Monte Carlo simulations of cyclization in hyperbranched system of AB<Subscript><Emphasis Type="Italic">g</Emphasis></Subscript> type with solvent effect

Cyclization in the hyperbranched polymerization system of AB _g type under different solvent conditions is studied by the method of Monte Carlo (MC) simulation. For this purpose, we apply a scheme of “generation” to specify the growth of polymers, by which a set of differential kinetic equations describing the growth of treelike and cyclic polymers are given. The rate constants of inter- and intramolecular reactions are further deduced to perform the MC simulation. As a result, the number of treelike polymers and cyclic polymers, the size distribution of rings, and the weight-average molecular weight are presented. Based on the simulation results, a significant effect of cyclization on the average properties of polymers is found. Furthermore, the dependence of cyclization on the monomer concentration, solvent effect, and functionality is also discussed. It is shown that cyclization is determined by the cooperation of these factors, of which the monomer concentration plays a leading role. It is expected that the present study may offer useful clues for designing related materials.     

Optimizing polymer reactivities for the solid-state polycondensation of AA and BB type monomers

A new method is presented to optimize the reactivities of a prepolymer for the solid-state polymerization of AA and BB type monomers to obtain high molecular weight polymers. The proposed method consists of blending the prepolymers of different end group mole ratios to maintain optimal reaction stoichiometry, and developing a computational procedure to calculate the molecular weight of the polymer in the solid-state polymerization. A molecular species model is used to calculate the molecular weight moments of the optimized prepolymer and to calculate the molecular weight development in a solid-state polymerization. The molecular weight moments of different polymer species in the prepolymer mixture are estimated by performing the dynamic simulations of a melt prepolymerization process model in conjunction with a numerical optimizer. The model simulation results show that the proposed method offers a significantly improved process performance to obtain high molecular weight condensation polymers in a solid-state polymerization. Bisphenol A polycarbonate is selected as an example to illustrate the proposed method.     

Toward living radical polymerization

Radical polymerization is one of the most widely used processes for the commercial production of high-molecular-weight polymers. The main factors responsible for the preeminent position of radical polymerization are the ability to polymerize a wide array of monomers, tolerance of unprotected functionality in monomer and solvent, and compatibility with a variety of reaction conditions. Radical polymerization is simple to implement and inexpensive in relation to competitive technologies. However, conventional radical polymerization severely limits the degree of control that researchers can assert over molecular-weight distribution, copolymer composition, and macromolecular architecture. This Account focuses on nitroxide-mediated polymerization (NMP) and polymerization with reversible addition-fragmentation chain transfer (RAFT), two of the more successful approaches for controlling radical polymerization. These processes illustrate two distinct mechanisms for conferring living characteristics on radical polymerization: reversible deactivation (in NMP) and reversible or degenerate chain transfer (in RAFT). We devised NMP in the early 1980s and have exploited this method extensively for the synthesis of styrenic and acrylic polymers. The technique has undergone significant evolution since that time. New nitroxides have led to faster polymerization rates at lower temperatures. However, NMP is only applicable to a restricted range of monomers. RAFT was also developed at CSIRO and has proven both more robust and more versatile. It is applicable to the majority of monomers subject to radical polymerization, but the success of the polymerization depends upon the selection of the RAFT agent for the monomers and reaction conditions. We and other groups have proposed guidelines for selection, and the polymerization of most monomers can be well-controlled to provide minimal retardation and a high fraction of living chains by using one of just two RAFT agents. For example, a tertiary cyanoalkyl trithiocarbonate is suited to (meth)acrylate, (meth)acrylamide, and styrenic monomers, while a cyanomethyl xanthate or dithiocarbamate works with vinyl monomers, such as vinyl acetate or N-vinylpyrrolidone. With the appropriate choice of reagents and polymerization conditions, these reactions possess most of the attributes of living polymerization. We have used these methods in the synthesis of well-defined homo-, gradient, diblock, triblock, and star polymers and more complex architectures, including microgels and polymer brushes. Applications of these polymers include novel surfactants, dispersants, coatings and adhesives, biomaterials, membranes, drug-delivery media, electroactive materials, and other nanomaterials.     

