Kinetic Monte Carlo simulations of surface reactions on supported nanoparticles: A novel approach and computer code

Speeding up the Detection of Adsorbate Lateral Interactions in Graph-Theoretical Kinetic Monte Carlo Simulations

Kinetic Monte Carlo (KMC) has become an indispensable tool in heterogeneous catalyst discovery, but realistic simulations remain computationally demanding on account of the need to capture complex and long-range lateral interactions between adsorbates. The Zacros software package (https://zacros.org) adopts a graph-theoretical cluster expansion (CE) framework that allows such interactions to be computed with a high degree of generality and fidelity. This involves solving a series of subgraph isomorphism problems in order to identify relevant interaction patterns in the lattice. In an effort to reduce the computational burden, we have adapted two well-known subgraph isomorphism algorithms, namely, VF2 and RI, for use in KMC simulations and implemented them in Zacros. To benchmark their performance, we simulate a previously established model of catalytic NO oxidation, treating the O* lateral interactions with a series of progressively larger CEs. For CEs with long-range interactions, VF2 and RI are found to provide impressive speedups relative to simpler algorithms. RI performs best, giving speedups reaching more than 150× when combined with OpenMP parallelization. We also simulate a recently developed methane cracking model, showing that RI offers significant improvements in performance at high surface coverages.

A review on microfluidic-assisted nanoparticle synthesis, and their applications using multiscale simulation methods

Recent years have witnessed an increased interest in the development of nanoparticles (NPs) owing to their potential use in a wide variety of biomedical applications, including drug delivery, imaging agents, gene therapy, and vaccines, where recently, lipid nanoparticle mRNA-based vaccines were developed to prevent SARS-CoV-2 causing COVID-19. NPs typically fall into two broad categories: organic and inorganic. Organic NPs mainly include lipid-based and polymer-based nanoparticles, such as liposomes, solid lipid nanoparticles, polymersomes, dendrimers, and polymer micelles. Gold and silver NPs, iron oxide NPs, quantum dots, and carbon and silica-based nanomaterials make up the bulk of the inorganic NPs. These NPs are prepared using a variety of top-down and bottom-up approaches. Microfluidics provide an attractive synthesis alternative and is advantageous compared to the conventional bulk methods. The microfluidic mixing-based production methods offer better control in achieving the desired size, morphology, shape, size distribution, and surface properties of the synthesized NPs. The technology also exhibits excellent process repeatability, fast handling, less sample usage, and yields greater encapsulation efficiencies. In this article, we provide a comprehensive review of the microfluidic-based passive and active mixing techniques for NP synthesis, and their latest developments. Additionally, a summary of microfluidic devices used for NP production is presented. Nonetheless, despite significant advancements in the experimental procedures, complete details of a nanoparticle-based system cannot be deduced from the experiments alone, and thus, multiscale computer simulations are utilized to perform systematic investigations. The work also details the most common multiscale simulation methods and their advancements in unveiling critical mechanisms involved in nanoparticle synthesis and the interaction of nanoparticles with other entities, especially in biomedical and therapeutic systems. Finally, an analysis is provided on the challenges in microfluidics related to nanoparticle synthesis and applications, and the future perspectives, such as large-scale NP synthesis, and hybrid formulations and devices.

Large-scale benchmarks of the time-warp/graph-theoretical kinetic Monte Carlo approach for distributed on-lattice simulations of catalytic kinetics

