Polymer melts viscous behavior

Melt Viscosity. The study of the viscosity of polymer melts (43—55) is important for the manufacturer who must supply suitable materials and for the fabrication engineer who must select polymers and fabrication methods. Thus melt viscosity as a function of temperature, pressure, rate of flow, and polymer molecular weight and stmcture is of considerable practical importance. Polymer melts exhibit elastic as well as viscous properties. This is evident in the swell of the polymer melt upon emergence from an extmsion die, a behavior that results from the recovery of stored elastic energy plus normal stress effects. 

Coating solutions often exhibit a mixture of viscous and elastic behavior, with the response of a particular system depending on the stmcture of the material and the extent of deformation. Eor example, polymer melts can be highly elastic if a polymer chain can stretch when subjected to deformation. 

PEs, as other polymers, exhibit nonlinear behavior in their viscous and elastic properties under practical processing conditions, i.e., at high-shear stresses. The MFI value is, therefore, of little importance in polymer processing as it is determined at a fixed low-shear rate and does not provide information on melt elasticity [38,39]. In order to understand the processing behavior of polymers, studies on melt viscosity are done in the high-shear rate range viz. 100-1000 s . Additionally, it is important to measure the elastic property of a polymer under similar conditions to achieve consistent product quality in terms of residual stress and/or dimensional accuracy of the processed product. 

Power law model fluid with temperature dependent viscosity m0 = e( a(-T Tm The rate of melting is strongly dependent on the shear thinning behavior and the temperature dependent viscosity of the polymer melt. However, we can simplify the problem significantly by assuming that the viscous dissipation is low enough that the temperature profile used to compute the viscosity is linear, i.e.,... 

Even at a phenomenological level, the flow behavior of polymers differs significandy from that of low-viscous liquids such as water. The flow behavior of polymer melts is markedly dependent on the applied shear stress o, the shear rate y, and on time. Elastic effects and normal stresses also occur in practice, and their effects can either help or hinder the processes underway. 

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. 

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. 

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). 

Discuss the effect of MWD and chain branching on the viscous behavior of a polymer melt. 

The frequency dependences of G (o)) and G"((o) for a typical polymer melt are reported in Figure 13.27. At low frequency G (ft)) < G"((0) and viscous behavior is dominant. This is the long-time or terminal region from which a measure of the zero shear rate viscosity can be derived. At intermediate frequencies, G ((o) > G"((0), and... 

The ribbon polymer is related to the less-flexible ladder and sheet polymers discussed before. One might expect very much different viscous behavior of such molecules in the melt. The interpenetrating networks [8] can have interesting elastic properties since each network may respond differently and interact with the other. The two-dimensional flexible polymers have recently been explored. They also belong to the sheet-like polymers. 

Unfortunately, the Reynolds-Nusselt dimensional analysis studies are not directly applicable to polymer melt and rubber processing for two important reasons. First, they are based on Newtonian fluid behavior, and second, they do not include viscous dissipation heating. 

In the quantitative analysis of most extrusion problems, the polymer melt generally is considered to be a viscous, time-independent fluid. This assumption is, of course, a simplification, but it usually allows one to find a relatively straightforward solution to the problem. This assumption will be used throughout the rest of this book, unless indicated otherwise. In the analysis of any flow problem, however, it should be remembered that elastic effects may play a role. Also, some flow phenomena, such as extrudate swell, clearly cannot be analyzed unless the elastic behavior of... 

Accurate description of flow of the polymer melt through the die requires knowledge of the viscoelastic behavior of the polymer melt. The polymer melt can no longer be considered a purely viscous fluid because elastic effects in the die region can be significant. Unfortunately, there are no simple constitutive equations that adequately describe the flow behavior of polymer melt over a wide range of flow conditions. Thus, a simple die flow analysis is generally very approximate, while more accurate die flow analyses tend to be quite complicated. 

The tendency of polymer molecules to curl-up while they are being stretched in shear flows results in normal stresses in the fluid that greatly affect the flow field in certain cases. Additionally, most polymer melts exhibit an elastic as well as a viscous response to strain. This puts them under the category of viscoelastic materials. There are no precise models accurately representing this behavior in polymers. 

However, various combinations of eiastic and viscous elements have been used to approximate the material behavior of polymer melts. Some models are combinations of springs and dashpots to represent the elastic and viscous responses, respectively. The most common ones being the Maxwell model for a polymer melt and the Kelvin or Voight model for a solid. One model that represents shear thinning behavior, normal stresses in shear flow and elastic behavior of certain polymer melts is the K-BKZ model [28-29]. 

Polymer melts and semidilute and concentrated solutions of polymer are highly viscous. Even at a concentration of 1 wt %, solutions of polymer with a molecular weight greater than several million g/mol can flow only slowly. Their behaviors are even elastic like rubber at accessible time and frequency ranges. These exquisite properties had eluded researchers for decades until the tube model and the reptation theory elegantly solved the mystery. The tube model and the reptation theory were introduced by de Gennes." They were refined and applied to the viscoelasticity of semidilute solutions of polymers and polymer melts in the late 1970s by Doi and Edwards." Until then, there had been no molecular theory to explain these phenomena. We will leam the tube model and the reptation theory here. 

In contrast to simple elastic solids and viscous liquids, the situation with polymeric fluids is somewhat more complicated. Polymer melts (and most adhesives are composed of polymers) display elements of both Newtonian fluid behavior and elastic solid behavior, depending on the temperature and the rate at which deformation takes place. One therefore characterizes polymers as viscoelastic materials. Furthermore, if either the total strain or the rate of strain is low, the behavior may be described as one of linear or infinitesimal viscoelasticity. In such a case, the stress-deformation relationship (the constitutive equation) involves not just a single time-independent constant but a set of constants called the relaxation spectrum,(2) and this, too, may be determined from a single stress relaxation experiment, or an experiment involving small-amplitude oscillatory motion. 

Many highly elastic polymer melts, including polypropylene, which is spun into fibers and hence is directly relevant to the discussion here, show considerably more complex behavior in extension than that given by Equation 7.11. Equation 7.11 does seem to be adequate for many polymers that are spun conamercially, however, including poly(ethylene terephthalate) hence, we will employ it in this chapter. (We use the qualifier seem because these polymers tend to be insufficiently viscous to carry out the extensional experiment as analyzed here, and the extensional behavior must be inferred from other measurements.) We therefore proceed with an analysis of spinning that, at the point where we require a constitutive equation, presumes the applicability of Equation 7.11. 

The viscoelastic nature of polymer melts and their pecularities in the viscous as well as elastic response to deformation under applied stresses bring them under the category of non-Newtonian fluids. There is a distinctive diGEerence in flow behavior between Newtonian and non-Newtonian fluids to an extent that, at times, certain aspects of non-Newtonian flow behavior may seem sdmormal or even paradoxical [12-16]. An interesting movie about polymer fluid medianics has been prepared [17] which clearly depicts certain peculiarities of sudi fluids. The dramatic differences between the qualitative responses of Newtonian and non-Newtonian fluids grossly affect the industrial and practical applications of them. 

All of these melt studies were based on consideration of the melt as a liquid, but the early work on application properties where from the solid mechanics point of view. Elastic effects were also very important in the melt state. Consideration of the viscoelastic characteristics of polymers in both the liquid and solid states led to the investigation of the elastic, or solid like, behavior of polymer melts. Studies of the recoverable strain in polymer melts indicated that if the molecular weight was high enough the melt exhibited almost a one-hundred percent recovery. Obviously true understanding of melt processing required consideration of both the viscous and elastic behavior. 

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