Molecular weight distribution formed during free‐radical polymerization in the presence of polyfunctional chain transfer agents

Free‐radical polymerization of styrene was carried out in the presence of chain transfer agents (CTAs) with functionality, f = 1–4. The size exclusion chromatography (SEC) with an ultraviolet absorption detector (UV) was used to measure the molecular weight distribution (MWD). A Monte Carlo simulation method proposed earlier was used to investigate the experimental results. In this simulation method, one can observe the structure of each polymer molecule directly, and very detailed information can be obtained in a straightforward manner, including the elution curve of SEC. It was found that up to the functionality f = 3, the equal reactivity model that assumes the reactivity of all functional groups in a CTA is equal agrees reasonably well with the experimental results. However, with f = 4, the reactivity of the fourth functional group seems to decrease and the substitution effects may need to be accounted for to fine control the formed branched structure. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1267–1275, 1999     

体积排阻色谱法测定胸腺肽分子量校准曲线条件的优化

在体积排阻色谱(SEC)法测定胸腺肽分子量校准曲线过程中,流动相中乙腈的比例对核糖核酸酶A、人胰岛素、胸腺肽α1和生长激素释放抑制因子4种蛋白的保留时间有重要影响,进而影响校准曲线的线性关系。当乙腈比例为75%时,胸腺肽分子量校准曲线线性最好,此时分子量校准方程为y=-3.138 6x+21.724,线性相关系数r2=0.988 5。4种蛋白的理论塔板数在45 783～63 345之间,拖尾因子在0.96～1.18之间,分离度在3.52～8.82之间。SEC法测定胸腺肽分子量校准曲线的液相色谱条件对4种蛋白的分离效果优异,分子量校准曲线线性良好,可用于胸腺肽制剂中高分子量物质的检测。     

Molecular weight distribution of emulsion-polymerized polyethylene

Emulsion polymerizations of ethylene were run using potassium persulfate as the initiator and either an anionic or a cationic surfactant, usually at five times the critical micellar concentration. The molecular weight distributions had at least two major peaks. The broadly distributed lower molecular weight component is formed in the early stages of polymerization. The higher molecular weight component has a narrow distribution characteristic of termination by the combination of chain radicals. The weight-average molecular weight of this component was about 400,000 when the surfactant was sodium laurate and 33,600,000 when the surfactant was dodecyl amine hydrochloride. © 1992 John Wiley & Sons, Inc.     

Effect of molecular weight in diketopyrrolopyrrole‐based polymers in transistor and photovoltaic applications

Uncovering the precise effect of the conjugated polymer chain length on the semiconducting properties in thin‐film devices is confounded by the step‐growth polymerization techniques typically used. Here, we use preparatory size exclusion chromatography to isolate fractions of two diketopyrrolopyrrole‐thiophene based co‐polymers with low molar‐mass dispersity, ?_M, and number average molecular weights up to 180 kDa. We find that the charge carrier mobility can vary over three orders of magnitude in the range from 9 to 70 kDa, while a factor of 3–4 increase in photovoltaic performance was noted over the same range. The effect of ?_M was found to be most drastic when the largest chains were mixed with the shortest. The study of the thin‐film morphology and crystallinity by GIWAXS give further insights into the origin of these effects. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2245–2253     

Molecular weight distribution in emulsion polymerization. I. The homopolymer case

A model for evaluating the instantaneous degree of polymerization distribution of homopolymers produced in emulsion, based on the mathematics of the Markov chains, is developed. The model accounts for any number of active chains per particle, as well as for the two fundamental mechanisms of chain termination: mono- and bi-molecular, both by combination and by disproportionation. The core of the model is the so called subprocessmain process treatment, which allows us to correctly evaluate the degree of polymerization of the chains growing in the polymer particles, by distinguishing between the events experienced by the polymer chain which imply a change of its degree of polymerization (subject transitions) and those which imply only a change in the particle state (environment transitions). This is obtained by properly defining the one-step transition probability matrix of the relevant Markov process. Once this is done, the evaluation of the distribution of the degrees of polymerization reduces to a few simple operations among matrices. Explicit expressions for the instantaneous probability density functions and the relative cumulative distributions are obtained. The application of such relationships is facilitated by the numerical procedures reported in the Appendices. The results of the model developed in this work are in agreement with those of earlier models in the range of parameter values of practical interest. In the limit of very low molecular weights, only the model developed in this work provides the correct answer. Moreover, a much more significant result is its applicability to the case of emulsion copolymerization, as it is shown in Part II.     

