Direct simulation Monte Carlo for simultaneous nucleation, coagulation, and surface growth in dispersed systems

A Monte Carlo simulation technique is developed to describe dispersed phase systems. The method is formulated for simultaneous coagulation, nucleation and surface growth, but can be extended to include other processes. These processes are considered in an initially constant simulation volume. The changes in the particle ensemble are determined by a random choice procedure, while the particle number in the simulation volume changes according to the chosen events. Every time, when the particle number in the simulation volume increases or decreases by a factor of two of its initial value, the simulation volume is halved or doubled, respectively. Therefore, this method is called a stepwise constant-volume Monte Carlo simulation. It allows to use only several thousands simulation particles, even if the particle number concentration experiences changes of several orders of magnitude. The simulations are validated through a comparison with the exact mathematical solutions for several simple cases. An example of simultaneous nucleation and coagulation in the free-molecular region demonstrates, that the stepwise constant-volume Monte Carlo simulations lead to more accurate results than the constant-number Monte Carlo simulations.     

Monte Carlo simulation of copolymerization and compositional inhomogeneity of copolymers: comparison to experimental data

A review is given of the methods used to calculate copolymer composition as a function of chain length. A Monte Carlo simulation of copolymerization, which considers the initiation and propagation steps and yields cumulative copolymer composition as a function of chain length, is described in detail. The results of the simulations for three copolymer systems show that the initiation step significantly influences the short chains but its effect rapidly vanishes with increasing chain length. The results of the simulations for the three copolymer systems are compared to experimentally determined composition-chain length distributions. The agreement of the simulations and the experimental data is good for long chains but poor for short chains.     

A hybrid stochastic-deterministic algorithm for lattice-gas models of catalytic reactions and the computation of TPD spectra

We present a hybrid numerical approach for modeling surface reactions in the framework of a lattice-gas model with lateral interactions between adsorbed particles. A hybrid multiscale algorithm, which we refer to as Quasi-Equilibrium Kinetic Monte Carlo (QE-KMC), comprises traditional Metropolis Monte Carlo (MMC) simulations of equilibrium systems and standard numerical methods for deterministic ordinary differential equations (ODEs). The functional dependence of these ODEs on the macroscopic state variables (adsorbate coverages) is not explicitly known, but their right-hand sides can be evaluated “on the fly” with prescribed accuracy by means of the MMC simulations. At the time scale of these ODEs it is assumed that an equilibrium statistical distribution of adsorbed particles on an infinite lattice is attained at every moment in time due to infinitely fast surface diffusion. QE-KMC and conventional KMC simulations are used to study the temperature-programmed desorption (TPD) spectra of adsorbed particles. We critically discuss results of previous studies that applied Monte Carlo simulations to describe the TPD spectra in the case of fast adsorbate diffusion and strong lateral interactions. We show that the quasi-equilibrium TPD spectra can be quickly and accurately estimated by the QE-KMC algorithm, while the KMC simulations require much more extensive computational resources to obtain the same results.     

The use of Monte Carlo simulation to evaluate the optical properties of polyester fabric treated with titanium dioxide nanopigments

The current study utilises Monte Carlo simulation and Mie scattering theory to estimate the reflectance spectra of fabric coated with titanium dioxide nanopigments of various diameters and concentrations. Image processing was carried out and experimental data were gathered to evaluate the performance of Monte Carlo simulation. The distribution and location of the nanopigments on the surface of fabric were determined using the Monte Carlo method. Reflection of the fabric was calculated based on Monte Carlo simulation with the partitive mixing method and Mie theory. According to the experimental and simulation results, the reflectance of coated samples was increased by increasing the concentration and number of titanium dioxide nanoparticles. There was a good match between the results obtained by Monte Carlo simulation and the experimental results. For coated samples (dTiO₂: 500 nm), the root mean square error between measured and predicted reflectance by the Monte Carlo and partitive mixing method and by Monte Carlo and Mie theory was 0.022 and 0.0078, respectively. The results indicate that the performance of the Monte Carlo and Mie method was better than that of the Monte Carlo and partitive mixing method. According to t-test analysis, there was no statistically significant difference between the experimental data and Monte Carlo simulation.     

