Isothermal elongational behavior of liquid-crystalline polymers and LCPs based blends

The rheological behavior of two flexible thermoplastics, Nylon-6 (Ny) and bisphenol-A polysulfone (PSu), and two wholly aromatic liquid crystalline polymers, Vectra-A900 (VA) and Vectra-B950 (VB), as well as that of Ny/VB and PSu/VA blends with 10% LCP, has been investigated by the use of capillary viscometers equipped with cylindrical dies having different length-to-diameter ratios. The elongational viscosity of all materials was calculated, from the results of isothermal measurements carried out at 290°C, by means of the Cogswell's analysis, based on the estimation of the pressure drop due to the converging flow at the die inlet. The behavior in elongational flow was compared with the rheological behavior in shear flow conditions. It was found that the elongational viscosities of VA and VB are very large and account for a fairly marked pressure drop at the die entrance, due to the orientation of the LCP domains taking place in the converging flow zone. For these materials, the ratio of the elongational viscosity to the Newtonian shear viscosity is up to two orders of magnitude higher than the value expected on the basis of the Trouton rule. For the flexible resins, the Trouton ratio is 3 and ca. 3–10, are common values for high molar mass linear polymers. The addition of 10% LCP into the flexible resins strongly increases their elongational viscosity and makes the blends resemble neat LCPs in their extensional flow behavior. In shear flow, on the contrary, the addition of LCP was shown to induce a marked reduction of the melt viscosity, even when, as for the Ny/VB blend, the LCP is more viscous than the matrix.     

Rheological behavior of poly(methyl methacrylate)/polystyrene (PMMA/PS) blends with the addition of PMMA-<Emphasis Type="BoldItalic">ran</Emphasis>-PS

In this work, the dynamic behavior of poly(methyl methacrylate)/polystyrene blend to which P(S_0.5-ran-MMA_0.5) was added was studied. Several blend (ranging from 5 to 20 wt% of dispersed phase) and copolymer (up to 20 wt% with respect to dispersed phase) concentrations were studied. The rheological behavior of the blends was compared to Bousmina’s (Rheol Acta 38:73–83, 1999) and Palierne’s (Rheol Acta 29:204–214, 1990) generalized models. The relaxation spectra of the blends were also inferred, and the results were analyzed in light of the analysis of Jacobs et al. [J Rheol 43:1495–1509, 1999]. The relaxation spectra of the blends with smaller dispersed phase (below 10 wt%) and larger copolymer concentrations (above 0.4 wt%) showed the presence of four relaxation times, two corresponding to the blend phases, τ _F , corresponding to the relaxation of the shape of the dispersed phase of the blend and that can be attributed to the relaxation of Marangoni stresses tangential to the interface between the dispersed phase and matrix. The experimental values of and were used to infer the interfacial tension (Γ) and the interfacial complex shear modulus (β) for the different blends, Γ decreased with increasing copolymer concentration. β decreased with increasing blend dispersed phase concentration and decreasing copolymer concentration. The predictions of Palierne’s generalized model were found to corroborate the experimental data once the values of Γ and β, found analyzing the relaxation spectra, were used in the calculations. Bousmina’s model was found to corroborate the data only for larger dispersed phase concentration. Paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

The influence of epoxy resin on the morphological and rheological properties of PET/PA66 blend

Interfacial reactions have dominant effects on the morphological and rheological properties of compatibilized polymer blends. This work aims to investigate the effect of epoxy resin, as a coupling agent, on the interface properties and subsequent influences on the morphological and rheological properties of polyethylene terephthalate/polyamide66 (PET/PA66) blend. PET/PA66 70/30 blends with different amount of bisphenol A epoxy resin (0, 1, 3, and 5 wt.%) were prepared. SEM micrographs show reduction in droplet size with increasing epoxy resin concentration, confirming the reactive compatibilizing effect of the epoxy resin. Reactions at the interface of the PET-EP-PA66 blend are confirmed by FTIR spectra. Shear viscosity results demonstrates that adding epoxy resin could suppress the interfacial slip at the blend interphase. Obtained results from storage modulus (G′) curves show the presence of one plateau for the blends at low frequency region; nevertheless, relaxation spectra indicate the presence of two more relaxation mechanisms than precursors which are related to the shape relaxation of droplets and the interface relaxation. The presence of the interface relaxation time in the blend without epoxy resin can prove the presence of reactions between two condensation polymers; however, adding the epoxy resin results in reducing both relaxation time and interfacial tension and increasing interfacial shear modulus. These observations indicate that the epoxy resin has been successful to boost the reactions at the interface between two polymers. Fitting the obtained experimental data using Palierne model indicates that the general Palierne model could describe rheological properties of the blends very well.     