Molecular weight distribution in emulsion polymerization. II. The copolymer case

A model for evaluating instantaneous degree of polymerization distribution and the chain composition distribution of copolymers produced in emulsion is developed. The approach adopted is based on the mathematics of Markov processes and represents an extension of the one developed for homopolymers in Part I. As in the homopolymer case, the main aspect of the theoretical treatment is the definition of the proper one step transition probability matrix through the so called subprocess-main process procedure. The model accounts for monomolecular and bimolecular termination (both by combination and disproportionation) and, in principle, it can be applied to any number of reacting monomer species as well as to any number of active chains per particle. However, only the 0–1–2 and 0–1–2–3 emulsion copolymerization systems are discussed in detail. In the case of the chain composition distribution, the model allows the calculation of its moments only, through the method of the Generating Function associated with the probability density function. The expression obtained for the instantaneous probability density functions, as well as for the corresponding cumulative distributions, are all in explicit form and involve only algebraic operations among matrices. Efficient numerical procedure for their application are reported in the Appendix. Illustrative calculations are reported for a 0–1–2–3 copolymerization system, simulating the copolymer styrene–methylmethacrylate. The effect of the various termination mechanisms on the distribution of degrees of polymerization and on the first two moments of the chain composition distribution is discussed in detail. Finally, the three dimensional overall distribution function of both chain length and composition is shown under the assumption of Gaussian type chain composition distribution.     

体积排阻色谱法测定低分子量肝素抗凝血因子Xa的活性

发展了一种基于体积排阻色谱测定低分子量肝素(LMWH)抗凝血活性的方法。利用肝素与抗凝血酶Ⅲ(ATⅢ)结合后可增强ATⅢ对凝血因子Xa(FXa)抑制作用的原理,通过测定加入LMWH后FXa水解其生色底物产生对硝基苯胺(pNA)这一反应的抑制程度确定LMWH的活性。首先将含有一定浓度LMWH的缓冲溶液与ATⅢ溶液混合,然后依次加入FXa和生色底物,分别孵育一段时间。底物被FXa水解,产生游离的pNA。体积排阻色谱可将小分子产物pNA与其他大分子分离开,因而可以在pNA的最大吸收波长下得到高灵敏度的测定,并且不再受其他成分的干扰。该方法重复性好,灵敏度高,极大地减少了样品的消耗量,降低了成本,并且还可进行各种复杂样品(如血浆)中LMWH抗FXa活性的监测。     

Effect of method of solution on observed molecular weight distribution of barley starch and starch derivatives in size exclusion chromatography

Summary Samples of native barley starch and six starch derivatives were suspended (0.1% sample concentration) in four different solvents: the eluent (pH 11 buffer), dimethylsulfoxide, 0.1 M NaOH or 0.5 M NaOH and kept in a boilling water bath for 5 to 60 minutes or shaken for 60 minutes. The average molecular weight values , and the polydispersity value were determined with a TSK PW-type column using narrow standard calibration. Only a small part of the samples dissolved in the eluent. The dissolution of sample in dimethylsulfoxide was dependent on sample type. Of the NaOH solutions, 0.5 M NaOH was the only one that dissolved all the samples. Therefore, 0.5 M NaOH appears to be the solvent of choice for starch molecules.     

Control of macromolecular architecture of polyamides by poly-functional agents. 2. Use of oligomerization in polycondensation study

In the first paper of the series, a statistical model for star-branched polycondenzation of AB type monomers in the presence of a polyfunctional agent RA_f was completely developed. The analytical expressions obtained for the number-average (D̄P̄_n̄) and weight-average (D̄P̄_w̄) degree of polymerization, and the dispersion index (D) for whole polymer species, linear and star macromolecular chains, are now derived as function of the feed and of end-group analysis. Also the important molecular parameter, mole fraction of star-branched polymer, can be evaluated. Some numerical examples are presented. It is illustrated that the molecular weight properties of the linear and star-branched polymers in the mixture of the products, very important factors for the application of this kind of polymeric materials, can be determined starting from the feed and terminal group analysis. Polymerization and oligomerization of 6-aminocaproic acid were carried out in the presence of trimesic (T3) acid and 2,2,6,6-tetra(β-carboxyethyl)cyclohexanone (T4) and EDTA as tri- and terra-functional agents. The molecular weights calculated are in good agreement with those obtained by Size Exclusion Chromatography (SEC), end group analysis and NMR spectra.     