Generalized initialization for the dynamic simulation and optimization of grade transition processes using two-dimensional collocation

Optimization modeling tools are essential to determine optimal design specifications and operation conditions of polymerization processes, especially when quality indices based on molecular weight distributions (MWDs) must be enforced. This study proposes a generalized MWD-based optimization strategy using orthogonal collocation in two dimensions, which can capture the dynamic features of MWDs accurately. To enable the strategy, this study considers generalized initialization methods for large-scale simulation and optimization. Here, a homotopy method based on intermediate solutions is adopted to generate initial values for general steady-state simulation models, starting from an arbitrary known solution for any steady-state simulation model. For dynamic simulation models, the response of a first-order linear system is adopted to initialize the state variables. Case studies show the effectiveness of this procedure to enable systematic, reliable, and efficient solution of the optimization problem.     

Monte Carlo simulation of radiation-induced solid state polymerization

A Monte Carlo method was used for a computer simulation of radiation-induced solid state polymerization. The propagation of polymer chains was simulated by means of self-avoiding random walks on a tetrahedral lattice. The initiation and termination of the chains were modelled by pseudorandom processes. The influence of conditions of the in-source process on the post-polymerization kinetics and on the degree of polymerization of the polymers was studied.     

Reducing Statistical Noise and Extending the Size Spectrum by Applying Weighted Simulation Particles in Monte Carlo Simulation of Coagulation

The direct simulation Monte Carlo (DSMC) method is widely utilized to simulate microscopic dynamic processes in dispersed systems that give rise to the population balance equation. In conventional DSMC approaches, simulation particles are equally weighted, even for broad size distributions where number concentrations in different size intervals are significantly different. The resulting statistical noise and limited size spectrum severely restrict the application of these DSMC methods. This study proposes a new Monte Carlo (MC) method, the differentially weighted time-driven method, which captures the coagulation dynamics in dispersed systems with low noise and is simultaneously able to track the size distribution over the full size range. Key elements of this method include constructing a new jump Markov process based on a new coagulation rule for two differentially weighted simulation particles, and restricting the number of simulation particles in each size interval within prescribed bounds. The method is validated by using an ideal coagulation kernel with a known analytical solution and a real coagulation kernel for which an accurate solution can be found numerically (self-preserving particle size distribution in the continuum regime).     

Dynamic evolution of the particle size distribution in suspension polymerization reactors: A comparative study on Monte Carlo and sectional grid methods

In the present study, an efficient Monte Carlo (MC) algorithm and a fixed pivot technique (FPT) are described for the prediction of the dynamic evolution of the droplet/particle size distribution (DSD/PSD) in both non‐reactive liquid–liquid dispersions and reactive liquid(solid)–liquid suspension polymerization systems. Semi‐empirical and phenomenological expressions are employed to describe the breakage and coalescence rates of dispersed monomer droplets/particles, in terms of the type and concentration of suspending agent, quality of agitation, and evolution of the physical, thermodynamic and transport properties of the polymerization system. Moreover, the validity of the numerical calculations is first examined via a direct comparison of simulation results obtained by both numerical methods with experimental data on average particle diameter and droplet/particle size distributions for both non‐reactive liquid–liquid dispersions and the free‐radical suspension polymerization of methyl methacrylate (MMA). Additional comparisons between the MC and the FP numerical methods are carried out under different polymerization conditions. The simulation results reveal that both numerical methods are capable of predicting the mean and the distributed particulate properties of both non‐reactive and reactive suspension processes.     

Conditional Monte Carlo sampling to find branching architectures of polymers from radical polymerizations with transfer to polymer and recombination termination

A model is developed that predicts branching architectures of polymers from radical polymerization with transfer to polymer and termination by disproportionation and recombination, in a continuously stirred tank reactor (CSTR). It is a so-called conditional Monte Carlo (MC) method generating architectures of molecules of specified dimensions. The relevant dimensions in the present case are the number of branch points, n_p, and the number of combined parts a molecule consists of, n_c. These branch points and combination points together are decisive for the connectivity inside molecules. The modeling strategy is based on backtracking of the molecular growth history in terms of the chemical events determining connectivity, transfer to polymer and recombination termination. The recombination termination mechanism requires the model to develop parts of the architecture following several paths back to the initial primary polymers that form the starting points for the molecules. The algorithm requires the construction of probability density functions being evaluated using a fast Galerkin-FEM method. The architectures generated by the conditional Monte Carlo method are compared to those from a full MC method using several qualifiers. One of these is the number of initial primary polymers in a molecule as well as their lengths, another is the radius of gyration contraction factor. Perfect agreement is found between the architectures found by the conditional and full MC methods.     

