Details of Dynamic Mechanical Properties of Dendritic Poly(ether ketone)s in Conjunction with their Highly Branched Structure and Degree of Branching

To investigate the effects of unique hyperbranched structure on viscoelastic properties, three fluoro‐terminated hyperbranched poly(ether ketone)s (HPEKs) with different degrees of branching (i. e., 0.49; HPEK49, 0.62; HPEK62, and 0.67; HPEK67) and the analogous linear poly(ether ketone) (LPEK), whose chemical structure and molecular weights were similar to those of HPEKs, were synthesized and characterized. From the analysis of plots of the dynamic loss modulus G ″(ω) versus the storage modulus G ′(ω) of the individual polymers, it was confirmed that the amount of entanglements between polymer molecules decreased as the degree of branching increased, exhibiting a nearly Newtonian behavior particular for the HPEK with degree of branching of 0.67 (HPEK67). Furthermore, the G ″(ω) versus G ′(ω) plots indicated the narrowing of molecular weight distribution and/or shortening of branches with increasing degree of branching, being shown to shift the curves from lower to higher G ″(ω) values. From the master curves of HPEKs obtained by the time‐temperature superposition principle, it was investigated that the rubbery plateau region and the crossover of G ′(ω) and G ″(ω) started to disappear at a critical value (> 0.62–0.67) of the degree of branching, indicating a nearly Newtonian or little entanglement flow. Moreover, it could be predicted from the tendency of the shift factor a_T, obtained from the master curve, that the molecular mobility and temperature dependence of individual HPEKs increased as the degree of branching increased. The shift factors of HPEKs fit with the Williams‐Landel‐Ferry (WLF) equation resulted in a more temperature dependent non‐Arrhenius behavior than that of LPEK as the degree of branching increased, implying a fragile amorphous polymer. From the nonlinear curve fittings of shift factors by the Vogel‐Tamman‐Fulcher (VTF) equation, it was further quantified that the HPEKs were more fragile than the LPEK and the fragility increased with increasing degree of branching, which indicated that the branching structure induced the fragility in the materials.     

Role of capillary end correction in flow analysis of molten polyethylene

The role of the capillary end correction in flow analysis of molten low-density polyethylenes has been analyzed. In spite of limitations of accuracy a quantitative approach has been undertaken. The results are much more complicated than predicted by Bagley in his early reports. The elastic component of the end correction is controlled by shear stress and shear modulus. The latter is affected by the size of the subchain between entangles, M_e, and by the degree of long-chain branches. Both are eventually dependent on the length of the chain, i.e., its molecular weight. In addition shear stress and temperature affect the process of disentanglement. Capillary end correction increases with increasing molecular weight and shear stress and with decreasing temperature. The available analysis of branching is still in controversy, and therefore no numerical parameters are yet proposed. A consistent theory of the response of entanglement couplings to shear forces and temperature is evaluated.     

Rheological behavior of polymer blends

Steady and oscillatory shearing flow properties of compatible and incompatible polymer blend systems were measured, using a cone-and-plate rheometer. The compatible blend systems investigated are blends of two low-density polyethylenes (LDPE) having different values of molecular weight and blends of poly(methyl methacrylate) (PMMA) with poly(vinylidene fluoride) (PVDF). The incompatible blend system investigated is a blend of poly(methyl methacrylate) (PMMA) with polystyrene (PS). It was found that (1) plots of first normal stress difference (τ₁₁ – τ₂₂) vs. shear stress (τ₁₂) and plots of storage modulus (G′) vs. loss modulus (G″) for the LDPE blends become independent of temperature and blend composition; (2) plots of τ₁₁ – τ₂₂ vs. τ₁₂, and G′ vs. G″ for the PMMA/PVDF blends become independent of temperature but dependent upon blend composition. It was found further that, for the incompatible PMMA/PS blends, the dependence of τ₁₁ – τ₂₂ on blend composition, when plotted against τ₁₂, is different from the dependence of G′ on blend composition, when plotted against G″. However, in both compatible and incompatible blend systems, plots of τ₁₁ – τ₂₂ vs. τ₁₂ and plots of G′ versus G″ are independent of temperature. The seemingly complicated composition-dependent rheological behavior of the incompatible blend system is explained with the aid of photomicrographs describing the state of dispersion.     

