Kinetic Monte Carlo Approach Research Articles

Second-order mean-field approximation for calculating dynamics in Au-nanoparticle networks.

Exploiting physical processes for fast and energy-efficient computation bears great potential in the advancement of modern hardware components. This paper explores nonlinear charge tunneling in nanoparticle networks, controlled by external voltages. The dynamics are described by a master equation, which expresses the time-evolution of a distribution function over the set of charge occupation numbers. The driving force behind this evolution is charge tunneling events among nanoparticles and their associated rates. We introduce two mean-field approximations to this master equation. By parametrization of the distribution function using its first- and second-order statistical moments, and a subsequent projection of the dynamics onto the resulting moment manifold, one can deterministically calculate expected charges and currents. Unlike a kinetic Monte Carlo approach, which extracts samples from the distribution function, this mean-field approach avoids any random elements. A comparison of results between the mean-field approximation and an already available kinetic Monte Carlo simulation demonstrates great accuracy. Our analysis also reveals that transitioning from a first-order to a second-order approximation significantly enhances the accuracy. Furthermore, we demonstrate the applicability of our approach to time-dependent simulations, using Eulerian time-integration schemes.

Dissolution Mechanisms and Surface Charge of Clay Mineral Nanoparticles: Insights from Kinetic Monte Carlo Simulations

The widespread use of clay minerals and clays in environmental engineering, industry, medicine, and cosmetics largely stems from their adsorption properties and surface charge, as well as their ability to react with water. The dissolution and growth of minerals as a function of pH are closely related to acid–base reactions at their surface sites and their surface charge. The vivid tapestry of different types of surface sites across different types of clay minerals generates difficulties in experimental studies of structure–property relationships. The aim of this paper is to demonstrate how a mesoscale stochastic kinetic Monte Carlo (kMC) approach altogether with atomistic acid-base models and empirical data can be used for understanding the mechanisms of dissolution and surface charge behavior of clay minerals. The surface charge is modeled based on equilibrium equations for de/protonated site populations, which are defined by the pH and site-specific acidity constants (pKas). Lowered activation energy barriers for these sites in de/protonated states introduce pH-dependent effects into the dissolution kinetics. The V-shaped curve observed in laboratory experiments is reproduced with the new kMC model. A generic rate law for clay mineral dissolution as a function of pH is derived from this study. Thus, the kMC approach can be used as a hypothesis-testing tool for the verification of acid–base models for clay and other minerals and their influence on the kinetics of mineral dissolution and growth.

Kinetic Monte Carlo Simulations of Low-Temperature NH3-SCR over Cu-Exchanged Chabazite.

Cu-exchanged chabazite (Cu-CHA) is widely used for ammonia assisted selective catalytic reduction of nitrogen oxides (NH3-SCR). The Cu+ ions are at low temperatures solvated by NH3 forming mobile [Cu(NH3)2]+ complexes. The dynamic behaviour of the complexes is critical as O2 adsorption requires a pair of complexes to form a [Cu2(NH3)4O2]2+ peroxo-species over which NO couples with NH3. Here we introduce a first principles-based kinetic Monte Carlo approach to explore the effect of the Al-distribution on the reaction kinetics of NH3-SCR over Cu-CHA. The method allows us to scrutinize the interplay between the pairing of [Cu(NH3)2]+ complexes and the reaction landscape for the NH3-SCR reaction over the peroxo-complex. The Al-distribution affects the stability of the [Cu(NH3)2]+ pairs as well as the kinetic parameters of the SCR-reaction. The turn-over frequency is determined by the stability of the [Cu(NH3)2]+ pairs and the relative strength of NO and NH3 adsorption once a pair is present. The results establish the hierarchy of effects that influences the performance of Cu-CHA over NH3-SCR and provide a computational basis for further development of the Cu-CHA material.