Orientation dynamics in commercial thermotropic liquid crystalline polymers in transient shear flows

In situ X-ray scattering measurements of molecular orientation under shear are reported for two commercial thermotropic liquid crystalline polymers (TLCPs), Vectra A950® and Vectra B950®. Transient shear flow protocols (reversals, step changes, and flow cessation) are used to investigate the underlying director dynamics. Synchrotron X-ray scattering in conjunction with a high-speed area detector provides sufficient time resolution to limit the total time spent in the melt during testing, whereas a redesigned X-ray capable shear cell provides a more robust platform for working with TLCP melts at high temperatures. The transient orientation response upon flow inception or flow reversal does not provide definitive signatures of either tumbling or shear alignment. However, the observation of clear transient responses to step increases or step decreases in shear rate contrasts with expectations and experience with shear-aligning nematics and suggests that these polymers are of the tumbling class. Finally, these two polymers show opposite trends in orientation following flow cessation, which appears to correlate with the evolution of dynamic modulus during relaxation. Specifically, Vectra B shows an increase in orientation upon flow cessation, an observation that can only be rationalized by the assumption of tumbling dynamics in shear. Together with prior observations of commercial LCP melts in channel flows, these results suggest that this class of materials, as a rule, exhibits director tumbling.     

Effects of strong anchoring on the dynamic moduli of heterogeneous nematic polymers II: oblique anchoring angles

We extend previous work on the linear viscoelastic moduli of heterogeneous nematic polymers in a small-amplitude oscillatory shear flow, focusing on the role of the orientational anchoring conditions at the plates. When tangential or normal anchoring conditions are applied, the Doi–Marrucci–Greco orientation tensor-flow model effectively reduces to the Leslie–Ericksen director-flow model, predicting that director distortions control the dynamic moduli with negligible contributions from tensor-order parameters. In this paper, we examine oblique anchoring angles. We use a combination of analysis and numerical simulation on the generalized tensor-flow system for arbitrary anchoring conditions to show that any oblique anchoring condition induces a nontrivial order parameter contribution to the dynamic moduli, which vanishes only in the limit of tangential or normal anchoring. Our approach reveals that the storage and loss moduli admit an approximate decomposition in terms of two reduced problems that are exactly solvable: the heterogeneous director–flow response plus the monodomain tensor response to an imposed shear. The importance of this result is that we gain scaling properties of the moduli with respect to material parameters and experimental conditions without having to compute and assimilate across the full parameter space. These results provide insight into the relative importance of the distortional vs bulk nematic elastic stress in determining the viscoelastic moduli, predicting that anchoring conditions tune the relative contributions.     

