Viscosity of polymer melts

Before we are in a position to discuss the viscosity of polymer melts, we must first give a quantitative definition of what is meant by viscosity and then say something about how this property is measured. This will not be our only exposure to experimental viscosity in this volume—other methods for determining bulk viscosity will be taken up in the next chapter and the viscosity of solutions will be discussed in Chap. 9—so the discussion of viscometry will only be introductory. Throughout we shall be concerned with constant temperature experiments conducted under nonturbulent flow conditions. 

Polymer solutions are often characterized by their high viscosities compared to solutions of nonpolymeric solutes at similar mass concentrations. This is due to the mechanical entanglements formed between polymer chains. In fact, where entanglements dominate flow, the (zero-shear) viscosity of polymer melts and solutions varies with the 3.4 power of weight-average molecular weight. 

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. 

Extensional Viscosity. AH three types of extensional viscosity can be measured (101,103) uniaxial, biaxial, and pure shear. Only a few commercial instmments are available, however, and most measurements are made with improvised equipment. Extensional viscosity of polymer melts can be estimated from converging flow (entrance pressure) or from a melt strength drawdown test (208). 

As a starting point it is useful to plot the relationship between shear stress and shear rate as shown in Fig. 5.1 since this is similar to the stress-strain characteristics for a solid. However, in practice it is often more convenient to rearrange the variables and plot viscosity against strain rate as shown in Fig. 5.2. Logarithmic scales are common so that several decades of stress and viscosity can be included. Fig. 5.2 also illustrates the effect of temperature on the viscosity of polymer melts. 

Aggregation of particles may occur, in general, due to Brownian motion, buoyancy-induced motion (creaming), and relative motion between particles due to an applied flow. Flow-induced aggregation dominates in polymer processing applications because of the high viscosities of polymer melts. Controlled studies—the conterpart of the fragmentation studies described in the previous section—may be carried out in simple flows, such as in the shear field produced in a cone and plate device (Chimmili, 1996). The number of such studies appears to be small. 

The z average molecular weight has been found to correlate with the shear viscosity of polymer melts when the molecular weight distribution is very broad and where very large molecules appear to dominate the resistance to fluid flow. 

We will now turn our attention from the viscosity of dilute solutions and look at the viscosity of melted polymers. The viscosity of melted polymers is important in transferring resins and in polymer processing such as determining the correct conditions to have a specific flow rate for injection processing and in determining the optimum conditions to get the necessary dimensions of extruded shapes. Fillers, plasticizers, temperature, solvents, and molecular weight are just some of the variables that influence the viscosity of polymer melts. Here we will look at the dependence of melt viscosity on polymer molecular weight. Polymer melts have viscosities on the order of 10,000 MPa (1 centipoise =0.001 Pa/sec). 

In order to obtain an impression as to the usefulness of eqs. (1.6), (2.11) and (2.20), measurements have, amongst others, been carried out on polymer melts. These materials seem particularly suitable for the determination of shear recovery, as the problems arising in connection with the inertia of parts of the apparatus become much less important than with polymer solutions of low and intermediate concentrations, on which previous measurements have been carried out. In fact, the viscosity of polymer melts is, in general, very much higher than that of the mentioned solutions. At this Institute, Den Otter (26) carried out shear recovery measurements on polymer melts with the aid of a simple cone-and-plate arrangement. 

Originally, Fox and Flory (121) found that the zero shear viscosity of polymer melts increases with the 3.4-th power of the molecular weight. Bueche (122) has shown that this relationship holds only above a certain critical molecular weight Mc which depends on the structure of the polymer chain. Below Mc the zero shear viscosity is found to depend on a significantly lower power of molecular weight. A theoretical interpretation of these facts has been given by the latter author on the basis of the free-draining model (Section 3.4.1.). 

If the present author would be asked why he did not first try to investigate the flow birefringence of polymer melts with the aid of a concentric cylinder apparatus, he could only answer because of the inconveniences experienced with such a type of an apparatus, when the viscosity of polymer melts is measured. As a matter of fact, the apparatus for polymer solutions, as described in the previous sections, would not.be suitable because of the impossibility to fill it with a polymer melt. As a consequence, a new type of apparatus had to be designed in any case. 