A kinetic Monte Carlo approach for Boolean logic functionality in gold nanoparticle networks

Nanoparticles interconnected by insulating organic molecules exhibit nonlinear switching behavior at low temperatures. By assembling these switches into a network and manipulating charge transport dynamics through surrounding electrodes, the network can be reconfigurably functionalized to act as any Boolean logic gate. This work introduces a kinetic Monte Carlo-based simulation tool, applying established principles of single electronics to model charge transport dynamics in nanoparticle networks. We functionalize nanoparticle networks as Boolean logic gates and assess their quality using a fitness function. Based on the definition of fitness, we derive new metrics to quantify essential nonlinear properties of the network, including negative differential resistance and nonlinear separability. These nonlinear properties are crucial not only for functionalizing the network as Boolean logic gates but also when our networks are functionalized for brain-inspired computing applications in the future. We address fundamental questions about the dependence of fitness and nonlinear properties on system size, number of surrounding electrodes, and electrode positioning. We assert the overall benefit of having more electrodes, with proximity to the network’s output being pivotal for functionality and nonlinearity. Additionally, we demonstrate an optimal system size and argue for breaking symmetry in electrode positioning to favor nonlinear properties.

Excitation energy transfer in photosynthetic complexes using a kinetic Monte Carlo approach

Excitation energy transfer in photosynthetic complexes using a kinetic Monte Carlo approach

Kinetic Monte Carlo simulation of selective area growth of mix deposited organic molecules

The selective area growth approach (namely the self-assembly of molecules on pre-patterned surfaces) that takes into account the properties of organic molecular materials and traditional lithography techniques, is expected to play a significant role in manufacturing organic micro-nano patterns for photoelectric and full-color display. The manufacture of organic devices with tunable multicolor patterned films depends on the control of nucleation distribution of two or more organic molecules by using a selective area growth approach, particularly through the application of mixed deposition growth that can enhance the nucleation efficiency of multicolor thin films. However, till now the issue of mixed deposition growth of two kinds of organic molecules has been rarely reported, owing to the complexity in experimental operation. In this work, the selective area growth of mixed deposition of two kinds of molecules is studied by molecular kinetic Monte Carlo approach in order to find the experimental conditions for separating two kinds of molecular growth. In the simulation, the interaction energy between the two molecules is adjusted and controlled to study its influence on the separately selective area growth of the two molecules. The results show that when the intermolecular interaction energy is weak, the planar molecules and the non-planar molecules exhibit completely different growth behaviors. The most of non-planar molecules gather at the top of the electrode in an island mode, while planar molecules mainly accumulate in a layer-by-layer mode on the sides of the electrode. On the contrary, when the intermolecular interaction energy is strong, the number of non-planar particles on the tops decreases and a large number of planar particles appear. Moreover, on the sides of the electrode, the doping nucleation of planar molecules and non-planar molecules also exists, resulting in the failure of molecular phase separation growth. It proves that the intermolecular interaction energy can affect separately area-selective growth of various organic molecules. Therefore, when several different kinds of molecules are mixed and deposited, relatively pure crystalline monochromatic films can be obtained at the top and on the sides of the electrode, respectively, by appropriately adjusting the intermolecular interaction energy, which can further facilitate the application of multi-color organic micro-nano pattern in display and other fields.

A combined kinetic Monte Carlo and phase field approach to model thermally activated dislocation motion

In this work, a kinetic Monte Carlo (KMC) scheme is integrated into a phase field dislocation dynamics (PFDD) model to account for thermal activation. While the implementation is general and could be applied to many different thermally activated processes, we apply the model to simulate a dislocation transmitting through an interface. Two cases are analyzed: a dislocation transmitting through a strong interface, and a dislocation transmitting through a more realistic grain boundary in tungsten. Results and trends for both cases are discussed in detail, and ultimately show that the combined KMC-PFDD algorithm is effective in capturing thermally activated dislocation processes.

Carbonation and self-healing in concrete: Kinetic Monte Carlo simulations of mineralization

Industrial applications of carbonation such as self-healing and carbon capture and storage have been limited, due to a lack of reliable predictive models linking the chemistry of carbonation at the molecular scale to microstructure development and macroscopic properties. This work proposes a coarse-grained Kinetic Monte Carlo (KMC) approach to simulate microstructural evolution of a model cement paste during carbonation, along with evolution of pore solution chemistry and saturation indexes of solid species involved. The simulations predict the effective rate constants for Ca(OH)2 dissolution and CaCO3 precipitation as kCa(OH)2 = 2.20 × 10−5 kg/m3/s and kCaCO3 = 4.24 × 10−6 kg/m3/s. These values are directly fed to a macroscale reactive transport model to predict carbonate penetration depth. The rate constants from the molecular scale are used in a boundary nucleation and growth model to predict self-healing of cracks. Subsequently these results are compared with experimental data, and provide good agreement. This proposed multiscale approach can help understand and manage the carbonation of both traditional and new concretes, supporting applications in residual lifetime assessment, carbon capture, and self-healing.