Coupled simulation of heat transfer and reaction in a steam reforming furnace

For design and simulation of chemical process furnaces in accordance with present-day standards, the temperature distributions in the firebox and in the reactors must be generated simultaneously. This calls for coupling of the simulations of the firebox and of the reactor. For the calculation of heat transfer in the firebox, a generalized furnace simulations program, based on the zone method, is applied. Monte Carlo simulation techniques are used to determine the view factors. The location of the burners is explicitly accounted for. Absorption and emission of radiation by the flue gas are calculated by considering band contributions for carbon dioxide and water. For the simulation of the steam reforming reactors, a one-dimensional heterogeneous model, which accounts for the presence of intraparticle partial pressure gradients, is used. The simulated temperature distribution in the furnace is in excellent agreement with industrial results, as is the simulated product distribution.     

D4/APAEDMS本体开环共聚反应的Monte Carlo模拟

Monte Carlo方法模拟八甲基环四硅氧烷与N-β-氨乙基-γ-氨丙基甲基二甲氧基硅烷（D₄/APAEDMS）的本体开环共聚动力学.在兼顾模拟精度与计算经济性基础上,模拟过程采用自由体积理论简化处理扩散效应并与本征反应动力学耦合.本征动力学常数通过模拟主要共聚基元反应得到,基于优化的动力学常数通过模拟从分子水平揭示：（1）D₄/APAEDMS本体开环共聚存在总活性基团的“稳态”行为;（2）D₄/APAEDMS本体开环共聚反应过程的重均分子量与数均分子量以及分子量分布系数存在“突变”特性.     

Acceleration of kinetic monte carlo simulations of free radical copolymerization: A hybrid approach with scaling

Kinetic Monte Carlo (KMC) has been widely used in the simulation of polymeric reactions. The power of KMC is highlighted by its ability to keep track of the length and sequence of every radical or polymer chain, while it is computationally more expensive than deterministic kinetic models. This paper introduces an acceleration method that significantly reduces the computational cost of KMC simulations, while keeping the same features as the full kinetic Monte Carlo simulations. Case studies are used to demonstrate the general applicability of this method to free radical copolymerization. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4013–4021, 2017     

Monte Carlo simulation of microstructure evolution in biphasic-systems

Over the past few decades, a variety of models have been proposed in order to investigate the grain growth kinetics and the development of crystallographic textures in polycrystalline materials. In particular, a full understanding of the microstructure evolution is a key issue for ceramic systems, since their mechanical or thermal behaviour is intimately related to their microstructure. Moreover, the development of appropriate simulative tools is crucial to reproduce, control and finally optimize the solid-state sintering process of ceramics. Monte Carlo simulations are particularly attractive because of their ability to reproduce the statistical behaviour of atoms and grain boundaries with time. However, Monte Carlo simulations applied to two-phase materials, such as many ceramic systems, result complex because both grain growth and diffusion processes should be taken into account. Here the Monte Carlo Potts model, which is widely used to investigate the crystallization kinetics for monophasic systems, is modified and extended to biphasic ones. The proposed model maps the microstructure onto a discrete lattice. Each lattice element contains a number representing its phase and its crystallographic orientation. The grain formation and growth are simulated by appropriate switching and reorientation attempts involving the lattice elements. The effect of temperature is also discussed.     

Monte Carlo Prediction of Non-Newtonian Viscous Sintering: Experimental Validation for the Two-Glass-Cylinder System

From the Monte Carlo methodology based on a non-discrete potential and developed to model capillary-driven mass transport, a relation between the Monte Carlo step and the physical time has been defined as a function of the viscosity coefficient. The experimental kinetics of the shortening of a unique glass cylinder and the sintering of two-glass cylinders at 950°C then have been compared with the numerically obtained results. The original result indicates that the active sintering mechanism for a glass under the given sintering conditions is not Newtonian viscous flow alone, a finding that corresponds perfectly well with the Monte Carlo simulation.     

