A new method for calculating and correcting molecular weight distributions from gel permeation chromatography

A new method for calculating and correcting molecular weight distributions of polymer samples from GPC chromatograms is presented. The integral equation which relates the true molecular weight distribution of polymer sample to the chromatogram is reformulated into an equivalent variational problem of quadratic functional. The method of steepest descent in the function space is then applied to the minimization problem to obtain the true molecular weight distribution. This method is efficient and reduces some of the oscillation problems encountered in the previous methods. Examples are given.     

A method for determining sequence distributions in ethylene-1-butene copolymers by 13C NMR

Sequence distributions of the 1-butene comonomers in ethylene-1-butene copolymers were determined by analyzing the ¹³C NMR spectra using an optimization calculation technique. The proposed method takes the possible errors in NMR measurements into account. Applying the method to the spectra of some linear low density polyethylenes with 1-butene as the comonomer gave physically reasonable values of triad comonomer distribution. The method was thought to be useful by giving the possible maximum and minimum triad concentrations reflecting the chain structures. We also tried to use the method for determination of larger sequence structures over triad distribution. Received: 10 February 1997/Revised: 31 March 1997/Accepted: 2 April 1997     

Molecular weight distributions of tetrafluoroethylene-hexafluoropropylene copolymers

A new methodology has been developed to determine molecular weight distributions (MWD) from dynamic rheometry data. The present work extends and modifies previous results and illustrates that the MWDs of tetrafluoroethylenehexafluoropropylene copolymers (FEP) are broader than previously thought. The major change in methodology involves the relationship between a reduced form of the elastic shear modulus as a function of frequency, G′(ω), and the cumulative weight fraction as a function of molecular weight. The new method uses a square root versus the former linear relationship. Spectroscopic analysis of the end group concentration was used to determine the number-average molecular weight. These data were used to reference the MWDs determined by dynamic rheometry and indicate that the molecular weights of these polymers are 20% lower than previously found.     

Modality of molecular weight distributions

Even restricting attention to weight distributions, it is ambiguous to merely say that a polymer is “not bimodal.” A simple example is shown wherein the weight distribution of log (molecular weight) is bimodal, but the weight distribution of molecular weight is not bimodal.     

A segment probability method for calculating the molecular weight distributions of linear polycondensates in a continuous reactor

The molecular weight distribution (MWD) of polymers is a target of the optimization and control of industrial polymerization processes, as it dictates the processability and properties of polymers. A method, named as segment probability method, is developed to calculate the MWD of polycondensates produced by monomers of types A₂ and B₂ in a continuous reactor. It considers a growing chain as being composed of A and B segments in the middle of the chain and two terminal segments at the chain ends. It calculates the propagation probabilities of these different types of segments upon taking into account both the polycondensation and side reaction kinetics as well as the residence time distribution of the continuous reactor. The method is validated by poly(butylene terephthalate) (PBT) obtained from an industrial polymerization process composed of a continuous esterification reactor. The MWDs of the PBT calculated by this method are in agreement with those measured by size exclusion chromatography with mean square errors less than 10%.     

Low molecular weight block copolymers as plasticizers for polystyrene

Polystyrene‐b‐alkyl, polystyrene‐b‐polybutadiene‐b‐polystyrene, and polystyrene‐b‐poly(propylene glycol)monotridecyl ether were synthesized using macro initiators and atom transfer radical polymerization or by esterifications of homopolymers. The aim was a maximum molecular weight of 4 kg/mol and minimum polystyrene content of 50 w/w %, which by us is predicted as the limits for solubility of polystyrene‐b‐alkyl in polystyrene. DSC showed polystyrene was plasticized, as seen by a reduction in glass transition temperature, by block copolymers consisting of a polystyrene block with molecular weight of approximately 1 kg/mol and an alkyl block with a molecular weight of approximately of 0.3 kg/mol. The efficiency of the block copolymers as plasticizers increases with decreasing molecular weight and polystyrene content. In addition, polystyrene‐b‐alkyl is found to be an efficient plasticizer also for polystyrene‐b‐polyisoprene‐b‐polystyrene (SIS) block copolymers. The end use properties of SIS plasticized with polystyrene‐b‐alkyl, measured as tensile strength, is higher than for SIS plasticized with dioctyl adipate. The polystyrene‐b‐polybutadiene‐b‐polystyrene and polystyrene‐b‐poly(propylene glycol)monotridecyl ether series were only partially soluble in polystyrene and insoluble in the polystyrene phase of SIS. For the lowest molecular weight samples, this leads to measurable plasticization of polystyrene but no plasticization of SIS. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 95: 981–991, 2005     

A continuum of molecular weight distributions applicable to linear homopolymers

An array or continuum of molecular weight distributions was set up, based upon the numerical solutions found for the theoretical log-normal (LN) and generalized exponential (Gex) distribution functions, for a range of M_w/M_n = H ratios. For the Gex distributions, m > 0 in the continuum, and the theoretical Schulz–Zimm and Tung–Weibull distributions, in which m ≥ 1 for H ≤ 31, are located within the continuum. The LN distribution is the broadest, and the Gex-related distributions become narrower as the numerical value of m increases. From literature data for polystyrene, poly(vinyl chloride), linear polyethylene, and polypropylene, one can assign to these polymers specific molecular weight distributions that fall within the continuum.     

