Simulation of Degradation Processes. III. Testing of Some Relations for Random Chain Scission

Abstract

By means of the Monte Cario method a course of random chain scission was simulated and the following were decermined: the number-average moiecular weight and the degree of polymerization of the system, the weight-average moiecular weight and the degree of polymerization of the system, the number of molecules of degree of polymerization higher than an arbitrarily chosen value, and the number of molecules of a given degree of polymerization. Values obtained by simulation were compared with some analytical relations. Some hitherto unknown characteristics of the whole process have been established.     

Dynamic analysis of branching in radical polymerization

A method for the theoretical analysis of branching in radical polymerization is presented which includes the dynamics of the process. In particular, the method is applied to a polymerization that occurs by decomposition of initiator, propagation, termination by radical combination, and chain transfer with polymer. By a numerical solution of the kinetic equations (suitably transformed), the time dependence of the number-average degree of polymerization (DP), the weight-average DP, the mean number of branches, and the monomer conversion are obtained. The parameters of the process, that is the rate coefficients and initial concentrations, have the following effects: (1) An increase in the chain transfer coefficient increases the ratio of weight-average to number-average X_w/X_n and the mean number of branches X_b, but does not change the number-average X_n. (2) For a given value of the chain transfer coefficient, a change in the parameters of the process such that X_n increases, causes X_w/X_n and X_b to increase also. (3) Chain transfer with polymer seems to produce relatively few polymer molecules having many branches and a large number of smaller polymer molecules having no branches; consequently, the polymer size (or molecular weight) distribution broadens.     

Emulsion copolymerization of styrene and methyl methacrylate. II. Molecular weights

A mathematical model for the time evolution of both number-average molecular weight and weight-average molecular weight is described. The model results in a set of ordinary differential equations and its application is not limited by the maximum number of radicals per particle. The model was used to analyze the effect of the monomer molar ratio in the initial charge on the weight-average molecular weight during the emulsion copolymerization of styrene and methyl methacrylate in a batch reactor.     

Influence of catalyst depletion or deactivation on polymerization kinetics. II. Nonsteady-state polymerization

The number-average and weight-average degrees of polymerization at the end of the polymerization process have been calculated in terms of the initial monomer concentration, initial catalyst concentration, and rate constants for various polymerization processes, all of which assume instantaneous initiation. The mechanisms differ among themselves in that there is either first-order catalyst deactivation, or transfer to monomer, or both. The calculation is greatly simplified if only the molecular weights at the end of polymerization are considered. The method given is particularly useful for systems where the calculation of the distribution function as a function of time is complicated. The fact that the monomer concentration and catalyst concentration have a marked effect on the molecular weight provides a good test of the validity of the mechanism under consideration. A comparison of the calculated and observed molecular weights obtained for the homogeneous polymerization of acrylonitrile with an organometallic catalyst will be given in a later communication.     

Kinetics of radical polymerization. XXX. Polymerization of styrene in solution

A study was made on the AIBN-initiated polymerization of styrene in benzene and dimethyl formamide at 50°C. The overall rate and the rate of initiation of the polymerization were determined and the number-average and weight-average molecular weights of the polymers formed were measured. The decrease in the rate and degree of polymerization with the decrease in styrene concentration was caused by the corresponding decreases in the rate constants of chain propagation and initiation steps. In the systems studied no chain transfer process occurred with an experimentally measurable rate.     

Continuous precipitation polymerization of vinylidene fluoride in supercritical carbon dioxide: molecular weight distribution

The surfactant-free precipitation polymerization of vinylidene fluoride (VF2) in supercritical carbon dioxide was studied in a continuous stirred autoclave. The polymerization temperature ranged from 65 to 85°C, the average residence time in the reactor varied from 10 to 50 min., and the pressure was between 210 and 305 bar. Diethyl peroxydicarbonate was used as the initiator. The fractional conversion of monomer varied from 7 to 26%, the number-average molecular weight of the polymer was between about 14,000 and 79,000, and the weight-average molecular weight was between about 21,000 and 700,000. In many cases, the polymer exhibited a bimodal molecular-weight distribution, especially at high monomer concentrations.     