Interfacial welding of dynamic covalent network polymers

Dynamic covalent network (or covalent adaptable network) polymers can rearrange their macromolecular chain network by bond exchange reactions (BERs) where an active unit replaces a unit in an existing bond to form a new bond. Such macromolecular events, when they occur in large amounts, can attribute to unusual properties that are not seen in conventional covalent network polymers, such as shape reforming and surface welding; the latter further enables the important attributes of material malleability and powder-based reprocessing. In this paper, a multiscale modeling framework is developed to study the surface welding of thermally induced dynamic covalent network polymers. At the macromolecular network level, a lattice model is developed to describe the chain density evolution across the interface and its connection to bulk stress relaxation due to BERs. The chain density evolution rule is then fed into a continuum level interfacial model that takes into account surface roughness and applied pressure to predict the effective elastic modulus and interfacial fracture energy of welded polymers. The model yields particularly accessible results where the moduli and interfacial strength of the welded samples as a function of temperature and pressure can be predicted with four parameters, three of which can be measured directly. The model identifies the dependency of surface welding efficiency on the applied thermal and mechanical fields: the pressure will affect the real contact area under the consideration of surface roughness of dynamic covalent network polymers; the chain density increment on the real contact area of interface is only dependent on the welding time and temperature. The modeling approach shows good agreement with experiments and can be extended to other types of dynamic covalent network polymers using different stimuli for BERs, such as light and moisture etc.     

Theory of interfacial dynamics of nematic polymers

 The interfacial momentum and torque balance equations for deforming interfaces between nematic polymers and isotropic viscous fluids are derived and analyzed with respect to shape selection and interfacial nematic ordering. It is found that the interfacial momentum balance equation for nematic interfaces involves bending forces that act normal to the interface, and that interfacial pressure jumps may exist even for planar surfaces. In addition tangential forces on nematic interfaces arise in the presence of surface gradients of the tensor order parameter. The torque balance equation shows that couple stress jumps are balanced by the surface molecular field. The interfacial balance equations are shown to be coupled such that nematic ordering depends on shape and vice versa. The governing dimensionless numbers for deforming nematic polymer interfaces are identified and the limiting regimes are discussed in reference to related experimental data. It is found that the ratio of Frank elasticity to surface anchoring controls whether the surface tensor order parameter deviates from its preferred equilibrium value. Whether the shape is affected, depends on the relative magnitudes of the isotropic surface tension, Frank bulk elasticity, and anchoring energy, and capillary number. Received: 16 April 1999/Accepted: 19 August 1999     

Dependence of the dynamic moduli of heterogeneous nematic polymers on planar anchoring relative to flow direction

We analyze the dynamic moduli of nematic polymers in a parallel plate oscillatory shear experiment from a Doi?CMarrucci?CGreco orientation tensor formulation, paying special attention to the inherent connection between rheological properties and wall anchoring conditions. We assume standard experimental procedures in which the plates have been rubbed to achieve strong nematic anchoring parallel to the rubbing direction. We derive the heterogeneous, harmonic response of the nematic liquid in the weak oscillatory shear regime of linear viscoelasticity. The response function is parameterized by the orientational anchoring condition and, in particular, by the angle of rotation between the rubbing direction and the flow direction. From this analysis, we read off the frequency-dependent storage and loss moduli. The dominant effect is in the storage modulus where for high frequencies rubbing aligned with the vorticity axis can cause G ^?? to be two to three orders of magnitude larger than rubbing in the flow direction. This anchoring dependency shows the significance of the order parameter fluctuations of tensor-based models: the Leslie?CEricksen theory predicts zero storage modulus for vorticity-aligned anchoring. For low frequencies, this effect is reversed with flow-aligned anchoring maximizing G ^?? in a manner similar to the Leslie?CEricksen theory although we predict a nonzero modulus for vorticity-aligned anchoring.     

Effects of strong anchoring on the dynamic moduli of heterogeneous nematic polymers

We focus on the linear viscoelastic response of heterogeneous nematic polymers to small amplitude oscillatory shear, paying special attention to the macroscopic influence of strong plate anchoring conditions. The model consists of the Stokes hydrodynamic equations with viscous and nematic stresses, coupled to orientational dynamics and structure driven by the flow gradient, an excluded-volume potential, and a two-constant distortional elasticity potential. We show that the dynamical response simplifies when plate anchoring is either tangential or homeotropic, recovering explicitly solvable Leslie–Ericksen–Frank behavior together with weakly varying order parameters across the plate gap. With these plate conditions, we establish “model consistency” so that all experimental driving conditions (plate-controlled velocity [strain] or shear stress, imposed oscillatory pressure) yield identical dynamic moduli for the same material parameters and anchoring conditions, eliminating the culpability of device influence in scaling behavior. Two physical predictions emerge that imply significant macroscopic elastic and viscous effects controlled by plate anchoring relative to flow geometry: (1) The storage modulus is enhanced by two to three orders of magnitude for homeotropic relative to parallel anchoring, across all frequencies. (2) The loss modulus exhibits enhancement of a factor of two to three for homeotropic over tangential anchoring, restricted to low frequencies. We further deduce a scaling law for the dynamic moduli versus anisotropy of the distortional elasticity potential.

