STEADY-STATE MODELLING OF A LATEX REACTOR TRAIN FOR THE PRODUCTION OF STYRENE-BUTADIENE RUBBER

A mathematical model is developed for the emulsion copolymerization of styrene and butadiene carried out in a continuous train of stirred tank reactors. The model predicts copolymer composition, conversion, molecular weight averages, and long chain branching frequencies, as well as the latex particle size distribution for all reactors in the train. It is capable of simulating closely the behaviour of industrial SBR processes.

Several simulation studies are performed. Topics investigated include: process operating modifications to improve productivity; the effect of chain transfer agent flow rate and number of reactors on the molecular weight development; the effect of process modifications on the development of the particle size distribution down the reactor train; and the effect of reactor design on particle generation rates.     

Effect of the operating conditions of synthesizing diene rubber with a neodymium-based catalytic system on its branching characteristics

A mathematical model taking into account the branching of a polymer is developed for the synthesis of diene rubber with a neodymium-based catalytic system (NBCS) in a cascade of continuous reactors. The model is used to study the main branching characteristics of NBCS diene rubber. Relations for calculating the average number of branches per macromolecule, average length of a main chain, average length of side chains, weight fraction of a polymer in side chains and G-factor are derived.     

Mathematical modeling of the continuous process of butadiene polymerization over a neodymium-based catalyst with allowance for its polycentric nature and chain transfer to the polymer in a cascade of stirred reactors

A mathematical model for continuous butadiene polymerization under the effect of a neodymium versatate-diisobutylaluminum hydride-hexachloro-p-xylene catalytic system is developed that takes into account its polycentric nature and chain transfer to the polymer in a cascade of stirred reactors. The constructed mathematical model adequately describes industrial data and makes it possible to calculate not only the average molecular weights, but also the characteristics of polymer branching at the outlet of the kth reactor of the cascade.     

Chain branching in high pressure polymerized polyethylene

We have combined the techniques of ¹³C nuclear magnetic resonance (n.m.r.) and nitric acid degradation to obtain information on the location of the side chains in branches polyethylene. Surprisingly, we have found that the ethyl and butyl groups are mainly excluded from the crystalline zones. The longer branches can cocrystallize with the main chain. Knowledge of the numbers and types of branch in polymers is of some technological important in polymer science. Short chain branching has a marked effect on the mechanical properties of the polymer, whilst the long chain branching affects the properties of melts.     

搅拌反应器内气液两相流的CFD研究进展

搅拌式气液反应器因其操作灵活、适用性强等优点,在过程工业中应用广泛.综述了采用计算流体力学CFD技术对搅拌反应器内气液两相流动行为的数值模拟研究.Euler-Euler双流体模型作为主要方法用于描述气液两相流动,在其基础上耦合相对简单的气泡数密度函数模型或复杂的群体平衡模型,可较为准确地预测搅拌反应器内气泡尺寸和局部气含率及其分布规律.CFD模拟结果可用以分析和评价不同搅拌桨叶、搅拌桨组合和气体分布器的气液分散性能,对气液反应器的结构优化和过程强化提供了有效手段.     

群体平衡方程在搅拌反应器模拟中的应用

群体平衡方程（population balance equation,PBE）是描述多相流体系中分散相大小与分布随时空变化的通用方程。搅拌反应器内多为多相流体系,考虑到颗粒聚并、破碎等微观机制对颗粒大小、分布、粒数密度等宏观参量的影响,采用PBE对搅拌槽内多相流体系进行数值模拟,可以较准确预测搅拌槽内流场和颗粒的大小与分布。对群体平衡方程在搅拌反应器数值模拟中的应用进行了综述,在简要介绍PBE的基本形式后,讨论了PBE的主要数值求解方法,然后着重介绍近年来采用PBE对搅拌槽内液固沉淀过程、气液及液液体系进行数值模拟的情况,并对今后的研究方向进行了展望。     

Short chain branching distribution and thermal behavior of high density polyethylene

High-density polyethylenes with unimodal and bimodal molecular weight distribution have been fractionated according to crystallizability using preparative temperature rising elution fractionation. The molecular structure and thermal properties of the fractions with their whole polymers have been characterized. The average short chain branching content of the fractions obtained ranged from 0 to 8 branches per 1000 carbon atoms while that of the whole polymers is about 2 branches per 1000 carbon atoms. The bimodal resins have a slightly higher frequency of short chain branch in higher molecular weight species than in those of the unimodal resins. The short chain branching distribution as well as the low molecular weight species in the fractions seem to be important parameters to determine thermal behavior of the fractions. The fractions with the short chain branching content above 3 branches per 1000 carbon atoms showed a significantly different thermal behavior from those with less than 3 branches per 1000 carbon atoms. © 1996 John Wiley & Sons, Inc.     

