Molecular theories of polymer rheology are reviewed with emphasis on predictions of the more familiar properties: non-Newtonian viscosity and normal stress in steady shear, complex viscosity in oscillatory shear, and elongational viscosity in extensional flow. Both dilute and concentrated solutions are discussed, with emphasis on the former. An important objective is clarification of polymer modeling strategies and how they are related to polymer structure. The intended readership consists of those engineers familiar in a general way with continuum polymer rheology, but with no special expertise in polymer physical or theoretical chemistry.
MICHAEL C. WILLIAMS Chemical Engineering Department
University of CaliforniaBerkeley, California 94720 SCOPE Rheology, the study of material deformation and flow, can be defined more precisely as the establishment of relationships between stress a and strain rate A (including their respective histories in terms of integral or derivative functions). Among the theoretical tools for doing this are the continuum and the molecular/structural approaches. Continuum methods have been used to generate admissible frameworks for rheological models, but have a generality which permits ambiguity and cannot be used to evaluate model parameters. Thus the basic utility of molecular theory is its capability of yielding specific information on how rheological parameters vary with molecular variables under the control of chemists and chemical engineers.Polymeric fluids-melts and solutions-possess the quality of viscoelasticity which has stimulated most of modern rheological research. This quality affects all properties of engineering interest, most prominently the non-Newtonian viscosity ~( y ) = oZl/y as a function of steady shear rate y.More recently it became evident that processing anomalies such as die swell, melt fracture, and certain instabilities in flow as well as many final product anomalies also had their origin in viscoelasticity; many of these can be correlated in terms of the normal stress functions N l ( y ) = ull -uZ2 = (y2 and N 2 ( y ) = uZ2 -u33 = 8,/2 in steady shear. Fluid elasticity is essential to the synthetic fiber industry, and therefore the behavior of the elongational (tensile) viscosity ? ( K ) as a function of tensile strain rate K is important to many engineers.Other material properties can be defined for other types of flows, including the transient conditions of creep, relaxation, and start-up. Probably the most important of the time-dependent flows is sinusoidal oscillation of small amplitude, characterized by the complex viscosity q * ( 0 ) dependent only on the frequency 0 . This property, widely used by chemists to evaluate viscoelasticity of polymers, is becoming increasingly relevant to engineering operations as well.Defining "basic material properties" for all possible flow situations, and evaluating them separately, is an endless AlChE Journal Wol. 21, No. 1) and unnecessary task. Instead, use of a rheological model will in principle permit predictions of...