Viscoelastic behavior of polymerizing systems

Experimental data of the dynamic viscoelastic properties, storage modulus (G′), loss modulus (G′′), and phase shift (δ) as well as of the viscosity, η, are reported for the polymerization of a free radical polymerization system (methyl methacrylate) which exhibits the Trommsdorff effect. A rheometer-reactor assembly developed in our laboratory is used for this purpose. It is observed that in the early stages of reaction, data lie in the terminal zone. As the polymerization progresses, the Trommsdorff effect leads to a sharp increase in both the polymer concentration and the weight average molecular weight, and the viscoelastic properties then lie in the entanglement zone. A modulus crossover point (when G′ = G′′) is identified that could be used as an identification of the point where the Trommsdorff effect starts assuming significance. Received: 17 September 1998 Accepted: 9 December 1998     

Nonlinearly Viscoelastic Nanoindentation of PMMA Under a Spherical Tip

The Oliver-Pharr method has been well established to measure Young’s modulus and hardness of materials without time-dependent behavior in nanoindentation. The method, however, is not appropriate for measuring the viscoelastic properties of materials with pronounced viscoelastic effects. One well-known phenomenon is the formation of unloading “nose” or negative stiffness during unloading that often occurs during slow loading-unloading in nanoindentation on a viscoelastic material. Most methods in literature have only considered the loading curve for analysis of viscoelastic nanoindentation data while the unloading portion is not analyzed adequately to determine the nonlinearly viscoelastic properties. In this paper, nonlinearly viscoelastic effects are considered and modeled using the nonlinear Burgers model. Nanoindentation was conducted on poly-methylmethacrylate (PMMA) using a spherical indenter tip. An inverse problem solving approach is used to allow the finite element simulation results to agree with the nanoindentation load–displacement curve during the entire loading and unloading stage. This approach has allowed the determination of the nonlinearly viscoelastic behavior of PMMA at submicron scale. In addition, the nanoindentation unloading “nose” has been captured by simulation, indicating that the negative stiffness in the viscoelastic material is the result of memory effect in time-dependent materials.     

Stress relaxation behavior of PMMA/PS polymer blends

In this work, the stress relaxation behavior of PMMA/PS blends, with or without random copolymer addition, submitted to step shear strain experiments in the linear and nonlinear regime was studied. The effect of blend composition (ranging from 10 to 30 wt.% of dispersed phase), viscosity ratio (ranging from 0.1 to 7.5), and random copolymer addition (for concentrations up to 8 wt.% with respect to the dispersed phase) was evaluated and correlated to the evolution of the morphology of the blends. All blends presented three relaxation stages: a first fast relaxation which was attributed to the relaxation of the pure phases, a second one which was characterized by the presence of a plateau, and a third fast one. The relaxation was shown to be faster for less extended and smaller droplets and to be influenced by coalescence for blends with a dispersed phase concentration larger than 20 wt.%. The relaxation of the blend was strongly influenced by the matrix viscosity. The addition of random copolymer resulted in a slower relaxation of the droplets.     

Rheology and structural changes of plasticized zeins in the molten state

Zeins, storage proteins from maize, are suitable for making biobased thermoplastic materials. The rheological behavior of a commercial zein plasticized with 20 w% glycerol was studied in the molten state by steady-state flow experiments in extrusion conditions and oscillatory rheometry. For low residence times, a shear-thinning viscoelastic behavior was observed, with G″ exceeding G′. After 300 s at 130 °C, the complex viscosity |η ^?|?=?7?×?10³ ω ^?0.46 was found to be similar to that of thermoplastic polymer melts used in fused deposition modeling. However, the ratio between the exponents of the power laws describing G′(ω) and G″(ω) did not meet the typical value of 2 for entangled polymer melts. Moreover, for longer residence times, the viscosity increased and a gelation phenomenon was observed with a crossing over of G′(ω) and G″(ω). Gel times ranged from 6000 s at 120 °C to 1700 s at 150 °C. The evolution of the macromolecular structure assessed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis and high-performance size exclusion chromatography suggested that this gelation phenomenon involves various types of covalent and non-covalent cross-links. Disulfide bonds played a significant role in gelation kinetics despite a very low cysteine residue content in the protein primary structure (about 1 mol%). These results suggested that plasticized zeins initially behave like a low-viscosity non-entangled polymer melt, before cross-linking progressively led to a continuous network.     