Transient shear and elongational behavior of blends of PET with a LCP

Blends of polyethylene terephthalate (PET) with a liquid crystalline polymer (LCP) and a compatibilizer were produced by twin screw extrusion and injection molding. Transesterification and compatibilization studies were made in a torque rheometer. The morphology of the injection-molded plaques was studied by scanning electron microscopy. The blends shear growth function was measured in a cone and plate rheometer. The elongational growth function was measured in a modified rotational rheometer. Transesterification was observed in the PET/LCP/compatibilizer 95/5/0 blend. The injection-molded plaques displayed the usual “skin-core” morphology. All the blends were highly shear-thinning, even at low shear rates; thus, a zero-shear viscosity could not be calculated. The compatibilized blend had the highest shear viscosity of all the blends, confirming the strong PET/LCP interphase and the effectiveness of the compatibilizing agent. On the other hand, the 90/10/0 blend had the lowest shear viscosity. All the blends showed strain softening behavior, similar to the PET. The 90/10/0 blend had the highest elongational growth function, while the 95/5/0 had the lowest. The compatibilized blend had an intermediate behavior between both blends.     

Analytical rheology of blends of linear and star polymers using a Bayesian formulation

A Bayesian data analysis technique is presented as a general tool for inverting linear viscoelastic models of branched polymers. The proposed method takes rheological data of an unknown polymer sample as input and provides a distribution of compositions and structures consistent with the rheology, as its output. It does so by converting the inverse problem of analytical rheology into a sampling problem, using the idea of Bayesian inference. A Markov chain Monte Carlo method with delayed rejection is proposed to sample the resulting posterior distribution. As an example, the method is applied to pure linear and star polymers and linear–linear, star–star, and star–linear blends. It is able to (a) discriminate between pure and blend systems, (b) accurately predict the composition of the mixtures, in the absence of degenerate solutions, and (c) describe multiple solutions, when more than one possible combination of constituents is consistent with the rheology.     

Effect of temperature and molecular weight on the interfacial tension of PS/PDMS blends

The imbedded-fiber retraction (IFR) method was used to study the effect of temperature and PDMS molecular weight on the interfacial tension of PS/PDMS blends. The interfacial tension decreased with increasing temperature and analysis of the temperature dependence using a simple linear fit gave –dγ/dT value of 0.058±0.010 dyn/cm-deg. Reported –dγ/dT values of PS/PDMS blends are highly dependent on the molecular weights of the polymers and can have values that are <0, 0, or >0. Our interfacial tension values were independent of the molecular weight of PDMS and this was attributed to the molecular weights studied here being well above the entanglement values of both polymers. However, analysis of interfacial tension data from this work and the literature showed the following empirical relationship between apparent blend molecular weight, M_b, and interfacial tension of PS/PDMS blends with a correlation of 0.94: γ₁₂=γ₀+k₂M_b ^(–2/3), where γ₀=7.3±0.3 dyn/cm; k₂=–517±41 (dyn/cm)(g/mol)^2/3.     

