Kinetic Monte Carlo Algorithm Research Articles

Kinetic Monte Carlo study on the effect of growth conditions on the epitaxial growth of 3C–SiC (0001) vicinal surface

Due to the lack of research on the microscopic evolution process and the formation of step growth patterns for SiC crystals, it is of great importance to deepen the understanding of the epitaxial growth of a SiC vicinal surface from a microscopic point of view. In this study, a three-dimensional lattice kinetic Monte Carlo algorithm was used to study the step flow growth characteristics of SiC crystals. The microscopic evolution of the step flow growth patterns for SiC vicinal surfaces was shown. C and Si were treated as the basic particles, and the net deposition and diffusion of atoms were considered in this model. The periodic boundary conditions were applied along the step edge and the helical boundary conditions were applied in the direction perpendicular to the step. The surface morphology evolution of SiC crystals grown on step substrates was simulated at different growth temperatures, partial deposition fluxes, and terrace widths. The results indicated that the growth patterns of the SiC vicinal surface could be transformed from a step flow growth to a nucleation growth pattern by decreasing the growth temperature, increasing the deposition flux, and increasing the terrace width.

Advancing biomass fractionation with real-time prediction of lignin content and MWd: A kMC-based multiscale model for optimized lignin extraction

Recently, lignin has garnered significant research attention due to its abundance in nature. However, lignin is viewed as a recalcitrance factor as it impedes the overall biomass fractionation. In this regard, harsh operating conditions have been applied for the effective separation of the biomass components but they may cause substantial lignin degradation. Another problem is that the overall kinetics of lignin reactions remain limited since current models primarily focus on the cellulose fiber. These pose a challenge when developing effective fractionation strategies for industrial lignin extraction. To this end, we propose a multiscale model and develop a controller to determine the optimal operation strategy. In terms of lignin, delignification and de/repolymerization happen simultaneously but in different length and time scales. We adopted a bilayer structure of the ODEs and kinetic Monte Carlo (kMC) algorithm, accounting for the multiscale reaction kinetics. Our model provides the key outputs including the lignin content in the bulk chip and lignin molecular weight distribution, which were validated with the experiments. Subsequently, we developed a reduced-order model (ROM) for soft sensor design and formulated a model predictive controller (MPC) to determine the optimal operation strategy and then maximize the profitability.

A DFT-based FD-KMC Simulation for Electrodeposition of Copper Nanoparticles on Carbon Electrode Surface

Electrodeposition is often used to load catalysts onto electrode surfaces to enhance their electrochemical activity, thereby improving the performance of redox flow batteries. The kinetic Monte Carlo (KMC) method was used to successfully simulate the nucleation and growth of nanoparticles during the electrodeposition process. However, the reliability of KMC simulation results is closely related to the atomic kinetic parameters derived from quantum-scale calculations. Meanwhile, the electrochemical reaction behaviors during electrodeposition rely on the mass transport of electroactive ions near the electrode surface. To address these issues, density functional theory (DFT) was introduced to obtain the energy barriers required in the calculation of KMC. Simultaneously, the finite difference (FD) method was integrated into the KMC algorithm to provide the transient concentration distribution of the diffusion layer near the electrode surface. This DFT-based FD-KMC method was used to simulate the early stage of electrodeposition of copper (Cu) nanoparticles on carbon electrode surfaces and investigate the effects of bulk concentration and applied potential on the characteristics of deposition morphology of Cu nanoparticles. Additionally, carbon electrode surfaces with different defect site numbers were generated to reveal the influence of surface defect sites on the morphology of the deposited Cu nanoparticles during electrodeposition process.

