Rheological behavior of a semi-crystalline polymer during isothermal crystallization

The theological behavior of a molten semi-crystalline polymer, namely, a high density polyethylene (HDPE), was investigated during isothermal crystallization from the melt, using dynamic oscillatory experiments at 1 tad/s in a parallel plates rheometer. The theological results were compared with those obtained from differential scanning calorimetry in the same conditions. During the crystallization, the molten and crystallizing polymer provides a useful model for filled polymers, the crystalline phase being the filler and the liquid phase being the matrix. In most cases, the filler can be considered to be spherical shaped (spherulites). Owing to the amorphous phase linking liquid and crystallites, the adhesion between matrix and filler in this system is perfect. The filler content increases continuously during the crystallization. This model might be used to test laws relating the theological parameters to the volume fraction of filler. Problems related to the rheometry for such systems are discussed and the key parameters insuring reproducibility and accuracy in the measurements are pointed out. The relative sensitivity of the various theological parameters (storage and loss moduli, loss angle) to structural changes of the liquid has been out forward. Some preliminary equations relating the variation of these parameters to the volume fraction of filler, through the use of simple fractal exponents have been derived and discussed in comparison with laws provided by various authors.     

Towards a rheological classification of flow induced crystallization experiments of polymer melts

Departing from molecular based rheology and rubber theory, four different flow regimes are identified associated to (1) the equilibrium configuration of the chains, (2) orientation of the contour path, (3) stretching of the contour path, and (4) rotational isomerization and a deviation from the Gaussian configuration of the polymer chain under strong stretching conditions. The influence of the ordering of the polymer chains on the enhanced point nucleation, from which spherulites grow, and on fibrous nucleation, from which the shish-kebab structure develops, is discussed in terms of kinetic and thermodynamic processes. The transitions between the different flow regimes, and the associated physical processes governing the flow induced crystallization process, are defined by Deborah numbers based on the reptation and stretching time of the chain, respectively, as well as a critical chain stretch. An evaluation of flow induced crystallization experiments reported in the literature performed in shear, uniaxial and planar elongational flows quantitatively illustrates that the transition from an enhanced nucleation rate of spherulites towards the development of the shish-kebab structure correlates with the transition from the orientation of the chain segments to the rotational isomerization of the high molecular weight chains in the melt. For one particular case this correlation is quantified by coupling the wide angle X-ray diffraction and birefringence measurements of the crystallization process to numerical simulations of the chain stretch of the high molecular weight chains using the extended Pom-Pom model in a cross-slot flow.     

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.     

Phase morphology and rheological behavior of polymer/layered silicate nanocomposites

Rheological behavior of polymer/layered silicate nanocomposites are strongly dependent not only upon their microstructure but also upon the interfacial characteristics. Different phase morphology (intercalated or exfoliated) of polymer/clay is obtained according to interfacial characteristics between polymer chains and clay. In intercalated structure, the presence of randomly oriented anisotropic stacks of silicate layers is responsible for the enhancement of both moduli. The PS/clay nanocomposites exhibit a slight enhancement at low frequency because of its simple intercalated structure and little interaction. On the other hand, the PS-co-ma/clay nanocomposites have a similar intercalated structure but exhibit a distinct plateau-like behavior at low frequency since the PS-co-ma has a strong attractive interaction with the silicate layers. Finally, PE-g-ma/clay nanocomposites display an exfoliated structure, which exhibit both a distinct plateau-like behavior at low frequency and enhanced moduli at high frequency. Percolation structure as well as large interfacial area between polymer chains and clay are responsible for the rheological behavior. Received: 20 March 2000   Accepted: 11 September 2000     

A rheological study of shear induced crystallization

The isothermal crystallization of three isotactic polypropylene (iPP) types, with different molar mass (distributions), was studied after a well defined shear treatment of the melt at an elevated temperature and a subsequent quench to the crystallization temperature. For these experiments a standard rheometer of the cone and plate configuration was used. The development of the crystallization was monitored by dynamic oscillatory measurements. Shearing in the melt was shown to enhance subsequent crystallization at lower temperatures. Not only the total shear at constant rate is of importance, but also the chosen combination of rate and shearing time. Moreover, a pronounced influence of molar mass was detected. The exploration of the melting temperatures and times which are necessary for an erasion of the memory effects showed that the effect of shearing could not completely be erased, possibly as a consequence of mechanical degradation.     

