A rheology theory and method on polydispersity and polymer long-chain branching

Model calculations were performed to investigate the sensitivity of zero-shear melt viscosity (η₀ or Eta0) on the molecular weight (MW) polydispersity of linear polymers. Simulated MW distributions (MWD) were generated with the generalized exponential (GEX) distribution function for various levels of polydispersity M_w/M_n and M_z/M_w. For linear entangled polymeric chains in the melt, the linear viscoelastic properties were predicted by using the double reptation blending rule and the so-called BSW relaxation time spectrum, named after the authors: Baumgaertel, Schausberger and Winter [Baumgaertel M, Schausberger A, Winter HH. Rheol Acta 1990;29:400-8]. Published rheological parameters appropriate for polyethylene were used in the calculations. It was found that Eta0 depended mostly on M_w, but it also significantly depended on the extent of high-MW polydispersity M_z/M_w. A revision to the fundamental MW dependency of Eta0 was proposed to compensate for this polydispersity effect. To offset the polymer polydispersity differences, we propose a new MW average (M_HV or M_x with x = 1.5) to replace M_w in the historical rheological power-law equation of Eta0 ∝ M_w^a, where the literature value of exponent “a” ranges from 3.2 to 3.6. The use of M_HV instead of M_w in the power-law equation made the calculated Eta0 independent of the sample high-MW polydispersity. With the removal of the complication from polydispersity effect, the new Eta0 power law can now provide a more robust base for studying polymer long-chain branching (LCB). A new LCB index is thus proposed based on this new melt-viscosity power law. The values of M_HV in the new power law can be calculated for polymer samples from the conventional gel permeation chromatographic (GPC) slice data.     

Chemical modification of PP architecture: Strategies for introducing long-chain branching

Two strategies for introducing long chain branching (LCB) to a polypropylene homopolymer (PP) are evaluated in terms of the product's molecular weight and branching distributions, and in terms of melt-state shear and extensional rheological properties. Single step processes involving radical-mediated addition of PP to triallyl phosphate are shown to generate bimodal products with highly differentiated chain populations, while a two step sequence involving PP addition to vinyltriethoxysilane followed by moisture-curing is shown to generate more uniform architectures. As a result, the sequential approach can improve low-frequency shear viscosity and extensional strain hardening characteristics while staying below the polyolefin's gel point. The composition and molecular weight distribution transformations that underlie sequential LCB techniques are discussed.     

SEC-MALS method for the determination of long-chain branching and long-chain branching distribution in polyethylene

This paper systematically describes a LCB determination method that can quantify both LCB content and LCB distribution across the molecular weight distribution in polyethylene homopolymers as well as copolymers. Coupling size-exclusion chromatography with multi-angle light scattering (SEC-MALS), this method quantifies molecular weights (MW) and radii of gyration (R_g) simultaneously. The number of LCB per molecule and LCB frequency as a function of MW can be calculated by comparing R_g of a branched polymer with that of a linear control at the same MW using the Zimm-Stockmayer approach. Because the presence of short-chain branching in copolymers results in changes in R_g of the copolymers, their LCB contents cannot be obtained before the short-chain branching (SCB) effect is corrected. Using well-characterized linear PE copolymers as standards, an empirical method is successfully established in this paper to correct the SCB effect. Consequently, this method can be applied to determine LCB in PE copolymers as well. Some practical aspects, such as the selection of formalism for data processing, the LCB detection sensitivity and precision, and long-term reproducibility of this method are also discussed. Finally, examples are given to demonstrate how this method is applied to determine LCB and LCB distribution in practical PE homopolymers and copolymers.     