The effect of grafting density on the crystallization behavior of one-dimensional confined polymers

Grafting density and confinement scale of the nano-area are significant elements affecting the crystallization behavior of polymers. In this work, the crystallization processes of confined and unconfined polymer systems with different grafting density were systematically studied by MC simulation. The results show that when the grafting density of confined systems is low, the crystallization rate is faster and the final crystallinity is higher. However, the crystallization ability is reduced for higher grafting density. We found that for this confined system, the segmental density of interfacial region is larger, and the movement of chain segment is lower. Due to the higher grafting density, the crowding effect of polymer chains is strong, which leads to the intermolecular nucleation. The critical nucleation free energy barrier is higher. Moreover, only homogeneous nucleation occurs in confined polymer systems. With the increasing grafting density, the crystals change from lying on the substrate surface to being perpendicular to the substrate surface in unconfined polymer systems. The crystals are mainly lying on the substrate surface in confined polymer systems. These simulation results are helpful to understand the microscopic mechanism of crystallization behaviors of polymer nanocomposites and provide a theoretical basis for the design of nanocomposites with excellent physical properties.     

Acrylamide‐based anionic polyelectrolytes and their applications: A survey

Water‐soluble polymers are found in a very broad range of industrial applications. An important class of these is acrylamide‐based polymers which bear negative charges along the polymer chain and are called anionic polyelectrolytes. These negatively charged polymers are widely used as flocculants, rheology control agents, and adhesives. They are employed especially in oil field operations as viscosity control agents for enhanced oil recovery and to a lesser degree in engineering fluids used for lubrication, for effluent reclaiming, and for opening oil passage channels in oil‐bearing rock. Paper manufacture, mining, and water treatment processes also benefit from the use of acrylamide‐based polymers to flocculate solids in aqueous dispersions. The acrylamide‐based polymers are made by the free‐radical polymerization of acrylamide and its derivatives via bulk, solution, precipitation, suspension, emulsion, and copolymerization techniques. Among these, solution polymerization is a preferred technique because of difficulty with temperature and agitation control in bulk polymerization and the cost of surfactants and solvents for suspension, emulsion, and precipitation polymerization. The anionic polymers may interact with particles in aqueous dispersions in several ways that result in the stability or instability of the dispersions. The particles in solid‐liquid phases can be destabilized through three main mechanisms which promote flocculation and cause destabilization. These mechanisms are polymer bridging, charge neutralization, and polymer adsorption. The particles in solid‐liquid phases can be stabilized by the anionic polymers through both electrostatic and steric repulsive forces. J. VINYL ADDIT. TECHNOL., 2010. © 2010 Society of Plastics Engineers     

Modeling and theoretical development in controlled radical polymerization

Controlled radical polymerization (CRP) systems have gained increasing interests for the past two decades. Numerous publications may be found in the literature reporting experimental and modeling work on various CRP processes, including their use in surface modification through grafting. Knowledge of underlying mechanism behind polymerization systems is valuable for product design and process optimization. This information may be obtained through the combination of modeling and experimental studies. In this review, published studies on kinetic and stochastic based modeling for CRP systems are summarized. Their relevance in model discrimination of proposed mechanisms is discussed. This review also includes various parameter estimation studies, that is crucial to obtain accurate simulation predictions. Existing issues on the fundamental mechanism in CRP processes are also addressed.     

Microwave-Assisted RAFT Polymerization

Advances in controlled radical polymerization (CRP) have facilitated access to well-defined polymers with controlled molecular weight, topology, and functionality. However, despite the benefits afforded by many CRP techniques, control over these key polymer attributes often comes at the expense of polymerization rate. One method proposed for accelerating chemical synthesis is microwave heating. This review highlights recent examples of microwave heating being applied during reversible addition-fragmentation chain transfer (RAFT) polymerization. In addition to successfully leading to homopolymers from a variety of monomers, block copolymers have also been prepared by microwave-assisted RAFT, which suggests that the high polymerization rates observed do not necessarily lead to significant end group loss from termination. Despite significant debate regarding the origin of rate enhancement observed during microwave-assisted reactions, the reports included herein provide insight into mechanisms by which well-defined functional polymers can be prepared in an accelerated fashion.     

Multiscale optimization using hybrid PDE/kMC process systems with application to thin film growth

The problem of optimal time-constant and time-varying operation for transport-reaction processes is considered, when the cost functional and/or equality constraints necessitate the consideration of phenomena that occur over disparate length scales. Multiscale process models are initially developed, linking continuum conservation laws with microscopic scale simulators. Subsequently, order reduction techniques for dissipative partial-differential equations are combined with adaptive tabulation of microscopic simulation data to reduce the computational requirements of the optimization problem, which is then solved using standard search algorithms. The method is applied to a conceptual thin film deposition process to compute optimal substrate-surface temperature profiles that simultaneously maximize film-deposition-rate uniformity (macroscale objective) and minimize surface roughness (microscale objective) across the film surface for a steady-state process operation. Subsequently, optimal time-varying policies of substrate temperature and precursor inlet concentrations are computed under the assumption of quasi-steady-state process operation.     

