selective towards the RWGS+CO hydrogenation pathway in this temperature range. It also means that the addition of certain supports can change the dominant pathway to the RWGS+CO hydrogenation rather than the formate pathway. This agrees with the results of the thermodynamic study by Ou et al. which showed that RWGS+CO hydrogenation is more dominant than the formate pathway on the catalyst [14]. Comparing the TOF of the best pathway between the three catalysts (formate pathway on and , and RWGS+CO hydrogenation on has the highest TOF over the whole temperature range, while has the lowest TOF. This
shows that the presence of the right metal oxide support can increase the reaction rate of hydrogenation, thus improving the catalytic activity of Pd clusters.

Fig. 1. TOF profiles as a function of temperature for hydrogenation to methanol via formate and RWGS+CO hydrogenation pathways over , and . TOF was calculated at bar with pressure ratio of 1:3.

Fig. 1. TOF profiles as a function of temperature for hydrogenation to methanol via formate and RWGS+CO hydrogenation pathways over , and . TOF was calculated at bar with pressure ratio of 1:3.

The surface coverage profiles versus temperature of each species involved in the hydrogenation reaction via the formate pathway and the RWGS+CO hydrogenation pathway is shown in Fig 3. We can see that the dominating coverage for each pathway is different. For in the formate pathway (Fig. 3a) and in both pathways (Fig. 3c and f), there is a high coverage in the low temperature region which indicates that has not been consumed. The coverage decreases as the temperature increases, indicating that more is consumed. Meanwhile, from the surface coverage profile for (see Fig. 3b and e), there is a high coverage at temperatures lower than 700 K , where the formate pathway has a higher coverage than the RWGS+CO hydrogenation pathway. This explains why the RWGS+CO hydrogenation pathway on catalyst exhibits higher TOF than the format pathway at temperatures lower than 700 K. Furthermore, we can see that for the RWGS+CO hydrogenation pathway on Pd 7 (Fig. 3d) and (Fig. 3e) there is CO* poisoning. For Pd 7 catalyst, CO* poisoning has occurred even in the low temperature region so that the RWGS+CO hydrogenation pathway on Pd 7 has a lower TOF than the formate pathway. Meanwhile, for poisoning occurs at temperatures higher than 700 K . This causes the RWGS pathway to produce a lower TOF than the formate pathway at temperatures higher than 700 K .

Fig. 2. Surface coverage of each species involved in hydrogenation via the formate pathway on (a) , (b) (110), (c) (110), and via the RWGS+CO hydrogenation pathway on (d) Pd 7 , (e) (110), and (f) (110).

Fig. 2. Surface coverage of each species involved in hydrogenation via the formate pathway on (a) , (b) (110), (c) (110), and via the RWGS+CO hydrogenation pathway on (d) Pd 7 , (e) (110), and (f) (110).

Conclusions

The original version of this paper is available on https://www.scientific.net/EC.13.7.pdf

In this work, we study the kinetics of hydrogenation to produce methanol on cluster (without support), , and using microkinetic model. Our results show that the presence of metal oxide support on subnanometer cluster can improve the reaction rate of hydrogenation, as can produce higher TOF than cluster. Furthermore, the presence of a support can also alters the dominant reaction pathway. For example, can change the pathway to be more selective towards RWGS+CO hydrogenation than formate pathway. Therefore, the type of support material must be considered in designing a catalyst for hydrogenation with the desired catalytic activity.

Acknowledgments

The original version of this paper is available on https://www.scientific.net/EC.13.7.pdf

We acknowledge the research fund granted by Institut Teknologi Bandung, under grant scheme "Riset Unggulan ITB 2023".

References

The original version of this paper is available on https://www.scientific.net/EC.13.7.pdf

P. Schwiderowski, H. Ruland, M. Muhler, Current developments in CO2 hydrogenation towards methanol: A review related to industrial application, Curr Opin Green Sustain Chem 38 (2022) 100688.

