Long-Chain Branching under Conditions of Nonuniform Branching Probability

Abstract

Long-chain branching can occur during free radical polymerization and is especially important for polyethylene. An improved method of calculating the effect of long-chain branching on molecular weight distribution was presented in an earlier paper in which the assumption was made that the probability of branching at each monomer unit was constant throughout the polymerization. A method of including a nonuniform probability of branching in the calculations is presented. Calculation results show that the predictions of the two mathematical models are similar and both models fit published data on polyethylene equally well.     

Dilute solution properties and phase separation of branched low-density polyethylene

Viscosity, light scattering, and precipitation temperature measurements on dilute solutions of high-density and low-density polyethylene fractions have been carried out and a theory by Flory for phase equilibrium of linear polymers has been extended to branched polymer. From the results, it is shown that the entropy parameter ψ, depends on branching; a method for the determination of long-chain branching in polymer fractions is proposed combining precipitation temperature and molecular weight measurements. The method has been applied to the evaluation of long-chain branching in low-density polyethylene.     

Long-chain branching in low-density polyethylene

A method is given for the analysis of long-chain branching in polymers by using combined GPC and intrinsic viscosity measurements. A computer program was written to evaluate branching indices by a tabular, iterative method. The method was applied to the evaluation of long-chain branching in low-density polyethylene.     

分子结构参数对顺丁胶浓溶液流变性质的影响

本工作用GPC-Automatic Viscometer方法测定了顺丁胶样的分子量、分子量分布和支化因子,用同轴圆筒粘度计及落球法测定了顺丁胶浓溶液的粘度,主要研究了分子量分布和长链支化对顺丁胶浓溶液非牛顿流动的影响。提出了描述不同分子量分布的顺丁胶浓溶液粘度的切变速率依赖性的简单公式,并讨论了长链支化对顺丁胶浓溶液非牛顿流动的影响。     

用GPC-级分特性粘数法表征高顺式-1,4聚丁二烯的长链支化

本文在Ambler方法和kraus方法的基础上,用GPC-级分特性粘数法来测定聚合物的长链支化度,能同时以g_i、λ_i、G_i、m_i、支化重量百分数等支化参数来表征聚合物的支化分布、支化程度和支化含量等;得到了相应的计算gi、λi、[η]_i等有关的计算公式和计算方法;还研制成了以光导纤维为冷光源的高精度光电自动计时毛细管粘度计和60小时内恒温精度优于±5×10~(-4)℃的超级恒温水浴,使计时精度达到≤±4×10~(-3)秒;并以国产和进口的镍系顺丁橡胶为例,讨论了分子量和支化度多分散性之间的某些关系;从而确定了该法比较合理地、全面地相对比较聚合物的长链支化度。     

Molecular weight and long-chain branching distributions of some polybutadienes and styrene–butadiene rubbers. Determination by GPC and dilute solution viscometry

A method described for the determination of molecular weight and long-chain branching distributions of polymers requires no prior knowledge of the functional relation between branching frequency and molecular weight. It is based on preparative fractionation and viscometric and gel-permeation chromatographic measurements on both fractions and whole polymer. The technique is applied to several polybutadienes and butadiene-styrene copolymers differing widely in method of synthesis and pattern of long-chain branching.     

Temperature rising elution fractionation, infra red and rheology study on gamma irradiated HMSPP

It is well known that polypropylene undergoes simultaneous crosslinking and degradation under irradiation. However, there are speculations regarding the formation of branching under special conditions. It is also well known that the melt-strength property of a polymer increases with molecular weight and with long-chain branching due to the increase in the entanglement level. This study was a contribution to the understanding of the following points: the role of molecular weight, the role of structural modifications on nucleation properties; the structural changes on polypropylene.

The results showed that degradation was the major reaction in the initial step of irradiation, however, the largely modified molecules concentrated in the high molecular weight fraction. The results also confirm that the branching formation is likely to occur.     

Molecular weight distribution and molecular structure of polyethylene produced by radiation-induced polymerization

The molecular weight distribution of polyethylene produced by radiation was calculated according to a kinetic scheme. The calculated molecular weight distribution was compared with the results deduced from gel-permeation chromatography. The observed distribution curve from GPC was broader and showed a lower degree of polymerization than the calculated one. Discrepancies between observed and calculated curves can be explained if the polymer contains nonsteady-state products and if the reaction mechanism includes chain transfer to dead polymer. By this reaction long-chain branching would occur. Several long-chain branches per polymer molecule were indeed found, as inferred from solution properties.     