A moving front kinetic Monte Carlo approach to model sessile droplet spreading on superhydrophobic surfaces

This study reports the development of a Moving Front kinetic Monte Carlo (MFkMC) algorithm to capture the behaviour of sessile droplets on pillared superhydrophobic surfaces (SHSs). This model depicts the stochastic evolution a droplet on an SHS as a state-by-state process based on the balance of forces acting locally along the droplet interface length. The proposed SHS-based MFkMC (SHS-MFkMC) model was adapted based on a previously-established MFkMC model that captured droplet spreading on an ideally-smooth surface, and it was developed to accommodate for both Cassie mode wetting and to capture Cassie-to-Wenzel (C2W) transitions of the droplet on the SHS. Furthermore, the SHS-MFkMC model incorporates several novel features needed to accommodate for the geometry and the physics of SHS-based droplet spreading. In particular, the proposed approach incorporates the Periodic Unit (PU) method, which was developed to efficiently map a periodic array of SHS pillars for use in models such as MFkMC. Furthermore, the SHS-MFkMC model accommodates for the additional physics necessary to capture the droplet spreading behaviour across the gaps between the pillars of an SHS (i.e., Cassie mode wetting), as well as to incorporate spontaneous and inertia-driven C2W droplet transitions on the solid surface. The capabilities of the full SHS-MFkMC model to capture both radial sessile droplet spread and C2W transitions are compared to experimental results from within the literature. Furthermore, the developed model’s predictive capabilities are further examined via sensitivity analysis to assess the effects of the various system parameters on the model performance and compare them with the expected system results. Overall, these results demonstrate the SHS-MFkMC model’s ability to predict the droplet spreading behaviour of a given SHS design and to assess its likelihood to undergo C2W transitions.

Exact distributed kinetic Monte Carlo simulations for on-lattice chemical kinetics: lessons learnt from medium- and large-scale benchmarks.

Kinetic Monte Carlo (KMC) simulations have been instrumental in multiscale catalysis studies, enabling the elucidation of the complex dynamics of heterogeneous catalysts and the prediction of macroscopic performance metrics, such as activity and selectivity. However, the accessible length- and time-scales have been a limiting factor in such simulations. For instance, handling lattices containing millions of sites with 'traditional' sequential KMC implementations is prohibitive owing to large memory requirements and long simulation times. We have recently established an approach for exact, distributed, lattice-based simulations of catalytic kinetics which couples the Time-Warp algorithm with the Graph-Theoretical KMC framework, enabling the handling of complex adsorbate lateral interactions and reaction events within large lattices. In this work, we develop a lattice-based variant of the Brusselator system, a prototype chemical oscillator pioneered by Prigogine and Lefever in the late 60s, to benchmark and demonstrate our approach. This system can form spiral wave patterns, which would be computationally intractable with sequential KMC, while our distributed KMC approach can simulate such patterns 15 and 36 times faster with 625 and 1600 processors, respectively. The medium- and large-scale benchmarks thus conducted, demonstrate the robustness of the approach, and reveal computational bottlenecks that could be targeted in further development efforts. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Site Communication in Direct Formation of H2O2 over Single-Atom Pd@Au Nanoparticles

Single atom alloy catalysts offer possibilities to obtain turnover frequencies and selectivities unattainable by their monometallic counterparts. One example is direct formation of H2O2 from O2 and H2 over Pd embedded in Au hosts. Here, a first-principles-based kinetic Monte Carlo approach is developed to investigate the catalytic performance of Pd embedded in Au nanoparticles in an aqueous solution. The simulations reveal an efficient site separation where Pd monomers act as active centers for H2 dissociation, whereas H2O2 is formed over undercoordinated Au sites. After dissociation, atomic H may undergo an exothermic redox reaction, forming a hydronium ion in the solution and a negative charge on the surface. H2O2 is preferably formed from reactions between dissolved H+ and oxygen species on the Au surface. The simulations show that tuning the nanoparticle composition and reaction conditions can enhance the selectivity toward H2O2. The outlined approach is general and applicable for a range of different hydrogenation reactions over single atom alloy nanoparticles.

