Realistic Modelling of Dynamics at Nanostructured Interfaces Relevant to Heterogeneous Catalysis

Abstract

The focus of this short review is directed towards investigations of the dynamics of nanostructured metallic heterogeneous catalysts and the evolution of interfaces during reaction—namely, the metal–gas, metal–liquid, and metal–support interfaces. Indeed, it is of considerable interest to know how a metal catalyst surface responds to gas or liquid adsorption under reaction conditions, and how its structure and catalytic properties evolve as a function of its interaction with the support. This short review aims to offer the reader a birds-eye view of state-of-the-art methods that enable more realistic simulation of dynamical phenomena at nanostructured interfaces by exploiting resource-efficient methods and/or the development of computational hardware and software.

1. Introduction

In heterogeneous catalysis, atomic and electronic structures of surface atoms and their specific interactions with the local environment (gas, liquid solvent, support) govern the binding and the release of reactant molecules, thus controlling the catalytic reaction mechanisms [1]. In this context, computational models have a long-standing tradition in the study of phenomena at solid–gas and solid–liquid interfaces, which determine the activity, selectivity, and lifetime of a catalyst [2,3]. In fact, numerical simulations can provide a full atomistic and electronic structural insight into the process of interest. Furthermore, numerical simulations are of great aid in the deconvolution and control of input parameters, such as temperature, pressure, chemical composition, and the nature of the species in the system—i.e., the manifold variables that strongly contribute to the complexity of dynamical processes at the interfaces. This is rarely accessible to current characterization measurements—especially for the case of in situ and in operando studies, where the interface structure may undergo frequent changes [4,5], notwithstanding the recent advancements in the field, which have been reviewed in great detail elsewhere [6,7,8]. The purpose of this short review is to survey some significant milestones in the modelling of dynamic phenomena occurring at the interfaces in the heterogeneous catalysts, with an emphasis on works related to metallic or oxide nanoparticle (NP) catalysts. Advancements in the theory-guided understandings of the dynamical organization of three relevant interfaces in heterogeneous catalysis—namely, the catalyst–solvent, catalyst–gas, and catalyst–support interfaces—will be discussed.

2. Catalyst-Solvent Interface

An understanding of the solvent–metal structures is key to rationalizing catalytic processes. Indeed, depending on the reaction of interest, the solvent may act as a relatively innocent spectator, influence activity and selectivity by interacting with adsorbates—e.g., by hydrogen bonding with key intermediates—or serve as a proton donor. Because of the ubiquitous relevance of water in catalytic reactions, water–metal and water–metal oxide interfaces have drawn great interest from the heterogeneous catalysis community. Ab initio density functional theory (DFT) modelling has been adopted, together with molecular-dynamics-based sampling, to probe the structure, dynamics, and acidity of water monolayers, double-layers, and over the surfaces of many late transition metals—Cu [9,10], Ag [10,11], Au [9,11,12], Pt [10,12,13,14], Pd [12,13,15], Rh [13], Ru [16], Ni [17], and their alloys [9]—under a number of different conditions. Similarly, the interface between oxides and water was assessed for systems of different natures—namely, silica [18,19], ZnO [20,21,22], goethite [23], and alumina [24,25]. In the field of electrocatalysis, the dynamics at electrified metal surface–water [26,27,28,29,30,31] and oxide surface–water [32,33] interfaces have also been recently modelled and characterized in detail.

When moving from studies on pristine, flat surfaces to those on nanostructured catalysts, we find that they are lesser in number and more recent. We could rationalize this trend in terms of the computational cost required to achieve accurate and realistic simulations of these systems. While works on pristine surfaces can provide information transferable to surface science experiments or to studies involving large and pristine nanocrystals, we believe that it is only by explicitly considering nanoscale features in the catalyst—e.g., curvature effects, edges, vertices, and step sites unique to nanocatalysts—that insightful and non-trivial inferences on nanostructured water–metal interface properties can be obtained.