基于MPLS的间歇过程终点质量迭代优化控制

提出了多向偏最小二乘(MPLS)模型和迭代学习控制相结合的方法,实现间歇过程终点时刻产品质量指标的控制.利用间歇过程的重复特性,根据前一批次的终点质量偏差调整下-批次控制变量的轨迹,从而使质量指标逐步接近于理想指标.本文提出的方法可以有效地消除由于模型误差和未知扰动引起的质量偏差.在苯乙烯间歇聚合反应模型上进行了仿真分析,验证了该方法的有效性.     

细颗粒物的声凝并数值模拟研究进展

采用数值模拟方法研究细颗粒物的声凝并具有实验研究无法比拟的灵活性和经济性,是获得声凝并微观机理和宏观效果的重要途径之一。本文对国内外相关研究进展和现状进行评述,介绍了细颗粒物声凝并的同向作用机理、流体力学作用机理、声致湍流机理,阐述了声凝并数值模拟的区域算法、矩量法、蒙特卡罗方法,指出考虑各凝并机理之间的耦合,利用多重蒙特卡罗方法结合可视化编程技术,对声凝并过程进行可视化数值模拟是声凝并数值模拟研究的重要发展方向。     

INTEGRATING THE EFFECTS OF PROCESS CONTROLLERS WITH STEADY-STATE, EQUATION-BASED SIMULATION

Process controllers have a significant influence on the steady-state, as well as the dynamic, behavior of chemical processes. Thus, the steady-state simulation of processes should include the effects of control. A new method for including controllers in steady-state simulation is presented in this paper. The method provides equations that represent the steady-state control algorithm and can be solved simultaneously with the process model to yield the steady-slate behaviour of the closed-loop system. Most importantly, the controller models include saturation effects and can be formulated and solved within an open-form model. The method is general and can be applied to single-loop controllers, to complex control designs including split range and signal select, and to several single-loop controllers in a multiloop controller design.     

Molecular simulation of plasma polymerized polyaniline-iodine compounds

This work presents a molecular simulation study of plasma-polymerized polyaniline-iodine compounds. The simulation is focused on the ortho, meta and para substitutions of aniline benzene rings where the polymers can grow into the maximum and partially reduced and oxidized states of polyanilines. This simulation offers the possibility of visualizing the spatial conformation of polyanilines while interacting with iodine atoms with and without chemical bonds between them. Such cases are often found in plasma polymerization and doping processes.     

A multi-thread parallel computation method for dynamic simulation of molecular weight distribution of multisite polymerization

Molecular weight distribution (MWD) is an important quality index of polymer products. Many methods have been proposed to dynamically simulate the MWD of polymerization, but these methods are normally designed for serial computations. In this paper, a multi-thread parallel computation method was proposed for multisite free-radical polymerization. Analysis of the relationship among different subtasks revealed a combined parallel strategy by fully exploiting the parallel feature of the process. A good performance was obtained to accelerate the dynamic simulation of MWD based on Flory method. We theoretically analyzed the speedup ratio (SR) and parallel efficiency (PE). Results showed that software algorithm and hardware configuration exhibited a good match. The efficiency of the proposed parallel method was presented through industrial slurry processes that used high-density polyethylene (HDPE).     

End‐functional polymers,thiocarbonylthio group removal/transformation and reversible addition–fragmentation–chain transfer (RAFT) polymerization

This review focuses on processes for thiocarbonylthio group removal/transformation of polymers synthesized by radical polymerization with reversible addition‐fragmentation‐chain transfer (RAFT). A variety of processes have now been reported in this context. These include reactions with nucleophiles, radical‐induced reactions, thermolysis, electrocyclic reactions and ‘click’ processes. We also consider the use of RAFT‐synthesized polymers in the construction of block or graft copolymers, functional nanoparticles and biopolymer conjugates where transformation of the thiocarbonylthio group is an integral part of the process. This includes the use of RAFT‐synthesized polymers in other forms of radical polymerization such as atom transfer radical polymerization or nitroxide‐mediated polymerization, and the ‘switching’ of thiocarbonylthio groups to enable control over polymerization of a wider range of monomers in the RAFT process. With each process we provide information on the scope and, where known, indicate the mechanism, advantages and limitations. Copyright © 2011 Society of Chemical Industry