Determination of long-chain branching in model polystyrene samples by the GPC-sedimentation method

The GPC–sedimentation velocity method proposed earlier for the determination of long-chain branches was examined quantitatively by using model star-shaped and comb-shaped polystyrene samples of known degree of branching. The results showed that separation by sedimentation velocity was more sensitive to branching variations than separation by GPC. The results showed also that at low and moderate levels of branching the GPC–sedimentation velocity method reflected accurately the amounts of branching in the model samples. At high levels of branching, the method underestimated the amount of branching. The discrepancy, however, appears to have been caused by the inadequacy of the theories used in the interpretation of the raw data and not by any inherent problem in the method itself. The relative sensitivities of the GPC-sedimentation, GPC-viscosity, and GPC–light scattering methods are discussed.     

用凝胶渗透色谱测定聚合物中的支化度

本文在Ambler报导的测定聚合物中支化度的工作基础上,提出了支化度的计算方法和电子计算机计算程序,可用ALGOL-60语言在国产DJS-6电子计算机上计算。讨论了支化模型、短链支化和长链支化分布函数等对计算结果的影响,确定了该方法可以相对比较镍系顺式聚丁二烯中的支化度。     

Processability improvement of polyolefins through radiation-induced branching

Radiation-induced long-chain branching for the purpose of improving melt strength and hence the processability of polypropylene (PP) and polyethylene (PE) is reviewed. Long-chain branching without significant gel content can be created by low dose irradiation of PP or PE under different atmospheres, with or without multifunctional branching promoters. The creation of long-chain branching generally leads to improvement of melt strength, which in turn may be translated into processability improvement for specific applications in which melt strength plays an important role. In this paper, the changes of the melt flow rate and the melt strength of the irradiated polymer and the relationship between long-chain branching and melt strength are reviewed. The effects of the atmosphere and the branching promoter on long-chain branching vs. degradation are discussed. The benefits of improved melt strength on the processability, e.g., sag resistance and strain hardening, are illustrated. The implications on practical polymer processing applications such as foams and films are also discussed.     

Determination of branching distribution by concurrent GPC and sedimentation velocity experiments

A method of determining the distribution of branching in polydisperse polymer samples is proposed. This method uses data from concurrent gel permeation chromatography and sedimentation-velocity experiments. Tedious fractionation, which must precede other methods of determining long-chain branching, is eliminated. An example of use of the method on the data of a sample of styrene–divinylbenzene copolymer is given.     

The application of the size exclusion chromatography/ viscometry technique to the determination of molar-mass and long-chain branching in polychloroprene

The coupling of a low-pressure size exclusion chromatography (SEC) with a modified Ubbelohde capillary viscometer is described. This SEC/viscometry system measures the flow time of aliquot fractions (5ml) of the SEC effluent along with the refractive index change. This dual detection leads to the determination of the intrinsic viscosity as a function of the elution volume, thus allowing a precise use of Benoit's universal calibration. Moreover information of the branching factors (degree of long-chain branching, long-chain branching frequency) can be calculated under certain assumptions. As an example the changes in molar-mass distribution and branching factors during mechanical shear degradation (mastication) of special polychloroprene samples were investigated. It is shown that the SEC/viscometry system is especially suitable for the characterization of polymers with broad molar-mass distribution and extremely high molecular tails. The data provided by this method are useful for the investigation of the viscoelastic behaviour of concentated polychloroprene solutions and for quality control of polymers in the rubber and adhesives industries.     

Rate Constant for Long-Chain Branch Formation in Free-Radical Polymerization of Ethylene

Quantitative measurements on the rate constant for long-chain branching in radical polymerization of ethylene have not yet been cited. This paper presents a convenient method of calculating the ratio of the rate constant for long-chain branching to that for propagation, by means of polymerization parameters, average degrees of polymerization (X_n and X_w), and amount of total unsaturation. The results of calculation based on our experimental data show that the activation energy E_trp -E_p, and the activation volume ΔV ^trp _?-ΔV ?_p were 3.6 kcal/mole and 24 cc/mole, respectively, in radical polymerization of ethylene. The validity of these values is discussed.     