Motivated by the need to perform large-scale kinetic Monte Carlo (KMC) simulations, in the context of unravelling complex phenomena such as catalyst reconstruction and pattern formation, we extend the work of Ravipati et al. [S. Ravipati, G. D. Savva, I.-A. Christidi, R. Guichard, J. Nielsen, R. Réocreux and M. Stamatakis, Comput. Phys. Commun., 2022, 270, 108148] in benchmarking the performance of a distributed-computing, on-lattice KMC approach. The latter, implemented in our software package Zacros, combines the graph-theoretical KMC framework with the Time-Warp algorithm for parallel discrete event simulations, and entails dividing the lattice into subdomains, each assigned to a processor. The cornerstone of the Time-Warp algorithm is the state queue, to which snapshots of the simulation state are saved regularly, enabling historical KMC information to be corrected when conflicts occur at subdomain boundaries. Focusing on three model systems, we highlight the key Time-Warp parameters that can be tuned to optimise performance. The frequency of state saving, controlled by the state saving interval, δ_snap, is shown to have the largest effect on performance, which favours balancing the overhead of re-simulating KMC history with that of writing state snapshots to memory. Also important is the global virtual time (GVT) computation interval, Δτ_GVT, which has little direct effect on the progress of the simulation but controls how often the state queue memory can be freed up. We also find that pre-allocating memory for the state queue data structure favours performance. These findings will guide users in maximising the efficiency of Zacros or other distributed KMC software, which is a vital step towards realising accurate, meso-scale simulations of heterogeneous catalysis.

Kinetic Monte Carlo simulations for heterogeneous catalysis: Fundamentals, current status, and challenges

Kinetic Monte Carlo (KMC) simulations in combination with first-principles (1p)-based calculations are rapidly becoming the gold-standard computational framework for bridging the gap between the wide range of length scales and time scales over which heterogeneous catalysis unfolds. 1p-KMC simulations provide accurate insights into reactions over surfaces, a vital step toward the rational design of novel catalysts. In this Perspective, we briefly outline basic principles, computational challenges, successful applications, as well as future directions and opportunities of this promising and ever more popular kinetic modeling approach.

Bragg Coherent Diffraction Imaging for In Situ Studies in Electrocatalysis

Electrocatalysis is at the heart of a broad range of physicochemical applications that play an important role in the present and future of a sustainable economy. Among the myriad of different electrocatalysts used in this field, nanomaterials are of ubiquitous importance. An increased surface area/volume ratio compared to bulk makes nanoscale catalysts the preferred choice to perform electrocatalytic reactions. Bragg coherent diffraction imaging (BCDI) was introduced in 2006 and since has been applied to obtain 3D images of crystalline nanomaterials. BCDI provides information about the displacement field, which is directly related to strain. Lattice strain in the catalysts impacts their electronic configuration and, consequently, their binding energy with reaction intermediates. Even though there have been significant improvements since its birth, the fact that the experiments can only be performed at synchrotron facilities and its relatively low resolution to date (∼10 nm spatial resolution) have prevented the popularization of this technique. Herein, we will briefly describe the fundamentals of the technique, including the electrocatalysis relevant information that we can extract from it. Subsequently, we review some of the computational experiments that complement the BCDI data for enhanced information extraction and improved understanding of the underlying nanoscale electrocatalytic processes. We next highlight success stories of BCDI applied to different electrochemical systems and in heterogeneous catalysis to show how the technique can contribute to future studies in electrocatalysis. Finally, we outline current challenges in spatiotemporal resolution limits of BCDI and provide our perspectives on recent developments in synchrotron facilities as well as the role of machine learning and artificial intelligence in addressing them.

Comparison of Queueing Data-Structures for Kinetic Monte Carlo Simulations of Heterogeneous Catalysts

On-lattice kinetic Monte Carlo (KMC) is a computational method used to simulate (among others) physicochemical processes on catalytic surfaces. The KMC algorithm propagates the system through discrete configurations by selecting (with the use of random numbers) the next elementary process to be simulated, e.g., adsorption, desorption, diffusion, or reaction. An implementation of such a selection procedure is the first-reaction method in which all realizable elementary processes are identified and assigned a random occurrence time based on their rate constant. The next event to be executed will then be the one with the minimum interarrival time. Thus, a fast and efficient algorithm for selecting the most imminent process and performing all of the necessary updates on the list of realizable processes post execution is of great importance. In the current work, we implement five data-structures to handle the elementary process queue during a KMC run: an unsorted list, a binary heap, a pairing heap, a one-way skip list, and finally, a novel two-way skip list with a mapping array specialized for KMC simulations. We also investigate the effect of compiler optimizations on the performance of these data-structures on three benchmark models, capturing CO oxidation, a simplified water gas shift mechanism, and a temperature-programmed desorption run. Excluding the least efficient and impractical for large-problems unsorted list, we observe a 3× speedup of the binary or pairing heaps (most efficient) compared to the one-way skip list (least efficient). Compiler optimizations deliver a speedup of up to 1.8×. These benchmarks provide valuable insight into the importance of, often-overlooked, implementation-related aspects of KMC simulations, such as the queueing data-structures. Our results could be particularly useful in guiding the choice of data-structures and algorithms that would minimize the computational cost of large-scale simulations.