Structure-rheology relationships of long-chain branched polypropylene: Comparative analysis of acrylic and allylic coagent chemistry

The relationship between product structure and melt-state rheological properties is established for series of branched PP derivatives prepared by the radical-mediated grafting of tri-functional coagents. Peroxide-initiated, solvent-free additions of linear PP to triallyl trimesate (TAM), trimethylolpropane triacrylate (TMPTA) and triallyl phosphate (TAP) at high temperature are shown to produce bimodal molecular weight and branching distributions. Low-frequency dynamic shear viscosities as well as extensional viscosities are shown to be highly responsive to a hyper-branched chain population, whose abundance and molecular weight correlate with the kinetic chain length of the grafting process, and the propensity of a coagent to oligomerize.     

Influence of a metal–polymer interfacial interaction on dielectric relaxation properties of polyurethane

The influence of metal–polymer interaction on dielectric relaxation properties of polyurethane (PU), prepared from poly(oxypropylene)diol and hexamethylendiisocyanate, was investigated by means of dielectric relaxation spectroscopy in the frequency domain on the dependence of the thickness of the PU layer and electrode material (gold and steel). Strong electrostatic part of an adhesion interaction between steel substrate and PU results in changes of the -, β-, γ- and Maxwell–Wagner–Sillars relaxation of the PU, as compared to a gold substrate. The effect of the metal–polymer double layer results in the complication of the cooperative and local motions in the polymer. The influence of metal–polymer interaction on the relaxation parameters becomes pronounced at a thickness of less than 60 μm for the steel substrate. For the gold substrate the relaxation characteristics hardly depend on the thickness.     

Influence of long-chain branching on the viscoelastic properties of low-density polyethylenes

Melt How data has been determined for a series of fractionated and whole low density polyethylenes which has been characterized in terms of their molecular weights and degree of long-chain branching, (LCB). The resulting data indicate that low LCB influences melt flow both through a reduction in molecular size and an increased level of intermolecular interaction. Die swell measurements on whole polymers indicate an increase in melt elasticity with increase in degree of LCB for samples of similar melt flow (MI). Comparison of GPC data with observed die swell characteristics indicates that die swell is a molecular size dependent property and independent of intermolecular entanglement effects, suggesting that the measurement of elastic properties of LDPE melts will provide a means of determining relative degrees of LCB for commercial resins.     

Introduction of long-chain branches in linear polyethylene by light cross-linking with 1,3-benzenedisulfonyl azide

Metallocene synthesised HDPE with M_w=82,000 and M_n=40,000 was modified with small amounts of 1,3-benzenedisulfonyl azide by reactive extrusion at 200 °C with the purpose to form long-chain branches. At the processing temperature the two azide groups decompose to nitrenes that work as cross-linkers for PE. Cross-linking occurs primarily by insertion of singlet nitrenes into CH bonds. Size exclusion chromatography revealed that the modification resulted in the formation of a long-chain branched (LCB) high molecular weight fraction. The LCB was detectable with SEC for concentrations above 100 ppm corresponding to approximately 0.03–0.04 branch points pr 10⁴ carbon. No signs of the formation of low molecular species due to chain scission were observed. Dynamical mechanical analysis and shear creep test showed sign of long chain branching at concentrations down to the same limit as SEC (100 ppm). These signs were thermorheological complexity, increased zero shear viscosity, increased shear thinning and increased recovery compliance. The cross-linking efficiency of 1,3-BDSA were estimated to 40–60% from comparison of SEC data with random cross-linking theory and traditional SEC-LCB analyses.     

Influence of crystallinity on rheological properties of unfilled and particle-filled polycarbonates

Polycarbonates are modified, nowadays, with various kinds of fillers from the micro to the nano range in order to improve properties like the electrical conductivity, for example. Rheological measurements are often performed to support the characterisation of the compounds. In this communication it is demonstrated that the crystallisation of polycarbonates in the molten state has to be taken into account for a comprehensive assessment of rheological experiments. This is particularly evident in the case of filled materials as particles can act as nucleating agents. The crystallisation behaviour of neat and filled polycarbonates is investigated by differential scanning calorimetry and its influence on rheological properties presented by dynamic-mechanical and creep experiments. From the results, the role of crystallisation processes becomes evident for a reliable interpretation of rheological investigations on polycarbonates and their modelling. Comparative measurements on the non-crystallisable polymethylmethacrylate underline the importance of a thorough discussion of the crystallinity in the case of polycarbonates.     