Molecular simulation of CH4 adsorption behavior in slit nanopores: Verification of simulation methods and models

The aim of this study is to select an appropriate method for CH₄ adsorption in organic nanopores for shale-gas development. Molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) simulations were performed. Three comparison studies were included: (i) comparison of the adsorption behavior in kerogen nanopores using different schemes for dispersion correction, (ii) comparison of the adsorption behavior in graphite nanopores using MD and GCMC simulations, and (iii) comparison of the adsorption behavior in kerogen and graphite nanopores using MD simulations. The result was reliable when using a particle-mesh Ewald scheme or a cut-off ≥1.5 nm without dispersion correction. The simulation results were essentially identical for the MD and GCMC simulations. The free-gas CH₄ density inside the nanopores started to deviate from the bulk density at ~2 nm for the graphite model and at ~7–10 nm for the kerogen model, whereas the total CH₄ density deviates from the bulk density at ~20 nm.     

Motion and sorption of gas molecules in poly(octadecyl acrylate)

Monte Carlo simulations are reported on the sorption and motion of small gas molecules (CH₄ and CO₂) in poly(octadecyl acrylate), a typical comb-like polymer with biphasic structure. Calculations were performed using a computational procedure recently developed by us, which is suitable to simulate the motion and sorption of small molecules in dense comb-like polymers. To our knowledge, the problem of gas transport in comb-like polymers using explicit penetrant molecules is for the first time studied by computational techniques. The study involves more than 12 million Monte Carlo steps of systems constituted by more than 1470 explicit atoms/pseudoatoms. Solubility coefficients are discussed by comparison with recently reported experimental data.     

Monte Carlo simulation of particle breakage process during grinding

The Monte Carlo method is quite useful in the modeling of particulate systems. It is used here to simulate the particle brekage process during grinding that can be represented by a population balance equation. The simulation technique is free from discretization of time or size. The results of simulation under restricted conditions of grinding compare very well with the available analytical solution of the population balance equation. The procedure is extended to simulate the grinding process in its entirety. This method provides an alternative to the modeling of the grinding process where the governing population balance equation cannot be readily solved.     

分子模拟与化学工程

从分子水平来研究化工过程及产品的开发和设计是21世纪化学工程的一个重要方向.综述了计算机分子模拟中的MonteCarlo分子模拟和分子动力学模拟两种方法及其在化工中的应用,涉及分子模拟在建立状态方程和研究分子微观结构、相界面、扩散性质等方面的应用进展.指出分子模拟对化学工程的基础研究、工艺过程以及新产品开发将发挥巨大作用.     

高分子构象模拟研究中的Monte Carlo方法

介绍了Monte Carlo方法及其特点,进而分析了Monte Carlo用于高分子模拟的优势,并描述了两类模拟模型。论文重点综述了近年来Monte Carlo方法在高分子构象模拟中的一些研究与应用,并展望了Monte Carlo方法在高分子构象模拟中的发展趋势和前景。     

Molecular simulation,experiments and modelling of single adsorption capacity of 4A molecular sieve for CO2–CH4 separation

Monte Carlo simulation of CO₂ and CH₄ adsorption on zeolite 4A is carried out in grand canonical Monte Carlo (GCMC) simulation. LTA framework was used to reproduce the structure of zeolite 4A. A comparison between the structure and properties of this zeolite and 13X, ZSM-5, 4A and 3A is performed and the results are included in the article. Universal force field was used for calculation of intermolecular forces. Our own experiments were also carried out to reinvestigate the simulation results. Ewald summation method was used for calculating electrostatic forces and atom based method was applied for van der Waals forces. The simulation results show good agreement with experimental results. Highest CO₂ adsorption capacity of zeolite 4A was in good agreement with experiments at the same pressure ranges, and was found to be 3.17 mol/kg from GCMC. Isosteric heat of adsorption was calculated to find the heat released during adsorption of each gas. Finally simulation results were fitted to four isotherms to find the best fit.     

