Parameters Affecting Rheological Properties

Rheological properties are significantly affected by specific external or internal conditions. In addition to the kind of external applied load and the loading frequency, the most relevant properties affecting rheology are as follows:

  • • Temperature;
  • • Micro- or nanostructure of the system.

Effect of Temperature

Temperature is probably the most important parameter affecting rheological properties of systems. Viscosity widely depends on the temperature, and this dependence is generally expressed as a separate function from the effect of other parameters (e.g., the shear rate or the shear frequency):

The simpler form of the function f(T) commonly used is:

In this equation, the parameter a is called temperature sensitivity of the viscosity, while the temperature difference is calculated between the working temperature and the temperature at which viscosity is known.

Structure of the System

The structure of the system is particularly important in macromolecular formulations, e.g., in polymer solutions or melts.

Basically, intramolecular and intermolecular interactions determine mechanical properties of a polymer at the macromolecular scale.

Polymeric chains are obtained by covalently attaching a large number of repeating units. Intramolecular forces acting in polymers are prevalently related to the C-C bond (except, of course, in the presence of heteroatoms in the main polymer chain).

The energy of the C-C bond is around 350 kJ/mol, leading to a theoretical stiffness of 300-400 GPa. In the real case, polymer stiffness is considerably lower than the theoretical value. The difference between theoretical and actual stiffness is generally attributed to the macromolecular misaligning. This observation leads to consider also the intermolecular interactions as an important factor in polymer strength. Intermolecular interactions are mainly accounted to be van der Waals forces, and their entity is inversely proportional to the sixth power of the distance between atoms. Thus, in the presence of solvents or plasticizers, or when heated, the distance between two macromolecules increases, and the free volume increases; thus, intermolecular interactions, and consequently stiffness, decrease.

The degree of polymerization, or the number of repeating units per macromolecule, is another factor affecting macromolecular interactions.

Polymers with a low degree of polymerization are liquid or very soft at room temperature while, increasing the degree of polymerization, they gradually become stiffer at the same temperature and with the same additives. However, while the stiffness rapidly tends to a plateau, the viscosity steadily increases with molecular weight, generally with a power law (Figure 7.6).

Variation of stiffness and viscosity in polymers by increasing the molecular weight

FIGURE 7.6 Variation of stiffness and viscosity in polymers by increasing the molecular weight.

In systems containing macromolecular coils, soft particles, or vesicles, rheological properties are also affected by deformation of these components.

As a general rule, deformable structures dispersed in a liquid phase tend to get deformed in the direction of load application, while non-deformable structures tend to get aligned in the load direction.

In both cases, the most general rule is that systems become shear thinning during load application, while thixotropy dominates when loading is stopped, and systems tend to return thicker with time.

Industrial Uses of Rheological Analysis

Industrial systems are often related to fluid flow and rheology. In this inventory, polymer coatings and polymer-based paints are the major example of industrial rheological systems.

The terms “coating” and “paint” are synonymous. However, coating commonly refers to industrial applications such as in automotive applications, food cans, and papers. On the other hand, paint commonly refers to architectural coatings such as wall and house paints, for both interior and exterior surfaces.

Paints and coatings are used for a variety of applications, from surface protection to aesthetic decorations. From production to final use, paints and coatings formulations, containing solvents, fillers, resins, and pigments, should remain uniformly mixed. These products should remain stable during production and storage and then should be easily applied providing smooth surfaces. For all these reasons, rheological properties of paints and coatings must be carefully analyzed and optimized.

In this section, we will analyze some practical concerns of polymer-based paints and coatings and their rheological characterization, in order to understand how rheology is so important in quality check and product performances.

Commercial Formulations of Coatings and Paints

Formulations for coatings and paints are colloidal suspensions that solidify to give homogeneous solid films. Conventional formulations contain solvents, plasticizers, inorganic fillers, a polymeric film former, and pigments. More innovative formulations also contain additives to improve some performances, such as stability, surface properties, and durability.

From their production to the final use, such formulations should remain uniformly mixed and stable also after prolonged storage, also in different conditions. The ideal formulation should be pumpable, stirrable, mixable, and dispersible to fulfill all the requirements needed in the whole life cycle.

The Importance of Rheology in Paints and Coatings Formulations

Rheological properties of paints and coatings formulations are crucial for their performances and quality; thus, their optimization is vital. Generally, such formulations are developed to be non-Newtonian fluids, in order to have more than one parameter (e.g., temperature) governing their behavior.

Production processes, transportation, and storage, as well as their application on the substrate, imply different shear stress regimes. Thus, formulations have to be optimized to be correctly manipulated, and to ensure correct product performances at all stages.

