The Rheology of Polymer Alloys and Blends
Rheology is part of continuum mechanics. Thus, the basic principles of continuity, homogeneity and isotropy are incorporated into the basic rheological relations. The continuity principle requires that there is no discontinuity of material properties from
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THE RHEOLOGY OF POLYMER ALLOYS AND BLENDS
L. A. Utracki1 and M. R. Kamal2
1
National Research Council Canada, Industrials Materials Institute, Boucherville, QC, Canada 2
McGill University, Montreal, QC, Canada
7.1
Introduction
7.1.1
Rheology of Multiphase Systems
Rheology is part of continuum mechanics. Thus, the basic principles of continuity, homogeneity and isotropy are incorporated into the basic rheological relations. The continuity principle requires that there is no discontinuity of material properties from one mathematical point to another; homogeneity demands that there is no concentration gradient, and isotropy implies that the flow does not impose orientation on the flow elements. In multiphase systems that comprise polymer alloys and blends, these three principles are seldom obeyed [Utracki, 1995]. The rheology of the multiphase systems follows its own sub-set of principles, extending the use of the general rheological dependencies. Obviously, the basic definitions of rheological functions, e.g., viscosity, η, dynamic shear moduli, G’ and G”, dynamic shear compliance, J’ and J”, etc., are identical. However, owing to the numerous influences, viz., concentration, morphology, flow geometry, time scale, type of flow field, thermodynamic interactions between the phases, and many others, it is difficult to relate the measured rheological functions to the intrinsic physical properties of the fluid. The rheological measurements of a multiphase system should be carried out in such a way that the length-scale of the flow is significantly larger than the size of the flow element. This makes it possible to treat the multiphase system as a homogeneous one, having an average, “specific” rheological behavior. For example, Brenner [1970] showed that relative viscosity, ηr, of diluted spherical suspensions, as measured in capillary flows, depends on the (d/D)2 factor, where d is the sphere diameter and D is the diameter of the capillary — for D ≅ 10d, the error in ηr, was 1%. Thus, if 1% error is the acceptable limit, the size of the dispersion should be at least 10 times smaller than the characteristic dimension of the measuring device, viz. radius of a capillary in capillary viscometers, distance between stationary and rotating cylinders or L.A. Utracki (Ed.), Polymer Blends Handbook, 449-546. © 2003 Kluwer Academic Publishers. Printed in the Netherlands.
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L. A. Utracki and M. R. Kamal
tion gradient and orientation of domains. Both of these depend on the magnitude of strain imposed on the fluid during the measurements, thus on the type of flow. Three types of flow are mainly used in the rheological measurements: steady state shearing, dynamic shearing, and elongation. The three can be classified according to the strain, γ, vorticity, as well as uniformity of stress, σ, and strain within the measuring space (see Table 7.1). The flow characteristics listed in Table 7.1 indicate that the steady-state flows strongly affect the morphology, whereas the dynamic flows have less influence. The extensional flows are characterized by
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