Understanding differential microemulsion polymerization in continuous slug flow through kinetic Monte Carlo simulation

Microreactors have been universal in polymerization and will help mitigate the residence time distribution and viscosity if conducted in a slug flow regime. The numerical simulation of this practice remains uncharted. Herein, based on our previous study, we proposed a kinetic Monte Carlo algorithm to describe the differential microemulsion polymerization in a biphasic slug flow. Propelled by an automatically spaced refreshment method and other accelerating approaches, the performance of the algorithm was boosted by over forty times. The sensitivity to the model-fitting parameters was analyzed to help understand the underlying mechanisms. After a thorough investigation on the effects of miscellaneous operating conditions regulatable in the continuous slug flow regime, the feasibility of product customization was demonstrated with case studies. Bridging the studies upon kinetics of microemulsion polymerization and interphase mass transfer in microreactors, this work should be able to provide deeper understanding of the process and guide the actual operation.

Calculation of the recombination radii between various point defects and defect clusters in nickel via kinetic Activation Relaxation Technique

The recombination radii between various point defects and defect clusters are essential input parameters for mathematical and computational models of radiation-induced damage evolution. In this work, such recombination radii is calculated by the kinetic Activation Relaxation Technique (k-ART)—an off-lattice, self-learning kinetic Monte Carlo algorithm—in conjunction with molecular dynamics simulations. We found vacancy clusters exhibit larger average recombination radii with interstitials than single vacancies, reaching as large as 2.2a0 (a0 is the lattice parameter of nickel). Such recombination enhancement can be attributed to the intensified distortion near cluster surfaces. Unlike vacancy clusters, free surfaces feature smaller recombination radii than single vacancies. Their recombination radii are correlated with the angle between surface normal and <110> directions. Finally, the recombination radii of interstitial clusters are larger than vacancy clusters and strongly depends on the cluster configurations. Overall, the recombination radii of most internal defect clusters range from ∼2a0 to ∼2.4a0. Because previous research has found that recombination radii affect the density-size distribution of point defect clusters but not the fraction of a particular defect, our analysis suggests that given an accurate initial estimate of cluster density-size distributions, choosing a uniform recombination radius for different clusters in object kinetic Monte Carlo simulations should be sufficient to predict subsequent microstructural evolution.

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.

Achieving Optimal Paper Properties: A Layered Multiscale kMC and LSTM-ANN-Based Control Approach for Kraft Pulping

The growing demand for various types of paper highlights the importance of optimizing the kraft pulping process to achieve desired paper properties. This work proposes a novel multiscale model to optimize the kraft pulping process and obtain desired paper properties. The model combines mass and energy balance equations with a layered kinetic Monte Carlo (kMC) algorithm to predict the degradation of wood chips, the depolymerization of cellulose, and the spatio-temporal evolution of the Kappa number and cellulose degree of polymerization (DP). A surrogate LSTM-ANN model is trained on data generated from the multiscale model under different operating conditions, dealing with both time-varying and time-invariant inputs, and an LSTM-ANN-based model predictive controller is designed to achieve desired set-point values of the Kappa number and cellulose DP while considering process constraints. The results show that the LSTM-ANN-based controller is able to drive the process to desired set-point values with the use of a computationally faster surrogate model with high accuracy and low offset.

Boundary homogenization for patchy surfaces trapping patchy particles.

Trapping diffusive particles at surfaces is a key step in many systems in chemical and biological physics. Trapping often occurs via reactive patches on the surface and/or the particle. The theory of boundary homogenization has been used in many prior works to estimate the effective trapping rate for such a system in the case that either (i) the surface is patchy and the particle is uniformly reactive or (ii) the particle is patchy and the surface is uniformly reactive. In this paper, we estimate the trapping rate for the case that the surface and the particle are both patchy. In particular, the particle diffuses translationally and rotationally and reacts with the surface when a patch on the particle contacts a patch on the surface. We first formulate a stochastic model and derive a five-dimensional partial differential equation describing the reaction time. We then use matched asymptotic analysis to derive the effective trapping rate, assuming that the patches are roughly evenly distributed and occupy a small fraction of the surface and the particle. This trapping rate involves the electrostatic capacitance of a four-dimensional duocylinder, which we compute using a kinetic Monte Carlo algorithm. We further use Brownian local time theory to derive a simple heuristic estimate of the trapping rate and show that it is remarkably close to the asymptotic estimate. Finally, we develop a kinetic Monte Carlo algorithm to simulate the full stochastic system and then use these simulations to confirm the accuracy of our trapping rate estimates and homogenization theory.

