The Rheology Handbook. Thomas Mezger

or a roller. Therefore, this coating shows pronounced shear-

       thinning flow behavior throughout the entire shear rate range.

       Figure 3.33: Principal shape of viscosity curves of pigmented water-based coatings containing

      different additives as rheology thickeners: 1) clay, as an inorganic gellant, 2) dissolved polymer,

      3a) polymer dispersion without an additive, 3b) polymer dispersion including an associative thickener

      3.1.2.1.2b) Water-based dispersions containing dissolved polymer as the thickening agent

      Dissolved polymer macromolecules exhibit the form of coils when at rest, see Figure 3.32. At a sufficiently high concentration there are entanglements between the long, thread-like molecules when at rest, and a loose, non-permanent network of entanglements is built up as a continuous phase (see also Chapter 3.3.2.1). Its strength is only based on mechanical forces, such as the relatively high frictional forces between the long polymer molecules. However, this network is not held together by chemical or physical forces. For hydrophilic polymers, e. g. hydrocolloids (such as starch, carrageen, agar or carob bean gum), cellulose derivatives or polyacrylic acid, a pronounced hydration shell may develop additionally like an envelope around the individual molecules. Hydrogen bridges can also build up a superstructure “surrounding the molecules like fog”. In this case, there is a network of interactions which is also strengthened by the physical-chemical secondary forces of the hydrogen bridges. Therefore, if the additive is incorporated in an appropriate way, a relatively high – but not in all cases “infinitely high” – viscosity value may result in the state of rest. Then towards the low-shear range, the shape of the viscosity curve is becoming flatter on a high level (see Figure 3.33), showing the tendency to end on the plateau value of zero-shear viscosity . Indeed, this plateau only appears for uncrosslinked polymer solutions, thus without showing a gel-like structure (see Chapter 3.3.2.1a). With a high thickener concentration, however, a gel-like structure with a yield point may occur as a superstructure. In this case, the shape of the vicosity curve towards low shear rates is steadily increasing towards an “infinitely high” value.

      Under a sufficiently high shear force, the network disintegrates, and the molecules are disentangling more and more. Therefore, at increasing shear rates the viscosity values are decreasing considerably and the individual molecules of the additive are more and more oriented into shear direction. At a typical concentration of around 0.2 % as used in practice, dissolved polymer molecules in the flowing state display no longer a significant thickening effect at high shear rates.

      Dimensions: The chains of individual polymer molecules exhibit diameters of around 0.5 nm. At rest, typical diameters of individual polymer coils are between 5 and 100 nm depending on the degree of dissolution, which of course again is influenced by temperature and pH value. Here as a measure, often is taken the “hydrodynamic radius ” RH which is derived from the “hydro­-dynamic volume” of a freely moveable molecule appearing in a spherical shape when rotating together with its hydration shell. In this case however, instead of a “radius” it would be better to talk of a diameter.

      Figure 3.33 presents a typical viscosity function of a pigmented water-based coating containing a dissolved polymer as the thickener. On the one hand it shows a pronounced thickening effect in the low-shear range of γ ̇ < 1 s-1, which may lead to the same problems as described above for the clay thickener. On the other hand, there is no more thickening effect at high shear rates, e. g. at γ ̇ > 1000 s-1, with the same consequences as described above. The coating displays pronounced shear-thinning flow behavior throughout the entire shear rate range.

      c) Water-based polymer dispersion without a thickener

      In polymer dispersions, the macromolecules are a component of discrete particles which consist of a shell of surface-active small molecules (surfactants), whose hydrophilic part points outwards into the water phase, whereas the hydrophobic part points inwards into the core of the particles containing the organic polymer molecules (polymer dispersion particles, “latex particles”; see also Chapter 9.1.3). Despite of their relatively high molar mass and also at a high polymer concentration, there is no possibility for the macromolecules to entangle like in polymer solutions, because they are enclosed in their spheres and therefore are shielded from their surrounding; see Figure 3.32. Without additional additive, no network can occur between the particles. If the polymer concentration remains within the corresponding limits, for example at a volume fraction of Φ < 50 %, the individual particles do not prevent each other’s motion by direct contact and corresponding friction. Therefore, the viscosity values remain relatively low, as well at rest as well as also in the sheared state. Since the individual dispersed polymer particles do not break even at higher shear rates, also here, the viscosity values are still remaining almost on a constant level. As a comparison: Being in a flowing state, dissolved polymer molecules are oriented and stretched out in shear direction showing continuously decreasing flow resistance as they glide increasingly easier along one another.

      Dimensions: Individual particles of polymer dispersion may exhibit diameters of 20 nm to 20 μm, and often are around 50 to 500 nm.

      Figure 3.33 presents a typical viscosity function of a pigmented water-based coating without a thickener (at Φ < 50 %). As well in the low-shear range of γ ̇ < 1 s-1 as well as at higher shear rates, e. g. at γ ̇ > 1000 s-1, viscosity remains usually relatively low. As this value hardly depends on the shear rate, these dispersions are showing nearly ideal-viscous (Newtonian) behavior. Usually under these conditions, polymer dispersions without thickener are not useful in practice since their viscosity is mostly too low. Neither their stability against sedimentation nor their matrix is strong enough to prevent spattering during application. They usually also display a highly pronounced tendency for sagging after application.

      3.1.2.1.3d) Water-based polymer dispersion containing an associative thickener

      Associative thickeners consist of molecules which are able to connect to one another. This occurs in water-based systems via hydrophobic molecular groups, whose connections and association takes place via non-permanent secondary bonds. Connections of these surface-active groups of the thickener molecules can take place between one another or via other hydrophobic components such as particle surfaces (see also Chapter 9.1.3: Surfactant-like polymers). At rest a loose, non-permanent network is built up which is only held together by the physical-chemical secondary forces of the hydrophobic interactions; see Figure 3.32. This Figure also displays small surfactant molecules which by self-organization can integrate themselves into these clusters. The thickener molecules are not remaining permanently in one place, they are continuously changing positions; they show fluctuation. The result is a weaker network, if compared as well to the network of entangled polymers as well as to the gel structure mentioned above; see Figure 3.33. In the range of very low shear rates, viscosity can be adjusted to the required value if the concentration of the dispersion components remains within the corresponding limits. Therefore, flow behavior can be controlled and optimized as desired for any requirement. A higher proportion of hydrophobic groups or longer hydrophobic molecule segments will lead to a higher structural strength at rest. In a sheared state, an increased number of hydrophobic molecule clusters and associative bridges are breaking, and the thickener molecules are oriented more and more into shear direction. The viscosity values may still decrease but only to a limited extent since also here, the particles of the polymer dispersion are not destroyed, even at high shear rates. Due to their size they are showing also here considerably more friction between one another compared to dissolved polymer molecules, and therefore, correspondingly higher viscosity values.

      Dimensions: Surface-active polymers exhibit a length of around 50 to 100 nm when stretched. Comparison: Many surfactant molecules are merely 0.5 to 5 nm long.

      Figure 3.33 presents a typical viscosity function of a pigmented water-based coating (at Φ < 50 %) including an associative thickener (with a concentration of around 0.1 to 0.2 % of the active components). In the low-shear range of γ ̇ < 1 s-1 there