Long chain branching and polydispersity effects on the rheological properties of polyethylenes

The rheological behavior of linear, and branched polyethylenes is studied as a function of the weight average molecular weight (M_w) and its distribution (MWD) as well as the level of long chain branching in an attempt to identify correlations between long chain branching, polydispersity and rheological properties. It is found that a need for vertical shift of the viscoelastic moduli data to obtain the master curves using the time‐temperature superposition principle is associated with the existence of long chain branching in the structure of the polymer. The degree of vertical shift is found to correlate with the level of long chain branching. This correlation corroborates with the observation that long chain branching correlates with the horizontal flow energy of activation. Plots of atan(G″/G′) vs. G* (known as Van Gurp plots) also reveal some important features that can be used as signs of specific features in the structure of polymers. More specifically, the area included below the Van Gurp curves correlates with the level of long chain branching and polydispersity index. The correlations are presented in graphical form and they can be used to associate rheological properties with the presence of long chain branching and/or polydispersity.     

Rheological behavior of compatible polymer blends. I. Blends of poly(styrene-Co-acrylonitrile) and poly(ε-caprolactone)

The rheological behavior of blends of poly(styrene-co-acrylonitrile) (SAN) and poly(ε-caprolactone) (PCL) was investigated, using a cone-and-plate rheometer. For the study, blends of various compositions were prepared by melt blending using a twin-screw compounding machine. The rheological properties measured were shear stress (σ₁₂), viscosity (η), and first normal stress difference (N₁) as functions of shear rate (γ) in steady shearing flow, and dynamic storage modulus (G′) and loss modulus (G″) as functions of angular frequency (ω) in oscillatory shearing flow, at various temperatures. It has been found that logarithmic plots of N₁ versus σ₁₂, and logarithmic plots of G′ versus G″, become virtually independent of temperature but vary regularly with blend composition, and that the zero-shear viscosity of the blends, (η_o)_blend, follows the relationship, 1/log(η_o)_blend = w_A/log η_0A + w_B/log η_0B, where η_0A and η_0B are the zero-shear viscosities of components A and B, respectively, and w_A and w_B are the weight fractions of components A and B, respectively. The physical implications of the relationship found are discussed.     

Influence of molecular weight distribution on the linear viscoelastic properties of polymer blends

Literature data for the dynamic viscoelastic properties of binary blends of nearly monodisperse polybutadienes, polystyrenes, and poly(methyl methacrylate)s was analyzed using logarithmic plots of dynamic storage modulus G′ versus loss modulus G″, based on a recent theoretical study by Han and John.²⁸ It has been found that for binary blends of monodisperse polymers with molecular weights M much greater than the entanglement molecular weight M_e, the value of G′ in log G′ ? log G″ plots becomes independent of molecular weight, increases sharply as small amounts of a high-molecular-weight component are added to a low-molecular-weight component, and passes through a maximum G′_max at a critical blend composition (?₂)_max, and that G′_max becomes larger and (?₂)_max becomes smaller as the ratio of component molecular weights increases. However, as the molecular weight distribution of the constituent components becomes broader, the effect of blend composition on G′ in log G′ ? log G″ plots becomes less pronounced. This observation has enabled us to explain why log G′ ? log G″ plots of binary blends of commercial polymers, namely, blends of two low-density polyethylenes, blends of poly(?-caprolactone) and poly(styrene-co-acrylonitrile), and blends of poly(methyl methacrylate) and poly(vinylidene fluoride), all having broad molecular weight distributions, give rise to values of G′ between those of the constituent components. When one of the constituent components has molecular weight smaller than M_e, while the other has molecular weight larger, and as small amounts of the high-molecular-weight component are added to the low-molecular-weight component, log G′ ? log G″ plots of binary blends give rise to values of G′ larger than those of the constituent components at low values of G″, but approaches the value of G′ for the low-molecular-weight component as the value of G″ is increased. However as the amount of the high-molecular-weight component is increased above a certain critical composition, binary blends give rise to values of G′ close to that of the high-molecular-weight component at all values of G″. The experimentally observed dependence of G′ on blend composition in log G′ ? log G″ plots is favorably compared to the theoretical prediction of a blending law proposed by Montfort and co-workers.^14,15     