Prediction of glassy silica etching with hydrogen fluoride gas by kinetic Monte Carlo simulations.

Understanding the surface properties of glass during the hydrogen fluoride (HF)-based vapor etching process is essential to optimize treatment processes in semiconductor and glass industries. In this work, we investigate an etching process of fused glassy silica by HF gas with kinetic Monte Carlo (KMC) simulations. Detailed pathways of surface reactions between gas molecules and the silica surface with activation energy sets are explicitly implemented in the KMC algorithm for both dry and humid conditions. The KMC model successfully describes the etching of the silica surface with the evolution of surface morphology up to the micron regime. The simulation results show that the calculated etch rate and surface roughness are in good agreement with the experimental results, and the effect of humidity on the etch rate is also confirmed. Development of roughness is theoretically analyzed in terms of surface roughening phenomena, and it is predicted that the values of growth and roughening exponents are 0.19 and 0.33, respectively, suggesting that our model belongs to the Kardar-Parisi-Zhang universality class. Furthermore, the temporal evolution of surface chemistry, specifically surface hydroxyls and fluorine groups, is monitored. The surface density of fluorine moieties is 2.5 times higher than that of the hydroxyl groups, implying that the surface is well fluorinated during vapor etching.

The impact of endoplasmic reticulum morphology on IRE1 protein clustering.

The Unfolded Protein Response (UPR) is a signaling network that responds to an increased load of unfolded proteins within the Endoplasmic Reticulum (ER), referred to as ER stress. ER stress activates the transmembrane signaling protein IRE1, which subsequently forms oligomers and clusters with signaling activity that modifies target gene expression to reestablish ER homeostasis. Experiments have shown that IRE1 clusters can have complex shapes that form along the ER tube structure, including wrapping around an ER tube, and suggest that IRE1 protein clusters tend to be found on narrower ER tubes. However, the influence of ER morphology on the dynamics of these IRE1 clusters remains largely unexplored. We quantitatively modeled the dynamics of IRE1 protein clusters on a tubular surface, using a kinetic Monte Carlo algorithm that treats the IRE1 proteins as particles undergoing stochastic diffusion. We show that cluster shape exhibits a phase transition from approximately round clusters to clusters that wrap around the ER tube as a cluster becomes sufficiently large or on sufficiently narrow tubes. These wrapped clusters, which easily form on narrow tubes, evaporate much slower compared to circular clusters of equal size that form on larger tubes. The threshold concentration between cluster growth and decay is also lower for wrapped clusters compared to circular clusters, exhibiting greater stability of wrapped clusters under varying cellular concentrations of IRE1. This modeled behavior aligns with experimental observations and suggests cluster wrapping around the ER tube is important to understanding IRE1 cluster dynamics and corresponding signaling. UPR malfunction is implicated in the development of many diseases including neurodegeneration and cancer. By furthering understanding of IRE1 protein clustering, we gain insight into how ER morphology controls the IRE1 behavior and impacts UPR signaling

Accelerated kinetic Monte Carlo methods for general nonlocal traffic flow models

This paper presents a class of one-dimensional cellular automata (CA) models on traffic flows, featuring nonlocal look-ahead interactions. We develop kinetic Monte Carlo (KMC) algorithms to simulate the dynamics. The standard KMC method can be inefficient for models with global interactions. We design an accelerated KMC method to reduce the computational complexity in the evaluation of the nonlocal transition rates. We investigate several numerical experiments to demonstrate the efficiency of the accelerated algorithm, and obtain the fundamental diagrams of the dynamics under various parameter settings.

