Inference of polymer structure by simultaneous analysis of chromatographic and rheological measurements

A Bayesian framework that integrates chromatographic and rheological measurements to infer the structure of an unknown binary linear blend, with a high molar mass tail, is proposed and explored. A visualization method based on clustering of multidimensional data is introduced to facilitate the comprehension of the joint probability distribution that results from the Bayesian analysis. The relationship between the rheological and chromatographic data is found to be synergetic: the simultaneous analysis of both sets of data circumvents problems of degeneracy and insensitivity associated with rheology and chromatography, respectively.     

Phase structure change and ER effect in liquid crystalline polymer/dimethylsiloxane blends

The mechanism of the electrorheological (ER) effect in two types of liquid crystalline polymer (LCP)/dimethylsiloxane (DMS) blends was investigated by rheological measurements and by structure observation under electric field and shear flow. The results show that the phase structures of these immiscible blends can be categorized into slipping (low viscosity) and non-slipping (high viscosity) states. In the non-slipping state, higher viscosity LCP domains connect the electrodes. In the slipping state, on the other hand, LCP domains do not connect the electrodes and the shear is mainly confined in the lower viscosity DMS domains. The ER effect (electrically induced viscosity increase) originates from the electrically induced slipping to non-slipping transition. In one of the blends, the ER effect occurs only at high shear rate, since this blend is in non-slipping state even under no field if the shear rate is low. Received: 29 April 1997 Accepted: 3 November 1997     

Quantitative rheological evaluation of phase inversion in two-phase polymer blends with cocontinuous morphology

 The present work is focused on the rheological properties of two-phase polymer blends in the phase inversion region. A large number of PS/PMMA- and PSAN/PMMA-blends has been investigated in order to establish a rheological criterion which allows the quantitative determination of the phase inversion concentration φ_PI by rheological means. Three rheological criteria based on the viscous and elastic blend properties such as maximum of dynamic viscosity η′, slope of G′, and maximum of G′ at a constant evaluation frequency have been tested. By correlating the rheological results to data from quantitative morphological analysis we could prove that the chosen rheological criteria are differently suitable for the determination of φ_PI. It has turned out that the G′ criterion is the most robust and most suitable one yielding an excellent correlation with morphological data. Based on these findings we propose a new simple equation for the prediction of φ_PI-values. Received: 14 March 2001 Accepted: 15 May 2001     

The effect of instrument compliance on dynamic rheological measurements

The effect of instrument compliance on ERD and forced oscillation experiments is examined. A relationship for the determination of correct experimental conditions in ERD measurements is presented. It is concluded that the applicability of shear compliance corrections is doubtful whenever their magnitude is over 50% of the measured quantity and |G ^*| > 5 × 10⁵ Pa. Compressive compliance is found to have a negligible effect in all practical cases. Torsional compliance can be important in oscillatory experiments when sample torsional stiffness is high relative to instrument stiffness. Numerical values for Rheometrics equipment are used throughout the discussion.     

Some general rheological properties of dilute polymer solutions predicted from intrinsic viscosity measurements

Expressions for the rheological properties of dilute polymer solutions at low and moderate deformation rates are established through the computation and analysis of exact Zimm's eigenvalues. It is shown that they can be expressed in terms of measurable parameters from intrinsic viscosity data. Under moderate deformation rates one needs to introduce a slippage between the solvent and the smoothed polymer to be able to describe shear-thinning behaviour.     

Quasi-linear rheological behaviour of polymer melts: Comparison between mechanical and improved flow birefringence measurements

Summary The latest improvement of the rotor unit (cone- and plate-type) for the measurement of the flow-birefringence of polymer melts is described. As a consequence of this improvement, the influence of parasitic birefringences, as produced in the corners near the windows, is minimized. It is shown that the limitation of the range of available rates of shear, as experienced with previous versions of the apparatus, was due to those parasitic birefringences which predominated at rates of shear where the main birefringence caused an optical path difference of one, two or more whole wavelengths (fringes) and was, as a consequence, virtually zero. This explains why great troubles were experienced in particular with polymers possessing a high back-bone anisotropy. The validity of the linear stress-optical rule up to shear rates, where melt fracture occurs in capillary flow, is well understood in terms of the wriggling motion of chain molecules. Comparison with direct mechanical measurements was very satisfactory.

