Kinetic model for short-cycle bulk styrene polymerization through bifunctional initiators

A model describing the kinetics of bulk styrene polymerization through bifunctional initiators has been developed. The diffusion-controlled propagation and termination reactions at high monomer conversions are modeled with the free volume theory for polymer solutions. Three different commercially available bifunctional initiators were experimentally evaluated for a wide range of polymerization conditions to study the effect of the reaction rate on the molecular weight and molecular weight distribution. The model predictions for the same polymerization conditions show excellent agreement with the experimental data, for the whole range of conversions, for both reaction rate and molecular weight distribution development, under all the conditions tested. It is demonstrated throughout this study that high molecular weights, very high reaction rates, and narrow molecular weight distributions can be achieved simultaneously by using bifunctional initiators. A comparison between monofunctionally initiated systems with the bifunctionally initiated ones shows that short-cycle reactions with reductions in polymerization time of up to 75% may be achieved with the bifunctional initiators for a wider range of conditions without significantly affecting the molecular weight and molecular weight distribution of the final product.     

Optimal operations of semibatch solution polymerization of acrylamide with molecular distribution as constraints

In this work, optimal control profiles of a semibatch solution polymerization of an acrylamide system are investigated for the first time. The control variables are the monomer and initiator feed rates. The objective function is the operating time of each batch. One of the operating constraints is the maximum of the polymerization rate of the reaction, which is important due to the limitation of the heat-removal equipment. The expected number-average molecular weight and molecular weight distribution are also included as constraints in order to guarantee the quality of the products. A nonlinear programming approach developed by Jang and Yang is used for solving the equations. Several simulation and experimental runs show that the operation of this semibatch system is very smooth and conversions are fitted well by the model. The molecular weights and molecular weight distributions of the polymer products are also well controlled. © 1993 John Wiley & Sons, Inc.     

Development of a unified framework for calculating molecular weight distribution in diffusion controlled free radical bulk homo-polymerization

In the present work, two different approaches to model diffusion controlled free radical polymerization, namely the free volume model and the entanglement theory are compared. These approaches are applied to methyl methacrylate bulk polymerization in a batch reactor to calculate the conversion, total radical concentration, the number and weight average molecular weights as well as the entire molecular weight distribution as a function of the polymerization time and the process conditions. All the diffusion-controlled phenomena were taken into account, including gel, glass and cage effects as well as residual termination. The molecular weight distribution is calculated by direct numerical integration of a large system of non-linear ordinary differential equations describing the conservation of the mass of macromolecular species in the batch reactor. Model predictions are in good agreement with available experimental data for conversion, number and weight average molecular weights as well as the entire molecular weight distribution, thus justifying the ability of these models to describe the main issues of the diffusion-controlled free radical polymerization.     

Modeling methyl methacrylate free radical polymerization in nanoporous confinement

Nanoconfinement of methyl methacrylate free radical polymerization is known to impact the molecular weight and molecular weight distribution of the polymer produced, with results in the literature generally indicating an increase in molecular weight and a concomitant decrease in polydispersity index. In the present work, the mathematical model described by Verros et al. (2005) for free radical bulk polymerization of methyl methacrylate is extended to account for polymerization in nanopores. The model of Verros et al. (2005) incorporates diffusion effects and is capable of describing the conversion and the number- and weight-average molecular weights of the resulting poly(methyl methacrylate) as a function of polymerization time and process conditions. The model is extended by incorporating the effect of nanoconfinement on diffusivity using the scaling reported in the literature. The calculations indicate that nanoconfinement will lead to higher molecular weights and lower polydispersity, and the gel effect will occur earlier. The results are compared to experimental work and implications discussed.     

Polymerization of olefins through heterogeneous catalysis. VI. Effect of particle heat and mass transfer on polymerization behavior and polymer properties

The multigrain model for polymerization of olefins over solid catalysts is used to predict kinetic behavior, molecular weights, and polydispersities. The effects of intraparticle and external boundary layer transport resistance on the kinetic behavior and polymer properties are explored. Means for the experimental detection of intraparticle diffusion resistance are suggested. The importance of catalyst physical properties, such as the porosity, and the catalyst loading is illustrated through simulation. Finally, the hypotheses of diffusion resistance and site heterogeneity as explanations for the broad molecular weight distributions of olefin polymers are critically evaluated, and molecular weight distribution control in industrial catalysts is discussed.     