用于吸附过程开发的从分子水平级开始的多尺度模拟

This article presents a multiscale simulation approach starting at the molecular level for the adsorption process development. A grand canonical Monte Carlo method is used for the prediction of adsorption isotherms of methanol on an activated carbon at the molecular level. The adsorption isotherms obtained in the linear region （or adsorption constant） are exploited as a model parameter required for the adsorption process simulation. The adsorption process model described by a set of partial differential equations （PDEs） is solved by using the conservation element and solution element method, which produces a fast and an accurate numerical solution to PDEs. The simulation results obtained from the adsorption constant estimated at the molecular level are in good agreement with the experimental results of the pulse response. The systematical multiscale simulation approach addressed in this study may be useful to accelerate the adsorption process development by reducing the number of experiments.     

Curing of styrene‐free unsaturated polyester alkyd: synthesis,characterization and simulation

Experimental and simulation studies of the crosslinking process of styrene‐free unsaturated polyester (UP) alkyd chains are presented. The thermal and mechanical properties of the crosslinked UP alkyd are studied as a function of the peroxide concentration. The characterized and simulated thermoset matrix properties are compared. Simulation of the crosslinking reaction is used to improve the understanding of the process and to define the species involved in it. The main experimental characterization tools used were differential scanning calorimetry and dynamic mechanical analysis. The main simulation tools used were a Monte Carlo procedure for the crosslinking process and a density functional theory‐based quantum code for the scission process. Good agreement between the experimental and simulation results was achieved. Copyright © 2010 Society of Chemical Industry     

聚合物材料力学性能的计算机模拟

聚合物材料的宏观力学性能与其微观结构具有密切的关系,计算机模拟是研究这种结构与性能关系的重要手段之一,近年来国内外学者已经发展了多种模拟方法并从不同尺度来模拟聚合物材料的力学性能。本文综述了不同方法在聚合物材料力学性能模拟研究中的应用,重点介绍了Monte Carlo模拟、分子动力学模拟和基于弹簧格子模型的多尺度模拟这3种常见模拟方法的应用情况,如在分子动力学模拟中重点关注无定形聚合物玻璃态、结晶聚乙烯和部分非均质体系,而在多尺度模拟中则重点关注复杂的非均质聚合物体系,并讨论了各种方法的应用前景及亟待解决的问题。     

Molecular-Level Characterization of Heterogeneous Catalytic Systems by Algorithmic Time Dependent Monte Carlo

Monte Carlo algorithms and codes, used to study heterogeneous catalytic systems in the frame of the computational section of the NANOCAT project, are presented along with some exemplifying applications and results. In particular, time dependent Monte Carlo methods supported by high level quantum chemical information employed in the field of heterogeneous catalysis are focused. Technical details of the present algorithmic Monte Carlo development as well as possible evolution aimed at a deeper interrelationship of quantum and stochastic methods are discussed, pointing to two different aspects: the thermal-effect involvement and the three-dimensional catalytic matrix simulation. As topical applications, (i) the isothermal and isobaric adsorption of CO on Group 10 metal surfaces, (ii) the hydrogenation on metal supported catalysts of organic substrates in two-phase and three-phase reactors, and (iii) the isomerization of but-2-ene species in three-dimensional supported and unsupported zeolite models are presented.     

Monte Carlo simulation of polyampholyte-nanoparticle complexation

The complexation between a polyampholyte and a charged particle was investigated via Monte Carlo simulations on an off-lattice. The simulations revealed that there are three regions for the conformation of the complex formed between a positively charged particle and a polyampholyte chain. When the charge density and the size of the particle were small, the chain adsorbed on the particle surface maintained to a large extent its configuration from the bulk (spherical, dumb-bell, necklace or rod-like). By increasing the charge density and the particle size, the polyampholyte chain has collapsed on the surface. Further increases of the charge density and size of the particle caused a segregation of the beads of the sub-chains with mostly positive charges from those with mostly negative charges, those richer in positive charges being repelled by the particle. The simulation results are compared with some analytical results.