(184f) Modeling of Multi-Dimensional Dynamics Using Layered Algorithms: Application to Lignin Depolymerization and Self-Assembly Simulation with Experimental Validation

Unlike some existing simulation techniques like the molecular dynamic (MD) [1], a kinetic Monte Carlo (kMC) algorithm provides us with feasible simulation results especially for multiscale phenomena, by giving access to the microscopic and stochastic phenomena, and filling the gaps between the processes whose time and length scales are considerably different. It becomes available to incorporate various processes as the kMC algorithm is based on the rate expressions of all involving reactions in the system. Here, the rate constants from those rate expressions form a rate distribution; that is, an event selection pool is generated to randomly pick one event to be executed. Following Poisson distribution, a chosen microscopic event has the same probability of more than one path, so the simulation time is advanced as much as that calculated from an exponential equation [2]. The macroscopic properties can be tracked by the first-principle equations, and the microscopic phenomena are normally described in an properly-sized simulation lattices [3]. Taking advantage of these characteristics, the kMC approach is applied to the broad fields of research, where understanding of the stochastic events is important, such as surface effects [4,5], dissolution events [6,7], polymerization [8], and so on.

However, because of the nature of the kMC algorithm, it is difficult to simulate the processes with substantially different time and length scales. Due to the large dependence on the rate distribution, the probability of slower events can be overlooked [9]. Besides, since the kMC algorithm can only handle one event for each reaction time which is small enough, it is not possible to promote multiscale events simultaneously. In this sense, some slow but vital events tend not to occur frequently enough, thus there is a risk that the entire process can be misrepresented. Moreover, it is sometimes worth to note that the kMC lattice is represented by a coarse-grained model. This reduces the computational requirement significantly by not considering all constituent atoms subject to individual calculation but grouping molecules in a reaction unit to behave identically. However, in case the interactions among grouped atoms become considerable, the kMC algorithm cannot applied to those reacting systems.

In this study, a layered-kMC algorithm is proposed to address this challenge. In a layered approach, the events are classified based on the time scales. Also, the spatial domains are also separated by dividing the simulation lattice sites. In this way, the entire simulation operates avoiding direct competition between different time and length domains. In detail, the events of a smaller scale are performed separately during a series of larger-scale events. In this layered algorithm, therefore, the events having various time and length scales can take place at the same time. In order to address the practicality and feasibility of the layered-kMC approach, it is employed to represent some chemical operations such as lignin depolymerization as well as self assembly with the experimental validation. It is exhibited well that the experimental observation and the simulation results agree with each other.

Literature cited:

[1] Ustinov E. (2019). Kinetic Monte Carlo approach for molecular modeling of adsorption. Curr. Opin. Chem. Eng., 24, 1-11.

[2] Chib S., & Greenberg E. (1995). Understanding the Metropolis-Hastings Algorithm. Am. Stat., 49, 327-335.

[3] Gillespie D.T. (1976). A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys., 22, 403-434.

[4] Martin-Bragado I., Borges R., Balbuena J.P., & Jaraiz M. (2018). Kinetic Monte Carlo simulation for semiconductor processing: A review. Prog. Mater. Sci., 92, 1-32.

[5] Cheimarios N., To D., Kokkoris G., Memos G., & Boudouvis A. (2021). Monte Carlo and Kinetic Monte Carlo Models for Deposition Processes: A Review of Recent Works. Front. Phys., 9, 631918.

[6] Izadifar M., Ukrainczyk N., Salah Uddin K.M., Middendorf B., & Koenders E. (2022). Dissolution of Portlandite in Pure Water: Part 2 Atomistic Kinetic Monte Carlo (KMC) Approach. Materials, 15, 1442.

[7] Martin P., Gaitero J.J., Dolado J.S., & Manzano H. (2021). New Kinetic Monte Carlo Model to Study the Dissolution of Quartz. ACS Earth Space Chem., 5, 516-524.

[8] Rego A.S.C., & Brandão A.L.T. (2021). Parameter Estimation and Kinetic Monte Carlo Simulation of Styrene and n-Butyl Acrylate Copolymerization through ATRP. Ind. Eng. Chem. Res. 60, 8396-8408.

[9] Dybeck E.C., Plaisance C.P., & Neurock M. (2017). Generalized Temporal Acceleration Scheme for Kinetic Monte Carlo Simulations of Surface Catalytic Processes by Scaling the Rates of Fast Reactions. J. Chem. Theory Comput., 13, 1525-1538.