Viscoelastic properties of poly(ethylene-co-styrene) copolymers

The viscoelastic properties of narrowly distributed linear poly(ethylene-co-styrene) copolymers with different mole fractions of styrene (x_S = 0–20.5 mol %) and molecular weights (M_w = 64–214 kg/mol) were analyzed in the molten state at different temperatures by means of oscillatory rheometry. Analyzing the thermorheological properties of the polymers, we found that the time temperature superposition principle is fulfilled. The corresponding shift factors follow up to 16.5 mol % of styrene units the Arrhenius behavior of neat polyethylene. For a styrene content of about 20 mol %, the polymers no longer crystallize and a transition from Arrhenius to WLF behavior of pure polystyrene was observed. The zero shear viscosity, η₀, of the polymers was derived from the mastercurves. The determination of the plateau modulus by the well-known tan δ-min criterion is not possible due to the beginning crystallization in the corresponding temperature range. An approximate calculation of this value is based on the characteristic relaxation time λ_x = 1/ω_x, corresponding to the crossover of G′ and G′. Indeed, the characteristic modulus G_px calculated as η₀/λ_x is a good approximation for the plateau modulus G_p. The viscosity–molecular weight and relaxation time–molecular weight scaling relations were established for three copolymers with different molecular weights and nearly the same styrene content. For both material parameters, the scaling exponent is around 3.4, confirming the linear architecture of the investigated polymers. The mixing rules describing the change of such material parameters like zero shear viscosity or plateau modulus independent of styrene content are of logarithmic linear character using the weight fraction of styrene units instead of the mole fraction. The relations found allow the prediction of melt state properties for polymers with arbitrary styrene content. In the future, when catalysts with sufficient activity for the synthesis of high styrene content copolymers are available, these predictions will have to be checked. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65:209–215, 1997     

Elastic behavior of concentrated solutions of acrylonitrile copolymers

The elastic behavior of concentrated solution of acrylonitrile copolymer was investigated by the capillary end correction method. The results were as follows. (1) The shear stress is proportional to recoverable shear strain in accordance with Hooke's law below critical concentration; above a critical concentration, however, the shear modulus depends on shear stress. (2) The log–log plots of zero shear modulus against polymer concentration and molecular weight fall on two straight lines with different slopes. The intersection of lines is considered to be the onset of elastically deformable entanglement network. We denote this inflection point as (C_c)_e or (M_c)_e. (3) The log–log plot of viscosity against polymer concentration does not show a change of slope at the critical concentration (C_c)_e. (4) By the application of the kinetic theory of rubberlike elasticity to the pseudo-network structure of concentrated polymer solution, in the range of C_c < C < (C_c)_e or M_c < M < (M_c)_e, the number of chain entanglement per molecule is kept one; moreover, in the range of C > (C_c)_e, or M > (M_c)_e, the number of chain entanglement increases to three.     

Structure‐property relationships of blends of polycarbonate

Three grades of bisphenol‐A polycarbonate—high molecular weight linear, high molecular weight branched and low molecular weight linear—and their blends have been studied by GPC, DMTA, DSC, rheometry and impact measurements. The molecular weight distribution of the blends agred with that predicted from the component's distributions, indicating that no transesterification reactions had occurred during melt blending. The T_g of the blends varied with blend composition according to the Fox equation and was related to the reciprocal molecular weight predicted by the Flory‐Fox equation. The low shear rate viscosity of the blends agreed with a logarithmic rule of mixtures and showed power‐law dependence on the weight average molecular weight. At higher shear rates, shear thinning was observed. The steady shear viscosity correlated well with the dynamic viscosity, as suggested by the Cox‐Merz relation. The stress relaxation behavior of the melt was very sensitive to the blend composition and molecular weight and correlated well with the real modulus. Temperature studies of the dart impact energy showed that only the low molecular weight polymer underwent a brittle‐duetile transition at ea ?30°C and that all the blends were tough at room temperature. The enhanced stress triaxiality inherent in the notched lzod test caused the impact strenght at room temperature to decrease almost linealy with blend composition.     

Rheological behavior of blends of poly(methyl methacrylate) (PMMA) and poly(acrylonitrile-stat-styrene)-graft-polybutadiene (ABS)

The rheological behavior of blends of poly(methyl methacrylate) (PMMA) and poly(acrylonitrile-stat-styrene)-graft-polybutadiene (ABS) was investigated using a cone-and-plate rheometer. The rheological properties measured were shear stress (σ₁₂), viscosity (η), and first normal stress difference (N₁) as functions of shear rate (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma$ \end{document}) in steady shearing flow, and storage modulus (G′) and loss modulus (G″) as functions of frequency (ω) in oscillatory shearing flow. It has been found that the rheological behavior of blends of ABS and PMMA was very similar to that of blends of poly(styrene-stat-acrylonitrile) (SAN) and PMMA, in that N₁ in logarithmic plots of N₁ versus σ₁₂, and G′ in logarithmic plots of G′ versus G″, vary regularly with blend composition. This has led us to conclude that the rubber particles that are grafted on an SAN resinous matrix in ABS resin plays only a minor role in influencing the compatibility of ABS/PMMA blends, and that the SAN chains attached to the surface of rubber particles, and the SAN matrix phase, play a major role in compatibilizing ABS resin with PMMA.     