Supercritical carbon dioxide-assisted reactive extrusion for preparation long-chain branching polypropylene and its rheology

An environmental benign process, which uses supercritical carbon dioxide (ScCO₂) as a processing aid, is developed in this work to prepare long chain branching polypropylene (LCB-PP). Results from the oscillatory shear rheology, melt elongational behavior and Fourier transformed infrared spectroscopy (FTIR) show that long chains have been linked as branches to the original linear PP chains using scCO₂-assisted reactive extrusion in the presence of cumene hydroperoxide and 1,6-hexanediol diacrylate. Compared to the initial linear PP, the branched samples show higher storage modulus (G′) at low frequency, distinct strain hardening of elongational viscosity, lower melt flow rate, increased crystallization temperature and improvement of the melt strength. ScCO₂ can improve the branching efficiency of modified PPs. The elastic response, melt strength and strain hardening parameter of the modified PPs increase with increasing scCO₂ concentration, which is ascribed to scCO₂ acting as a plasticizer for reducing PP viscosity and a carrier for active chemical species.     

Influence of Sr ions on the structure and dielectric properties of Cu/Nb Co-doped BaTiO3 ceramics

Sr-modified Cu/Nb co-doped BaTiO₃ ceramics were prepared using solid-state reactions and the structures and dielectric properties were studied. All the samples had single-phase perovskite structures with no detectable secondary phases. In the low-temperature range, the dielectric constant decreased as the Sr content increased in the high- and low-frequency ranges. Two dielectric constant plateaus accompanied by dielectric relaxation peaks were present in the loss curves, and the relaxation process deviated from the Arrhenius law at low temperatures. The dielectric constants of different plateaus were related to inhomogeneous structures such as grain interiors and grain boundaries. The polarization strength of the grain boundaries in the low-frequency range increased with the temperature and that of the grain interiors demonstrated paraelectric behaviour in high-temperature ranges. An analysis of the electric modulus spectra indicated a close relationship between the relaxation process and resistivity of the grains for high-frequency relaxation. The impedance spectra at high temperatures consist of three electrical responses, corresponding to the effects of grains, grain boundaries, and electrodes. The dielectric relaxation appeared in high temperature range was related to the electrical properties of the grain boundaries.     

Low-frequency dielectric properties of SrLaAlO4 ceramics

SrLaAlO₄ ceramic samples were prepared via solid state reaction method. The low-frequency (20–10⁷ Hz) dielectric properties were investigated in the temperature range from room temperature to 700 °C. It was found that SrLaAlO₄ shows intrinsic dielectric behavior with a dielectric constant of 13 in the temperature range below ~300 °C. In the temperature range from 300 °C to 560 °C, the bulk dielectric contribution due to oxygen-vacancy-related polarons dominates the dielectric properties of the samples. However, the dielectric properties are controlled by sample/electrode contacts when the temperature is risen to above 560 °C. Our results indicate that the bulk effect instead of interfacial effect is the main contribution to dielectric loss in the lower temperature range.     

Study of mechanical and rheological behaviors of linear and branched polycarbonates blends

A study of the mechanical and rheological properties of linear and branched polycarbonates blends is presented. Phase separations of the blends were checked through DSC and SEM, and, subsequently, mechanical and rheological properties were investigated. Phase separations were not observed in the blends. The mechanical properties were examined through tensile, flexural, and impact tests. All the mechanical properties of the blends were relatively independent of the compositions. For study of the rheological properties, melt viscosity, storage and loss moduli, and melt tension of the blends with various compositions were examined at various temperatures. The dependence of the viscosity on the molecular weight was also studied. As the content of branched polycarbonate increases, the dependence of the viscosity on the molecular weight and the shear thinning behavior became more marked. Melt tensions were also increased as the branched polycarbonate content increased in the blends for all tested temperatures. In this study, the blend systems which have same mechanical properties but different rheological properties can be obtained through blending of linear and branched polycarbonates. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1814–1824, 2001     