Viscoelastic fluid behavior in annulus using Giesekus model

An analytical solution is derived for the steady state, laminar, axial, fully developed flow of a viscoelastic fluid obeying the Giesekus model without any retardation time in a concentric annulus.An approximation is used for the estimation of radial normal stress. The influence of Deborah number (De) and the mobility factor (α) on the velocity profile, axial pressure gradient are investigated and results show strong effects of mobility factor and Deborah number on above parameters.     

Stress relaxation behavior of co-continuous PS/PMMA blends after step shear strain

Stress relaxation probing on the immiscible blends is an attractive route to reveal the time-dependent morphology–viscoelasticity correlations under/after flow. However, a comprehensive understanding on the stress relaxation of co-continuous blends, especially after subjected to a shear strain, is still lacking. In this work, the stress relaxation behavior of co-continuous polystyrene/poly(methyl methacrylate) (50/50) blends with different annealing times, strain levels, and temperatures was examined under step shear strain and was correlated with the development of their morphologies. It was found that co-continuous blends display a fast relaxation process which corresponded to the relaxation of bulk polymer and a second slower relaxation process due to the recovery of co-continuous morphology. The stress relaxation rates of co-continuous blends tend to decrease due to the coarsening of instable co-continuous structure during annealing. Furthermore, the stress relaxation of the co-continuous blends is strongly affected by the change of viscosity and interfacial tension caused by the temperature. The contribution of morphological coarsening, viscosity, and interfacial tension variation on the stress relaxation behavior of co-continuous blends was discussed based on the Lee–Park model and time–temperature superposition principle, respectively.     

The stress relaxation of molten PMMA at large deformations and its theoretical interpretation

Summary The stress relaxation behaviour of molten PMMA under large tensile deformations has been studied. Maximum values of the extension ratio were larger than 3.5. Similarly with previous results, the time dependence of the relaxing stress was found to be approximatively the same at all deformations. The deformation dependence was compared with the predictions of a theory byDoi andEdwards as well as with a modification of that theory which proves to agree better with the experimental results.

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Zusammenfassung Es wurde das Spannungsrelaxations-Verhalten von PMMA-Schmelzen unter großer Dehnbeanspruchung untersucht. Die maximalen Dehnungen waren dabei größer als 3,5. Ähnlich wie bei früheren Untersuchungen ergab sich die Zeitabhängigkeit der relaxierenden Spannung bei allen Deformationen als nahezu gleich. Der Deformationsverlauf wird mit den Voraussagen der Theorie vonDoi undEdwards, sowie denjenigen einer modifizierten Theorie verglichen. Es erweist sich, daß letztere die experimentellen Ergebnisse noch besser zu beschreiben vermag.

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With 5 figures     

Temperature dependence of the interfacial tension of PS/PMMA, PS/PE, and PMMA/PE blends

The effect of temperature on the interfacial tension for PS/PMMA, PS/PE, and PMMA/PE was measured using the imbedded fiber retraction method. Interfacial tensions for PS/PMMA, PS/PE, and PMMA/PE were measured over temperature ranges of 160–250 °C, 140–220 °C, and 140–220 °C, respectively. The interfacial tension was found to follow a dependence of 3.6–0.013 T dyn/cm, 7.6–0.051 T dyn/cm and 11.8–0.017 T dyn/cm for PS/PMMA, PS/PE, and PMMA/PE, respectively. Comparison of the data with the mean field theory of Helfand and Sapse were made; however, a simple linear fit to the data described the temperature dependence in the experimental window as well as the predictions of the mean field theory. Received: 6 July 1999 Accepted: 23 March 2000     