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Zusammenfassung Eine Beschreibung der jüngsten Verbesserung an der Rotorzelle (Kegel-Platte-Typ) für die Messung der Strömungsdoppelbrechung polymerer Schmelzen wird gegeben. Als Folge dieser Verbesserung wird der Einfluß der parasitären Doppelbrechung, die in den Ecken neben den Fenstern auftritt, minimalisiert. Es wird gezeigt, daß die Begrenzung des Bereiches der verfügbaren Schergeschwindigkeiten, wie sie in früheren Versionen des Apparates gefunden wurde, auf das Vorherrschen der parasitären Doppelbrechungen bei Schergeschwindigkeiten zurückzuführen ist, bei denen die Hauptdoppelbrechung optische Weglängen von einer, zwei oder mehreren ganzen Wellenlängen verursacht und daher effektiv null wird. Dies erklärt, warum große Schwierigkeiten gerade bei solchen Polymeren auftraten, die eine stärkere Kettenanisotropie aufweisen. Die Gültigkeit der linearen spannungsoptischen Regel bis zu Schergeschwindigkeiten, bei denen in der Kapillaren Schmelzbruch auftritt, kann man aufgrund der Ringelbewegung der Makromoleküle gut verstehen. Ein Vergleich mit direkten mechanischen Messungen ergab sehr befriedigende Ergebnisse.

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With 8 figures and 2 tables     

The effect of liquid crystal structure on the rheological properties of nitrocellulose-dimethylacetamide solutions

Solutions of Pyro grade nitrocellulose (NC) in dimethyl acetamide (DMA), containing between 42.5% and 60% NC (w/w), have been studied by differential scanning calorimetry and polarised light microscopy. The results showed that NC forms a lyotropic liquid crystal structure in DMA. A transition from the liquid crystal phase to an isotropic phase occurred over the temperature range 27 °C to 67 °C, and the enthalpy of transition increased with NC concentration. Rheological properties were determined using an extrusion rheometer with a slit die. The solutions were shown to have a yield stress for flow which increased with increasing NC concentration. The solutions were also found to be thixotropic.     

On-line measurements of the rheological properties of fermentation broth

The paper is concerned with measurements of rheological properties of fermentation broth. An on-line rheometer, Rheohelix-1, based on the application of a helical screw impeller rotating in a draught tube has been constructed. The instrument was used for measurements of the rheological parameters of fermentation broth of Aspergillus niger in a submerged fermentation process. The results of rheological and some standard measurements have been compared and proved the applicability of the instrument.Presented at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Interfacial activity of reactive compatibilizers in polymer blends

The influence of a reactive block copolymer compatibilizer on the breakup of polymer fibers in the quiescent conditions is investigated using the breaking thread method (BTM). The compatibilizer is either localized at the interface of two polymers or incorporated in the bulk of thread phase. Moreover, the nominal interfacial tension between two polymers is estimated as a function of compatibilizer concentration for both types of samples using Tomotika theory. It is shown that assembling of compatibilizer molecules at the interface of two immiscible polymers can result in very different dynamic of thread breakup compared to samples containing the compatibilizer in the bulk phase. We observe a reduction in the rate of thread breakup (kinetic of stabilization) when compatibilizer is incorporated in the bulk of thread phase. Such effect is more significant when compatibilizer is localized at the interface of two fluids. Additionally, the mode of thread breakup is sensitive to the compatibilizer location since a beads-on-a-string (BOAS) morphology is observed when compatibilizer is localized at the interface. In conclusion, the usual attribution of interfacial activity of compatibilizer in polymer blends may be originated from their random presence at the interface rather than thermodynamically favored diffusion to the interface.     