The few reports appearing in the literature support this statement. Ferreira de Morais et al. [34] utilized MD with a DFT potential energy landscape (ab initio MD) to characterize the interface between a Pt nanoparticle of 201 atoms and 689 explicitly considered water molecules. They observed a re-organization of water molecules at the water–Pt₂₀₁ interface. This interface consists of an average of two physisorbed water molecules on terraces, which is twice the number of chemisorbed water molecules on edges and corners. The unique adsorption properties of low-coordinated atoms were also highlighted by Soria et al. [35]. These authors adopted a ReaxFF interaction modelling scheme and molecular dynamics to characterize the hydration shells of spherical TiO₂ nanoparticles. Their simulations showed that water molecules adsorb in both molecular and dissociative states on the surface. Depending on water concentration, single water molecules’ dissociation mechanisms (low coverage) or Grotthuss-like mechanisms (high coverage) are observed. Several water molecules can bind to the nanoparticle surface simultaneously, with adsorption being enhanced at low-coordinated Ti atoms that do not find a counterpart in low-energy TiO₂ surface terminations. Previously, Fazio et al. [36] focused on the same system, and adopted a multiscale multistep integration scheme to prove that the nanoparticle–water interface affects the water molecules’ dipolar orientation in a solvation shell with a thickness of 5 Å, while water structuring was observed up to a distance of 8 Å from the nanoparticle surface. The hydration shell structures around oxide nanoparticles have been also discussed by Liu et al. [37], who used multiscale quantum mechanics/molecular mechanics (QM/MM) simulations exploiting force fields and tight-binding methods to unravel the short-range and long-range arrangement of water molecules around a spherical Fe₃O₄ nanoparticle. Almost half of the water molecules in the first hydration shell dissociate and hydroxylate the nanoparticle. Clear signatures in the radial distribution function of water around the nanoparticle enable the detection of a well-structured second and third hydration shell, while water molecules at distances ≥5 Å from the nanoparticle organize in bulk-like arrangements. The immersion of Fe₃O₄ nanoparticles in water was further found to improve their magnetic properties.

Solvent–catalyst interaction may also induce significant restructuring of the catalyst itself. Thermodynamic models indeed predict rich adsorbate coverage–temperature-phase diagrams, growth increasingly complex when further including eventual external electrochemical potential [38,39]. Zhu et al. [40] developed an environmental model based on the density functional theory, the Wulff construction, and the Langmuir adsorption isotherm to explore the shape evolutions of several transition metal NPs exposed to water vapor pressure at different temperatures. The predicted results show that despite the weak metal–water interactions, the evolution of water coverage on different facets could induce dramatic shape changes, depending on the temperature and the water vapor pressure. More recently, Chan et al. [41] adopted a first-principles approach and a micro-solvation model (one water layer) to draw insight on the stability of different closed-shell Au nanoparticles and determine the nature of the rearrangement mechanisms, which stabilize icosahedral shapes with respect to Ino decahedra. These authors found that the adsorption strength per water molecule following a rearrangement is independent of the nanoparticle size and shape, while the water molecule networks around the nanoparticles consist of H₂O molecules linked, by and average of two hydrogen bonds. To sample longer time scales, Delgado et al. [42] utilized an implicit potential to model the attractive interaction between metal atoms and solvent molecules. They showed that such metal–adsorbate interactions diminish the nanoparticles’ thermal stability against solid–solid and solid–liquid transitions. Similarly, Braunwarth et al. [43] observed the long-term stability of Pt cubes solvated in water by means of a ReaxFF potential. The cubes underwent a strong restructuring into concave disordered cuboids after a few ns of simulation.