Preparation and rheological characterization of long chain branching polylactide

Long chain branching (LCB) of polylactide (PLA) was successfully prepared by the successive reactions of PLA with pyromellitic dianhydride (PMDA) and 1,4-phenylene-bis-oxazoline (PBOZ) together. The topological structures of the LCB generated from functional group reactions were investigated thoroughly by gel permeation chromatography (GPC) and rheology. Qualitative information about the branching structures could be readily obtained from linear viscoelasticity, nonlinear oscillatory shear experiments and strain hardening in elongational experiments. For quantitative information on chain structure, linear viscoelasticity combined with branch-on-branch (BOB) dynamic model was used to predict probable compositions and chain topologies of the products, which were reasonably explained by the suggested mechanism of functional group reactions. It was found out that the star-like LCB structure generated in these reactions contributed remarkably to the enhancement of strain hardening under elongational flow.     

Computation of the linear viscoelastic relaxation spectrum from experimental data

Accurate and reliable determination of the linear viscoelastic relaxation spectrum is a critical step in the application of any constitutive equation. The experimental data used to determine the relaxation spectrum always include noise and are over a limited time or frequency range, both of which can affect the determination of the spectrum. Regularization with quadratic programming has been used to derive the spectrum; however, because both the experimental data and the spectrum change by more than an order of magnitude, the input data and the spectrum are normalized in order for the numerical procedure to be accurate. Accurate determination of the relaxation spectrum requires that the spectrum extend about two logarithmic decades on either side of the frequency range of the input data. The spectrum calculated from G′ alone is more accurate at shorter relaxation times, while that from G′ data alone is obtained from a combination of G′ and G′ data, blended in the manner described herein. Comparison with existing methods in the literature shows a consistently improved performance of the present method illustrated with both model as well as experimental data. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 2177–2189, 1997     

Dielectric relaxation behavior and energy storage properties of Sn modified SrTiO3 based ceramics

SrSn_xTi_(1−x)O₃ (x=0, 0.01, 0.03, 0.05, 0.07) dielectric ceramics were fabricated by the solid state reaction method. Significant refinement of grain size and improved resistivity were observed with the addition of Sn, accounting for effectively enhanced dielectric breakdown strength, beneficial for the energy storage applications. Impedance analysis was employed to calculate the conductivities of grain and grain boundary and resistance ratios (R_gb/R_g) of grain boundary to grain. The grain boundary effect was believed to dominate the modified macroscopic performance, which was confirmed by the complex impedance analysis. The optimal properties were achieved for samples with x=0.05, exhibiting a charge energy density of 1.1 J/cm³ and an energy efficiency of 87%.     

Rubber-modified epoxy resins: 3. Influence of filler on the dielectric relaxation properties

Dielectric measurements are reported on the effect of addition of glass (wool and beads) to a rubber modified epoxy resin. A parallel study of the influence of the addition of polydimethylsiloxane is also reported. It is found that there are significant shifts in the position of the dielectric relaxation associated with the acrylonitrile/butadiene phase. Analysis of the data indicates that the activation energy of the relaxation is little affected by the additives and the observed effects can be explained by the change in internal field brought about by the addition of filler through its effect on the permittivity of the material.     