Molecular weight distribution of living polymers in a semi-batch reactor

For anionic polymerization with slow initiation and rapid propagation step analytical expressions are presented to calculate average molecular weights and molecular weight distributions for a semi-batch process, in which a monomer solution contaminated by impurities is fed to an initiator solution in the reactor. The validity of the model was checked for the case of the polymerization of isoprene by n-butyllithium in n-heptane. The differences observed between theoretical and experimental values are explained by the changes in the rate constants of the initiation and the propagation step caused by the change in the polarity of the reaction solution by the continuously fed impurities. Furthermore it is shown that polymers with bimodal molecular weight distributions are formed if the semi-batch procedure is followed by a batch one to increase the monomer conversion.     

多分散聚合物稀溶液体系的Rouse模型

本文将Rouse提出的均一分布球簧链式分子模型加以推广.得到了多分散体系的本构方程.对几种最常见的分子量分布,在稳态剪切流中,分别计算了它们的物质函数以及特性粘数与重均聚合度的关系.结果表明,这一线性模型的流变性质与聚合物的分子量分布有密切的关系;若通过物质函数的监测,则还能预示聚合反应的动态过程.     

Unusual Effect of α-olefins as Chain Transfer Agents in Ethylene Polymerization over the Catalyst with Nonsymmetrical Bis(imino)pyridine Complex of Fe(II) and Modified Methylalumoxane (MMAO) Cocatalyst

Ethylene polymerization with bis(imino)pyridlyiron precatalysts generally produces linear polyethylene (PE) even with the presence of α-olefins because α-olefins are not incorporated into polymeric products. Interestingly, α-olefins, such as hexene-1 or butene-1, have been found to act as effective chain transfer agents in the ethylene polymerization promoted by nonsymmetrical bis(imino)pyridyliron complexes with modified methylalumoxane (MMAO), resulting in higher catalytic activities with higher amounts of polymers with lower molecular weights, and, more importantly, narrower molecular weight distributions of the resultant polyethylenes (PE). This phenomenon confirms the assistance of α-olefins in the chain-termination reaction of iron-initiated polymerization and regeneration of the active species for further polymerization. Besides higher activities of the catalytic system, the formation of linear PE with trans-vinylene terminal groups and lower molecular weights are explained. The observation will provide a new pathway for enhancing catalytic activity and improving the quality of polyethylenes obtained by regulation of molecular weights and molecular weight distribution.     

Ultrasonic degradation of poly(methyl methacrylate

Ultrasonic degradation studies on a variety of molecular weights and molecular weight distributions of poly(methyl methacrylate) are reported. The extent of degradation was measured using gel permeation chromatography. Polydispersity decreased as a function of irradiation time for polymers with initial broad distributions. In contrast, polymers with an initial narrow distribution increased in polydispersity, passed through a maximum and then gradually decreased in polydispersity. Results appear to show no limiting degree of polymerization for poly(methyl methacrylate).     

Molecular weight distribution of polyacrylonitrile produced in supercritical CO2

An effectively linear molecular weight calibration curve of polyacrylonitrile (PAN) was obtained using a copolymer standard with a single broad molecular weight distribution. The molecular weights and molecular weight distributions of PAN obtained from precipitation polymerization of acrylonitrile in supercritical CO₂ were quantitated by the calibration curve. The effects of monomer concentration, initiator concentration, the CO₂ pressure, and the total reaction time on the molecular weight and molecular weight distribution were studied in detail. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 2338–2341, 2002     

Melting Properties of Syndiotactic Polystyrenes and Effect of Hydrogen on Molecular Weight Distribution