A fast species redistribution approach to accelerate the kinetic Monte Carlo simulation for heterogeneous catalysis

The first-principles kinetic Monte Carlo (kMC) simulation has been demonstrated as a reliable multiscale modeling approach in silico to disclose the interplay among all the elementary steps in a complex reaction network for heterogeneous catalysis. Heterogeneous catalytic systems frequently contain fast surface diffusion processes of some adsorbates while the elementary steps in it would be much slower than those in fast diffusion. Consequently, the kMC simulation for these systems is easily trapped in the sub-basins of a super basin on a potential energy surface due to the continuous and repeated sampling of these fast processes, which would significantly increase the total accessible simulation time and even make it impossible to get the reasonable simulation results using the kMC simulation. In this work, we present an improved fast species redistribution (FSR) method for the kMC simulation to overcome the stiffness problem resulting from the low-barrier surface diffusion to accelerate the heterogeneous catalytic kMC simulation. Taking CO oxidations on Pt(111) and Pt(100) as examples, we demonstrate that the FSR approach can properly reproduce the results of an equivalent first-principles microkinetic model simulation with more reasonable reaction rates. The improved kMC simulation based on the FSR method can accurately incorporate the effect of the fast diffusion of species on the surface and provide several orders of magnitude of acceleration compared to the standard kMC simulation.

Dynamic vs static behaviour of a supported nanoparticle with reaction-induced catalytic sites in a lattice model

Modern literature shows a rapidly growing interest to the supported nanocatalysts with dynamic behaviour under reaction conditions. This new frontier of heterogeneous catalysis is recognized as one of the most challenging and worthy of consideration from all possible angles. In this context, a previously suggested lattice model is used to get an insight, by means of kinetic Monte Carlo, into the influence of the mobility of reaction-induced catalytic sites of a two-dimensional supported nanoparticle on the system behaviour. The results speak in favour of feasibility of dynamic nanocatalysts with self-organized structures capable of robust functioning. This approach, from the macroscopic end, is believed to be a useful complement to ever developing experimental and first principle approaches.

A Lattice Kinetic Monte Carlo Solver for First-Principles Microkinetic Trend Studies

Mean-field microkinetic models in combination with Brønsted-Evans-Polanyi like scaling relations have proven highly successful in identifying catalyst materials with good or promising reactivity and selectivity. Analysis of the microkinetic model by means of lattice kinetic Monte Carlo promises a faithful description of a range of atomistic features involving short-range ordering of species in the vicinity of an active site. In this paper, we use the "fruit fly" example reaction of CO oxidation on fcc(111) transition and coinage metals to motivate and develop a lattice kinetic Monte Carlo solver suitable for the numerically challenging case of vastly disparate rate constants. As a result, we show that for the case of infinitely fast diffusion and absence of adsorbate-adsorbate interaction it is, in fact, possible to match the prediction of the mean-field-theory method and the lattice kinetic Monte Carlo method. As a corollary, we conclude that lattice kinetic Monte Carlo simulations of surface chemical reactions are most likely to provide additional insight over mean-field simulations if diffusion limitations or adsorbate-adsorbate interactions have a significant influence on the mixing of the adsorbates.

A Review of Multiscale Computational Methods in Polymeric Materials

Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.