Monte Carlo Simulation of Ethylene Copolymers: A Look into the Monomer Sequence Distribution

A comprehensive mathematical model was developed using Monte Carlo simulation to describe the mechanism of ethylene and α-olefin copolymerization. The model studies the polymerization mechanism using coordination catalysts and is able to predict molecular weight and detailed chemical composition distributions. This work is considered to be a useful tool that enables us to understand and described the monomer sequence distribution as a function of chain length in semi-batch polymerization reactors.     

Atom-transfer radical polymerization of styrene with bifunctional and monofunctional initiators: Experimental and mathematical modeling results

Bulk atom transfer radical polymerization (ATRP) of styrene was carried out at 110 °C using benzal bromide as bifunctional initiator and 1-bromoethyl benzene as monofunctional initiator. CuBr/2,2′-bipyridyl was used as the ATRP catalyst. The polymerization kinetic data for styrene with both initiators was measured and compared with a mathematical model based on the method of moments and another one using Monte Carlo simulation. An empirical correlation was incorporated into the model to account for diffusion-controlled termination reactions. Both models can predict monomer conversion, polymer molecular weight averages, and polydispersity index. In addition, the Monte Carlo model can also predict the full molecular weight distribution of the polymer. Our experimental results agree with our model predictions that bifunctional initiators can produce polymers with higher molecular weights and narrower molecular weight distributions than monofunctional initiators. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2212–2224, 2007     

Self-optimizing Diffusion Quantum Monte Carlo Calculation: the Potential Energy Curve of C_2

11NTRODUCTIONDiffusionquantumMonteCarlo(DMC)isoneofthesimplestofthevariousMonteCarlotechniquesavailabletosolvetheSchrodingerequation,forarecentre-viewofDMC(seeRef[1i).Foravarietyofsmallatomsandmolecules,DMChasbeenshowntobecapableofprovidinganestimateoftheground-state(nonrelativistic)energywithanaccuracycomparabletogoodqualityClcalculations,evenwhenarelativelysimpletrialwavefunctionisemployed.However,todate,thereareseveralobstaclesinaDMCcalculation:(1)BeforetheDMCcomputation,thepar…     

Molecular Weight Distribution Simulation in Equilibrium Ring‐Opening Polymerization: A New Macroscopic Model

Compared with other types of polymerization, the molecular weight and its distribution (MWD) of equilibrium ring‐opening polymerization (EROP) are complicated and have not been extensively studied. By using statistic method, a series of equations based on polymerization mechanism is established to describe numbers of rings, chains, and active centers. Using this new model, the predicted results of polydimethylsiloxane synthesized by EROP agree well with experimental results. This model has advantages in molecule number, calculation speed, and stability when compared with the Monte Carlo simulation. It also has the potential to replace Monte Carlo simulation in MWD prediction.     

Simulation of styrene free radical polymerization over bi-functional initiators using Monte Carlo simulation method and comparison with mono-functional initiators

In the present study, based on a complete mechanism, a Monte Carlo simulation method is employed to investigate the kinetics of styrene free radical polymerization over bi-functional initiators in a bulk medium. The effects of the concentration of initiator and the monomer, of the temperature on monomer conversion, average molecular weights, polydispersity index, and molecular weight distribution are inspected and compared with mono-functional initiators. According to the simulation results, an increase in either the concentration of initiator or the temperature leads to the rise of the monomer conversion and to the reduction of the average molecular weights, while the increase of the monomer concentration results in the rise of both monomer conversion and molecular weights, which is in accord with predictions of the theory of free-radical polymerization. In addition, application of bi-functional initiators increases both monomer conversion and average molecular weight and results in narrower chain length distributions.     

Statistical mechanical theory for steady state systems. V. Nonequilibrium probability density

The phase space probability density for steady heat flow is given. This generalizes the Boltzmann distribution to a nonequilibrium system. The expression includes the nonequilibrium partition function, which is a generating function for statistical averages and which can be related to a nonequilibrium free energy. The probability density is shown to give the Green-Kubo formula in the linear regime. A Monte Carlo algorithm is developed based upon a Metropolis sampling of the probability distribution using an umbrella weight. The nonequilibrium simulation scheme is shown to be much more efficient for the thermal conductivity of a Lennard-Jones fluid than the Green-Kubo equilibrium fluctuation method. The theory for heat flow is generalized to give the generic nonequilibrium probability densities for hydrodynamic transport, for time-dependent mechanical work, and for nonequilibrium quantum statistical mechanics.     