An Atomistic Model of Field-Induced Resistive Switching in Valence Change Memory

In valence change memory (VCM) cells, the conductance of an insulating switching layer is reversibly modulated by creating and redistributing point defects under an external field. Accurately simulating the switching dynamics of these devices can be difficult due to their typically disordered atomic structures and inhomogeneous arrangements of defects. To address this, we introduce an atomistic framework for modeling VCM cells. It combines a stochastic kinetic Monte Carlo approach for atomic rearrangement with a quantum transport scheme, both parametrized at the ab initio level by using inputs from density functional theory. Each of these steps operates directly on the underlying atomic structure. The model thus directly relates the energy landscape and electronic structure of the device to its switching characteristics. We apply this model to simulate field-induced nonvolatile switching between high- and low-resistance states in a TiN/HfO2/Ti/TiN stack and analyze both the kinetics and stochasticity of the conductance transitions. We also resolve the atomic nature of current flow resulting from the valence change mechanism, finding that conductive paths are formed between the undercoordinated Hf atoms neighboring oxygen vacancies. The model developed here can be applied to different material systems to evaluate their resistive switching potential, both for use as conventional memory cells and as neuromorphic computing primitives.

Methanol Synthesis on Copper-Doped F Centers

We investigate the influence of single copper atoms adsorbed at F centers on the KCl (100) surface on the reaction of adsorbed hydrogen and carbon monoxide with density functional theory methods. Adsorption at an F center strongly stabilizes and reduces the copper atom, as its 4s electron pairs with the defect electron to form a closed-shell state. The Cu-doped F center readily reduces adsorbed formaldehyde and strongly interacts with carbon monoxide and methanol, weakening and activating intramolecular bonds, but unlike the empty F center, it does not dissociate methanol. During hydrogenation of adsorbed CO and CH3OH, hydrogen reacts with the adsorbed copper atom to form a stable linear HCuH complex. The hydrogen affinity of the copper atom facilitates the reaction of adsorbed molecules with hydrogen molecules as well as the attachment and removal of hydrogen atoms, enabling a fast synthesis route from carbon monoxide to methanol. The rate-limiting step of the reaction is the final hydrogenation, which recovers the active center and liberates methanol. Computing the thermodynamic and kinetic parameters of the intermediates and transition states and simulating the reaction pathway with a kinetic Monte Carlo approach, we obtained a turnover frequency of 230 s–1 per active site at 500 K and 50 bar with a 1:9 ratio of CO/H2, exceeding the rate on the empty defect by 3 orders of magnitude and the conventional catalyst by 4 orders of magnitude. The present results indicate that the addition of a metal atom to the alkali halide F center can enhance, stabilize, and control its reactivity. In the case of copper, they point toward the existence of a synthesis route for methanol with an overall activity comparable to the conventional copper-based catalysts but with much smaller metal loading.

Exchange bias model including setting process: Investigation of antiferromagnetic alignment fraction due to thermal activation

An exchange bias (EB) model taking the setting process into account is developed to study the effect of the crucial parameters, such as the AFM anisotropy constant (KAF), the setting temperature (Tset), and the physical microstructure on the exchange bias field of an AFM/FM system. The magnetization dynamics of the EB system is treated using the kinetic Monte Carlo approach and by integrating the Landau–Lifshitz–Gilbert equation for AFM and FM layers, respectively. We first investigate the variation of the exchange bias field (HEB) as a function of KAF in the IrMn/CoFe system. It is found that HEB strongly depends on the energy barrier dispersion determined by dispersions of KAF and the grain volume. It is shown that the HEB is affected by the physical microstructure of the IrMn layer: film thickness and grain diameter. We also demonstrate that the maximum setting fraction (fset) related to HEB can be achieved by optimizing the value of KAF and Tset. The simulation results of the setting process are in good agreement with previous experimental works. This confirms the validity of the EB model, including the setting process that can be used as a powerful tool for the application of spintronics, especially for read sensor design to achieve high thermal stability with scaling down of components.

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, δsnap, 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, ΔτGVT, 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.

Prediction of the evolution of defects induced by the heated implantation process: Contribution of kinetic Monte Carlo in a multi-scale modeling framework

Extended defects formed as a result of heated implantation and thermal annealing are studied using transmission electron microscopy and kinetic Monte Carlo simulations. We highlight the relevance of using kinetic Monte Carlo approach to provide information to continuum-scale simulations as well as the value of integrating data from atomic-scale calculations for its calibration.