Effect of internal viscosity and elasticity of ellipsoidal macromolecules on the rheological behavior of dilute polymer solutions. rheological equations of state

The structural-continuum approach is used to obtain the Theological equations of state for dilute polymer solutions whose macromolecules can be modeled by an ellipsoid of rotation with internal viscosity and elasticity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 94–98, May–June, 1976.     

Quantitative description of rheological properties of dilute polymer solutions I. The prediction of rheological behavior at low deformation rates using the Rouse-Zimm model

Analytical expressions for the rheological properties of dilute polymer solutions at low deformation rates are established through the computation and analysis of exact Zimm's eigenvalues. These expressions include only measurable molecular parameters without the need for adjustable model parameters. In all the expressions the polydispersity of the molecular weight is considered. The theoretical predictions show good agreement with published experimental results.     

Heat transfer and crystallization kinetics during fast cooling of thin polymer films

In this work, the heat transfer phenomena taking place during the cooling of thin films of crystallizable polymers were analyzed. The thermal histories, as recorded during experimental cooling runs carried out at various cooling rates, were compared with the predictions of a general purpose numerical code, which was resulted able to capture all the main features of the process. Thus, the conditions which allow homogeneous cooling (negligible temperature gradient within the sample) or homogeneous cooling history (the same cooling history for all the positions within the sample) were predicted by the simulation code.     

Suspension-based rheological modeling of crystallizing polymer melts

The applicability of suspension models to polymer crystallization is discussed. Although direct numerical simulations of flowing particle-filled melts are useful for gaining understanding about the rheological phenomena involved, they are computationally expensive. A more coarse-grained suspension model, which can relate the parameters in a constitutive equation for the two-phase material to morphological features, such as the volume fractions of differently shaped crystallites and the rheological properties of both phases, will be more practical in numerical polymer processing simulations. General issues, concerning the modeling of linear and nonlinear viscoelastic phenomena induced by rigid and deformable particles, are discussed. A phenomenological extension of linear viscoelastic suspension models into the nonlinear regime is proposed. A number of linear viscoelastic models for deformable particles are discussed, focusing on their possibilities in the context of polymer crystallization. The predictions of the most suitable model are compared to direct numerical simulation results and experimental data.     

Acoustical validation of the rheological models for a structural bond

The purpose of this study is to characterize by ultrasound a bonded structure metal/adhesive/metal. At first, we investigate the guided modes of the structure for the adhesive layer in its entirety; this is the exact model. Secondly, we assume that the adhesive layer is described by one geometrical interface, with a superficial distribution of longitudinal and transversal springs with or without mass; this is the rheological model. A comparison of the guided modes for the two models allows to determinate the validity limits for the rheological modelling and define the equivalent stiffness coefficients and the mass as a function of the frequency. Some cutoff-frequencies are better evaluated when the springs mass is taken into account.     

Homogeneous rheological behavior of nanoparticle-based melt

The present work explores nonlinear rheological behavior of a strongly viscoelastic paste made of nano-sized polybutadiene particles. Apart from conventional rheometric measurements, particle-tracking velocimetric observations are carried out to determine the macroscopic state of deformation during startup shear and after step strain. Despite its highly nonlinear rheological characteristics, the system shows no sign of inhomogeneous response to large shear deformations in sharp contrast to well-entangled polymeric liquids made of linear chains. Apparently strongly nonlinear rheological behavior can occur in absence of inhomogeneous macroscopic deformation.     

