Modeling of branching and gelation in living copolymerization of monomer and divinyl cross-linker using dynamic lattice liquid model (DLL) and Flory-Stockmayer model

The random living copolymerization of vinyl and divinyl monomers with fast initiation and slow propagation was simulated using two Monte Carlo methods: one, purely statistical, corresponding to the mean-field Flory-Stockmayer (FS) theory and the dynamic lattice liquid model (DLL). The results were compared with experiments in which atom transfer radical polymerization (ATRP) method was used. Molecular weights, polydispersities and the cross-linking/cyclization of macromolecules were modeled as a function of conversion for various cross-linker concentrations. The results obtained by the DLL and FS methods and experiments are presented and the sources of discrepancies are discussed. The DLL method yields gel points, molecular weight distributions and critical exponents closer to experimental values and gives an insight into cross-linking processes near the gel point (leading to gelation). More realistic gel structure is obtained due to an appropriate modeling of intra-chain cyclization and diffusion effects, especially close to and above the gel point.     

Cyclic poly(dimethylsiloxane) from kinetically controlled cyclodepolymerization of linear precursors in dilute solution

Cyclic poly(dimethylsiloxane) (PDMS), [(CH₃)₂SiO]_x or D_x, was prepared in high yield (>70% for x > 12) from commercially available linear α,ω-dihydroxy-PDMS by base-catalyzed unimolecular ring closure in dilute solution. Cyclization, which occurs with formation of charged linear byproducts, was confirmed by GPC, FTIR, MALDI-ToF and NMR spectroscopy. Product mixtures were analyzed with a newly developed dual-detector GPC method in which the linear byproducts were end-labeled with a UV-absorbing group and separately detectable with a UV detector. Alternatively, charged linear byproducts were removed with anion-exchange resin. Yields and molecular weight distributions of the cyclic products are consistent with Monte Carlo simulations of kinetically controlled cyclodepolymerization. Large cycles from this cyclodepolymerization route are obtained in much higher yields (>70% for x > 12) than those reported for the traditional base-catalyzed ring-chain equilibration of D₄ and D₅ (∼13% for x > 6) [1].     

丙烯聚合的Monte Carlo模拟(Ⅰ)活性杂质对丙烯聚合的影响

1 INTRODUCTION Polypropylene is a popular thermoplastic polymer, and produced via bulk polymerization in petroleum chemical industry. The molecular configuration of polypropylene and the characteristics of polymer can be controlled by the catalyst and polymerization method. Furthermore, other factors, such as impurities in the material and polymerization conditions, also influence the industrial production. Catalyst influences the rate and the quality of polymer, is a key factor of the in…     

丙烯聚合的Monte Carlo模拟(Ⅰ)活性杂质对丙烯聚合的影响

A comprehensive mechanism for propylene polymerization was proposed by considering the effects of main impurities in the material on propylene polymerization. According to the proposed mechanism, Monte Carlo simulation was employed to investigate the polymerization kinetics in order to determine the effects of the main impurities on the polymerization. Significant influences of the main impurities on the rate, number-average degree and controlling capability of hydrogen of the polymerization were analyzed.     

Some Results on Specification Search and Pre-testing in an ARMA(1,1) Process

In this study we consider simple autoregressive moving-average (ARMA) models of order at most 1. Pre-testing, on the moving-average coefficient θ, is used to choose between an ARMA(1,1) and an AR(1) in a Monte Carlo design. We find that the pre-test estimator is not always dominated by the others, and that the bias and the mean square error of the estimate of the autoregressive coefficient φ very often depend on the sign of the autoregressive and moving-average parameters of the ARMA(1,1) model in the data-generating process. Further, we note that the degrees of size and power distortion of the t test on φ, after pre-testing for θ, are generally associated with model misspecification.     

Personal Exposure of Children to Particle-Associated Polycyclic Aromatic Hydrocarbons in Tianjin,China

Polycyclic aromatic hydrocarbons (PAHs) associated with fine particles are harmful to human health, particularly to children, who are most vulnerable. To evaluate the respiratory exposure of children to particle-associated PAHs properly, personal air sampling near breathing zone of 36 schoolchildren were conducted in Tianjin, China. Sixteen priority PAHs designated by the United States Environmental Protection Agency were measured using GC-MS. The average concentrations of personal exposure to ∑₁₆PAH were 27.31 ± 3.91 ng/m³ in summer and 58.18 ± 24.68 ng/m³ in winter. Moreover, PAH profiles were studied and the results showed NAP, BbF, and IPY were the most abundant PAHs. Five rings PAH species made up the largest proportion, accounting for 25.7% in summer and 32.6% in winter. Diagnostic ratios and principal component analysis indicated combustion activities were the major source for children exposure to particle-associated PAHs in this study. According to the risk assessment results, the inhalation exposure risk for children were higher than the acceptable risk level of 10–⁶, indicating the health issues of children should be paid more attention. On the basis of sensitivity analysis results, further research should be done to improve the inhalation cancer slope factor of BaP and the concentration distribution of PAHs in order to improve the accuracy of the health risk assessment.     

