Properties of Viscoelastic Liquids

This section summarizes results of the phenomenological theory of viscoelasticity as they apply to homogeneous polymer liquids. The theory of incompressible simple fluids (76, 77) is based on a very general set of ideas about the nature of mechanical response. According to this theory the flow-induced stress at any point in a substance at time t depends only on the deformations experienced by material in an arbitrarily small neighborhood of that point in all times prior to t. The relationship between stress at the current time and deformation history is the constitutive equation for the substance. 

The stress tensor describes the forces transmitted to an element of material through its contacts with adjacent elements (78). Traction is the force per unit area acting outwardly on the material adjacent to a material plane, and transmitted through its contact with material across the plane. If the components of traction are known for any set of three planes passing through a point, the traction across any plane through the point can be calculated. The stress at a material point is determined by an assembly erf nine components of traction, three for each plane. If the orientations of the three planes are chosen to be normal to the coordinate directions of a rectangular Cartesian coordinate system, the Cartesian components of the stress are obtained  

The response of simple fluids to certain classes of deformation history can be analyzed. That is, a limited number of material functions can be identified which contain all the information necessary to describe the behavior of a substance in any member of that class of deformations. Examples are the viscometric or steady shear flows which require, at most, three independent functions of the shear rate (79), and linear viscoelastic behavior (80,81) which requires only a single function, in this case a relaxation function. The functions themselves must be determined experimentally for each substance. 

The utility of the simple fluid theory lies in the plausibility and generality erf its assumptions about how materials behave and in the exactness with which its conclusions are worked out. In particular, one is inclined to believe, as a working hypothesis and in the absence of contradictory evidence, that the theory is general enough to encompass the behavior of homogeneous polymeric liquids. On this basis the role of molecular theories is a complementary one, to provide forms for the material functions and to account for their systematic change with molecular structure and temperature. 

Most rheological data on polymer liquids of known structure has been obtained in simple shearing deformations. The velocity field for homogeneous simple shear in rectangular Cartesian coordinates may be expressed  

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Contents Chain Configuration in Amorphous Polymer Systems. Material Properties of Viscoelastic Liquids. Molecular Models in Polymer Rheology. Experimental Results on Linear Viscoelastic Behavior. Molecular Entan-lement Theories of Linear iscoelastic Behavior. Entanglement in Cross-linked Systems. Non-linear Viscoelastic-Properties. 

Note 3 Deformations and flows used in conventional measurements of properties of viscoelastic liquids and solids are usually interpreted assuming incompressibility. 

Figure 3.22 illustrates die swell at the exit of a flow channel, a characteristic property of viscoelastic liquids for high-shear-rate flows (yw o ) The extrudate emerging... 

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