The hydrosilylation cure of polyisobutene

Summary A liquid polyisobutene oligomer with unsaturated chain ends undergoes hydrosilylation with HMe₂SiOMe₂SiOMe₂SiH or Si(OMe₂SiH)₄ to give higher molecular weight polymers or elastomers. A major side reaction consumes SiH to give redistributed siloxane in the resulting polymers and gaseous silanes and siloxanes as by-products. A second side reaction results in loss of reactivity in the oligomer due to a shift of the terminal double bond to an internal position. If the side reactions are taken into account, it is possible to forecast quantitatively molecular weight, gel point and modulus from the conversions of >SiH, >C=CH_f2 and the chain entanglement concentration reported for polyisobutene in the literature.     

Crystal modulus of a new semiaromatic polyamide 9‐T

The elastic modulus (E_l) of crystalline regions in the direction parallel to the chain axis in a new semiaromatic polyamide 9‐T (PA9‐T) containing a long aliphatic chain unit was measured by X‐ray diffraction and the derived E_l value was discussed in terms of its molecular conformation and mechanical properties. For low and high molecular weight PA9‐Ts, the E_l value of 40 GPa was obtained. The low E_l value for PA9‐T is due to the presence of aromatic groups with long crankshaft arms, which result in a greater moment of force during deformation compared with those polymers with planner zigzag molecular conformation like polyethylene and nylon 6 α‐form. Another factor for the low E_l is due to the contraction of its molecular chains that is likely originated from the existence of a torsional conformation. The presence of contraction causes some internal rotation in the polymer chain during extensional deformation, which results in low E_l. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Experimental arguments on the conformation of molecules in molten and glassy polymers

In molten non-crystallising polymers we find normal random coil conformations of the molecules. This is inferred from the theoretically predicted and experimentally observed relationships between the properties of solutions (relaxational modulus, viscosity, osmotic pressure and specific volume) and melts. It is also derived from the intrinsic viscosities (η) and the diffusion constants of molecules with a very high molecular weight in polymeric solvents (M = 10⁴?10⁵) of the same chemical constitution. Moreover the properties of melts (relaxational modulus, flow curve, viscosity) depend on chemical structure and long chain branching in the manner predicted assuming a random coil conformation. At the glass temperature T_g the conformation resembles that in the melt as the temperature dependence of the conformation at T > T_g shows ((η) in polymeric solvents, diameters of the domains in block copolymers). However, on cooling below T_g an irreversible volume shrinking process may lead to an inhomogeneous distribution of densities and possibly to an extended conformation of molecules in grain boundaries. Experiments show that only strong deviations from random coil conformations decrease the ultimate strength of a glass.     

Correlations involving modulae and cross-polarization time constants for a series of polyurethane elastomers

Correlations between the macroscopic bulk polymer properties storage modulus (E′) and loss modulus (E″) and the microscopic property of cross-polarization as represented by the time constant T_CH have been established for a series of polyurethane elastomers. The dependence of E′, E″, and T_CH as a function of molecular weight, rigid domain concentration, and temperature are graphically presented as a series of log plots. An experimental relationship is presented that shows that the distribution of motions of the flexible domains appears to be the major factor in the success of these correlations.     

Viscoelastic properties of linear chain macromolecular gels. Growth of stress at the onset of steady shear flow

The growth of stress (shear stress and normal stress) at the onset of steady shear flow was investigated for linear chain macromolecular fluids to determine nonlinear viscoelasticity. The polyacrylamides (PAAm) were dissolved in H₂O, formamide and ethyleneglycol. The polymers were prepared in this laboratory. They were unbranched and free of initiator. The polystyrene (PS) samples from Pressure Chemical Company were studied in decalin solutions. PAAm shows increasingly typical gel character—in all 3 solvents—with increasing molecular weight and polymer concentration. For homogeneous systems gel fracture and undershoot were observed. Further for the first time overshoot due to entangled molecules and overshoot due to energetically associated chains have been distinguished. This behaviour is a strong contrast to the PS/decalin system and demonstrates the strength of the second valence bondings in the PAAm-systems.     

Criteria for rheological compatibility of polymer blends

Criteria for rheological compatibility of polymer blends are suggested. The criteria suggested make use of plots of first normal stress difference (N₁) against shear stress (σ₁₂), and of storage modulus (G′) against loss modulus (G″). Compatible blend systems considered are (1) blends of two different grades of low-density polyethylene, (2) blends of poly(vinylidene fluoride) and poly(methyl methacrylate), (3) blends of poly(2,6-dimethyl-1,4-phenylene oxide) and polystyrene, and (4) blends of poly(styrene-co-acrylonitrile) and poly(styrene-co-maleic anhyride). And incompatible blend systems considered are (1) blends of nylon 6 and poly(ethylene-co-vinyl acetate) and (2) blends of nylon 6 and an ethylene-based multifunctional polymer. It has been found that plots of N₁ vs. σ₁₂ and G′ vs. G″ give (a) temperature-independent correlations for both compatible and incompatible blend systems; (b) composition-independent correlations for compatible blends; (c) composition-dependent correlations for incompatible blends.     