Molecular dynamics based kinetic Monte Carlo simulation for accelerated diffusion

Molecular dynamics (MD) simulations have long been unable to provide significant insights into large-scale processes involving diffusion. Here, we implement a kinetic Monte Carlo (kMC) algorithm to circumvent such issues. We have implemented this approach in the widely used MD simulation package, LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). Validation of the MD/kMC algorithm is achieved by replicating results predicted by diffusion equations. Comparisons are made between a traditional MC approach and the kMC algorithm for the case of L12 phase growth in Ni-Al alloys. These examples highlight the unique advantages provided by the kMC approach to unlock new capabilities for MD simulations.

Area-selective growth for patterning and separation of molecules at allocated sites: Designed kinetic Monte Carlo simulation for anisotropic molecules

Micro-patterning of organic thin films plays a crucial role for organic electronics. Due to the high resolution over large areas, several photo-lithography compatible techniques for the patterning of organic films were developed. As a promising candidate, area-selective growth (ASG), i.e., the growth of molecules on patterned surface for nucleation control, has been proposed. Experimentally, two typical molecules, categorized into non-planar and planar molecular configuration, exhibit different growth behavior, which is mechanistically attributed to binding energy difference and step-edge induction on patterned surface. Benefiting from the diffusion and nucleation sites control of the different configuration molecules, patterning and separation of multi-species molecules at micro-scale were demonstrated. For the ASG of non-planar molecules, the molecular dynamics has been well explored using the kinetic Monte Carlo (KMC) simulations. However, little attention is paid to the step-edge induced ASG for anisotropic molecules. Here, we introduce a coarse-grained anisotropic interaction model in the KMC algorithm to simulate the step-edge induced ASG. Our results reveal that the edges of electrode (Au) patterns become preferential nucleation sites at initial stage, followed by the lateral growth of subsequent particles due to the strong π-π interactions. In combination with the KMC simulation for binding energy difference mechanism, separation of different particles on designed locations are theoretically demonstrated to mimic the molecular separation that experimentally observed. Our results also validate the KMC simulation as a powerful means for the ASG process of anisotropic molecules in a microscopic view, in addition to the ASG process of isotropic molecules. We believe that the KMC method will provide a deeper insight of the ASG method for organic molecules with different molecular architectures.

Accelerated Diffusion Following Deprotection in Chemically Amplified Resists.

Polymeric chemically amplified resists (CARs) are critical materials for high-throughput lithographic processes. A photoactivated acid-anion catalyst changes the polymer's solubility via a deprotection reaction, which enables pattern development through selective dissolution. To capture observed reaction kinetics, reaction-diffusion models employ a catalyst diffusivity that is accelerated by reaction. However, the microscopic origin and factors contributing to this phenomena remain unclear. Herein, we employ detailed atomistic molecular dynamics simulations to examine the impact of protecting group removal and material relaxation on catalyst mobility. We report data on polymer density, catalyst dispersion, excess free volume, and segmental dynamics with increasing time/extent of deprotection. We then propose simple kinetic Monte Carlo algorithms that can describe both molecular dynamics simulations of deprotection reactions and experimental data.

Kinetic modeling of simultaneous polycondensation and free radical polymerization for polyurethane/poly(methyl methacrylate) interpenetrating polymer network

AbstractA comprehensive kinetic Monte Carlo algorithm has been developed to investigate the formation process of a polyurethane/poly(methyl methacrylate) (PU/PMMA) interpenetrating polymer network (IPN), in which a component independent strategy is proposed to perform the simulation of simultaneous polycondensation and free radical polymerization. An empiric diffusion model based on the mass fraction of polymer is used to quantify the effect of diffusional limitations on MMA polymerization. Results show that the presence of acrylic monomers has little impact on the formation rate of PU, but the presence of the PU network can accelerate the polymerization of MMA. In addition, the effects of component mass ratio, acrylic cross‐linker concentration, and [NCO]/[OH] ratio on the IPN formation kinetics are investigated based on the kinetic model. It is believed that the as‐developed modeling strategy can be extended to other IPN systems and provide a better understanding of the interactions between chemically independent networks.