Effects of long-chain branching on distribution of degree of polymerization

The method of generating functions is used to calculate the number fraction of molecules having any specified degree of polymerization and number of long branches for polymers produced under conditions in which the probabilities of chain propagation and of branching on a monomer unit incorporated in the polymer are both constant; termination by combination is assumed absent. Expressions are given for the moments of degree of polymerization and the first two moments of branch number. It is shown that all moments of degree of polymerization are finite, for this model. An asymptotic expression for the number distribution at very high degrees of polymerization is obtained. The way in which the average number of branches per monomer unit varies with degree of polymerization is studied.     

Kinetics of high conversion polymerization of vinyl acetate. Effects of mixing and reactor type on polymer properties

In the present article the kinetics of polymerization of vinyl acetate in suspension up to high conversion was studied. The molecular weight distribution and the side chain branching of polyvinyl acetate produced were examined with respect to micro and macro mixing as well as to reactor type. The following results were achieved: the time–activity curves of the polymerization can be described up to high conversions considering the exponential increase in viscosity of the polymerizing system and combining the viscosity with rate constants of the polymerization. The change of volume of the polymerizing system has no significant influence on kinetics. The narrowest molecular weight distribution of the poly(vinyl acetate) produced was achieved when polymerizing in the homogeneous continuous stirred tank reactor while the broadest molecular weight distribution was observed in the segregated continuous stirred tank reactor. The batch reactor and the flow tube reactor produce polymers with molecular weight distributions lying in between. Considering the side chain branching, another order was found. The batch reactor and the tube reactor show the lowest side chain branching, the homogeneous continuous stirred tank reactor shows a larger one and the segregated continuous stirred tank reactor shows the largest. Possible reasons for the different behavior of the different reactors are discussed. The degree of segregation was determined by experiments.     

Dynamic modelling of the continuous emulsion polymerization of vinyl chloride

A dynamic model for the continuous emulsion polymerization of vinyl chloride (VCM) in a train of stirred tank reactors has been developed. This model can predict monomer conversion, polymer particle size distribution (PSD), molecular weight distribution and long and short chain branching frequencies under non-steady reactor operation during startup, reactor switching and during unstable operation when conversion and polymer and polymer particle properties oscillate with time. The model has been used to design a flexible reactor train configuration which operates in a stable mode and can produce latexes with a wide range of properties including a bimodal polymer particle size distribution.     

Impact of branching on the UV degradation of metallocene LLDPE

The effect of UV degradation on metallocene linear low density polyethylenes (LLDPEs) of different branching characteristics was studied. The samples were exposed to natural weather condition. The extent of the degradation on these LLDPEs was measured by Mechanical, FTIR and GPC testings. This paper addressed the structural modifications due to UV degradation of metallocene LLDPE (m-LLDPE). The results suggested that Z-N HDPE is very stable. Carbonyl absorbance and degradation of mechanical properties of m-LLDPEs increased with increasing branch content of the polymers. For short exposure times, the results suggested increase in the degree of cross-linking of m-PEs with the increase in BC leading to brittle behavior. However, at high exposure times chain scission dominates and it is branch content dependent. Most of the mechanical properties show a sharp rate of drop at branch contents less than 20 branches/1000 C followed by a slow drop rate. The results of the mechanical properties correlate very well with the carbonyl absorbance. GPC results confirmed that chain scission leading to a broader MWD is dominant at high exposure times and for LLDPEs with high branch contents. Branch type did not show any influence on mechanical properties.     

A computational model for predicting particle size distribution and performance of fluidized bed polypropylene reactor

Gas phase polymerization of propylene is one of the most widely accepted and commercially used processes for manufacturing of polypropylene. The present work describes a comprehensive mathematical model for simulating fluidized bed polypropylene reactors. Unlike previously published models, the present model simultaneously predicts both polymer properties as well as particle size distribution. A generalized framework of a dynamic model based on mixing cell approach and detailed polymerization kinetics coupled with population balance model for particle size distribution (PSD) is developed. Need for coupling the reaction engineering model with population balance models is demonstrated. The coupled model was then used to understand influence of operating parameters on polymer properties and particle size distribution. The model is also used to understand the effects of multiple active sites and reaction kinetics on macroscopic variables. The developed framework is useful for simulating multi-monomer, multi-site Ziegler-Natta type olefin fluidized bed polymerization reactors.     

Modeling and Simulation of Ethylene Polymerization in Industrial Slurry Reactor Series

A five-site comprehensive mathematical model was developed to simulate the steady-state behavior of industrial slurry polymerization of ethylene in multistage continuous stirred tank reactors. More spe...     

A molecular dynamics study of the effects of branching characteristics of LDPE on its miscibility with HDPE

The effects of branching characteristics of low-density polyethylene (LDPE) on its melt miscibility with high-density polyethylene (HDPE) were studied using molecular simulation. In particular, molecular dynamics (MD) was applied to compute Hildebrand solubility parameters (δ) of models of HDPE and LDPE with different branch contents at five temperatures that are well above their melting temperatures. Values computed for δ agreed very well with experiment. The Flory-Huggins interaction parameters (χ) for blends of HDPE and different LDPE models were then calculated using the computed δ values. The level of branch content for LDPE above which the blends are immiscible and segregate in the melt was found to be around 30 branches/1000 long chain carbons at the chosen simulation temperatures. This value is significantly lower than that of butene-based linear low-density polyethylene (LLDPE) (40 branches/1000 carbons) in the blends with HDPE computed by one of the authors (polymer 2000; 41:8741). The major difference between LDPE and LLDPE models is that each modeled LDPE molecule has three long chains while each modeled LLDPE molecule had only one long chain. The present results together with those of the LLDPE/HDPE blends suggest that the long chain branching may have significant influence on the miscibility of polyethylene blends at elevated temperatures.     