Preparation of polyethylene block copolymers by a combination of postmetallocene catalysis of ethylene polymerization and atom transfer radical polymerization

The synthesis of block copolymers consisting of a polyethylene segment and either a poly(meth)acrylate or polystyrene segment was accomplished through the combination of postmetallocene-mediated ethylene polymerization and subsequent atom transfer radical polymerization. A vinyl-terminated polyethylene (number-average molecular weight = 1800, weight-average molecular weight/number-average molecular weight =1.70) was synthesized by the polymerization of ethylene with a phenoxyimine zirconium complex as a catalyst activated with methylalumoxane (MAO). This polyethylene was efficiently converted into an atom transfer radical polymerization macroinitiator by the addition of α-bromoisobutyric acid to the vinyl chain end, and the polyethylene macroinitiator was used for the atom transfer radical polymerization of n-butyl acrylate, methyl methacrylate, or styrene; this resulted in defined polyethylene-b-poly(n-butyl acrylate), polyethylene-b-poly(methyl methacrylate), and polyethylene-b-polystyrene block copolymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 496–504, 2004     

Emulsion polymerization of styrene in a single continuous stirred-tank reactor

The effects of mean residence time, initiation rate, and emulsifier concentration on particle formation, particle growth, and polymerization rate are examined for the emulsion polymerization of styrene in a completely mixed continuous stirred-tank reactor. Experimental measurements of number of particles, particle size distribution, polymerization rate, and molecular weights are compared with theoretical predictions. A theoretical model which incorporates Stockmayer's modification of the Smith-Ewart theory into the particle growth equation allows reasonably accurate prediction of polymerization rate, particle formation rate, and particle size distribution. Agreement between experimental measurements of number-average and weight-average molecular weights and a theory based on Smith-Ewart case 2 kinetics is also reasonable.     

A Study of the Molecular Weight and Chain Length Distribution of Cyclocopolymers of Divinyl Ether and Maleic Anhydride

Some physical properties of a cyclocopolymer formed by an intra-inter-molecular polymerization mechanism were studied. The cyclic copolymer of divinyl ether and maleic anhydride was chosen for study. Intrinsic viscosities were determined in two solvents. The weight-average molecular weight was determined by light-scattering measurements and the number-average molecular weight was determined by osmometry. Results from a sedimentation velocity pattern indicated that the chain length distribution is much broader than random, which is in agreement with the ratio of the two molecular weight determinations. The polymer was fractionated by precipitation from acetone with hexane as precipitant. Addition of sodium tetraphenyl boron was necessary to obtain separation. Correlation of intrinsic viscosity and weight-average molecular weights was not obtained because of anomalous solubility effects preventing light-scattering determinations.     

Molecular weights in polymerization as a function of conversion

A relatively novel method of calculating molecular weight changes and broadening during a polymerization is proposed. It differs from others in that the distribution is considered implicitly rather than explicitly. This allows direct use of kinetic rate equations in the derivation of weight-average and number-average degree of polymerization etc.; the mathematics simplifies to simple integration rather than sums of complicated series. The method is illustrated by applying it to several cases. These range from various models where only monomer concentration changes, to where both monomer and initiator or monomer and chain transfer agent are changing. Cases previously unsolvable can now be handled.     

茂基二价钐配合物高效催化己内酯开环聚合

研究了二茂基二价钐配合物(C5H5)2Sm(THF)作为单组分催化剂催化己内脂开环聚合反应,考察了催化剂用量、聚合反应时间、聚合反应温度对己内酯聚合反应的影响。结果表明,配合物(C5H5)2Sm(THF)对己内酯聚合有极高的催化活性且产物的数均分子量较高,当催化剂与单体摩尔比为1：5000时,聚合产率仍可达50.3%,数均分子量可高达32.4万;温度升高,聚合反应的转化率增加,聚合产物数均分子量降低;催化剂用量增加,聚合转化率增加,聚合产物分子量降低;聚合产物的分子量分布较窄;通过凝胶色谱法对聚合产物的分子量及分子量分布进行了表征。     

Solution Polymerization of Acrylonitrile Catalyzed by Sodium Triethylthioisopropoxyaluminate: A Polyacrylonitrile with High Structural Regularity