Application of the Monte Carlo simulation method to the investigation of peculiar free‐radical copolymerization reactions: Systems with both reactivity ratios greater than unity (rA > 1 and rB > 1)

With a Monte Carlo simulationmethod, copolymer properties have been thoroughly studied, and the influence of the reactivity ratios and feed composition has been taken into consideration. Instantaneous alterations of the copolymer composition and copolymer heterogeneity, which is also called a randomness parameter, have been examined with data obtained from the simulation at each stage of the copolymerization reaction. The results prove the azeotropic behavior of copolymerization reactions in which both reactivity ratios are greater than unity, although some special reactivity ratio combinations ignore the azeotropic behavior. The copolymer composition reaches an azeotrope point at the end of the copolymerization reaction when the copolymerization is an azeotropic reaction. In addition, the randomness parameter takes its maximum value at the azeotrope point when reactivity ratio r_A is equal to reactivity ratio r_B. Finally, increasing the reactivity ratios causes no change in the trend of copolymer composition/feed composition curves when r_A is equal to r_B. However, the curves produced with larger r_A and r_B values show more fluctuations. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

Monte Carlo Simulation of Kinetics of Ammonia Oxidative Decomposition over the Commercial Propylene Ammoxidation Catalyst (Mo-Bi)

Monte Carlo method is applied to investigate the kinetics of ammonia oxidative decomposition over the commercial propylene ammoxidation catalyst(Mo-Bi). The simulation is quite in agreement with experimental results. Monte Carlo simulation proves that the process of ammonia oxidation decomposition is a two-step reaction.     

Treating missing values in INAR(1) models: An application to syndromic surveillance data

Time-series models for count data have found increased interest in recent years. The existing literature refers to the case of data that have been fully observed. In this article, methods for estimating the parameters of the first-order integer-valued autoregressive model in the presence of missing data are proposed. The first method maximizes a conditional likelihood constructed via the observed data based on the k -step-ahead conditional distributions to account for the gaps in the data. The second approach is based on an iterative scheme where missing values are imputed so as to update the estimated parameters. The first method is useful when the predictive distributions have simple forms. We derive in full details this approach when the innovations are assumed to follow a finite mixture of Poisson distributions. The second method is applicable when there are no closed form expression for the conditional likelihood or they are hard to derive. The proposed methods are applied to a dataset concerning syndromic surveillance during the Athens 2004 Olympic Games.     

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.     

基于蒙特卡洛模拟法的钻井经济评价

对石油钻井进行投资决策时,要考虑各方面的风险因素和投资成本,为了降低石油钻井中的投资风险,在钻井之前就能预测到可能的成本,可以采用蒙特卡洛模拟法对钻井投资进行风险预估。本文通过对不同的地层分别运用蒙特卡洛模拟法,在不同的地层建立蒙特卡洛模的模型,并应用matlab模拟软件处理数据解释分析结果,最终得出钻井费用的预测值和误差,为投资决策提供依据。     

A simulation of oscillatory behavior in the NO+H2 reaction on Pt(100): effect of diffusion and blocking sites

The catalytic reduction of nitric oxide by H₂ over the Pt(100) surface is studied as a function of partial pressures of the reactants. The mathematical mean field model, originally proposed by Makeev and Nieuwenhuys (J. Chem. Phys. 108 (1998a) 3740) shows kinetic oscillations of the reaction products and near the critical point the dependence of the amplitude of oscillations on the partial pressures ratio p is shown to be very close to that predicted for the Hopf supercritical bifurcation. The model has been extended to include the effect of blocking sites (poisoning) on the catalyst surface. This effect changes the period of the oscillations. Diffusion of the adspecies NO has also been studied and we show in what way it modifies the nonlinear behavior of the kinetic oscillations and the transition to chaos through period-doubling bifurcations. The influence of defects on global coupling as they are increased continuously is also studied. Finally, we use Monte Carlo simulations to show the species distributions and growth as they oscillate in time.     

Self-condensing vinyl polymerization in the presence of multifunctional initiator with unequal rate constants: Monte Carlo simulation

Monte Carlo method was applied to simulate self-condensing vinyl polymerization (SCVP) in the presence of multifunctional initiator with unequal reactive rate constants. Simulations showed that, with the increase of reactivity of multifunctional initiator, the molecular weight distribution decreases, the fraction of multi-armed hyperbranched polymers increases, and the best reactivity ratio of multifunctional initiator to inimor is 10/1; the reactivity difference of two active sites in inimer has strong effects on the molecular weight distribution and degree of branching. The branch degree and fraction of branch-points depend on both the conversion of double bonds and reactivity difference of two active centers in inimer, and have no relation with the adding of multifunctional initiator. The density distribution of degree of branching further shows common self-similarity in SCVP.     

