Viscoelasticity polymer melt behavior

Constitutive Description of Polymer Melt Behavior K-BKZ and DE Descriptions. Although there are many nonlinear constitutive models that have been proposed, the focus here is on the K-BKZ model because it is relatively simple in structure, can be related conceptually to finite elasticity descriptions of elastic behavior, and because, in the mind of the current author and others (82), the model captures the major features of nonlinear viscoelastic behavior of polymeric fluids. In addition, the reptation model as proposed by Doi and Edwards provides a molecular basis for understanding the K-BKZ model. The following sections first describe the K-BKZ model, followed by a description of the DE model. 

The cone-n-plate viscometer can be used for osdllatory shear measurements as well. In this case, the sanq>le is deformed by an osdllating driver which may be mechanical or electromagnetic. The amplitude of the sinusoidal deformation is measured by a strain transducer. The force deforming the sample is measured by the small deformation of a relatively rigid spring or tension bar to wbidi a stress transducer is attached. Because of the energy dissipated 1 the viscoelastic polymer melt, a phase difference develops between the stress and the straiiL The complex viscosity behavior is determined from the amplitudes of stress and strain and the phase angle between them. The results are usually interpreted in terms of the material functions G, G", and others [21-28]. 

The significance of G G tan 5, Tj, and Tj is that they can be determined experimentally and used to characterize real materials. These parameters depend on frequency and temperature, and this dependence can be used to define behavior. For example, viscoelastic fluids are often characterized by log—log plots of one or more of these quantities vs the angular frequency CO, as shown in Figure 21, which illustrates the behavior of a polymer melt (149). 

Viscoelastic Measurement. A number of methods measure the various quantities that describe viscoelastic behavior. Some requite expensive commercial rheometers, others depend on custom-made research instmments, and a few requite only simple devices. Even quaHtative observations can be useful in the case of polymer melts, paints, and resins, where elasticity may indicate an inferior batch or unusable formulation. Eor example, the extmsion sweU of a material from a syringe can be observed with a microscope. The Weissenberg effect is seen in the separation of a cone and plate during viscosity measurements or the climbing of a resin up the stirrer shaft during polymerization or mixing. 

In Section 4.2.2 the central role of atomic diffusion in many aspects of materials science was underlined. This is equally true for polymers, but the nature of diffusion is quite different in these materials, because polymer chains get mutually entangled and one chain cannot cross another. An important aspect of viscoelastic behavior of polymer melts is memory such a material can be deformed by hundreds of per cent and still recover its original shape almost completely if the stress is removed after a short time (Ferry 1980). This underlies the use of shrink-fit cling-film in supermarkets. On the other hand, because of diffusion, if the original stress is maintained for a long time, the memory of the original shape fades. 

Though experimental data on suspensions of fibers in Newtonian dispersion media give more or less regular picture, a transition to non-Newtonian viscoelastic liquids, as Metzner noted [21], makes the whole picture far or less clear. Probably, the possibility to make somewhat general conclusions on a longitudinal flow of suspensions in polymer melts requires first of all establishing clear rules of behavior of pure melts at uniaxial extension this problem by itself has no solution as yet. 

The above considerations illustrate the difficulties of trying to formulate equations descriptive of rheological behavior of polymer melts with gas bubbles. An optimistic approach to the solution of this task is contained in [60, 61]. The content of these works is revealed by their titles On the Use of the Theory of Viscoelasticity for Describing of the Behaviour of Porous Material and for the Calculation of construction... 

In order to illustrate the specific material properties of polymers, we compare a viscous fluid (silicone oil) with a viscoelastic shear thinning fluid (aqueous polyethylene oxide solution). These fluids are used as model fluids in order to show the flow behavior limits for polymer melts, which corresponds to the behavior of a viscous fluid at very low shear rates and to the behavior of a shear thinning fluid at very high shear rates. 

On a global scale, the linear viscoelastic behavior of the polymer chains in the nanocomposites, as detected by conventional rheometry, is dramatically altered when the chains are tethered to the surface of the silicate or are in close proximity to the silicate layers as in intercalated nanocomposites. Some of these systems show close analogies to other intrinsically anisotropic materials such as block copolymers and smectic liquid crystalline polymers and provide model systems to understand the dynamics of polymer brushes. Finally, the polymer melt-brushes exhibit intriguing non-linear viscoelastic behavior, which shows strainhardening with a characteric critical strain amplitude that is only a function of the interlayer distance. These results provide complementary information to that obtained for solution brushes using the SFA, and are attributed to chain stretching associated with the space-filling requirements of a melt brush. 