Theoretical study of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction by a diffusion quantum Monte Carlo approach

Ab initio calculations of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction has been carried out by the fixed-node diffusion quantum Monte Carlo method in this study. The Monte Carlo sampling is based on the Ornstein-Uhlenbeck random walks guided by a trial wave function constructed from the floating spherical Gaussian orbitals and spherical Gaussian geminals. The Monte Carlo calculated barrier height of 1.09(16) kcal/mol is consistent with the experimental values, 0.86(10)/1.18(10) kcal/mol, and the calculated value from the multireference-type coupled-cluster (MRCC) calculation with the aug-cc-pVQZ(F)/cc-pVQZ(H) basis set, 1.11 kcal/mol. The Monte Carlo-based calculation also gives a similar value of the reaction enthalpy, -32.00(4) kcal/mol, compared with the experimental value, -32.06(17) kcal/mol, and the calculated value from a MRCC/aug-cc-pVQZ(F)/cc-pVQZ(H) calculation, -31.94 kcal/mol. This study clearly indicates a further application of the random-walk-based approach in the field of quantum chemical calculation.     

Monte Carlo simulation of the self-assembly and phase behavior of semiflexible equilibrium polymers

Grand canonical Monte Carlo simulations of a simple model semiflexible equilibrium polymer system, consisting of hard sphere monomers reversibly self-assembling into chains of arbitrary length, have been performed using a novel sampling method to add or remove multiple monomers during a single MC move. Systems with two different persistence lengths and a range of bond association constants have been studied. We find first-order lyotropic phase transitions between isotropic and nematic phases near the concentrations predicted by a statistical thermodynamic theory, but with significantly narrower coexistence regions. A possible contribution to the discrepancy between theory and simulation is that the length distribution of chains in the nematic phase is bi-exponential, differing from the simple exponential distribution found in the isotropic phase and predicted from a mean-field treatment of the nematic. The additional short length-scale characterizing the distribution appears to arise from the lower orientational order of short chains. The dependence of this length-scale on chemical potential, bond association constant, and total monomer concentration has been examined.     

具有RAFT链转移过程的活性自由基聚合的Monte Carlo模拟

活性自由基聚合是近年来高分子合成领域中研究的热点之一 .目前主要有两种体系 ,其一是ＴＥＭＰＯ调控的自由基聚合[1],但单体选择面窄 ,聚合速率慢 ;其二是原子转移聚合 ,单体适用面较广 ,但产物中常含有难以除去的金属离子[2 ].因此寻找单体适用性广 ,产物纯净的聚合体系 ,具有十分重要的意义 .近两年来 ,Ｔｈａｎｇ等[36 ]发现用双硫酯调聚的自由基聚合具有活性特征 ,并指出其原因是这类体系中的链转移具有可逆性 ,称为可逆加成 裂解链转移过程 (ＲＡＦＴ) ,可示意如下 :Ｒｉ·+ ＣＳＺＳＲｊ(ＤＳＥ)ｋａｄｄｋｄｉｓＣ·ＳＲｉＺＳＲｊ…     

用隐函数方法处理不断引发,链增长自由基聚合反应

利用图形分析方法给出了不断引发、链增长自由基聚合反应的分子量分布函数，结合反应转化率曲线，利用隐函数方法和数学随机模拟法，得到了分子量分布曲线，利用计算结果计算结果讨论了不同终止形式及反应速率对聚合物分子量分布的影响，考虑反应体的扩散控制。给出了苯乙烯本体聚合的分子量分布，得到与实验事实相一致的结论。     

V／Sb催化剂上丙烷氨氧化反应机理的Monte Carlo模拟

本文应用Ｍｏｎｔｅ Ｃａｒｌｏ方法对丙烷氨氧化的反应机理进行了初步研究。首先在分析了Ｖ／Ｓｂ金红石构催化剂的各个晶面之后，以１００面为模板建立了Ｖ／Ｓｂ双活性中心模型。在此基础上，对丙烷，氨及氧的不同进料摩尔比率对丙烯腈，丙烯及ＣＯＸ三种产物的影响规律进行了详细考察。     

Simulation of Molecular Weight Distribution After Polymer Breakdown. I. A Least-Squares Parameter Estimation Method on Monte Carlo Models

The degradation index (DI) has been used in previous work for Monte Carlo simulation of breakdown of polymers with narrow initial molecular weight distribution. However, the definition of DI is inadequate for polymers of broader molecular weight distribution. A least-squares method for estimating DI for such systems is described.     