3. Catalyst-Gas Interface

In gas-phase reactions, the dynamic interaction takes place between the surface of the nanostructured catalyst and the gas molecules, adsorbed intermediates, and products form the catalyst−gas interface, which directly impact the available reaction pathways. In addition, the catalyst−gas interactions are expected to modify the catalyst structure by changing its shape and surface organization [44,45,46], as well as the atomic ordering in the case of alloy catalysts [47,48,49,50,51,52]. As these dynamic structural changes modulate the activity, selectivity, and stability of NP catalysts, probing the dynamic evolution of surface structure and chemical ordering at the atomic scale under reaction conditions is crucial to providing a fundamental understanding of reaction mechanisms.

In spite of the huge number of studies in the literature devoted to metal or metal oxide catalyst–gas interactions, few theoretical studies have been dedicated to the investigation of the dynamics of nanostructured catalysts under reactive conditions. In general, to predict the effects of gas adsorption on metallic nanocatalysts, DFT-based geometric optimization methods are used to calculate and compare the stability of different conformations of small metal clusters interacting with adsorbed gas molecules [53]; however, this method is limited to systems of a few dozen atoms. The prediction of equilibrium shape evolution of larger metallic nanoparticles interacting with gas molecules has been generally resolved by means of Wulff constructions based on DFT calculations instead. This approach, however, does not account for dynamical contributions. In addition, Wulff’s construction theorem is only reliable for NP size > 5 nm, and disregards the possibilities of disordered surfaces and twinning.

In the last few years, thanks to the strong progress in computational resources, it has been feasible to sample DFT potential energy surfaces via ab initio molecular dynamics (AIMD), exploiting the Born–Oppenheimer (BOMD) or Car–Parrinello (CPMD) formalism. These approaches have emerged as powerful tools to explore the conformational changes of metal NPs when exposed to different pressures of molecules. Very recently, Nassereddine et al. [54] employed BOMD simulations to provide insights on the atomic-scale mechanisms that underpin the experimentally observed size-dependent structural dynamics of Au NPs exposed to atmospheric hydrogen pressure. These authors monitored the structural evolution of hydrogen-covered Au NPs of 2 nm in size for more than 60 ps of simulation time, in order to demonstrate that the strong Au–H interactions may induce a high mobility of gold atoms, which drastically change the shape and the symmetry of the whole NP at room temperature (Figure 1). Similarly, by performing AIMD simulations, He et al. [55] revealed size-dependent order-to-disorder transformation of ultrasmall gold clusters supported on ceria upon exposure to carbon monoxide and oxygen. This transformation was found to lead to the generation of dynamic low-coordinated atoms, which may boost the oxidation reaction of carbon monoxide. Thermodynamic models of gas–catalyst interaction inducing dynamical changes become even more complex when it comes to the case of nanoalloys. Restructuring, reshaping, segregation, and many other processes may occur, and must be taken in account [56].

In addition to the well-known solid-state nanosized alloy catalysts, new emerging classes of materials—namely, single-atom alloy catalysts (SAACs) [50,51] and supported catalytically active liquid metal solutions (SCALMSs)—have been shown to undergo significant changes during reactions. In a recent work, Wang et al. [52] reported the stability phase diagram of single-atom Pt anchored in various metal host NPs as a function of hydrogen pressures and temperatures. This work shows non-intuitive segregation behavior of SAACs where the stability of diluted single atoms is found to depend on either the electronic and geometric ensembles or the affinity of both alloy elements to the reactive gas. Humphrey et al. [57] performed picosecond-long AIMD to show that the diffusion properties of single Pt atoms on a rutile TiO₂ (110) support are dictated by the interaction strength with adsorbates and supports, where strong metal–adsorbate interactions determine higher diffusion coefficients. Bauer et al. [58] have recently reported in operando DRIFT and DFT results of Ga_xPt_y catalyst systems, showing interesting dynamical behavior of isolated Pt atoms. Running AIMD simulations of Pt atoms evolving in Ga matrixes as a function of time and temperature, these authors showed that the rate of appearance at the surface of a single Pt atom depends on several factors, such as the size of the NP and the mobility of the atoms which, in turn, depend on the temperature and the composition of the catalyst. At temperatures higher than 350 °C, a homogeneous and liquid Ga/Pt metal phase appears, leading to a higher mobility of atoms; thus, the ability of Pt to reach the surface and to interact with the reactant becomes stronger. In addition, the residence time of Pt at the surface is found to be strongly influenced.

