Filled polymer rheology

The fourth chapter presents some constitutive theories and equations for suspensions. Suspension rheology normally deals with the flow behavior of two-phase systems in which one phase is solid particles like fillers but the other phase is water, organic liquids or pol)oner solutions. Literature on suspension rheology does not include flow characteristics of filled polymer systems. Neverttieless, ttiis chapter needs to be included as the foimdations for understanding ttie basics of filled polymer rheology stem from the flow behavior of suspensions. In fact, most of the constitutive theories and equations that are used for filled polymer systems are borrowed firom those that were initially developed for suspension rheology. 

Filled polymer rheology is basically concerned with the description of the deformation of filled polymer systems under the influence of applied stresses. Softened or molten filled polymers are viscoelastic materials in the sense that their response to deformation lies in varying extent between that of viscous liquids and elastic solids. In purely viscous liquids, the mechanical energy is dissipated into the systems in the form of heat and cannot be recovered by releasing the stresses. Ideal solids, on the other hand, deform elastically such fliat the deformation is reversible and the energy of deformation is fully recoverable when the stresses are released. 

There are a number of reviews [49-61] which discuss various aspects of the rheology of suspensions and may be referred to for detailed study. In the present chapter, the topic is touched upon rather briefly and only certain aspects are discussed in a limited manner just enough to lay the foundations for understanding the basics of filled polymer rheology. 

Chapter 4 deals witii constitutive theories and equations for suspensions and lays down the foundations for understanding the basics of filled polymer rheology. Starting from the simplest dilute... 

Rheological properties of filled polymers are characterized by the same parameters as any fluid media [1]. These are ... 

All these quantities may depend on the content and behavior of a filler and to a certain extent on the prehistory of the material. This is a specific character of rheological properties of filled polymers. 

The manifestation of rheological properties of filled polymer melts is a combination... 

Analysis of rheological properties of filled polymers consists, in essence, of answers to a few general questions. They may be stated as follows ... 

Some of these questions have strict and unambiguous answers, in a mathematical model, to other answers are derived from extensive empirical material. The present paper will discuss the problems formulated above, but concerning only rheological properties of filled polymer melts, leaving out the discussion of specific hydrodynamic effects occurring during their flow in channels of different geometrical form. 

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. 

First. The problem of a limit of linearity has assumed a certain importance for investigating dynamic properties of filled polymers [4, 5], Even for very small (from the point of view of measuring rheological properties of pure polymer melts) amplitudes of deformation, the values of a modulus depend on the amplitude. 

The fact that the appearance of a wall slip at sufficiently high shear rates is a property inwardly inherent in filled polymers or an external manifestation of these properties may be discussed, but obviously, the role of this effect during the flow of compositions with a disperse filler is great. The wall slip, beginning in the region of high shear rates, was marked many times as the effect that must be taken into account in the analysis of rheological properties of filled polymer melts [24, 25], and the appearance of a slip is initiated in the entry (transitional) zone of the channel [26]. It is quite possible that in reality not a true wall slip takes place, but the formation of a low-viscosity wall layer depleted of a filler. This is most characteristic for the systems with low-viscosity binders. From the point of view of hydrodynamics, an exact mechanism of motion of a material near the wall is immaterial, since in any case it appears as a wall slip. 

The dependence of Vs on rheological parameters-shear stress on the wall and /notion coefficient — as far as the author knows, for filled polymers was not investigated somewhat completely, though its determination is necessary for a specific solution of hydrodynamic problems related to the flow of filled polymers. 

Nikolaeva NE, Sabsai OYu, Fridman ML (1985) Rheological properties of gas-filled polymers and their effects on processing Ser. Pererabotka plastmass. NIITEHIM, Moscow... 

The book contains rather complete reviews of papers published in the last 5-10 years in the USSR and abroad on various problems of filled polymers of differing nature. The discussion is centered on the physico-chemical problems of these complex systems, their structure, mechanical, rheological, dielectric and other properties in a word, important aspects of theory and technology of filled composites. We hope the topical nature of the subjects discussed and the selection of authors that appear in the book all help to throw more light on this area of science and technology. The interested reader will be able not only to appreciate the book as a source of additional literature or a snapshot of the state-of-... 

Rheological properties of filled polymers can be characterised by the same parameters as any fluid medium, including shear viscosity and its interdependence with applied shear stress and shear rate elongational viscosity under conditions of uniaxial extension and real and imaginary components of a complex dynamic modulus which depend on applied frequency [1]. The presence of fillers in viscoelastic polymers is generally considered to reduce melt elasticity and hence influence dependent phenomena such as die swell [2]. 

Further factors influencing rheological characterization of filled polymers include changes in the degree of filler dispersion or inter-particle structure forma-... 

---