Influence of azobenzene concentration on the dielectric behavior of amorphous comb-like copolymers with photochromic side groups

Dielectric spectroscopy in the frequency range from 10⁻² to 10⁶ Hz and in the temperature range from 190 to 440 K is employed to study the effect of azobenzene concentration on the dielectric relaxation processes of an amorphous comb-like copolymethacrylate. Four concentrations (x=29, 45.5, 54, and 74.5 mol%) of photochromic group 4-amino-azobenzene were investigated, where as comonomer a methacrylate unit having a derivative of benzanilide in the side group is used. Two prominent processes, the β-relaxation at low temperatures which is related to rotational fluctuations of the mesogenic unit around its long axes and the dynamic glass transition (α-relaxation, segmental dynamics) at higher temperatures are observed for all azobenzene concentrations. In addition in between the α- and the β-relaxation a β′-process is observed for the polymers with the two lowest azobenzene concentrations, which seems to be related to the azobenzene unit. The dependence of the dielectric strength and the relaxation rate of the relaxation processes on the azobenzene concentration is discussed and interpreted in a simple phenomenological model, where also data obtained by semi empirical quantum chemical calculations are used.     

High dielectric permittivity and dielectric relaxation behavior in a Y2/3Cu3Ti4O12 ceramic prepared by a modified Sol−Gel route

In this work, Y_2/3Cu₃Ti₄O₁₂ ceramics were fabricated via a modified sol?gel route. Structural, dielectric, and electrical parameters were systematically investigated. The XRD results indicate that a CaCu₃Ti₄O₁₂ phase (JCPDS No. 75–2188) is present in every sintered sample. SEM images of Y_2/3Cu₃Ti₄O₁₂ ceramics disclose a fine-grained ceramic microstructure. Interestingly, high dielectric permittivity, ～6600–7600, with loss tangents of ～0.918–1.086 were achieved in the sintered Y_2/3Cu₃Ti₄O₁₂ samples. Density functional theory (DFT) calculations were used to investigate the most stable structure of the Y_2/3Cu₃Ti₄O₁₂ ceramics. Our DFT results reveal that two calcium vacancies (V_Ca) are isolated from each other. We also determined the lowest energy configuration of an oxygen vacancy (V_O) in the Y_2/3Cu₃Ti₄O₁₂ ceramics occurred during the sintering process. We found that the V_O is trapped close to the Y atom in this structure. Both computational and experimental studies specify that the oxygen vacancy is located close to the Y atom in the Y_2/3Cu₃Ti₄O₁₂ lattice and it might be a bivalent oxygen vacancy. As a result, due to charge balance, charge compensation of the transition ions, i.e., Cu and Ti ions, might take place. The charge compensation mechanisms in the Y_2/3Cu₃Ti₄O₁₂ lattice were verified using an XPS technique. Impedance spectroscopy confirms the presence of an inhomogeneous microstructure consisting of semiconducting grains and insulating grain boundaries in the sintered Y_2/3Cu₃Ti₄O₁₂ ceramics. This electrical result is consistent with the computational analysis, showing that a charge compensation mechanism might be involved in generation of the grains' semiconductive region due to the presence of a V_O. Consequently, high dielectric permittivity in Y_2/3Cu₃Ti₄O₁₂ may have originated from an internal barrier layer capacitor (IBLC) effect.     

Effect of Sm doping on structure,dielectric and magnetic properties of GdFeO3

Nano-particles of GdFeO₃ (GFO) and Gd_0.4Sm_0.6FeO₃ (GSFO) were synthesized by sol-gel auto-combustion method to study the effect of Sm³⁺doping on physical properties of GFO. Rietveld refinement of x-ray diffraction pattern confirms the proper phase formation of samples and the average octahedral <Fe–O1–Fe> angle of GSFO is found to be 145.54⁰ which is larger compared to GFO 142.53⁰. Temperature dependent DC magnetization measurements showed that Sm doping in GdFeO₃introduces spin-reorientation transition which is absent in pure GdFeO₃ phase. The dielectric constant of GSFO is found to be larger than that of GFO because of change in hybridization between the O-2p states and Fe-3d states. In both the ceramics at higher temperatures (above 150 °C) conduction mechanism is taking place via oxygen defect charge carrier hoping. The complex impedance analysis revealed that the distribution of relaxation time of charge carriers is temperature independent. Sm doping in GFO not only changed the dielectric properties but also changed the magnetic coercive field and shape of the magnetic isotherm of GFO.