Novel mechanism for the formation of long-chain branching in polyethylene

Polyethylene produced by a vanadium-based polymerization catalyst contains long-chain branching as determined by NMR and rheology, even though the polymer has very low levels of vinyl unsaturation. A new mechanism is proposed for the formation of the long-chain branching, which involves C H bond activation of the polyethylene backbone through a σ-bond metathesis reaction, followed by ethylene insertion at the new V C bond. Consistent with the proposed C H bond activation mechanism, the polymerization catalyst was also found to insert ethylene into the C H bonds of alkanes such as heptane. A bridged metallocene catalyst was also found to activate C H bonds of alkanes suggesting this new mechanism may explain the formation of long-chain branching in some metallocene-produced polyethylene. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2889–2898, 1998     

Theoretical determination of the rate constant for OH hydrogen abstraction from toluene

The OH abstraction of a hydrogen atom from both the side chain and the ring of toluene has been studied in the range 275-1000 K using quantum chemistry methods. It is found that the best method of calculation is to perform geometry optimization and frequency calculations at the BHandHLYP/6-311++G(d,p) level, followed by CCSD(T) calculations of the optimized structures with the same basis set. Four different reaction paths are considered, corresponding to the side chain and three possible ring hydrogen abstractions, and the branching ratio is determined as a function of temperature. Although negligible at low temperatures, at 1000 K ring-H abstraction is found to contribute 11% to the total abstraction reaction. The calculated rate coefficients agree very well with experimental results. Side chain abstraction is shown to occur through a complex mechanism that includes the reversible formation of a collisionally stabilized reactant complex.     

Branching kinetics in copolymerization of styrene with a chain-transfer monomer

In an earlier work it was shown that a random long-chain branching structure can be incorporated in polystyrene by copolymerizing styrene with a small amount of monomer that contains a chain transfer group. The use of vinylbenzylthiol as the chain transfer monomer produced a polystyrene with low number-average molecular weight and a degree of branching lower than expected. In this study polymerization kinetics were used to compute the theoretical molecular weight and degree of branching. The results show that if the chain-transfer constant of the chain transfer monomer is as high as that for vinylbenzylthiol the expected molecular weight and degree of branching will indeed be as low as those found experimentally. The theory also predicts that if the chain transfer constant is near one a highly branched bushy structure will result.     

Characterization of low-density polyethylene by gel permeation chromatography—II. Study on the Drott method using fractions

Polyethylenes of different structures were fractionated and the fractions characterized by light scattering, gel permeation chromatography and viscometry. Intrinsic viscosities were measured in solvents of different thermodynamical quality including a θ-solvent (diphenyl at 118° for low-density polyethylene and at 130° for high-density polyethylene and ethylene-butene-1 copolymer). The results were used for examining two aspects of the Drott iterative procedure: (a) the relationship between thermodynamical quality of the solvent and depression in the intrinsic viscosity due to branching; and (b) analytical form of expression relating the so-called g-factor to the number of long-chain branches. The ratio of intrinsic viscosities of branched and linear species at a given weight-average molecular weight has been clearly proved to be solvent independent, and the equation relating the g-factor to the number of branches for polymer monodisperse with respect to molecular weights appears to be a fair representation of long-chain branching in low-density polyethylene. For the polymers examined, the branching frequency λ is not independent of molecular weight.     

Polymerization of vinyl chloride at reduced monomer accessibility. II. Polymerization at subsaturation pressure with emulsion PVC as seed

Vinyl chloride was polymerized at 59–92% of saturation pressure in a water-suspended system at 45–65°C with an emulsion poly(vinyl chloride) (PVC) latex as a seed. A water-soluble initiator was used in various concentrations. The monomer was continuously charged as vapor from a storage vessel kept at lower temperature. Characterization included determination of molecular-weight distribution and degree of long-chain branching by gel permeation chromatography (GPC) and viscometry, thermal dehydrochlorination, and microscopy. The polymerization rate decreases with decreasing pressure but is reasonable even at the lowest pressure. The molecular weight decreases with decreasing pressure and increasing initiator concentration and also with increasing polymerization temperature, if the initiator concentrations are chosen to give a constant initiator radical concentration. The degree of long-chain branching increases with increasing initiator concentration and decreasing monomer pressure but is unaffected by the polymerization temperature, if the initiator radical concentration is kept constant. The thermal stability decreases with decreasing M _n, while the degree of long-chain branching has only a minor influence. The most important factor in the system influencing the molecular parameter is the monomer accessibility.     

Glycine in an electronically excited state: ab initio electronic structure and dynamical calculations

The goal of this study is to explore the photochemical processes following optical excitation of the glycine molecule into its two low-lying excited states. We employed electronic structure methods at various levels to map the PES of the ground state and the two low-lying excited states of glycine. It follows from our calculations that the photochemistry of glycine can be regarded as a combination of photochemical behavior of amines and carboxylic acid. The first channel (connected to the presence of amino group) results in ultrafast decay, while the channels characteristic for the carboxylic group occur on a longer time scale. Dynamical calculations provided the branching ratio for these channels. We also addressed the question whether conformationally dependent photochemistry can be observed for glycine. While electronic structure calculations favor this possibility, the ab initio multiple spawning (AIMS) calculations showed only minor relevance of the reaction path resulting in conformationally dependent dynamics.