Influence of the short‐chain branch length on the calibration of temperature rising elution fractionation systems

The effects of short‐chain branch (SCB) length on the calibration of temperature rising elution fractionation (TREF) were examined. Samples of ethylene–hexene, ethylene–octene, and a novel polyolefin produced using Eastman Chemical Company's Gavilan catalyst technology were used to prepare TREF calibration curves. Preparative TREF was used to collect fractions of the materials based on their crystallizability, and the branching frequencies of the fractions were determined by NMR. Calibration curves were generated by plotting the branching frequency as a function of the TREF elution temperature. The results indicate that the calibration curves shift to lower TREF elution temperatures as the length of the SCB increases from methyl to butyl to hexyl. Other factors that may contribute to this shift include chain microstructural differences from variations in catalyst structure and process conditions. The shift can be decreased by plotting the data in “number of branches per 1000 backbone carbons” versus TREF elution temperature instead of the more traditional “number of branches per 1000 total carbons.” These data indicate that the branch type must be known a priori to calculate SCB averages and SCB distributions and that unique calibration curves exist for copolymers made using different α‐olefin comonomers. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 722–728, 2003     

Untersuchungen zur Langkettenverzweigung in Polyäthylenen

Polyethylene samples of various densities and melt flow indices resulting from different polymerization processes have been investigated with respect to long chain branching (LKV). For that purpose several polymer fractions have been characterized by measurement of weight average molecular weights M_w and intrinsic viscosities [η], the latter ranging from 0,2 to 3,2 with high pressure samples and from 0,2 to 10 with low pressure material. The intrinsic viscosity difference of branched (high pressure) polyethylene compared to linear (low pressure) polyethylene is used as a measure of LKV. With high pressure polyethylene LKV increases with decreasing density. This dependence is strongest within the medium molecular weight range. Samples with varying LKV but constant density can be obtained by appropriate change of polymerization conditions. No LKV has been observed with low pressure polyethylene. This means a marked difference compared to high pressure material of equal density. Branching with low pressure polymers can therefore be ascribed to the short chain type only, which in particular results from copolymerization. Several mathematical approaches have been checked whether or not they can yield suitable information about n, the number of long chain branches per molecule. The best fit with our experimental data is obtained using the expression [η]v/[η]₁ = g^1,3 (n = f(g)) and assuming, that the average concentration of long chain branch points does not depend on molecular weight for fractions of the same sample (n/M = const.). If LKV ist taken into consideration, logarithmic normal molecular weight distributions are obtained for many high pressure polyethylenes (similar to low pressure material). Data are reported in support of the view, that performance characteristics are dependent on LKV. There is some evidence, that melt flow properties of polyethylene are improved with increasing LKV.     

Agitation scale-up effects during VCM suspension polymerization

Experimental data are presented showing the effect of reactor agitation intensity and reactor size on final resin properties during VCM suspension polymerization. Experiments were carried out in three stirred batch polymerization reactors covering a broad range of vessel sizes (bench scale, pilot plant, and commercial production units). Reactors' shapes were geometrically similar. The same charge recipe and operating procedure was also used for all three reactors. The effects of major agitation parameters such as impeller diameter, width, and speed are correlated against resin properties using the Weber number. The same characteristic U-shaped curve is found for all three reactors when mean particle diameter is plotted versus Weber number. However, the curves do not lie on top of one another but are spread apart, the larger reactors having a higher Weber number. Another interesting feature is that the coefficient of variation (particle size standard deviation divided by mean diameter) decreases dramatically as reactor size is increased. Other resin properties also show improvement upon scale-up. In summary, resin properties continue to improve as reactor size is increased over the range studied (bench-to-commercial large reactor scale), but a correct application of the complex scale-up technology must be employed to take advantage of this observation.     

1H-NMR/13C-NMR studies of branched structures in PVC obtained at atmospheric pressure

Summary The ¹H-NMR-spectra of raw poly (vinyl chloride) obtained at atmospheric pressure (U-PVC) have revealed the presence of high concentrations of branches. The content of labile chlorine was determined by reaction with phenole in order to estimate the branch points with tertiary chlorine. The branch length of reductively dehalogenated U-PVC by¹³C-NMR analysis have provided evidence for both short chain branches including chloromethyl groups and 2.4-dichloro-n-butyl groups and long chain branching. For a number of U-polymers the total amount of branching ranges from 7.5 to 13.5/1000 C. The ¹³C-NMR measurements point to a ratio of methyl/butyl branches of 1 1 and short chains/long chains of 6 1 .