Investigation of the band texture occurring in acetoxypropylcellulose thermotropic liquid crystalline polymer using rheo-optical, rheological and light scattering techniques

The optical evolution of the band texture occurring in acetoxypropylcellulose thermotropic polymer has been investigated as a function of temperature and primary shear rate. Two distinct kinds of band texture were observed which are referred to here as the `fast' and `slow' band textures with regard to their rate of evolution. The fast band texture appears very quickly following the cessation of shear and then disappears. The slow band texture is much finer than the fast band texture and appears to exist both during and after the appearance of the fast band texture. The evolution behaviour of the fast band texture is interpreted in terms of the shifting of a three-region evolution curve. Particular attention has been paid to investigating the influence of temperature on the formation of the fast band texture. Rheo-optical experiments show that the minimum shear rate required to form the fast band texture increases as a power-law function of the temperature. By subsequently performing steady flow measurements over a range of temperatures, the minimum shear stress required to form the fast band texture has been found to be independent of temperature and to increase linearly with the molecular weight of the sample. Results obtained from dynamic tests are compared with similar tests conducted previously on a lyotropic hydroxypropylcellulose water solution (Harrison and Navard 1999). The results of the comparison provide evidence in support of a connection between the behaviour of the dynamic functions and the optical evolution of the slow band texture. These results suggest that nematic and cholesteric fluids can relax through several different possible mechanisms, each of which results in a periodic band texture following the cessation of shear. Received: 2 March 1999/Accepted: 26 July 1999     

A rheological criterion to determine the percolation threshold in polymer nano-composites

In this work, the effect of multi-walled carbon nanotube (CNT) and montmorillonite nanoclay on polymer chain dynamics is investigated around the percolation concentration for systems based on ethylene vinyl acetate (EVA) copolymer. Then, the results obtained are compared with literature data to determine if, regardless of particle characteristics, a universal rheological behavior can be detected at percolation. To do so, rheological analyses are performed under small amplitude oscillatory shear (SAOS), large amplitude oscillatory shear (LAOS), and transient shear step. SAOS data showed that, while the dynamics related to the Rouse relaxation time (τ _R) were not significantly influenced, the reptation relaxation time (τ _D) was strongly increased by the presence of nanoparticles. In step shear transient tests, the critical shear rate \( \left({\dot{\upgamma}}_{\mathrm{cr}}\right) \) for overshoot appearance was decreased due to chain confinement, and the formation of particle network strongly increased the level of stress overshoot. Particle networks increased significantly the nonlinear parameters (I ₃/I ₁ and Q ₀) obtained under LAOS and quantified by FT-rheology. In all measurements, due to the higher surface area associated to its size and density as well as hollow structure, CNT showed stronger effects compared to clay. Moreover, while the percolation concentration was different for CNT and clay, both systems showed similar behavior at percolation: a 0.5 scaling for G′ indicating a Rouse-dominated behavior.     

Representation of the rheological properties of polymer melts in terms of complex fluidity

In dynamic rheological experiments melt behavior is usually expressed in terms of complex viscosity ^* () or complex modulusG ^* (). In contrast, we attempted to use the complex fluidity ^* () = 1/µ ^* () to represent this behavior. The main interest is to simplify the complex-plane diagram and to simplify the determination of fundamental parameters such as the Newtonian viscosity or the parameter of relaxation-time distribution when a Cole-Cole type distribution can be applied. ^* () complex shear viscosity - () real part of the complex viscosity - () imaginary part of the complex viscosity - G ^* () complex shear modulus - G() storage modulus in shear - G() loss modulus in shear - J ^* () complex shear compliance - J() storage compliance in shear - J() loss compliance in shear - shear strain - rate of strain - angular frequency (rad/s) - shear stress - loss angle - ^* () complex shear fluidity - () real part of the complex fluidity - () imaginary part of the complex fluidity - ₀ zero-viscosity - ₀ average relaxation time - h parameter of relaxation-time distribution     