Finally, in the case of oxides, one can observe similar behavior, Modelling complex interfaces involving both surfaces and gas-phase molecules is of crucial interest for improving the catalytic activity and selectivity [59,60].

4. Catalyst-Support Interface

It is well documented that the arrangements of the catalyst–support interface can have a tremendous impact on the reactivity of the catalyst’s adsorption sites which, in turn, may cause an increase in the catalyst’s activity and/or selectivity due to geometric and/or electronic effects. By the same token, support–catalyst interaction can dramatically affect the stability of the latter with respect to the gas phase. Conversely, the effects of electronic [61], reactive [62], and strong metal–support interactions [63,64] have been strong drivers in the study and analysis of the dynamics of supported nanostructured metal catalysts.

To investigate the dynamics at the support–catalyst interface, ab initio simulations stand as one of the most promising tools. These are key tools to monitor the time- and condition-dependent evolution of the structure of a supported nanocluster. Vila et al. [65] utilized DFT modelling and molecular dynamics to characterize the peculiar negative thermal expansion and large structural disorder of Pt nanoparticles supported on a gamma-Al₂O₃ surface in terms of a combination of thermal vibrations and low-frequency disorder. Vila et al. [66] previously fitted a hybrid version of the classical Sutton–Chen force field to predict diffusion coefficients and bond-breaking rates as a function of the nanocluster size. By looking at sizes between 10 and 20 atoms, they identified size-dependent dynamical changes in the thermally driven phase change and diffusion of the nanoparticles. Xu et al. [67] adopted AIMD to demonstrate the complexity of the structural evolution of Au–Pd nanoalloys deposited on rutile TiO₂, as a function of different in operando conditions. These authors ran simulations for 40–50 ps of the Au–Pd cluster of 38 atoms deposited on a four-layer (7 × 3) rutile TiO₂ (110) support. The results show that when simulating reducing conditions (the adsorption of one hydrogen atom), Pt atoms are more likely to lie at the metal–oxide interface. Conversely, under oxidizing conditions (interactions with oxygen), Pd atoms are more likely to be located at the surface of the nanocluster.

Structural properties and catalytic activity are intimately interlinked. In turn, simulations of the dynamical evolution of the system can capture and reveal non-trivial catalytic reaction pathways. Li et al. [68] utilized ab initio molecular dynamics to monitor the time-dependent evolution of the geometric and electronic structure in a Pt nanocluster supported on CeO₂. They identified the dynamic nature of the Pt⁰−O vacancy, with Ce³⁺ sites as the key to rationalizing activity trends for water gas shift catalyzed by this system. Similarly, Wang et al. [69] considered Au nanoclusters on ceria, and utilized AIMD to unravel a previously unreported single-atom mechanism through which the system can drive the oxidation of CO. A gold cation can momentarily break away from the gold nanoparticle to catalyze CO oxidation by moving adjacent to the metal–oxide interface (Figure 2), and then re-insert into the nanocluster after the reaction is completed. Additionally, in relation to the dynamical nature of active sites in supported catalysts, Daelman et al. exploited AIMD to show that metal charge of single Pt atoms on CeO₂ (100) surfaces evolves over time; they thus rationalized these strong metal–support interactions in terms of the relative position of the Ce 4f levels relative to the ones in Pt, allowing for electron injection and withdrawal between the two [70]. The dynamical modification of the metallic charge further enabled the rationalization of the high reactivity of single Pt atoms for CO oxidation.