A new catalyst for the polymerization of acrylonitrile has been found by reacting sodium aluminum tetraethyl with a stoichiometric amount of oxygen, alcohols, or mercaptans, etc. The catalyst prepared by reacting NaAlEt₄ with RSH remains active at temperatures as low as ?78°C., polymerizing acrylonitrile into high molecular weight polymers with high conversions. At ?78°C., the propagating chain remains active over a period of days, and the chain length increases with time or conversion. At high conversions the molecular weight of the polymer is directly proportional to the concentration of the monomer, the catalyst concentration being kept constant. The efficiency of the catalyst expressed as the ratio of the number of the polymer molecules produced to the number of the sulfur atoms used is in excess of 80%. The weight-average molecular weight of the polymer measured by light scattering is roughly equal to the number-average molecular weight determined by sulfur analysis assuming only onesulfur atom in each polymer molecule. Although the data given here are only qualitative in nature, it is nevertheless evident that this system bears great resemblances to anionic polymerizations resulting in “living polymers.” The polymer obtained with the NaAlEt₃S(i-Pr) catalyst at ?78°C. differs from free-radical polyacrylonitrile in exhibiting substantially lower solubility, higher melting point, and higher rate of crystallization than that for the free-radical polymer. The polymer is also free from structural mpurities; it does not cause fluorescence in dilute solutions and has no absorption peak at 265 mμ; both these effects are produced by impurities in free-radical polyacrylonitrile. It is concluded that the polymer reported here is more regular in structure than free-radical polyacrylonitrile.     

线型缩聚反应的计算机模拟

缩聚反应是一类重要的高分子合成方法。其中最简单的反应为线型缩聚体系,它可分为两类,分别是含有两个可缩合的官能团的单体或单体对进行的相互缩合的体系。Flory在上世纪四十年代采用统计方法对该缩聚体系做过系统的理论研究,并在官能团等活性的假定下提出了著名的Flory分布函数,由此揭示了反应体系中数均聚合度xn、重均聚合度xw、不同聚合度分子的分布情况与反应程度p的关系。本文利用计算机模拟的方法,同样在官能团等活性的假定下模拟了线性缩聚反应的全反应过程,所得到的结果与用统计方法所得到的结果完全一致。本方法是对整个真实反应过程的直观模拟,对研究相似的以逐步聚合反应机理进行的反应具有普适性,并具有可拓展到模拟更真实的粘性聚合体系以及研究反应动力学的潜力。     

Nonsteady-state kinetics for anionic polymerization of polar monomer initiated instantaneously by electron transfer

With the help of the nonsteady-state method, the kinetic differential equations for the anionic polymerization of polar monomer initiated instantaneously by electron transfer with monomer termination are treated rigorously. The expressions for the molecular weight distribution, the number-average and weight-average degrees of polymerization, and the functionality distribution are derived in closed form. A theoretical means is established by which all the molecular parameters of the polymer can be calculated from polymerization conditions, such as the reaction constants, the concentrations of initiator and monomer, and the monomer conversion.     

H_2O/TiCl_4/Py体系引发苯乙烯正离子聚合

研究了在少量吡啶(Py)存在下由水(H2O)四氯化钛(TiCl4)体系引发苯乙烯于二氯甲烷正己烷中进行碳正离子聚合,分别考察[Py]、[H2O]和[TiCl4]对聚合速率、产物分子量与分子量分布的影响.实验结果表明,少量亲核试剂吡啶(Py)对聚合反应起着重要作用,可有效地降低聚合速率和使分子量分布变窄;随着[H2O]和[Py]降低或[TiCl4]增加,聚合产物的分子量增加,而分子量分布指数(Mw Mn)基本维持在1.8左右;随着[Py]增加,聚合速率降低;随着[H2O]和[TiCl4]增加,聚合速率提高.聚合速率对单体浓度呈一级动力学关系,对Py、H2O和TiCl4的反应级数分别为-0.72、0.72和1.86.聚合速率对TiCl4浓度呈接近二级动力学关系,这可能与体系中TiCl4主要以二聚体形式存在有关.聚合转化率和产物分子量均随着反应时间延长而逐渐增大,PS的数均分子量与转化率呈线性增加关系.     

