Monte Carlo Study of Binary Copolymerizations. 1. Ultimate and Penultimate Effect,Applications

The Monte Carlo models of binary irreversible copolymeriza-tion with ultimate and penultimate effect are applied to the copolymerization of acrylic acid and methyl acrylate, and styrene and benzylidene malononitrile, respectively. The agreement with available experimental data is quite good. A comparative study between the formal kinetics model and the Monte Carlo model reveals that statements concerning the copolymer composition are robust, but statements concerning the sequence distribution are not always robust.     

D_4/N-β-氨乙基-γ-氨丙基甲基二甲氧基硅烷本体共聚反应聚合度变化的Monte Carlo模拟

用MonteCarlo方法模拟八甲基环四硅氧烷 (D4 )与N β 氨乙基 γ 氨丙基甲基二甲氧基硅烷(APAEDMS)的本体开环共聚动力学 .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D4 APAEDMS本体开环共聚反应过程主要表现为活性阴离子聚合行为 ,同时又伴有部分逐步聚合特征 .     

Zur kopolymerisation: Axiomatische formulierung eines mathematischen modells,das memory 3 programm—anwendungen

This paper presents an axiomatic mathematical model for binary copolymerization reactions. The FØRTRAN program entitled MEMØRY 3 is described. This program implements the Monte Carlo version of the axiomatic model, computing the most probable sequence distribution. Finally, a concrete copolymerization process is studied and good results are presented.     

Das Monte Carlo-studium der binären copolymerisation in der annahme des vorletzten Effektes. I. Theorie,MEMORY 5-programm,anwendungen

This paper presents a mathematical model (using the Monte Carlo technique) for the building of a binary copolymer considering the penultimate effect. One discusses the algorithm and the computer implementation. Finally, two applications are given. The purpose of this series of papers is to provide a Monte Carlo method to compute the sequence distribution for the hypothesis of penultimate effect (program MEMORY 5), ultimate effect (program MEMORY 3), and copolymerization with depolymerization (program MEMORY 6).     

STUDY ON THE SEQUENCE STRUCTURE OF SBR BY 13C-NMR METHOD Ⅵ MONTE CARLO SIMULATION OF THE SEQUENCE OF SBR

A program of Monte Carlo simulation of binary copolymerization for E-SBR (emulsion polymn. SB rubber) was made according to the terminal model. The simulation results obtained by this program were in good agreement with those experimental ones. A detail microstructure information of E-SBR molecular chain has been provided.     

二元共聚反应的蒙特卡罗模拟(Ⅰ)——末端模型与共聚物的序列分布

本文根据蒙特卡罗方法的原理,编写了微机用BASIC程序,供模拟末端模型二元共聚反应使用。形成的共聚物分子链中两单元的各种段的数目,是跟模拟一道统计的。用该程序获得的结果,与用一级马尔可夫链算出者极其接近,该程序可用来研究由末端模型形成的二元共聚物的序列分布。     

Equilibrium copolymerization of tetrahydrofuran-3-methyltetrahydrofuran

The bulk cationic copolymerization of tetrahydrofuran and 3-methyl-tetrahydrofuran was studied at 0°C with acetylhexafluoroantimonate as initiator. The experimental equilibrium concentrations of both monomers were determined in all the intervals of composition, and the results obtained were compared with those calculated by different methods developed to study copolymerization systems in which depropagation reactions play an important role. In particular, very good agreement between calculated and experimental values was obtained by using Monte Carlo methods of simulation that allow the determination of the unknown cross-propagation and cross-depropagation rate constants, a necessary condition to calculate the equilibrium monomer concentrations.     

Copolymerization kinetics of methyl methacrylate-styrene obtained by PLP-MALDI-ToF-MS

The combination of MALDI-ToF-MS and pulsed laser polymerization has been used to study the propagation rate coefficients for the copolymer system styrene-methyl methacrylate. For the first time, complete information regarding mode of termination, reactivity of photoinitiator-derived radicals, copolymer molecular mass, chemical composition, and copolymerization rates is obtained interrelated. The polymerizations were carried out in bulk with varying styrene concentrations at a temperature of 15.2 degrees C by an excimer pulsed laser with varying frequencies. Both chemical composition distributions and molecular weight distributions were determined by MALDI-ToF-MS. The data were fitted to the implicit penultimate unit model and have resulted in new point estimates of the monomer and radical reactivity ratios for the copolymer system styrene-methyl methacrylate: r(St) = 0.517, r(MMA) = 0.420, s(St) = 0.296, s(MMA) = 0.262. Comparison between Monte Carlo simulations and the obtained results further confirmed the very successful combination of pulsed laser copolymerization experiments with MALDI-ToF-MS. The obtained results are believed to be the most accurate and complete set of copolymerization parameters to date.     