Molecular weight characterization of soluble high performance polyimides. 2. Validity of universal SEC calibration and absolute molecular weight calculation

Six different soluble high-performance aromatic polyimides, each prepared by solution imidization to three controlled average molecular weights, were analyzed by size exclusion chromatography (SEC) using on-line parallel coupled refractometric and viscometric detectors. N-methylpyrrolidone (NMP) with 0.06 M LiBr and NMP stirred over P₂O₅ were used as mobile phase for four of the polyimides; NMP with 0.06 M LiBr and NMP stirred over P₂O₅ were used as mobile phases for four of the polyimides; NMP with 0.06 M LiBr tetrahydrofuran (THF) and chloroform served as mobile phases for the other two polyimides. For all the samples the stationary phase in the SEC columns was cross-linked polystyrene beads. Molecular weight averages of the polyimides were calculated using universal SEC calibration with polystyrene standards in each solvent. The agreement of the calculated molecular weight averages in the different solvents confirms that the universal SEC calibrations are valid for these semiflexible polymers. There was good agreement with weightaverage molecular weights obtained by low-angle laser light scattering (LALLS) performed in pure NMP. Intrinsic viscosity and molecular weight data for a series of nine samples of one polyimide covering a M_w = 20,000–70,000 g mol^–1 interval were treated to obtain Mark-Houwink-Sakurada constants. Unperturbed chain dimensions of this polyimide were obtained by application of the Stockmayer-Fixman extrapolation procedure to these data. ©1995 John Wiley & Sons, Inc.     

凝胶色谱法测定顺丁橡胶平均分子量及其分布的研究

通过一系列的条件试验,包括样品浓度、样品量及流动相流速对柱效的影响,确定了最佳的凝胶色谱（ＧＰＣ）试验条件;采用普适校正法将聚苯乙烯（ＰＳ）标定曲线转换成顺丁橡胶（ＰＢ）标定曲线,并对Ｍａｒｋ－Ｈｏｕｗｉｎｋ方程式中Ｋ,α值的选择进行了讨论;采用４种分子量加宽方程对色谱柱加宽效应进行改正计算,通过比较,选定适合本试验系统的加宽效应的改正方法;用粘度法测得的顺丁橡胶特性粘度（η）吻合ＧＰＣ所测得特性粘度值,证明了方法的可靠性。     

Molecular weight distributions of linear polymers: Detailed analysis from GPC data

The GPC method is used widely to measure molecular weights of linear polymers. High-quality GPC data contains detailed information on many aspects of the polymer's molecular weight distribution (MWD). This information can be extracted from the data using computer analysis. Equations have been derived for the two simplest MWD functions in the GPC coordinates: the Flory function (one growing polymer chain produces one polymer molecule), and for the case when two polymer radicals combine into one polymer molecule. The equations were used to analyze MWD of two classes of polymers. The first class includes polymers with narrow MWD: polyethylene, ethylene-propylene and ethylene-hexene copolymers, syndiotactic polystyrene, and radical polystyrene. The second class includes polymers with broad MWD: ethylene copolymers and polypropylene produced with heterogeneous, Ti-based catalysts. The examples demonstrate that the resolution of complex GPC curves into their constitutents serve as an important source of information about kinetics of polymerization reactions. © 1995 John Wiley & Sons, Inc.     

Quenched Instationary Polymerization Systems, 6. The Direct Determination of Axial Dispersion in Size Exclusion Chromatography by Comparison of Theoretical and Ideal Peak Widths

For the direct determination of axial dispersion in size exclusion chromatography a simple method is presented which makes use of the measured and ideal peak widths. The peak width can be defined in two ways: either absolute as the difference of successive points of inflection or relative as the ratio of these points. If the absolute peak width is invariant for the number, molar mass and hyper distribution then this distribution can unambiguously be classified as Poissonian. The relative peak width for such distributions is strictly determined by the experimental parameters. It is demonstrated that axial dispersion only leads to an additive increase in the peak variances for peaks with a relative peak width smaller than 1.25. Thus, it is possible to determine directly the axial dispersion of an experimental size exclusion chromatography set‐up by the use of Poisson distributions prepared by quenched instationary polymerization techniques or any other technique leading to ideal Poisson distributions.     