Interfacial tension reduction in PBT/PE/clay nanocomposite

We investigated the effect of organically modified nanoclay (organoclay) on immiscible polymer blends [polybutylene terephthalate (PBT)/polyethylene (PE)] with a special focus on the role of clay as a compatibilizer. When organoclay (Nanofil 919; Sud-Chemie, Inc.) is added to the blend, the clay first locates at the interface and then selectively locates in the PBT phase due to its affinity with PBT. This results in effective size reduction and narrowed size distribution of the dispersed phase. However, with a small amount of organoclay, it is observed that the clay locates at the interface regardless of its affinity for a specific component to minimize the chemical potential. The interfacial tension change of the blend with the addition of organoclay was quantitatively predicted from extensional force measurement. When the blend is subjected to an extension, the interfacial tension functions as a resistance against drop deformation. When we added organoclay to the blend, the extensional force was significantly reduced, which means that the contribution of the interfacial tension to the total force is reduced. For a 10/90 PBT/PE blend, the interfacial tension was reduced from 5.76 to 0.14 cN m⁻¹ when 1 wt% of organoclay was added. This interfacial tension reduction arises from the localization of the organoclay at the interface and its nonhomogeneous distribution along the interface, suppressing the coalescence between the droplets, which is a role of a compatibilizer. Conclusively, the immiscible polymer blends can be compatibilized with organoclay. The organoclay changes the blend morphology by interfacial tension reduction due to the localization of the organoclay at the interface and by the viscosity ratio change due to the selective localization by its affinity to a specific component in the blend.     

Dynamics and rheology of the morphology of immiscible polymer blends – on modeling and simulation

 The material properties of heterogeneous polymer blends are crucially influenced by their morphology, i.e., by the spatial structure of the blend components and by the specific configuration of the interfaces separating the phases. Hence, in order to understand the behavior of experimentally obtained morphologies, one is interested in modeling the relevant dynamics of the morphology subject to external flow. Thus one can study, e.g., through the interfacial stress tensor the rheological properties due to the interfaces. The balance equations used for that purpose are based on a Cahn-Hilliard equation for the local concentration, the continuity equation, and a modified Navier-Stokes equation for the local velocity. The essential material and processing parameters such as surface tension, viscosity and volume fraction of both polymers, and imposed shear rate are taken into consideration as model coefficients. By regarding hydrodynamic interaction, which is proved to be important in case of immiscible blends, the interfacial relaxation is described properly. Simulations in both three and two dimensions agree at least qualitatively with experimental results concerning droplet deformation, droplet coalescence, and interfacial rheological properties of the blend. Received: 25 September 2000 Accepted: 24 April 2001     

Uniaxial extensional flow behavior of immiscible and compatibilized polypropylene/liquid crystalline polymer blends

In this work liquid crystalline polymer (LCP) and thermoplastic (TP) blends with and without compatibilizer were studied with respect to their elongational flow behavior, under uniaxial extensional flow. This knowledge is important because in processes involving dominantly extensional deformations, like the case of the formation of the LCP fibrillation, transient extensional flow properties become more important than transient or steady-shear properties. In systems characterized by disperse phase morphologies (10 and 20 wt%) the LCP acts as a plasticizer, decreasing the viscosity of the system and increasing its durability with respect to that of the matrix. On the other hand, for a system in which a co-continuous morphology is present (40 wt% LCP) fibrils and droplets deformation occurs simultaneously, leading to a much higher strain hardening and durability. Moreover, the addition of compatibilizers to the blends gives rise to an increase of the strain hardening and to a decrease of the durability, which is in accordance with the mechanical properties, namely a higher Young’s modulus and lower elongation at break, in comparison with noncompatibilized systems.     

A kinetic–hydrodynamic simulation of microstructure of liquid crystal polymers in plane shear flow

We study the microstructure formation and defects dynamics arising in liquid crystalline polymers (LCPs) in plane shear flow by a kinetic–hydrodynamic coupled model. The kinetic model is an extension of the Doi theory with a non-local intermolecular potential, including translational diffusion and density variation. LCP molecules are ensured anchoring at the boundary by an additional boundary potential, meanwhile mass conservation of LCPs holds in the whole flow region. Plane Couette flow and Poiseuille flow are studied using the kinetic–hydrodynamic model and the molecular director is restricted in the shear plane. In plane Couette flow, the numerical results predict seven in-plane flow modes, including four in-plane modes reported by Rey and Tsuji [Macromol. Theory Simul. 7 (1998) 623–639] and three new complicated in-plane modes with inner defects. Furthermore, some significant scaling properties were verified, such as the thickness of the boundary layer is proportional to molecular length, the tumbling period is proportional to the inverse of shear rate. In plane Poiseuille flow, the micro-morph is quasi-periodic in time when flow viscosity and molecular elasticity are comparable. Different local states, such as flow-aligning, tumbling or wagging, arise in different flow region. The difference of the local states, or difference of the tumbling rates in near-by regions causes defects and form branch pattern in director spatial–temporal configuration figure.     