Copolymerization with depropagation. IV. Computer simulation of copolymerization with reversibility

The results of Monte Carlo computer simulations of vinyl copolymerizations with complete reversibility are described for a variety of hypothetical systems using values of thermodynamic quantities typically found. Composition of copolymer, sequence distributions, relative chain lengths and equilibrium behavior have all been investigated. The existence of thermodynamic control of copolymerization behavior becomes more obvious as temperature is increased in some systems but may be masked by kinetic factors in others.     

计算机Monte Carlo法模拟自由基交联共聚网络结构的增长

本文成功地用MonteCarlo方法模拟了以画面方式表示的苯乙烯-二乙烯苯交联共聚反应中大分子链增长、支化及交联的进化情况，并给出了相应的转化率，以定量模型的方式描述了该类反应。     

Das Monte Carlo-studium der verteilung der sequenzen in den copolymeren des methylmethacrylats mit chloropren und des 2-hydroxyäthyl-methacrylats mit alkylacrylaten

Using our Monte Carlo model of binary copolymerization, one studies the sequence distribution in methyl methacrylate/chloroprene and 2-hydroxyethyl methacrylate/alkyl acrylate copolymers. Our study points out incontestably that the copolymerization of methyl methacrylate is explainable through ultimate group effect (Ebdon has stated a penultimate group effect). In the case of 2-hydroxyethyl methacrylate/alkyl acrylate copolymers the agreement between computed and experimental data is satisfactory.     

Steady State and Equilibrium in Reversible Copolymerization at Constant Comonomer Concentrations

Selected aspects of copolymerization processes carried on at constant comonomer concentrations are analyzed theoretically and modeled by Monte Carlo method. It is confirmed that some combinations of initial parameters lead to stationary conditions of copolymer formation for both irreversible and reversible systems which can be regarded as the first‐order Markov chain process. However, this study shows that for many copolymerization systems the stationary conditions are attained only at high number‐average degree of polymerization DP _n, and for some reversible copolymerizations, attaining equilibrium, stationary conditions are not observed at all. The analysis shows that the chain length distribution (CLD) for copolymerization carried out under steady state conditions at constant comonomer concentrations, equal to equilibrium concentrations for infinitely high DP _n, is approximately described by the modified Bessel and exponential functions. This type of CLD is analytically proved and confirmed by the Monte Carlo simulations for the analogous homopolymerization process.     

Photon-electron energy deposition in CANDU reactor channels: Simulation and modelling

Simulation of photon-electron transport in a CANDU reactor fuel channel using the Monte Carlo method for calculating the energy deposition in the coolant is studied. The geometry of the CANDU fuel channel is very complex so methods that make such simulations more practicable, without adversely affecting the results, are introduced. In this regard, the use of simplifying assumptions and simplified geometrical models on the performance of two different Monte Carlo codes has been compared. An ETRAN-based code (SANDYL), and the code EGS4 produced comparable results, although the former performs faster in accounting for low energy electrons. A simplified computational model is also introduced. This model is based on decoupling photon-electron transport simulations by the use of electron-energy-transfer functions. The results obtained using the model are successfully validated using the EGS4 and SANDYL codes. A significant computational speedup (about a factor of seven compared to Monte Carlo simulations) is achieved with this model.     

Biospecific Properties of Random Copolymers, 1

The kinetic study of copolymer synthesis is important to understand how a material is built and how it can get some particular properties. The radical copolymerization of one, two or more monomers can be simulated with classical analytic models, but can also be simulated by a Monte Carlo model that allows a bigger flexibility and is a lot easier to compute and use. We have shown that this Monte Carlo simulation gives the same results of the kinetic study of the terpolymerization as the analytic model, and it can create easily a bank of virtual copolymers for all the compositions needed to analyze the structure of the macromolecular chains in terms of sequences of monomers occurring as a function of the global composition. The search for the sequences is very simple to compute as it consists in a simple reading of the virtual chains previously simulated. This result can thus be applied to make appear a simple correlation between the distribution of functional groups and some specific observed biological activities of biospecific copolymers.