M. Takht Ravanchi, S. Sahebdelfar, Catalytic conversions of CO2 to help mitigate climate change: Recent process developments, Process Safety and Environmental Protection 145 (2021) 172-194.

C. Mebrahtu, F. Krebs, S. Abate, S. Perathoner, G. Centi, R. Palkovits, Chapter 5 - CO2 Methanation: Principles and Challenges, in: S. Albonetti, S. Perathoner, E.A. Quadrelli (Eds.), Stud Surf Sci Catal, Elsevier, 2019: pp. 85-103.

A.G. Saputro, A.L. Maulana, F. Fathurrahman, G. Shukri, M.H. Mahyuddin, M.K. Agusta, T.D.K. Wungu, H.K. Dipojono, Density functional and microkinetic study of CO 2 hydrogenation to methanol on subnanometer Pd cluster doped by transition metal , Pt, Rh), Int J Hydrogen Energy 46 (2021) 14418-14428.

A.G. Saputro, R.I.D. Putra, A.L. Maulana, M.U. Karami, M.R. Pradana, M.K. Agusta, H.K. Dipojono, H. Kasai, Theoretical study of CO2 hydrogenation to methanol on isolated small Pdx clusters, Journal of Energy Chemistry 35 (2019) 79-87.

F. Brix, V. Desbuis, L. Piccolo, É. Gaudry, Tuning Adsorption Energies and Reaction Pathways by Alloying: PdZn versus Pd for CO2 Hydrogenation to Methanol, J Phys Chem Lett 11 (2020) 7672-7678.

D. Guo, J. Liu, X. Zhao, X. Yang, X. Chen, Comparative computational study of CO2 hydrogenation and dissociation on metal-doped Pd clusters, Sep Purif Technol 313 (2023) 123462.

N. Garg, A. Sarkar, B. Sundararaju, Recent developments on methanol as liquid organic hydrogen carrier in transfer hydrogenation reactions, Coord Chem Rev 433 (2021) 213728.

H. Li, L. Wang, X. Gao, F.-S. Xiao, Catalyst Modulated by Zirconia with Enhanced Performance in CO2 Hydrogenation to Methanol, Ind Eng Chem Res 61 (2022) 10446-10454.

K. Stangeland, H. Li, Z. Yu, CO2 hydrogenation to methanol: the structure-activity relationships of different catalyst systems, Energy Ecol Environ 5 (2020) 272-285.

J. Zhong, X. Yang, Z. Wu, B. Liang, Y. Huang, T. Zhang, State of the art and perspectives in heterogeneous catalysis of CO2 hydrogenation to methanol, Chem Soc Rev 49 (2020) 13851413.

T.P. Araújo, S. Mitchell, J. Pérez-Ramírez, Design Principles of Catalytic Materials for CO2 Hydrogenation to Methanol, Advanced Materials (2024) 2409322.

X. Jiang, X. Nie, X. Guo, C. Song, J.G. Chen, Recent Advances in Carbon Dioxide Hydrogenation to Methanol via Heterogeneous Catalysis, Chem Rev 120 (2020) 7984-8034.

Z. Ou, J. Ran, J. Niu, C. Qin, W. He, L. Yang, A density functional theory study of CO2 hydrogenation to methanol over catalyst: The role of interfacial site, Int J Hydrogen Energy 45 (2020) 6328-6340.

O.A. Ojelade, S.F. Zaman, A Review on Pd Based Catalysts for CO2 Hydrogenation to Methanol: In-Depth Activity and DRIFTS Mechanistic Study, Catalysis Surveys from Asia 24 (2020) 11-37.

J. Ye, C. Liu, D. Mei, Q. Ge, Methanol synthesis from CO2 hydrogenation over a Pd4/In2O3 model catalyst: A combined DFT and kinetic study, J Catal 317 (2014) 44-53.

H. Eyring, The Activated Complex in Chemical Reactions, J Chem Phys 3 (1935) 107-115.

This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.