Moving from nanoclusters (a few tens of atoms at maximum) to nanoparticles (i.e., systems with at least a few hundred of atoms), several works have focused on the development of accurate interatomic potential parameters to reproduce and predict the effect of the support on the stability of the nanostructured catalyst. Ngajdong et al. [71] fitted an explicit analytical potential to DFT in order to model dynamics at the Ag–SiO₂ interface; they demonstrated that the likelihood of observing Ag nanoparticles with twin boundaries decreases when a SiO₂ support is considered; furthermore, they observed that melting initiates at the interface between the nanoparticle and the substrate. In the same year, Rossi et al. [72] showed that the support induces a wetting of the nanoparticle, crystalline rather than polycrystalline morphologies, and plays a strong role in stabilizing the nanoparticles against solid–liquid transition. This conclusion was achieved from the analysis of simulations adopting an implicit metal oxide force field parametrized on DFT data.

In addition to oxide supports, carbon also finds an application in devices—often as a substrate where metallic nanocatalysts are deposited. This motivation, together with the accuracy with which carbon–carbon and carbon–metal interactions can be modelled while utilizing efficient approaches, has stimulated a number of investigations on carbon–metal interfaces. Foster et al. [73] utilized an implicit approach where atoms were fixed in contact with the implicit carbon support, in order to show that the substrate tends to increase the stability of the nanocatalysts against solid–liquid transitions. Previously, Morrow et al. [74] and Qiu et al. [75] fitted a semi-empirical force field to DFT data in order to study the stability of metal nanoparticles on carbon nanostructures, which are modelled explicitly. The carbon support nanostructure was identified as a tunable parameter to control nanoparticle size and chemical composition. Later, Cheng et al. [76] also adopted a reactive force field to present an additional proof that the carbon support structure is a free parameter to modify the coordination number distribution of surface sites in a Pt nanoparticle. These changes, in turn, affected the catalytic properties of the system, where the abundance of highly coordinated sites was found to correlate with the activity for CO oxidation.

5. Outlook: Reactive Events at Support/Catalyst/Gas-Liquid Interfaces

The accurate modelling of dynamical processes at the catalyst–solvent, catalyst–gas, and catalyst–support interfaces has thus far benefited greatly not only from the improvement in the hardware performance—which enables faster computations—but also from the advancement in the methods and algorithms with which interatomic interactions are predicted. The investigations we have reported in this short review, in our opinion, represent significant and paradigmatic examples of these trends.

In the future, we believe that the explicit simulation of reactive events—while adopting a non-idealized description of the catalyst, its support, the solvent or the gas environment, and the applied potential for electrified interfaces—is likely to become the state of the art. To date, the investigations have mostly been devoted to pristine surfaces. Example studies of the reconstruction of pristine surfaces in the presence of a solvent have been recently reported by Natarajan et al. [77] and Michalka et al. [78]. The former developed a neural network force field for Cu, H, and O interaction, and utilized it to sample the self-diffusion of adatoms at the interface between a Cu surface and bulk water; they concluded that hopping mechanisms are more favorable than exchange mechanisms, and that Cu–water interaction lowers the barrier associated with self-diffusion. The latter utilized an analytical force field fitted to DFT data to simulate CO-induced restructuring on stepped Pt surfaces, and identified a stochastic edge-doubling nucleation followed by zippering as the most likely reconstruction mechanism.

Notable examples for the case of chemical reactions on pristine surfaces are represented by the studies of Goddard III et al. [79,80]—who utilized ab initio MD and enhanced sampling methods to pinpoint critical intermediates in electrochemical CO₂ reduction—and by Vandermause et al. [81], who fitted a Gaussian process of many-body potential to probe reactive events at the H₂–Pt interface, and predicted an activation energy for H₂ splitting and recombination in striking agreement with the experimental value. Machine learning has also been instrumental in the simulation of reactions in solutions, such as urea decomposition in water [82], proton transfer in Na/water mixtures [83], and CH₃SO₃H deprotonation in phenol and phenol/H₂O₂ solvents [84].