Kinetics of self‐condensing vinyl hyperbranched polymerization in three‐dimensional space

Self‐condensing vinyl hyperbranched polymerization (SCVP) with A‐B* type monomer is simulated applying Monte Carlo method using 3d bond fluctuation lattice model in three‐dimensional space. The kinetics of SCVP with zero active energy of reaction is studied in detail. It is found that the maximal number–average and weight–average polymerization degrees and the maximal molecular weight distribution, at varying the initial monomer concentration and double bond conversion, are about 52, 190, and 3.93, respectively, which are much lower than theoretical values. The maximal average fraction of branching points is about 0.27, obtained at full conversion at the initial monomer concentration of 0.75. The simulation demonstrated the importance of steric effects and intramolecular cyclization in self‐condensing vinyl hyperbranched polymerization. The results are also compared with experiments qualitatively and a good agreement is achieved. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4486–4494, 2008     

铝酸钠熔体Monte Carlo法计算机模拟研究

用计算机Monte Carlo法研究铝酸钠熔体结构. 计算了径向分布函数和局部结构. 表明NaAlO_2熔体是由畸变的共隅AlO_4四面体离子集团、Na~+离子和xNa~+·yO~(2-)离子集团所组成.     

Perturbed-chain equation of state for the solid phase

A perturbed chain equation of state for the solid phase has been derived. Although the equation is general with respect to intermolecular potential, we incorporate the Lennard-Jones potential in this work in order to compare results from the model with available Monte Carlo simulation data. Two forms of the radial distribution function for the hard-sphere solid chain reference state are used in the model. First, a theoretically rigorous approach is taken by using a correlation of actual solid-phase Monte Carlo hard-sphere chain data for the radial distribution function. This results in good agreement with the Monte Carlo data only at high density. Second, a simple extended-density approximation was used for the radial distribution function. This second approach was found to work well across the entire density range including the vicinity of the solid-fluid equilibrium.     

Lectures for chemists on statistics II. The normal distribution: a briefer on the univariate case

Motivated by the introduction of a supplement to the GUM suggesting Monte Carlo simulation as a method for establishing a complete measurement uncertainty budget, some properties of the normal distribution are reviewed. The normal distribution is the central distribution of parametric statistics and sampling from normal distributions is a regularly occurring activity in statistical simulation by Monte Carlo methods. Algorithms for computer generation of normal deviates, areas under the normal curve, and the error function are given to encourage practical simulation. Some critical issues, e.g. coverage and influential observations, are presented. The discussion is restricted to the univariate situation. There is no intention to provide an exhaustive presentation. Statistics is a specialised field requiring sophisticated competences. The text may serve as a golden thread to acquire a quick survey on a subject of general interest.     

Algorithm and application of Monte Carlo simulation for multi-dispersive copolymerization system

A Monte Carlo algorithm has been established for multi-dispersive copolymerization system, based on the experimental data of copolymer molecular weight and dispersion via GPC measurement. The program simulates the insertion of every monomer unit and records the structure and microscopical sequence of every chain in various lengths. It has been applied successfully for the ring-opening copolymerization of 2,2-dimethyltrimethylene carbonate (DTC) with δ-caprolactone (δ-CL). The simulation coincides with the experimental results and provides microscopical data of triad fractions, lengths of homopolymer segments, etc., which are difficult to obtain by experiments. The algorithm presents also a uniform frame for copolymerization studies under other complicated mechanisms.     

Super-Monte Carlo: A photon/electron dose calculation algorithm for radiotherapy

Super-Monte Carlo (SMC) is a method of dose calculation for radiotherapy which combines both analytical calculations and Monte Carlo electron transport. Analytical calculations are used where possible, such as the determination of photon interaction density, to decrease computation time. A Monte Carlo method is used for the electron transport in order to obtain high accuracy of results. To further speed computation, Monte Carlo is used once only, to form an electron track kernel (etk). The etk is a dataset containing the lengths and energy deposition of each step of a number of electron tracks. The etk is transported from each incident particle interaction site, from which the dose is calculated. Dose distributions calculated in heterogeneous media show SMC results similar to those of Monte Carlo. For the same statistical uncertainty, SMC takes an order of magnitude less computation time than a full Monte Carlo simulation. SMC has only been implemented for photons and electrons, however the same basic method could be used for the transport of other particles. Current development includes the optimisation of the etks and the code in order to decrease computation time, and also the inclusion of SMC onto a clinical planning system.     

Calculation of weight function for reactive differential cross sections by monte carlo methods

A weight function which depends only on the center-of-mass (c.m.) angle and velocity is used to relate the c.m. differential cross section to a measured reactive scattering contour map. The weight function is calculated by Monte Carlo methods. Its calculation includes the viewing factor correction.     

Monte Carlo simulations for predicting the precision of results and for optimizing data acquisition schedules

Monte Carlo simulations can be used to determine the precision of an analytical method if the standard deviations of the component unit operations are estimated accurately. Alternative methods for estimating the standard deviation have been compared by evaluating the success of Monte Carlo simulations to predict the precision of a second-order rate constant determined by spectrophotometry and of an equivalent weight and acid dissociation constant determined by potentiometry. Monte Carlo simulation has also been used with simplex optimization to predict a data acquisition schedule which gives high precision in the equivalent weight determination. By comparison with a naive design, a 22-fold improvement was predicted. A 15-fold improvement was observed experimentally.