Polymer rheology shear strain

The existence of yield stress Y at shear strains seems to be the most typical feature of rheological properties of highly filled polymers. A formal meaing of this term is quite obvious. It means that at stresses lower than Y the material behaves like a solid, i.e. it deforms only elastically, while at stresses higher than Y, like a liquid, i.e. it can flow. At a first approximation it may be assumed that the material is not deformed at all, if stresses are lower than Y. In this sense, filled polymers behave as visco-plastic media with a low-molecular and low-viscosity dispersion medium. This analogy is not random as will be stressed below when the values of the yield stress are compared for the systems with different dispersion media. The existence of yield stress in its physical meaning must be correlated with the strength of a structure formed by the interaction between the particles of a filler. 

Philippoff, W., Gaskins,F.H., Brodnyan, J.G. Flow birefringence and stress. V. Correlation of recoverable shear strains with other rheological properties of polymer solutions. J. Appl. Phys. 28,1118-1123 (1957). 

The analysis of mould filling requires rheological and thermal data for the plastic, and the mould dimensions. Polymer manufacturers usually provide shear flow curves at a range of temperatures these can be approximated by a power law relationship over a limited range of shear strain rates. In the days before computer analysis, flow lengths of short shots were determined in spiral test cavities, as a function of the injection pressure. However, the geometry of this constant cross section mould differs so much from most other moulds that the flow lengths in the two types of mould do not correlate well. 

For characterization of polymer blends, low strain dynamic rheological measurements are preferred over steady-state shearing (e.g., in a capillary viscometer). Since... 

Most polymer processes are dominated by the shear strain rate. Consequently, the viscosity used to characterize the fluid is based on shear deformation measurement devices. The rheological models that are used for these types of flows are usually termed Generalized Newtonian Fluids (GNF). In a GNF model, the stress in a fluid is dependent on the second invariant of the stain rate tensor, which is approximated by the shear rate in most shear dominated flows. The temperature dependence of GNF fluids is generally included in the coefficients of the viscosity model. Various models are currently being used to represent the temperature and strain rate dependence of the viscosity. 

Molten polymers are viscoelastic materials, and so study of their behaviour can be complex. Polymers are also non-ideal in behaviour, i.e. they do not follow the Newtonian liquid relationship of simple liquids like water, where shear-stress is proportional to shear strain rate. Unlike Newtonian liquids, polymers show viscosity changes with shear rate, mainly in a pseudoplastic manner. As shear rate increases there is a reduction in melt viscosity. This is true of both heat-softened plastics and rubbers. Other time-dependent effects will also arise with polymer compounds to complicate the rheological process behaviour. These may be viscosity reductions due to molecular-mass breakdown or physical effects due to thixotropic behaviour, or viscosity increases due to crosslinking/branching reactions or degradation. Generally these effects will be studied in rotational-type rheometers and the extrusion-type capillary rheometer. 

DPD simulation has been applied to predict the rheological and viscoelastic behaviors of nanopartide-polymer nanocomposites and to examine the effects of particle shape, particle-particle interaction, and partide dispersion states of such behaviors. It was found that partide-particle interaction has a distinct effect on the dynamic shear modulus. Havet and Isayev [39,40] proposed a rheological model to predict the dependence of dynamic properties of highly interactive filler-polymer mixtures on strain and the dependence of shear stress on shear rate. 

The raison d itre of this book is that rheological properties of the melt are very sensitive to the molecular structure of a polymer. Rheological properties describe how stress develops in a sample undergoing a prescribed deformation. They also describe the deformation that is caused by a prescribed stress. The most fundamental rheological experiment for a viscoelastic material is a step-strain test, and for melts this nearly always means a step shear strain. In a step shear-strain test, a sample is subjected to a sudden shear strain of magnitude, % at time t=0. The shear stress is measured as a fimction of time, and the ratio of the stress to the applied strain defines the relaxation modulus, G t). 

Flows were also utilized to direct the assembly of submicrometer-diameter particles in ID structures. For dilute dispersions, their rheological characteristics such as viscosity and elasticity determined the type of the resulting stmcture. When particles are dispersed in a polymer solution, melt, or concentrated surfactant solution, flow can induce anisotropic viscoelastic stresses which govern ID particle self-assembly. The assembly of particles occurs at high shear rates such that the Weissenberg number (the ratio of the first normal stress difference over the shear stress) of the suspending medium exceeds a critical value. In addition to the shear rate and shear strain, particle concentration, polydispersity, and particle interaction potentials play a major role in the formation of ID stmctures. One example includes shear-induced... 

Experimentally, the dynamic shear moduli are usually measured by applying sinusoidal oscillatory shear in constant stress or constant strain rheometers. This can be in parallel plate, cone-and-plate or concentric cylinder (Couette) geometries. An excellent monograph on rheology, including its application to polymers, is provided by Macosko (1994). 

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