(4ez) Thermodynamic Limit of Nanoparticle Disintegration in the Presence of Atom-Trapping Sites

Losing surface atoms from supported metal particles due to sintering is prevalent issue in catalysis, especially for applications such as Diesel Oxidation Catalysts (DOC) where catalysts are exposed to harsh reaction conditions (10% H₂O, ≈ 1073 K and residual air). To combat metal sintering, various strategies such as encapsulating metal particles, increasing the metal support interaction strength by modifying the support, and alloying are proposed in literature. The most common mode of deactivation is Ostwald ripening (OR) mediated by mobile atomic species. These mobile atomic species are ejected from metal particles and facilitate sintering by travelling from smaller particles to bigger particles due to local concentration gradients. However, if the support has a large number of atomic environments (referred to as trapping sites: Figure 1a) that can capture and trap the mobile metal species, Jones et al.¹ showed that these mobile metal species could be beneficial for maintaining a high surface area of metal particles by isolating single atoms or small atomic clusters and prevent particle sintering. Later, Goodman et al.² also observed the same phenomenon of metal nanoparticles disintegrating into single atoms for 0.007% wt. Pd/Al₂O₃, causing deactivation of the methane oxidation catalysts, where single atoms are inactive. However, for high Pd loading (0.659% wt.) of the same Al₂O₃ support, a lower degree of deactivation was observed. Importantly, Pd particle sintering was the dominant process of deactivating high Pd loading catalysts, in which particle disintegration to single atoms was minimal.

Atom trapping has been used as a promising approach to design highly dispersed metal (Fe, Pt, Pd, Au, Ru, and Rh) atoms on various supports such as CeO₂, Al₂O₃, zeolites, and N doped graphene.^3-5 However, almost a decade after Jone’s experimental observations¹ and five years after Goodman’s analysis,² a comprehensive theoretical study on atom trapping and its implications on particle growth, is still lacking. Here, we theoretically investigate a general system consisting of metal nanoparticles and trapping sites using a statistical mechanics approach. Then, we used numerical simulations to test the validity of our findings.

To derive an analytical expression for the equilibrium fraction of single atoms on the support, we express the total free energy change of the nanoparticle to single atom process using the Gibbs free energy for trapping a metal atom (ΔG_bind) in an isolated vacancy site excluding the configurational entropy and the configurational entropy of all single atoms in the support. Then, by minimizing the total Gibbs free energy of the system (Figure 1a), we obtained the fraction of single metal atoms at equilibrium, X_trapped (Figure 1b). Our analysis shows X_trapped is defined by the dimensionless parameter ϕ=total metal atoms/total trapping sites and f=exp[-ΔG_bind/(k_BT)] indicating the pivotal role of support composition and metal-support interaction strength stabilizing single atoms.

Figure 1b shows exergonic binding energies (f > 1) and excess trapping sites (ϕ < 1), in most cases, lead to the complete disintegration of nanoparticles to form single atoms in the trapping sites (e.g., point C). However, if the binding energy is weakly exergonic (ΔG_bind closer to 0 but < 0), then the configurational entropy drives a small fraction (<50%) of metal atoms to particles despite the exothermic binding energy. However, in the first quadrant (e.g., point B), which is representative of systems with exergonic binding energies (f > 1) and a limited amount of trapping sites compared to M atoms in particles (ϕ > 1), the maximum fraction of atom trapping is limited by the number of trapping sites, despite favorable trapping reaction free energies.

In conclusion, thermodynamic analysis of atom trapping reveals the key limiting factors for atom trapping processes as (1) the relative density of trapping sites compared to the metal loading of the system and (2) the atom trapping reaction free energy. A simple analytical expression cannot be derived for the X_trapped without assuming all metal atoms in particles have the same energy and all trapping sites are identical. However, we implemented a numerical simulation that can be adapted to the size (and/or shape) dependent energies of metal atoms on particles and heterogeneity of the trapping sites. Currently, we are expanding the numerical simulation, including additional free energy-driven atom exchange processes such as Ostwald ripening (OR) that could simultaneously occur in a practical system.

Research Interests

My main areas of research interest are, 1) large scale simulations of solvents specifically in mesoporous materials using classical and machine learning potentials, 2) material screening using machine learning with easy to compute and intuitive descriptors, and 3) numerical simulation of electrochemical interfaces. Being a member of computational group (Paolucci group, UVA), I have only limited experience with experiments (6 months internship in Prof. Gounder’s lab at Purdue). However, I am open for experimental research groups work on fields relevant to one or more of above as well because I enjoy both computational and experimental aspects of research.

I did my PhD in Chemical Engineering at the University of Virginia, USA under the supervision of Prof. Christopher Paolucci. My PhD thesis is titled "Computational Modeling of Activation and Deactivation of Supported Metal Catalysts." I have expertise in developing models that capture the essence of physics in catalytic systems using Density Functional Theory (DFT) calculations, Monte Carlo simulations, microkinetic modeling, catalytic material characterization, and kinetic modeling.

Further, I assisted two classes (Numerical methods and Data Science) and participated in research proposal writing and undergraduate student supervision. I engaged in course module development, performing laboratory experiments, grading student coursework, and undergraduate student supervision. Further, I co-taught the CP-515 course module (Numerical Simulation of simultaneous Mass and Heat Transfer) at the University of Peradeniya, Sri Lanka. With these experience and expertise, in my future academic career, I aspire to teach courses related to transport phenomena, reaction engineering and numerical analysis. I believe a postdoc position will give me an opportunity to diversify my teaching and research skills to be successful in academia.