Rheological behavior in the transient state of PP/EPDM blends with carbon nanofillers

The rheological properties in the transient state of PP/EPDM blends with carbon nanofillers had been studied. The carbon nanofillers were incorporated into molten EPDM in an internal mixer at 150 °C. The rheological variables were determined in rotational rheometry at constant temperature of 200 °C. The results suggest that the magnitude of the difference of the normal stress differences (N₁-N₂) of PP/EPDM blends through the time, with and without nanofillers, and has a transition cycle from positive to negative values and vice versa, at constant and at zero shear rate in previously sheared samples. At constant shear rate, the transition cycle is random; meanwhile, it is constant at zero shear rate. This behavior is attributed to the polymeric chain movement, considering that the sheared samples have two molecular reorder processes: an immediate mechanism and another one slower. The fastest reorder process is attributed to the polymeric chains entanglement forming non-stable and stressed molecular structures. In the other hand, the second process is referred to the molecular mobility that takes place inside the stressed entangled polymer, in such a way that its structure tends to molecular stability as the rest time increases.     

Viscoelastic state of a three-layer cylindrical shell during impulsive thermomechanical loading

Belorussian Institute of Railroad Transportation Engineers, Gomel'. Translated from Prikladnaya Mekhanika, Vol. 27, No. 3, pp. 46–52, March, 1991.     

Identification of the state equation in complex non-linear systems

Building on the basic idea behind the Restoring Force Method for the non-parametric identification of non-linear systems, a general procedure is presented for the direct identification of the state equation of complex non-linear systems. No information about the system mass is required, and only the applied excitation(s) and resulting acceleration are needed to implement the procedure. Arbitrary non-linear phenomena spanning the range from polynomial non-linearities to the noisy Duffing-van der Pol oscillator (involving product-type non-linearities and multiple excitations) or hysteretic behavior such as the Bouc-Wen model can be handled without difficulty. In the case of polynomial-type non-linearities, the approach yields virtually exact results for sufficiently rich excitations. For other types of non-linearities, the approach yields the optimum (in least-squares sense) representation in non-parametric form of the dominant interaction forces induced by the motion of the system. Several examples involving synthetic data corresponding to a variety of highly non-linear phenomena are presented to demonstrate the utility as well as the range of validity of the proposed approach.     

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.     

The phase-lag concept in the thermal behavior of lumped systems

The phase-lag concept in the wave theory of heat conduction is extended to describe the thermal behavior of lumped systems. It is assumed that a phase-lag exists between the convection heat flux from the lumped system and the temperature difference between the lumped system and its surroundings. It is found that the dimensionless delay time τ is an important parameter in specifying the qualitative behavior of the lumped system. The phase-lag concept has no significant effects on the thermal behavior of lumped systems having τ < 1/4. In this case, the classical theory without delay can give an accurate prediction for the system thermal behavior. On the other hand, the phase-lag concept changes the quantitative and qualitative behavior of systems having τ > 1/4 and these changes are enhanced as τ increases. However, it is shown that the thermal behavior of systems having τ > 1/4 violates the second law of thermodynamics. The physical reasoning for this violation is explained. Also, the phase-lag concept is extended to describe the thermal behavior of composite system which consists of two domains each is lumped at different temperature.     

Exploring the qualitative behavior of uncertain dynamical systems

The global behavior of uncertain nonlinear systems by means of the cell mapping method is investigated. The systems under consideration are governed by ordinary differential equations where uncertainty is characterized by a bounded stationary noise process. In order to make cell mapping methods applicable to this particular situation generalizations of the theory become necessary. The numerical approach is based on a reformulation of the dynamics in terms of a Markov process whose qualitative behavior is analyzed. We demonstrate the usefulness of the presented scheme in the engineering field while addressing an example problem from technical mechanics.