Simplified schema of the numerical virtual terpolymerization.     

Investigations on the Structure and Properties of Neutral Polymer Bonding Agents (NPBA) Used for Composite Solid Propellant. I: Study of the Reactivity Ratios and Sequence Structure Control of Acrylonitrile (AN)/Methacrylate (MA)/Hydroxyethyl Acrylate (HEA) Terpolymer Type NPBA

The copolymerization activity and sequence structure of the typical neutral polymer bonding agent (NPBA) for improving the mechanical properties of a composite solid propellant plasticized by nitrate ester were investigated. The reactivity ratios of three monomers were calculated and compared. In addition, by using Monte Carlo simulation, the effects of the monomers’ feed amount on composition and sequence structure of the copolymer were also investigated and discussed. The prepared NPBA bonding agents were used in a propellant. It was found that the results of the mechanical properties tests have good correspondence with the data of reactivity ratios and Monte Carlo simulation.     

Win X-ray: a new Monte Carlo program that computes X-ray spectra obtained with a scanning electron microscope.

A new Monte Carlo program, Win X-ray, is presented that predicts X-ray spectra measured with an energy dispersive spectrometer (EDS) attached to a scanning electron microscope (SEM) operating between 10 and 40 keV. All the underlying equations of the Monte Carlo simulation model are included. By simulating X-ray spectra, it is possible to establish the optimum conditions to perform a specific analysis as well as establish detection limits or explore possible peak overlaps. Examples of simulations are also presented to demonstrate the utility of this new program. Although this article concentrates on the simulation of spectra obtained from what are considered conventional thick samples routinely explored by conventional microanalysis techniques, its real power will be in future refinements to address the analysis of sample classifications that include rough surfaces, fine structures, thin films, and inclined surfaces because many of these can be best characterized by Monte Carlo methods. The first step, however, is to develop, refine, and validate a viable Monte Carlo program for simulating spectra from conventional samples.     

Development of an Integrated Framework for Multiscale,Multiphase Modeling of Industrial Slurry‐Phase Reactors for Polyethylene Production

A framework based on the Monte Carlo/random‐pore polymeric flow model is proposed to simulate both single‐particle and continuous slurry reactor industrial polymerizations. The Sanchez–Lacombe equation of state describes the distributions of components in the different phases of these systems. The developed process model is applied to describe heterogeneously catalyzed polymerizations of ethylene in n‐hexane diluent with or without 1‐hexene as a comonomer, but the proposed methodology is applicable to any ethylene/1‐olefin copolymerization in slurry reactors. In addition to the effects of catalyst particle size and reactor residence time distributions, the proposed hybrid model is used to investigate the impact of several catalyst characteristics under different process conditions on polymer yield and microstructure. Particular attention is paid to the catalyst fragmentation process and active center distribution through the particle. These simulations demonstrate the versatility and thoroughness of combining Monte Carlo simulation with single‐particle models to analyze and predict the behavior of commercial polyolefin reactors.     

A version of diffusion Monte Carlo method based on random grids of coherent states. II. Six-dimensional simulation of electronic states of H2

We report a new version of the diffusion Monte Carlo (DMC) method, based on coherent-state quantum mechanics. Randomly selected grids of coherent states in phase space are used to obtain numerical imaginary time solutions of the Schrodinger equation, with an iterative refinement technique to improve the quality of the Monte Carlo grid. Accurate results were obtained, for the appropriately symmetrized two lowest states of the hydrogen molecule, by Monte Carlo sampling and six-dimensional propagation in the full phase space.     

Das Monte Carlo-studium der copolymerisation der ester der benzylidencyanessigsäure mit styrol

The Monte Carlo study of copolymerization of styrene with four esters of benzylidenecyanoacetic acid has pointed out that (a) for methyl and hexyl esters one cannot decide among the ultimate and penultimate effect (using copolymer composition and Fischer statistic), and (b) cyclohexyl and benzyl esters copolymerize following the kinetics of penultimate effect. Finally, the most probable sequence distribution in the studied copolymers is presented.