Gaining Insight into the Electrochemical Interface Dynamics in an Organic Redox Flow Battery with a Kinetic Monte Carlo Approach (Small 43/2022)

Gaining Insight into the Electrochemical Interface Dynamics in an Organic Redox Flow Battery with a Kinetic Monte Carlo Approach (Small 43/2022)

Dissolution of β-C2S Cement Clinker: Part 2 Atomistic Kinetic Monte Carlo (KMC) Upscaling Approach.

Cement clinkers containing mainly belite (β-C2S as a model crystal), replacing alite, offer a promising solution for the development of environmentally friendly solutions to reduce the high level of CO2 emissions in the production of Portland cement. However, the much lower reactivity of belite compared to alite limits the widespread use of belite cements. Therefore, this work presents a fundamental atomistic computational approach for comprehending and quantifying the mesoscopic forward dissolution rate of β-C2S, applied to two reactive crystal facets of (100) and (). For this, an atomistic kinetic Monte Carlo (KMC) upscaling approach for cement clinker was developed. It was based on the calculated activation energies (ΔG*) under far-from-equilibrium conditions obtained by a molecular dynamic simulation using the combined approach of ReaxFF and metadynamics, as described in the Part 1 paper in this Special Issue. Thus, the individual atomistic dissolution rates were used as input parameters for implementing the KMC upscaling approach coded in MATLAB to study the dissolution time and morphology changes at the mesoscopic scale. Four different cases and 21 event scenarios were considered for the dissolution of calcium atoms (Ca) and silicate monomers. For this purpose, the (100) and () facets of a β-C2S crystal were considered using periodic boundary conditions (PBCs). In order to demonstrate the statistical nature of the KMC approach, 40 numerical realizations were presented. The major findings showed a striking layer-by-layer dissolution mechanism in the case of an ideal crystal, where the total dissolution rate was limited by the much slower dissolution of the silicate monomer compared to Ca. The introduction of crystal defects, namely cutting the edges at two crystal boundaries, increased the overall average dissolution rate by a factor of 519.

Modeling of polystyrene degradation using kinetic Monte Carlo

Polystyrene chemical recycling via pyrolysis constitutes an appropriate route for disposal of post-consumption material as high styrene amounts can be obtained and used for the production of recycled styrene-based materials, avoiding the use of virgin fossil feedstocks. However, although significant amounts of experimental polystyrene pyrolysis data have been published for different operation conditions and reactors, modeling studies about the degradation mechanism are relatively scarce, which corroborates the existence of few investigations related to the scaling-up and optimization of these processes. In a scenario of urgency to solve post-consumer waste, global warming and depletion of natural resources, filling up this gap is mandatory. Therefore, in order to understand and describe the kinetic degradation dynamics of polystyrene through pyrolytic processes, a literature review was performed and a detailed mechanistic model was developed and implemented with help of a fast kinetic Monte Carlo approach. Three reaction temperatures were then used to validate the proposed model (500, 600, and 700 ∘C), based on experimental data obtained through micropyrolysis experiments. The quality of the obtained fits and, importantly, the fast computational time proved the methodology to be an easy and smart alternative for the implementation of kinetic polystyrene pyrolysis models.

Gaining Insight into the Electrochemical Interface Dynamics in an Organic Redox Flow Battery with a Kinetic Monte Carlo Approach.

Finding low-cost and nontoxic redox couples for organic redox flow batteries is challenging due to unrevealed reaction mechanisms and side reactions. In this study, a 3D kinetic Monte Carlo model to study the electrode-anolyte interface of a methyl viologen-based organic redox flow battery is presented. This model captures various electrode processes, such as ionic displacement and degradation of active materials. The workflow consists of input parameters obtained from density functional theory calculations, a kinetic Monte Carlo algorithm to simulate the discharging process, and an electric double layer model to account for the electric field distribution near the electrode surface. Galvanostatic discharge is simulated at different anolyte concentrations and input current densities, which demonstrate that the model captured the formation of the electrical double layer due to ionic transport. The simulated electrochemical kinetics (potential, charge density) are found to be in agreement with the Nernst equation and the obtained EDL structure corresponded with published molecular dynamics results. The model's flexibility allows further applications of simulating the behavior of different redox couples and makes it possible to consider other molecular-scale phenomena. This study paves the way for computational screening of active species by assessing their potential kinetics in electrochemical environments.