Diffusion effects on the interfacial tension of immiscible polymer blends

Most methods of measuring the interfacial tension between two immiscible polymers are based on the analysis of the shape that a drop of one polymer immersed in the other one exhibits under the action of flow or gravity. In such a situation, the small, yet nonzero mutual solubility between the two polymers acts toward mass transfer between the drop and the surrounding fluid. In this work, diffusion effects on the interfacial tension of the pair polyisobutylene/polydimethylsiloxane have been investigated by drop deformation under shear flow. When the drop was made of polyisobutylene, drop size decreased with time due to diffusion. Drop shrinkage was associated with a significant increase in interfacial tension, until an apparent plateau value was reached. The effect was attributed to a selective migration of molecular weights, which would act to enrich the drop with higher molar mass material. To support such an interpretation, drop viscosity was evaluated by drop shape analysis and it was actually found to increase with time. In some cases, the ratio between drop and continuous phase viscosity became higher than the critical value for drop breakup in shear flow. Upon inverting the phases (i.e., when the drop was made of polydimethylsiloxane), no significant transient effects were observed. In the light of these results, the problem of what are the correct values of interfacial tension and viscosity ratio for a polymer blend of a certain composition will also be discussed. Received: 25 January 1999 Accepted: 24 May 1999     

Process validation of the normalized rheological function behavior during polymer crystallization

The film casting process of an isotactic polypropylene was adopted as the source of data to evaluate the behavior of a crystallizing polymer. The increase in viscosity due to the crystallization was quantified, and a model was proposed to estimate the normalized rheological function (NRF) during the process. The estimation was based also on the availability of rich sets of data, i.e., the polymer temperature and crystallinity, the film velocity and width distribution along the draw direction, gathered during the process. The quasi-experimental NRF evolutions were compared with just two of the very numerous hardening models proposed in literature, and the main result is that the process is coherent with the choice of an NRF model which predicts the increase in viscosity only for substantial crystallinity amount.     

Investigation of vapor condensation in a vapor-air jet

A vapor-air axisymmetric submerged jet was calculated for various environmental conditions and a number of values of vapor concentration and temperature of the vapor-air mixture in the initial section of the jet. The process of condensation in a vapor-air jet was investigated experimentally with the use of the laser-optical method of measuring the degree of dispersion and concentration of condensate droplets.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 142–144, May–June, 1976.     

Peculiarities of rheological behavior of filled polymer melts in uniaxial stretching

The peculiarities of theological behavior of filled polymer melts in uniaxial extension in a wide range of strain rates (from 2× 10^–5 to 1 × 10^–1 s^–1) have been studied. Linear polyethylene and 1,4-polybutadiene containing up to 21.5 vol.% of carbon black, silica, calcium carbonate or glass fibers were used. It has been found that the transition from uniform to nonunion stretching due to the neck formation is typical of all specimen compositions, when they approach steady-state straining. Depending on the structure and rheological characteristics of the compositions general conditions for this transition have been established. The general regularities for varying the rheological characteristics of filled polymers in the course of their uniform stretching have been recognized. These regularities depend on the molecular characteristics of the polymer matrix and the presence in the compositions of the structural framework of high disperse filler or the network formed by the entangled fibers. Using polyethylene compositions it has been shown that the introduction of small amounts of disperse or fibrous fillers can give rise to acceleration of the relaxation process in filled polymers.     

The influence of matrix viscoelasticity on the rheology of polymer blends

We examine the effects of matrix phase viscoelasticity on the rheological modeling of polymer blends with a droplet morphology. Two contravariant, second-rank tensor variables are adopted along with the translational momentum density of the fluid to account for viscoelasticity of the matrix phase and the ellipsoidal droplet shapes. The first microstructural variable is a conformation tensor describing the average extension and orientation of the molecules in the matrix phase. The other microstructural variable is a configuration tensor to account for the average shape and orientation of constant-volume droplets. A Hamiltonian framework of non-equilibrium thermodynamics is then adopted to derive a set of continuum equations for the system variables. This set of equations accounts for local conformational changes of the matrix molecules due to droplet deformation and vice versa. The model is intended for dilute blends of both oblate and prolate droplets, and droplet breakup and coalescence are not taken into account. Only the matrix phase is considered as viscoelastic; i.e., the droplets are assumed to be Newtonian. The model equations are solved for various types of homogeneous deformations, and microstructure/rheology relationships are discussed for transient and steady-state conditions. A comparison with other constrained-volume rheological models and experimental data is made as well.     

On the equivalence of simplest non-linear rheological equations for viscoelastic polymer media

Some equivalence conditions are formulated for non-linear models of polymer melts and solutions that are analogous to known conditions for three-constant linear rheological equations. The resulting model is analysed in simple shear and elongational flows. The kinematics of finite elastoviscous strains is considered in an appendix.