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.

A Lattice Kinetic Monte Carlo method to study drug release from swelling porous delivery systems

We develop a flexible Lattice Kinetic Monte Carlo (LKMC) algorithm that allows us to simulate drug release from swelling systems such as hydrogels. Our algorithm can be used for a wide range of problems as long as the interactions between the drug particles and the medium can be described by a local effective diffusivity. Considering a spherically symmetric swelling system, we test the efficiency and accuracy of our LKMC algorithm by comparing our simulation data to the analytical solution of the diffusion equation in the adiabatic limit.

Multiscale computational fluid dynamics modeling of spatial thermal atomic layer etching

Spatial atomic layer deposition and etching processes have emerged to reduce the overall process time while maintaining the conformity of thin films by functioning continuously. This research constructs an multiscale computational fluid dynamics (CFD) model with a dynamic mesh that combines a microscopic kinetic Monte Carlo algorithm of the film etching with a CFD simulation of the gas phase for the spatial thermal atomic layer etching of Al2O3. Using this model, we evaluate the effect that design and operation variables including the gap distance, purge and precursor gas flow rates, substrate velocity, and vacuum pressure have on the substrate film etching per cycle and uniformity. Numerical results suggest that small gap distances with sufficiently high N2 flow are desired to accomplish effective precursor separation for reactor configuration and the process operation requires low substrate velocities and low vacuum pressures to achieve optimal film quality and conformance.

Efficiency of the vacancy pipe diffusion along an edge dislocation in MgO

This study focuses on the mechanisms of pipe diffusion and the kinetic of point defect diffusion along dislocation line in MgO. We developed a numerical approach, based on atomic scale calculations and the use of the elasticity theory, to determine the migration energies of point defects. The kinetic of diffusion along the dislocation is then evaluated according to a on-lattice atomistic kinetic Monte Carlo algorithm informed by atomistic simulations. We show that edge dislocation in MgO behaves as a strong sink for vacancies which, combined with a lower migration energy at dislocation core region, strongly enhances the diffusion of point defect in the vicinity of the dislocation with respect to the bulk material. At low and intermediate temperatures, pipe diffusion results in an increase of the diffusivity of several order of magnitude. Accounting more precisely for the effect of pipe diffusion may therefore be a key to reconcile the experimentally measured scattering of diffusivity in MgO.

Statistical distribution of spontaneous recombination radii of Frenkel pairs in FCC and BCC metals

The recombination radius of Frenkel pairs induced by incident high-energy particles represents a critical determinant of irradiation-induced microstructure evolution. A better understanding of the atomistic processes controlling recombination can help us determine more accurately the average recombination radius, an essential input parameter of mesoscale models of radiation damage evolution. This work used the kinetic activation relaxation technique—an off-lattice, self-learning kinetic Monte Carlo algorithm in conjunction with molecular dynamics simulations—to study the statistical distribution of the recombination radii in six FCC (nickel, copper, silver, gold, palladium, and platinum) and one BCC (iron) metals. We found that recombination can occur from the 2nd nearest neighbor site to as far as the 15th neighbor site. Long-range recombination is realized via crowdion formation along <110> directions. Vacancies were found to diminish the recombination energy barrier, yet no correlation was found between energy barriers and the average recombination radius. Instead, the average recombination radius increases linearly with elastic constants. Although the atomic displacement fields near self-interstitials are identical in different metals, metals with higher elastic constants exhibit larger local stresses and broader stress distribution, facilitating long-range recombination. Similarly, hydrostatic pressure enhances the average recombination radius by rising elastic constants of the compressed structure. Thus, it is the elastic constants that determine the average recombination radius, not energy barriers.