Three-parameter (3P) weibull distribution for characterization of strength of ceramics showing R-Curve behavior

Strength distribution of advanced ceramics is commonly characterized by two-Parameter (2P) Weibull distribution. However, deviation of strength distribution from 2P-Weibull distribution may occur in ceramics due to various mechanisms. R-curve behavior is one of these mechanisms where increase of fracture resistance with the extension of crack occurs. In such cases, 2P-Weibull distribution may not be the best fitting distribution function based on the goodness-of-fitness tests. This article examines the effectiveness of three-parameter (3P) Weibull distribution function for fitting the strength variation due to R-curve effect by using experimental and virtual strength data. The effect of Weibull parameters, degree of increase in crack resistance and number of samples on effectiveness of fitting via 3P-Weibull distribution is investigated. It is reported that 3P-Weibull distribution function fits the strength distribution better than 2P-Weibull distribution function for materials showing R-curve behavior when the crack resistance curve is steep and Weibull modulus is high. Furthermore, it is shown that at least 100 samples should be used for a reliable estimate when the material exhibits R-curve behavior.     

气溶胶在毛细管中输运Monte Carlo模拟

气溶胶在管道中的输运广泛应用于气溶胶采样、监测和气溶胶的危害评价中,前人基于对流扩散方程、流体速度分布规律,结合初始条件和边界条件,对气溶胶粒子在管道中的扩散特性进行了理论分析,取得了一定成功．Monte Carlo方法作为一种统计实验方法,在模拟中子或光子在介质中的Markoff输运过程中取得了巨大成功．另外,Monte Carlo方法也成功用于吸附质在多孔介质中的吸附和解吸特征研究．气溶胶粒子在气体介质中,由于受到气体分子的随机碰撞,     

Molecular simulations of the conformational properties of atactic poly(2-ethylbutyl methacrylate)

RIS Metropolis Monte Carlo (RMMC) simulations were used to determine the unperturbed theta-state chain dimensions of atactic stereoconfigurations of poly (2-ethylbutyl methacrylate) [PEBMA]. Root mean-squared end-to-end distance (〈r²〉_o/M)^1/2 and characteristic ratio (C_n) were calculated along with the backbone torsion angle distribution. The simulated properties are in very good agreement with experimental results. The values of the PEBMA chain dimensions are in-between those corresponding ones for poly(n-butyl methacrylate) and poly (n-hexyl methacrylate) thereby showing the effect of branching in the side-chain. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Water vapor/propylene sorption and diffusion behavior in PVA-P(AA-AMPS) blend membranes by GCMC and MD simulation

Detailed atomistic structures of blend membranes (poly vinyl alcohol (PVA)/(acrylic acid-co-2-acrylamido-2-methylpropylsulfonic acid) (P(AA-AMPS)) were constructed to investigate the sorption and diffusion behavior of gas molecules (water and propylene) in the membranes. Interaction and miscibility between PVA and P(AA-AMPS) were calculated, and it was found that strong intermolecular interaction resulted in good miscibility of PVA and P(AA-AMPS) in the blend. The polymer chains mobility and free volume properties of the blend membranes were characterized. The sorption quantities and sorption sites of water and propylene in the blend membranes were calculated using Grand Canonical Monte Carlo (GCMC) method. The diffusion coefficients of water in the blend membranes were calculated by molecular dynamics (MD) simulation. The simulated results of the membrane structure (chain mobility, free volume properties), the sorption quantities and diffusion coefficients of water/propylene in the blend membranes showed the identical changing trends as the experimental results. Hopefully, this study could offer qualitative insight into the mass transport phenomena within the blend membranes.     

Effect of molecular weight and average comonomer content on the crystallization analysis fractionation (Crystaf) of ethylene α-olefin copolymers

The effect of molecular weight and average comonomer content on the crystallization analysis fractionation (Crystaf) of ethylene/1-hexene copolymers was investigated experimentally and modeled via stochastic simulations. Molecular weight and comonomer content are the main structural parameters that affect the crystallizability of polymer molecules from dilute solutions. Sets of samples with varying molecular weight and comonomer content were prepared to study each effect separately. Although both structural parameters significantly affect the shape of Crystaf profiles, comonomer content is the main determining factor for Crystaf peak location for most molecular weights of interest. The results of the stochastic simulations show good qualitative agreement with the experimental data, but also indicate some clear limitations that might be related to the kinetics of crystallization effects during Crystaf analysis.