Dynamic mechanical behavior of copolymers containing carbon black

The storage and loss moduli of random copolymers of styrene and butyl methacrylate containing carbon black of varied surface area were determined by dynamic mechanical analysis at several temperatures about 100°C above the glass-transition temperature, T_g. At low frequencies, the pure polymers exhibit linear double log plots of moduli against frequency, with slopes of unity and approaching two for G″ and G′, respectively. With the addition of carbon black filler, both G′ and G″ become independent of frequency and temperature at low frequencies, consistent with yield behavior arid the formation of a carbon black network. The limiting dynamic complex modulus exceeds the yield stress from steady shear rheology, perhaps indicating the extent of the carbon black network, which was highest for low-molecular-weight copolymer and polystyrene. The filled random copolymers behaved Theologically like similarly filled polystyrenes of comparable molecular weights. Plasticization effects observed in the steady shear rheology of filled copolymers containing small concentrations of carbon black were not observed in dynamic mechanical analysis, although dynamic moduli converge at high frequency.     

Chain‐linked lactic acid polymers by benzene diisocyanate

Chain‐linked lactic acid polymers with high molecular weight were synthesized by two‐step polymerization method, including polycondensation and chain extending reactions. The effects of chain extender toluene diisocyanate (TDI) on the chain‐linked lactic acid polymers were studied. The polymers obtained were characterized by gel permeation chromatography, fourier transform infrared spectroscopy, ¹H NMR, and differential scanning calorimeter. Reactions between 1,4‐butanediol and lactic acid oligomers led to hydroxyl‐terminated prepolymer, which provided significant increase of molecular weight in the chain extending reaction. In addition, the glass transition temperature (T_g) and the melting temperature (T_m) were increased. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 1045–1049, 2006     

Influence of long‐chain branching on the rheological behavior of polyethylene in shear and extensional flow

In this work, a study of the influence of molecular structure on the viscoelastic behavior of melts of commercial polyethylene (PE) copolymers, particularly in extensional flows, will be performed. To enable this study to be performed, a series of four very low‐density polyethylenes (VLDPEs) (film and blow molding grades) with different parameters of molecular weight (M_W), molecular weight distribution (MWD), and degree of long‐chain branching (LCB) will be used. Experiments in shear flow (steady state and oscillatory regime) are complemented with experiments in uniaxial extension (constant strain rate and stress relaxation after a step strain). It will be shown that a qualitative correlation exists between both types of experiments; the stress relaxation experiments being particularly sensitive to the different molecular features of the polymers. In addition, the failure behavior in extension was also investigated and the results indicate that, within experimental error, the Hencky strain to failure is sensitive to the type of molecular structure but the corresponding tensile stress is not. POLYM. ENG. SCI., 45:984–997, 2005. © 2005 Society of Plastics Engineers     

Influence of melt stability on the crystallization of bis(4-aminophenoxy)benzene-oxydiphthalic anhydride based polyimides

Novel high performance semicrystalline polyimides, based on controlled molecular weight phthalic anhydride (PA) endcapped 1,4-bis(4-aminophenoxy)benzene (TPEQ diamine) and oxydiphthalic dianhydride (ODPA), were synthesized. They exhibited excellent thermal stability in nitrogen and air atmospheres as determined by thermogravimetric analysis (TGA). The glass transition temperatures (T_g) for these polymers ranged from 225°C for the 10,000 M_n (10K) polymer, to 238°C for the 30,000 (30K) M_n material. The observed melting temperatures for all the polymers were ∼420°C. The crystallization behavior of these polymers showed a strong molecular weight dependence, as illustrated by the observation that the 10K and 12.5K polymers crystallized with relative ease, whereas the 15K, 20K, and 30K polymers showed little or no ability to undergo thermal recrystallization. The thermal stability of these polymers above T_m was investigated by studying the effect of time and temperature in the melt on the cold crystallization and melting of these polymers. Increased time and temperature in the melt resulted in lower crystallinity because of melt state degradation, such as crosslinking and branching, as evidenced by an increase in melt viscosity, which was more prominent for the higher molecular weight polymers.