In-line measurement of rheological properties of polymer melts

Shear viscosity (), first normal stress difference (N ₁), and extensional viscosity ( _E ) of polymer melts measured under processing conditions are important in process modeling, quality control, and process control. A slit rheometer that could simultaneously measure , N ₁, and the planar extensional viscosity ( _p ) was designed and tested by attaching it in-line to a laboratory model single-screw extruder. A tube (circular cross-section) rheometer to measure and the uniaxial extensional viscosity ( _u ) simultaneously was also designed and tested. Two commercial grades of LDPE (low density polyethylene) with melt index values of 6 and 12 were used as test materials for the study. Exit and hole pressure methods were used to estimate N ₁, and the entrance pressure drop method using the analyses of Cogswell, Binding, and Gibson (the last analysis used with the axisymmetric case only) was used to estimate _E .The hole pressure method was considered better than the exit pressure method to estimate N ₁ (due to the greater susceptibility of the latter to experimental errors). From the hole pressure method N ₁ was obtained from 100 kPa to 500 kPa over a range of shear rates from 40 s^–1 to 700 s^–1. Among the analyses used to estimate the extensional viscosity, Cogswell's is recommended due to its simpler equations without loss of much information compared to the other analyses. The range of extension rates achieved was 1 to 30 s^–1. The combination of the hole pressure and entrance pressure drop methods in a slit rheometer is a feasible design for a process rheometer, allowing the simultaneous measurement of the shear viscosity, first normal stress difference and planar extensional viscosity under processing conditions. Similarly, combining the entrance pressure drop measurements with a tube rheometer is also feasible and convenient.     

Process of selective laser sintering of polymer powders: Modeling,simulation, and validation

Selective laser sintering (SLS) of polymer powders involves multiphysical transient phenomena. A numerical tool for simulating such a process is developed on the basis of the reliable modeling of the corresponding thermo-physical transient phenomena and appropriate numerical methods. The present paper addresses modeling, simulation, and validation aspects that are indispensable for studying and optimizing SLS process. The coupled multiphysical models are detailed, and the numerical tool based on the finite volume method is presented, with validations in terms of numerical and physical accuracy, by considering the shrinkage involved in the process and the successive layers deposition. A parametric analysis is finally proposed in order to test the reliability of the model in terms of representing real physical phenomena and thermal history experienced by the material during the process.     

Peculiar features in the rheological behavior of electrorheological suspensions

Studies have been made of concentrated (up to 60%) diatomite suspensions in transformer oil, the structure and theological properties of which depend on an applied electric field. Studies have been conducted of steady-state and transient regimes of straining involving continuous and periodic shear. The structure in such suspensions is formed in the presence of an electric field of 10^–3 –10² duration. The suspensions under continuous stationary strain behave as non-Newtonian fluids with a yield stress dependent on electric intensity. Under periodic deformation conditions the test suspensions exhibit elasticity which abruptly diminishes with increasing deformation amplitude.     

Quantitative description of rheological properties of dilute polymer solutions

The Rouse-Zimm model has been generalized to describe the rheology of dilute polymer solutions at moderate shear rates by allowing for a reduced-shear-rate dependent slippage of the carrier solvent in the neighbourhood of the polymer coil with respect to the macroscopic continuum. A comparison of the theoretical predictions with published viscosity data for monodisperse polymer systems shows good agreement. Thus it appears to be sufficient to measure the intrinsic viscosity in order to estimate all the material functions of interest for the steady and dynamic shear flow of dilute polymer solutions.     

Effect of ring closure on rheological behavior

A comparison is given between the rheological behavior of dilute solutions of linear polymers and ring-shaped polymers. Both types of molecules are modeled as freely jointed bead-spring structures, with Hookean springs. It is shown that the ring closure results in lowering the viscosity by a factor of two regardless of the number of beads, N. The first normal stress coefficient is lowered by a factor between 5 (for N = 3) and 8 (for N → ∞). The form of the constitutive equation for rings is the same as that for chains, but the spectrum of relaxation times is altered. Formal expressions are obtained for the ring configurational distribution function and the single link distribution function for an arbitrary time-dependent homogeneous flow.     

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.     

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.