低分子量硫酸化多糖的体积排阻色谱法分离及其组成定量分析

建立了用于分离并定量测定低分子量硫酸化多糖中不同糖链数的各个组分分布比例的体积排阻色谱方法。系统考察了流动相的组成、离子强度和pH值、流速、柱温等因素对分离的影响。最佳分离条件: 两支TSK-GEL G2000 SWxl色谱柱(300 mm×7.8 mm)串联,流动相100 mmol/L Na2HPO4-NaH2PO4 (pH 7.0),流速0.5 mL/min,柱温35 ℃,进样量5 μL,样品质量浓度10 g/L。在最佳的分离条件下,可以将低分子量硫酸化多糖样品中不同糖链数的各个组分分离并对各个组分的分布进行了定量分析。用该方法对美国药典标准品(USP)、商品和实验室制备的低分子量硫酸化多糖糖链数分布进行了定量化比较,证明该方法可用于低分子量硫酸化多糖类药物的组成成分的质量控制。     

Molecular weight distribution in nonlinear emulsion polymerization

A modelistic study of the molecular weight distribution (MWD) formed in emulsion polymerization that involves chain transfer to polymer is conducted, by focusing our attention to the effect of very small reaction volume on the formed MWD. In emulsion polymerization, a polymer radical that causes polymer transfer reaction must choose the partner only within the same particle, which makes the expected size of the polymer molecule to be chosen smaller compared with the corresponding polymerization system that involves an infinitely large number of polymeric species. The usual assumption for homogeneous polymerization that the rate of chain transfer to a particular polymer molecule is proportional to its chain length cannot be used, except when branching frequency is low and particle size is large enough. This fact invalidates the direct use of models developed for homogeneous nonlinear polymerizations to emulsion polymerizations. Model equations that could be used to assess the significance of the limited space effects on the MWD under a given polymerization condition are also proposed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1515–1532, 1997     

Molecular weight distribution of cellulose esters by gel permeation chromatography and fractional precipitation

Fractional precipitation and gel permeation chromatography yield comparable information on the molecular weight distribution of various cellulose esters. The GPC technique applied to samples obtained by fractional precipitation gives a much more definitive analytical tool than either method used independently. One practical application of this work showed the same molecular weight distribution of two cellulose acetates prepared by different methods.     

Molecular weight distribution in composition controlled emulsion copolymerization

The effect of different strategies for copolymer composition control on the molecular weight distribution (MWD) and gel fraction in the emulsion copolymerization of methyl methacrylate and butyl acrylate was investigated. Starved and semistarved processes for copolymer composition control were both considered. For gel‐forming systems it was found that the starved process gave more gel and lower molecular weights than the semistarved process. The feasibility of simultaneous control of the copolymer composition and the MWD was assessed. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1100–1109, 2000     

Studies on molecular weight distribution of carbon fiber polymer precursors synthesized using mixed solvents

The molecular weight distributions were estimated for carbon fiber polymer precursors such as poly（acrylonitrile-co -itaconic acid） synthesized by semi batch solution polymerization in mixed solvents media with the azonitrile compounds as initiator under the different ratios of solvent and non solvent from 0.75 to 2.5 in weight.The copolymer was characterized by using Fourier transform infrared spectroscopy（FTIR） and nuclear magnetic resonance（¹H-NMR） analyses.The molecular weight distributions were evaluated by M_v/M_n ratios estimated from viscosity and osmotic measurements,and M_w/M_n estimated from size exclusion chromatography.The molecular weight distributions of these polymers as determined from M_v/M_n and M_w/M_n are 2.9 to 3.2 and 2.0 to 2.5 respectively.The molecular distributions were close to a narrow distribution of 2.0 when the solvent/non-solvent ratio was varied between 1.4 and 2.0.Intrinsic viscosity[?]as a function of molecular weight of poly（acrylonitrile-co-itaconic acid） was evaluated by means of low angle laser light scattering with size exclusion chromatography（SEC-LALLS） and viscometry with SEC（SEC-VISCO）.The relationship between[?]and M_w for poly（acrylonitrile-co-itaconic acid） in DMF at 50℃was[?]= 1.1×10^-5M_w^0.79,where[?]is obtained in dL/g.