As in the case of low-molecular liquid crystals the majority of information about the structure of LC polymers is obtained from their optical textures and X-ray diffraction data. Because of high viscosity of polymer melts, which results in retardation of all structural and relaxation processes it is quite difficult to obtain characteristic textures for LC polymers. As is noted by the majority of investigators smectic LC polymers form strongly birefringent films as well from solutions, as from melts11 27-... 

Since pressure driven viscometers employ non-homogeneous flows, they can only measure steady shear functions such as viscosity, 77(7). However, they are widely used because they are relatively inexpensive to build and simple to operate. Despite their simplicity, long capillary viscometers give the most accurate viscosity data available. Another major advantage is that the capillary rheometer has no free surfaces in the test region, unlike other types of rheometers such as the cone and plate rheometers, which we will discuss in the next section. When the strain rate dependent viscosity of polymer melts is measured, capillary rheometers may provide the only satisfactory method of obtaining such data at shear rates... 

In Figure 1.21, experimental observations show that the viscosity of polymer melts is dependent on molecular weight (A/) as follows ... 

The shear viscosity of polymers depends on the average molecular weight, the molecular-weight distribution, the temperature, the shear stress (and shear rate) and the hydrostatic pressure. Semi-empirical relationships for these dependencies permit estimations of shear viscosities of polymer melts under arbitrary experimental... 

As is to be expected, the viscosity of polymer melts increases with increasing molar mass. The difference in behaviour of polymers from low-molar mass substances becomes striking, however, for molecular mass higher than a certain critical value, Mcr. In this instance... 

The very strong influence of molecular mass on the viscosity of polymer melts required some mechanism of molecular interaction for a theoretical interpretation. Bueche (1952) could derive Eq. (15.28) with certain assumptions on the influence of chain entanglements on polymer flow. Later, numerous other interpretations have been offered which will not be discussed here. 

This effect may be responsible for the popular belief that the extensional viscosity of polymer melts increases with increasing rate of deformation. Obviously, this statement is too simplistic, as one more parameter is needed to describe the relationship between extensional viscosity and rate of deformation. The situation is even more complicated. It is certain that the correlation of Fig. 15.22 has no universal validity, but depends on the nature of the polymer. Therefore, at this moment it is not possible to predict the extensional viscosity behaviour of an arbitrary polymer. 

Another conclusion is that the high viscosity of polymer melts is an important requirement for their spinnability. 

One of the potential ways how to improve CNT dispersion in polymer matrixes is in-situ polymerization of monomers in presence of nanotubes. Monomers have very small shear viscosity in orders of about lO -lO"3 Pa.s, compared to relatively high viscosity of polymer melts, 103-106 Pa.s. This low viscosity helps to better impregnation and wetting of CNT material, which leads to more efficient dispersion and debundling of the nanotubes aggregates, especially when ultrasound is used as a dispersing agent. 

T. Kitano, T. Kataoka, and T. Shirota, An Empirical Equation of the Relative Viscosity of Polymer Melts Filled with Various Inorganic Fillers, Rheol. Acta, 20, 207-209 (1981). 

The story of the Great Molasses Flood (it s true, you can t make up stuff like that) is a useful introduction to our discussion of the viscosity of polymer melts, because... 

Van Krevelen DW and Hoftyzer PJ (1976) Newtonian shear viscosity of polymer melts. Angew Makromol Chem 52 101-9. 

A variety of laboratory instruments have been used to measure the viscosity of polymer melts and solutions. The most common types are the coaxial cylinder, cone-and-plate, and capillary viscometers. Figure 11 -28 shows a typical flow curve for a thermoplastic melt of a moderate molecular weight polymer, along with representative shear rate ranges for cone-and-plate and capillary rheometers. The last viscometer type, which bears a superficial resemblance to the orifice in an extruder or injection molder, is the most widely used and will be the only type considered in this nonspecialized text. 

Kitano, X, Kataoka, X, and Shirota, X 1981. An empirical equation of the relative viscosity of polymer melts filled with various inorganic fillers. Rheol. Acta 20 207-209. 

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