Summary: The melting properties of syndiotactic polystyrenes are significantly affected by the structural molecular properties of the polymers. The most important influences on the melting behavior are stereoregularity, molecular weight and molecular weight distribution of the polymers. The melting temperature is increased by an enhanced syndiotacticity at sufficiently high molecular weights and at narrow molecular weight distributions. The degree of syndiotacticity obtained primarily depends on the kind and structure of the cyclopentadienyl ligand of the transition metal catalyst, whereas the effect of the other ancillary ligands on stereoregularity is negligible at the same cyclopentadienyl ligand. At narrow molecular weight distributions with below 2.8 and at constant stereoregularities, the molecular weight has a remarkable effect on the melting behavior at weight‐average molecular weights lower than about 80 000 g · mol^?1, resulting in a significant decrease of the melting temperature until below 230 °C. The presence of hydrogen during polymerization leads to a significant shift to lower molecular weights at comparably small amounts of hydrogen, but results in the occurrence of an additional peak in the molecular weight distribution at larger hydrogen concentrations giving evidence for the formation of a second active polymerization site producing lower molecular weight polymers. At constant stereoregularity, the broadening of the molecular weight distribution leads to decreased melting temperatures and to improved flow properties of the syndiotactic polystyrenes with increasing shear rates at moderate molecular weight distributions.

Detailed molecular weight distributions of syndiotactic polystyrenes in dependence on the hydrogen concentration.     

Thermal polymerization of styrene at high conversions and temperatures. An experimental study

An experimental study of thermal polymerization of styrene in the temperature range 100–200°C and conversion range 0–100% is reported. Conversions, molecular weight averages, and molecular weight distributions were measured. A kinetic model with third-order initiation gives a satisfactory fit of conversion and number- and weightaverage molecular weights over the ranges of temperature and conversion investigated. This model should find use in the design, simulation, and optimization of polystyrene reactors.     

EMULSION COPOLYMERIZATION OF ACRYLONITRILE AND BUTADIENE. CALCULATION OF THE DETAILED MACROMOLECULAR STRUCTURE

A novel mathematical model is developed that predicts the detailed macromolecular structure of an acrylonitrile-butadiene rubber (NBR) produced in an industrial emulsion polymerization. The model consists of: (i) a basic module that calculates the monomer conversion and the copolymer composition; (ii) a particle size distribution module; and (iii) a macromolecular structure module that calculates the bivariate chain length distributions of the linear fraction and of each branched topology (characterized by the number of branching points per molecule). From the bivariate distributions, the univariate distributions of molecular weights, copolymer composition, and degrees of branching are obtained. The model was validated from global measurements of conversion, average molecular weights, average composition, and average degrees of branching.     

The role of diffusion in the Ziegler polymerization of ethylene

A theoretical and experimental study has been made of the polymerization of ethylene in a slurry reactor using a highly active Ziegler catalyst in the presence of hydrogen. A model of the polymerization system has been set up in which polymerization is assumed to proceed with encapsulation of catalyst subparticles. Allowance is made for an experimentally observed first-order decay in intrinsic catalyst activity. The theoretical prediction of the model for the monomer absorption rate behavior and the molecular weight characteristics of the polymers formed are in agreement with experimental findings. Experimental evidence is presented that in the earliest moments of a polymerization significant amounts of polymer are formed with molecular weights 100 times those in the balance of the polymerization. It is concluded that in this system the polymerization is diffusion controlled throughout the major part of the catalyst lifetime. This diffusion phenomenon, together with the gradual loss of active sites, is of vital importance in determining the molecular weight and molecular weight distribution of the polyethylene product.     

Comparison of molecular weight distribution models for polymers characterized by g.p.c.

A semi-empirical model which employs polynomials based on general free radical polymerization kinetics, is developed to describe the molecular weight distribution data as well as to evaluate the average molecular weights of a variety of commercial thermoplastics including polystyrene, poly(methyl methacrylate) and low density polyethylene. These novel expressions are equally applicable to a natural rubber sample with a bimodal distribution. Least-squares methods for the classical Schulz and Flory distribution functions are introduced to handle the g.p.c. data of the above polymers. Comparison of the results collected from various analyses indicates clearly that the polynomial model is the most versatile one in the sense that it can be utilized to smooth out satisfactorily the molecular weight distribution data of many polymers. In general, the Wesslau distribution function is particularly good for the highly branched polyolefin and the Schulz model is fairly effective for the addition polymers of moderately sharp molecular weight distribution, presumably with $\text{M}\text{?}{}_{\mathrm{<mtext>w</mtext>}}\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}\text{=3.0}$. However, the Flory and Tung distributions are found to be rather inferior in the present studies. On the basis of the current findings, a new procedure is suggested to facilitate the computations of the true average molecular weights from g.p.c. data directly.     