测定压敏胶乳液表面张力的简易珠滴重量法

介绍了一种利用常用的酸式滴定管、移液管和电子天平测定乳液表面张力的简易方法。首先通过测定已知表面张力液体的珠滴质量 ,由σ =D×M计算出D值 ,然后测定压敏胶乳液的珠滴质量 ,并利用同样的公式计算出乳液的表面张力。我们利用此方法测定了 5种压敏胶乳液的表面张力。结果表明 ,这种测定乳液表面张力方法操作简便 ,实用性强 ,结果准确可靠。     

A new accelerated method for determining the potential alkali-carbonate reactivity

Many kinds of carbonate aggregates with different chemical compositions, structure, and geological characteristics have systematically been investigated. This research deals with chemical components and mineral analysis, petrographic examination of the aggregates, the dynamics of alkali-carbonate reaction with different cements, alkali contents, and particle sizes. A new method for evaluating the potential alkali-carbonate reactivity has been proposed according to the results, in which the major test factors include 1.5% Na₂O_eq. of alkali content, 1 M NaOH solution, 0.3 water-to-cement ratio, 5-10 mm particle size, and 4 weeks of test period at 80 °C. The results using this new method has also been compared with that of the performance of concrete structures in China.     

一种计算搅拌槽混合时间的新方法

基于对混合时间定义的思考,提出了一种新的定义方法,在湍流流场数值计算的基础上通过求解示踪剂的浓度输运方程,研究了单层涡轮桨搅拌槽内的混合过程。结果表明：搅拌转速和搅拌桨安装位置都影响混合时间的大小,而进料位置对混合时间的影响不大。对于不同的搅拌转速而言,随搅拌转速的增大,相同体积分数对应的混合时间逐渐减小。当搅拌桨安装在槽中间位置时所对应的混合时间最小。利用适宜的尺寸和安装位置的导流筒可有效降低混合时间。     

陶瓷泥料可塑性的一种新型测试方法

1　测试原理陶瓷泥料是由多种原料按一定的配比混和制成 ,不同的产品对其泥料的塑性要求不同 ,我们在实际生产过程中根据不同工艺的环境要求 ,通过研究试样在受力过程中应力与应变之间的关系来确定泥料的可塑性 ,该方法更科学、更先进。根据这一原理制取直径2 8 × 38 的圆柱体试样 ,放在专用的测试架上 ,检测试样的受压和变形。在试样变形为10 %时 ,记录其所受的压力Ｆ10 ,此时其压缩的截面积变形为Ｓ10 ;试样变形为 50 %时记录其所受压力Ｆ50 ,此时其压缩的截面积变形为Ｓ50 。定义其“可塑度”Ｒ ,根据公式Ｒ =(Ｓ50 /Ｓ10 )× (Ｆ10 /Ｆ…     

不锈钢酸洗过程酸度测定的新方法

为解决不锈钢酸洗过程中存在的一些有色金属离子会对废液酸度的测定造成干扰的问题,通过理论计算,建立了一种新型的酸度测定方法:根据强酸滴定强碱的突跃范围为4.31～9.70,已知K_(sp)[Fe(OH_2)]=4.87×10^(-17),所得突跃范围内Fe(-17),所得突跃范围内Fe⁽²⁺⁾的浓度范围为1.938 8×10(2+)的浓度范围为1.938 8×10^(-8)～1.168 2×10(-8)～1.168 2×10³。将废酸稀释一定倍数,使其溶液中Fe3。将废酸稀释一定倍数,使其溶液中Fe⁽²⁺⁾的浓度在该范围内时,直接以Fe(2+)的浓度在该范围内时,直接以Fe⁽²⁺⁾作为指示剂进行酸碱滴定,将Fe(2+)作为指示剂进行酸碱滴定,将Fe⁽³⁺⁾沉淀时刻作为基准时刻,计算原酸浓度。新方法使用范围较宽,适用于多种钢铁酸洗过程酸度的测定。实验均取1 mL废酸分别稀释10,20,30倍时,利用加标回收法计算得到相对误差为0.23%。     

Modeling of molecular weight and copolymer composition distributions for ethylene-propylene solution copolymerization

A comprehensive computational fluid dynamics (CFD) model was developed to investigate spatial distributions of molecular weight distribution (MWD) and copolymer composition distribution (CCD) for ethylene-propylene (EPM) copolymers in a bubble column reactor. The CFD approach incorporated Euler–Euler two-fluid model, copolymerization kinetics, and copolymer microstructural distribution model together by user-defined functions for ethylene-propylene heterogeneous copolymerization process. MWD and CCD distributions were calculated by introducing Flory's distribution and Stockmayer's distribution, respectively. CFD model results were validated with literature data. The multiphase hydrodynamics, interphase mass transfer, spatial–temporal variations of MWD and CCD distributions were analyzed. Both distributions are wider at the inlet of reactor for the inefficient mixing, but narrower at the outlet due to fully developed flow and polymerization. This model is beneficial to the improvement of polymer products and process control in industrial EPM reactor.     

High molecular weight 1-olefin/carbon monoxide copolymers: a new class of versatile polymers

The moderate electrophilicity of palladium(II)-phosphine catalysts compared to those of zirconocene dichlorides makes them more tolerant toward a variety of polar functionalities of olefinic monomers. This allows use of Pd(II) complexes as catalysts for the copolymerization of olefins with readily available polar monomers, like acrylic acid derivatives or carbon monoxide. In particular, developments during the recent years have opened the way to a new and broad family of high molecular weight 1-olefin/CO co- and terpolymers. These 1,4-polyketone materials show interesting and easily variable properties which can be tuned from insoluble, highly crystalline to thermoplastic elastic. The latter polymers resemble in some cases flexible PVC and even vulcanized natural rubbers. This revised version was published online in June 2006 with corrections to the Cover Date.     

One-point method for determination of number-average molecular weight

The following well-known equation permits the ready determination of M _n from a single osmotic pressure measurement at a known concentration, if the second virial coefficient is previously given: On this basis, the one-point method was investigated to determine the number-average molecular weight. It was found that this method was applicable to commercial polymers. However, in this application, the dependence of Γ₂ on molecular weight distribution has to be kept in mind.