So, polymer melts display elastic as well as viscous behavior. In other words they are viscoelastic. Do polymer solids display some viscous behavior Also, we ve used the word relaxation when we talk about time-dependent behavior, but what do we mean by this To find out we now need to explore the subject of viscoelasticity in more depth. 

The transient net work model is an adaptation of the network theory of rubber elasticity. In concentrated polymer solutions and polymer melts, the network junctions are temporary and not permanent as in chemically crosslinked rubber, so that existing junctions can be destroyed to form new junctions. It can predict many of the linear viscoelastic phenomena and to predict shear-thinning behavior, the rates of creation and loss of segments can be considered to be functions of shear rate. 

It is expected that the same picture that gives a good account of the linear viscoelastic behavior of polymer melts should also hold for semidilute and concentrated solutions. In the case of semidilute solutions some conclusions can be drawn from sealing arguments (19,3, p. 235). In this way, concentration dependence of the maximum relaxation time tmax the zero shear rate viscosity r Q, and the plateau modulus G% can be obtained, where t is the viscosity of the solvent. The relevant parameters needed to obtain Xmax as a function of concentration are b, c, N, kgT, and Dimensional analysis shows that... 

A major goal in the physics of polymer melts and concentrated solutions is to relate measurable viscoelastic constants, such as the zero shear viscosity, to molecular parameters, such as the dimensions of the polymer coil and the intermolecular friction constant. The results of investigations to this end on the viscosity were reviewed in 1955 (5). This review wiU be principaUy concerned with advances made since in both empirical correlation (Section 2) and theory of melt flow (Section 3). We shall avoid data confined to shear rates so high that the zero shear viscosity cannot be reliably obtained. The shear dq endent behavior would require an extensive review in itself. 

Most common fluids of simple structure are Newtonian (i.e., water, air, glycerine, oils, etc.). However, fluids with complex structures (i.e., high polymer melts or solutions, suspensions, emulsions, foams, etc.) are generally non-Newtonian. Examples of non-Newtonian behavior include mud, paint, ink, mayonnaise, shaving cream, polymer melts and solutions, toothpaste, etc. Many two-phase systems (e.g., suspensions, emulsions, foams, etc.) are purely viscous fluids and do not exhibit significant elastic or memory properties. However, many high polymer fluids (e.g., melts and solutions) are viscoelastic and exhibit both elastic (memory) as well as nonlinear viscous (flow) properties. A classification of material behavior is summarized in Table 5.1 (in which the subscripts have been omitted for simplicity). Only purely viscous Newtonian and non-Newtonian fluids are considered here. The properties and flow behavior of viscoelastic fluids are the subject of numerous books and papers (e.g., Darby, 1976 Bird et al., 1987). 

Figure 15.5 shows a plot of the friction factor versus the Reynolds number as defined in Eq. 15.10. Because the Reynolds number has been defined by Eq. 15.10, the laminar-flow data must fall on the line shown. For flow at Reynolds numbers greater than 2000, two possible kinds of behavior are known. All slurries and many polymer solutions are represented by the solid curve in Fig 15.5. These do not seem to significantly suppress the turbulent behavior of the fluid. However, some polymer solutions and polymer melts, particularly those which show distinct viscoelastic behavior (such as rubber cement) obey the curves shown dotted at the right in Fig. 15.5. Visual observation [7] indicates that for these fluids the turbulence in the fluid is much less than it would be for a newtonian fluid at the same Reynolds number.

Before examining the viscoelastic behavior of amorphous polymeric substances in more detail, some of the fundamental properties of polymer melts and elastic solids will be reviewed. 

Various instruments are available to measure the viscosity of polymer melts and solutions, and more generally their rheological behavior, which include capillary and rotational viscometers. The former can be used to measure parameters such as shear viscosity, melt fracture, and extensional viscosity, which are important for many polymer processes. The latter type of device can be used in either steady or oscillatory mode, thus providing a measure of the viscosity as well as viscoelasticity (G", G, and tan 5) as a function of frequency and temperature. 

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