Microstructural effects on the dynamic rheology of a discotic mesophase pitch

The dynamic rheology and accompanying microstructure of a synthetic mesophase pitch (AR-HP) is reported. The loss modulus (G″) was found to be higher than the storage modulus (G′) at all frequencies (∼0.1 to ∼100 rad/s) and temperatures (280–305 °C) tested. The slope of the low-frequency terminal zone for G′ was found to be approximately 0.8, much lower than a value of 2 that is observed for flexible chain polymers. Cross-polarized optical microscopy with full-wave retardation plate confirmed the presence of different textures of mesophase pitch processed under different conditions. While loss moduli remained fairly unchanged, finer textures led to significantly lower storage moduli. Consistent with this trend, coarsening of the microstructure during textural relaxation led to an increase in storage moduli. Therefore, for the discotic mesophase pitch, the viscous component was found to remain unaffected by the microstructure, but the elastic modulus was dependent on the orientation of layer-planes and size of the texture.     

Damage evolution and energy dissipation of polymers with crazes

Craze damage evolution and energy dissipation of amorphous polymers with crazes have been studied. A mathematical model of a single craze (SC) is proposed by adopting the fibril creep mechanism. The viscoelastic characteristics of craze fibrils are supposed to obey the Maxwell model and the craze fibrils are assumed to be compressible. The assumption of Kausch [H.H. Kausch, The role of network orientation and microstructure in fracture initiation, J. Polym. Sci. C 32 (1971) 1–44] is adopted to describe the rupture of stressed fibril bonds. The craze damage evolution and the energy dissipation equations of a SC are derived. The equations are solved numerically and the life of a SC is computed. In a significant range of far-field stress, the dissipated energy varies linearly with the stress. Using the proposed model, the uniaxial stress-strain relation of polymers with low-density craze arrays (PLDCA) is investigated. The damage evolution equation of PLDCA is derived, which shows the mathematical relation between the damage of a SC and that of PLDCA. Based on the computed results, the variation of life of PLDCA with respect to applied stress is determined. Discussions are then given to the results and some significant conclusions are drawn.     

Co-continuity interval in immiscible polymer blends by dynamic mechanical spectroscopy in the molten and solid state

The work focuses on the detection of the co-continuity window in immiscible polymer blends. The purpose of the paper is to describe how rheological techniques can help to evaluate the composition range of the co-continuous morphology through the study of a particular system: PEO/PVDF-HFP. First, the blends were characterized by selective dissolution experiments and SEM observations. Then the ability of dynamic mechanical spectroscopy to detect the co-continuity was investigated in the melt and in the solid state. The evolution of the storage modulus of molten blends with their composition at a constant low frequency gives information about the co-continuity interval, especially as far as the onset of the continuity of the PEO phase is concerned. Then the immiscibility of the polymers and the continuity of PVDF-HFP as a function of blend composition have been highlighted by means of dynamic mechanical spectrometry below the melting point of PVDF-HFP. Comparison with results from classical methods shows fair agreement.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

Orientational instability of a lyotropic nematic liquid crystal layer

The problem of periodic domain initiation in a thin lyotropic nematic liquid crystal layer is studied. This layer has a planar director initial orientation, but the anchoring energy is minimized by the homeotropic one. The periodic structures whose wave vector is perpendicular to the director exist during the director reorientation process from the planar orientation to the homeotropic one when the reorientation wave front appears. It is shown that the divergent terms of the Prank orientation elasticity energy plays an important role in this effect. The saddle-splay Prank constant and the anisotropic anchoring energy coefficient are estimated.