Direct quantification of mono- and di-D-α-tocopherol polyethylene glycol 1000 succinate by high performance liquid chromatography

A simple and direct reversed-phase high performance liquid chromatography (RP-HPLC) method with UV detection was developed and validated for the determination of mono- and di-D-α-tocopherol polyethylene glycol 1000 succinate (TPGS 1000) in TPGS mixture. Before the HPLC analysis, mono- and di-TPGS 1000 were separated by simulated moving bed (SMB) chromatography system and characterized by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). The mass spectrometric results confirmed that the molar mass distribution of TPGS prepared in our laboratory was very close to that of the product of Eastman Chemical Company with similar nˉ (average polymerization degree), M(n)ˉ (number-average molecular weight) and M(w)ˉ (weight-average molecular weight). The HPLC analysis was carried out on a C30 analytical column with mobile phases comprised of acetonitrile (A) and isopropanol (B) in gradient conditions. Validation of the analytical method was done on the following parameters: system suitability, linearity, limits of detection and quantification, accuracy and precision, method robustness and solution stability. The linearity of the calibration curves for mono- and di-TPGS 1000 from both sources was found to be good (r(2)>0.9996). The recovery values were from 94.6% to 103.3% for mono-TPGS, and 93.5% to 103.3% for di-TPGS. This method could be successfully used in the direct quantification of mono- and di-TPGS in TPGS 1000 mixture using TPGS standards with similar molecular mass distributions although derived from different sources.     

Highly stereospecific polymerization of isoprene with homogeneous binary Ziegler-Natta catalysts based on NCN-pincer neodymium precursor

The aryldiimine NCN-pincer stabilized neodymium dichloride combined with aluminum alkyls established a new type of homogeneous binary neutral Ziegler-Natta catalyst system. This system exhibited high activity and high cis-1,4 selectivity for the polymerization of isoprene (T _p = 20 °C, 98.2%; T _p = ?20 °C, > 99%). Such catalytic performances remained under a broad range of polymerization temperatures and monomer-to-neodymium ratios (from 500 to 8000), reaching high number-average molecular weight (M _n = 1582 kg/mol) and relatively narrow molecular weight distribution (PDI = 1.68), which was, however, influenced by the amount and bulkiness of aluminum alkyls. Dynamic investigation of the polymerization was performed, which showed the number-average molecular weight of the resultant polyisoprene had an almost linear correlation with the conversion, suggesting, in some degree, the polymerization with this catalytic system was controllable.     

Gamma Radiation-Induced Template Polymerization of Acrylic Acid in the Presence of Polyactrylamide

Abstract

Poly(acrylamide-acrylic acid) resin p(AM-AA) was prepared by gamma radiation-induced polymerization of acrylic acid in the presence of polyacrylamide as a template polymer. The polymerization was studied by a free radical mechanism at different experimental conditions such as: absorbed dose, monomer concentration, polymer/monomer molar ratio and the weight-average molecular weight or the swelling degree of added polymer. The resin was obtained at dose > 10 KGy and there is no significant change in the swelling degree of the resin. The results showed that the capacity of the resin increases by increasing the monomer concentration, the weight-average molecular weight of the added polymer and decreases by increasing polymer/monomer molar ratio and the swelling degree of the added polymer. It was also found that the capacity of the resin depends on the radiation dose.     

AGET ATRP of methyl methacrylate with poly(ethylene glycol) (PEG) as solvent and TMEDA as both ligand and reducing agent

Activator generated by electron transfer atom transfer radical polymerization of methyl methacrylate (MMA) in inexpensive, non-toxic poly(ethylene glycol) (PEG), with air-stable Cu(II)X₂(X = Br, Cl) as the catalyst and N,N,N′,N′-tetramethylethylenediamine (TMEDA) as both ligand and reducing agent was investigated. The polymerizations in PEG proceeded in a well-controlled manner as evidenced by kinetic studies and chain extension results. The polydispersity of the polymer obtained was quite narrow, with a weight-average molecular weight/number-average molecular weight ratio of less than 1.2. Effects of the TMEDA content and the catalysts on polymerization were also investigated, respectively.