Practical Continuous‐Flow Controlled/Living Anionic Polymerization

A continuous‐flow reaction system was developed, allowing flow conditions of the entire system to be maintained at a predetermined constant level, which is one of the most significant factors for successful industrial application. Controlled/living anionic polymerization was selected as a model reaction since the characteristics of its polymer products, molecular weights, and molecular weight distributions are highly susceptible to changes in the relative flow rates of a monomer and initiator solutions. In flow microreactors, controlled/living anionic polymerization of styrene in tetrahydrofuran (THF)/hexane initiated by THF‐diluted n‐butyllithium (n‐BuLi) was examined. Poly(styrenes) of larger molecule sizes such as Mn > 15 000 were successfully synthesized. After continuous operation for four hours, ca. 0.5 kg of the polymer was readily produced with narrow molecular weight distribution, demonstrating the applicability of this continuous‐flow system for controlled/living anionic polymerization on considerably large scale with a view to its industrial usage in the future.     

Molecular weight distribution of products of free radical nonisothermal polymerization with gel effect. Simulation for polymerization of poly(methyl methacrylate)

A gel effect model for the free radical polymerization of PMMA under nonisothermal conditions has been used to simulate the profiles of various system parameters, such as temperature, initiator concentration and conversion. Cumulative molecular weight and instantaneous radical molecular weight profiles for processes with greatly different histories have been computed using the method of moments. Continuous approximation of the discrete variable, degree of polymerization, renders the transformation of a large set of ordinary equations for species conservation into partial differential equations. The resulting radical and dead polymer molecular weight distributions give averages consistent with those found by the method of moments. Basic rules of thumb correlating the product molecular weights with the governing process parameters have been established based on simulations applicable to either plug flow or well-stirred batch reactors.     

Comparison of RAFT polymerization of methyl methacrylate in conventional emulsion and miniemulsion systems

In this study, we have conducted the reversible addition-fragmentation chain transfer (RAFT) polymerization of methyl methacrylate (MMA) in two heterogeneous systems, i.e. conventional emulsion and miniemulsion, with identical reaction conditions. The main objective is to compare the living character in both systems according to the nucleation mechanism, the latex stability, the particle sizes and particle size distributions of latexes, the molecular weights and molecular weight distributions (or polydispersity index, PDI) of PMMA, and the kinetics of the RAFT polymerization. The RAFT agent used in both systems was 2-cyanoprop-2-yl dithiobenzoate (CPDB). The effects of an oil-soluble initiator 2,2′-azobisisobutyronitrile (AIBN) and a water-soluble initiator kalium persulfate (KPS) on the RAFT/emulsion and RAFT/miniemulsion polymerizations were investigated. Methyl-β-cyclodextrin (Me-β-CD) was used as a solubilizer. The average molecular weights and molecular weight distributions (PDIs) of dried PMMA samples were characterized by gel permeation chromatography (GPC). The experimental results showed that the RAFT/miniemulsion polymerization of MMA exhibited better living character than that of RAFT/emulsion polymerization under the conditions of our experiment. The PDI of PMMA in RAFT/miniemulsion polymerization was decreased with the addition of Me-β-CD. However, Me-β-CD did not have influence on the PDI of PMMA prepared in RAFT/emulsion polymerization.     

Emulsion copolymers of alpha-methylstyrene and styrene

This article reports molecular weights and mechanical and processing properties of a series of styrene/alpha-methylstyrene copolymers produced by emulsion polymerization at various temperatures. Molecular weights were measured by solution viscosity, membrane osmometry, light scattering, and gel-permeation chromatography. Molecular weight development is controlled by chain transfer to monomer, but the molecular weight distributions are broader than would be expected for such reactions. This is attributed to polymer branching resulting from chain-transfer events. Molecular weight distributions of copolymers were multimodal. Thermal stability of the copolymers is somewhat lower than that of polystyrene, but addition of conventional antioxidants produces compositions with good stability in thermoplastic processing operations. Copolymers containing 25 wt. % of alpha-methylstyrene have usage temperatures about 12°C higher than that of polystyrene.     

ATRP技术在新型高分子材料合成中的应用

原子转移自由基聚合（ATRP）是用来设计一系列指定和拓朴结构和功能化聚合珠材料的一种用途广泛、简单易行、有工业前景的聚合技术。它适用于乙烯类单体在水相或有机相中合成梯形、嵌段、接枝、梳型、树枝状、星型以及有机／无机杂化材料。