Читать книгу The Rheology Handbook - Thomas Mezger - Страница 66

Example: A chain-like macromolecule of a linear polyethylene (PE) with a molar mass of M = approx. 100,000 g/mol shows a length L of approx. 1 μm = 10-6 m = 1000 nm and a diameter of approx. d = 0.5 nm [3.8]. Macromolecule: Greek makros means large. Therefore, the ratio L/d = 2000:1. Using an illustrative dimensional comparison, this corresponds to a single spaghetti noodle being 1 mm thick – and 2000 mm or 2 m long! So, it is easy to imagine that in a polymer melt or solution these relatively long molecules would entangle loosely with others many times. As a second comparison: A hair with the dia­meter of d = 50 µm showing the length L = 10 cm. For an ultra-high molecular weight PE (UHMW) with M = 3 to 6 mio g/mol, then L/d = 50,000:1 to 100,000:1 approximately. Here, using the illustrative comparison, the piece of spaghetti would be approx. 50 m to 100 m long, and the hair with 2.5 m to 5 m would be permanently out of control!

At rest, each individual macromolecule can be found in the state of the lowest level of energy consumption: Therefore, without any external load it will show the shape of a three-

dimensional coil (see Figure 3.8). Each coil shows an approximately spherical shape and each one is entangled many times with neighboring macromolecules.

During the shear process, the molecules are more or less oriented in shear direction, and their orientation is also influenced by the direction of the shear gradient. When in motion, the molecules disentangle to a certain extent which reduces their flow resistance. For diluted polymer solutions, the chains may even become completely disentangled finally if they are oriented to a high degree. Then, the individual molecules are no longer in the same close contact as before, therefore moving nearly independently of each other (see Figures 3.9 and 3.32: no. 2).

Figure 3.8: Macromolecules at rest, showing coiled and entangled chains

Figure 3.9: Macromolecules under high shear load, showing oriented and partially disentangled chains

Using this concept, the result of the double-tube test can be explained now as follows (see Chapter 2.3, Experiment 2.2 and Figure 2.4): Fluid F1 shows shear-thinning and fluid F2 ideal- viscous flow behavior. At the beginning, there is a certain load on the molecules at the bottom of each tube due to the weight of the column of liquid which is compressing vertically onto them due to the hydrostatic pressure. Regarding the polymer molecules of F1, shortly after the beginning of the Experiment they are moving faster because they are stretched into flow direction now. As a consequence, they are disentangled to a high degree then. Hence, they are able to glide off each other more easily also during the passage through the valve.

Along with the falling liquid levels, also the shear load or shear stress, respectively, is decreasing continuously. Therefore, the macromolecules are recoiling more and more, and as a consequence, the viscosity of F1 is increasing now. However, F2, the mineral oil, still shows constant viscosity, independent of the continuously changing shear load, since for this ideal-viscous liquid with its very short molecules counts, that there is no significant shear load-dependent change in the flow resistance.

Figure 3.10 presents the viscosity function of a polymer displaying three intervals on a double logarithmic scale. These three distinct ranges of the viscosity curve only occur for uncrosslinked and unfilled polymers showing loosely entangled macromolecules. However, this does not apply for polymer solutions with a concentration which is too low to form entanglements, and not for gels and paste-like dispersions exhibiting a network of chemical bonds or physical-chemical interactive forces between the molecules or particles. The three intervals are in detail:

1 The first Newtonian range with the plateau value of the zero-shear viscosity η0

2 The shear-thinning range with the shear rate-dependent viscosity function η = f( γ ̇ )

3 The second Newtonian range with the plateau value of the infinite-shear viscosity η∞ (sometimes it is called plateau value of the limiting high-shear viscosity)

Figure 3.10: Viscosity function of an uncrosslinked and unfilled polymer solution or melt

In order to explain this, you can imagine a volume element containing many entangled polymer molecules. Of course, in each sample there are millions and billions of them.