During the production process, components and products are enlivened across the plant piping, and the flow regime implies moderate-to-high shear stresses.

The storage of final products occurs in a static and shear stress-free manner, in which solid components should maintain their colloidal nature avoiding sedimentation, filler precipitation, or demixing.

Transportation is a low-shear-stress process in which formulations are only subjected to vibrations.

During the final use, formulations should be easily spreadable by brush or roller, or sprayable. Thus, shear stresses related to their application vary on the basis of the selected application process: as in the case of brush spreading (moderate-to-high shear) to spraying (very high shear).

After application and before drying or curing, colloidal formulations undergo surface tension and gravitational forces. During this step, formulations should show a surface-leveling behavior and the internal microstructure should ideally recover after the application of shear stresses. The recovery time should be adequate for deaeration, to give a smooth and droplet-free surface. During solidification, when the coating is almost dried, sagging should be avoided or significantly limited.

Each process is important, and the perfect scenario would be to have the optimal viscosity at each stage to meet all requirements.

Rheometry of Paints and Coatings

Such very complex systems cannot be Theologically described by a single-point measure, acquired at an arbitrary shear strain rate regime. As a general rule, rheological measurements are difficult to compare to the actual processes that paints and coatings undergo during their overall life cycle. It is due to the variety of external factors occurring in real applications which can be very complex or impossible to “simulate” in a rheometry experimental test.

At the same time, a comprehensive rheological characterization should be performed in both continuous and dynamic regimes, considering different shear strain rates, and thus applying different rheometry techniques. It is because in a real scenario, paints and coatings are subjected to large variations of viscosity.

Viscosity as a function of the shear rate in different processes involved in paints and coatings formulation/storage/application is qualitatively represented in Figure 7.7.

According to Figure 7.7, formulations with high low-shear viscosity are more stable to sedimentation, while formulations with high high-shear viscosity form thicker layers after spreading.

As a general rule, the characterization at low-shear regimes is associated with how the paint or the coating behaves during leveling, sagging, and drying. At low shear regimes, viscous paints are prone to form brush marks after their spreading. Such behavior is due to the high leveling stability of viscous formulations. Too low viscosities at low shear are accounted to paint flow off the surface, resulting in the inapplicability of the product.

Qualitative trend of viscosity in paints and coatings formulations, at the different shear rates imposed in processing and application; values range from high to low from sedimentation to spraying

FIGURE 7.7 Qualitative trend of viscosity in paints and coatings formulations, at the different shear rates imposed in processing and application; values range from high to low from sedimentation to spraying.

A preliminary rheological analysis of paints and coatings formulation can be performed in continuous flow, in order to calculate some basic parameters.

Formulations for paints and coatings generally behave as a Bingham fluid. Thus, an important parameter that can be evaluated in continuous flow is the yield stress. Its value can be used to discriminate whether a formulation can be manually spread (e.g., by brush) or needs to be applied with different techniques (e.g., spraying). It is because the yield stress is the value of loading that a formulation can withstand before it starts flowing. This value of stress is commonly indicated as static yield stress. The value of the static yield stress increases with time, during the drying process.

However, yield stress of paints and coatings formulations can be evaluated not only in continuous flow but also by different and more complex rheological tests, e.g., in dynamic conditions. Unlike the static yield stress, indicating the point at which formulations start flowing, the dynamic yield stress is related to the process occurring when a flowing fluid comes to a rest state. The value of the dynamic yield stress can be evaluated from the fitting of experimental flow curves, by using appropriate models (e.g., the power law or the Carreau empirical models).

After the application of the formulation on its substrate, rheology can help to understand the leveling, sagging, and drying processes.

The appropriate rheological characterization to catch aspects related to leveling is obtained with oscillatory measurements, as for all non-Newtonian fluids, coupled to a preshear conditioning. The preshear step is able to simulate the spreading of the formulation over the substrate surface, while the oscillatory low stress applied at a fixed frequency can simulate the rebuilding of the microstructure. The parameter to monitor is viscosity, which should increase with the analysis time. It is expected that the system should show a shear-thinning behavior once the prestress is imposed, to have a simple spreading over the substrate surface, and a shear-thickening behavior once the prestress is released, providing a flow at low-shear regimes, to maximize leveling properties.

In this step of characterization, the G" modulus is expected to dominate the G' part at low-shear-strain regimes.

After the characterization of parameters related to leveling, a further step of analysis consists in the evaluation of rheological parameters affecting sagging. The formulation should flow at low shear to provide the surface leveling, but this flow should be limited to avoid sagging. This behavior is obtained in materials in which the loss modulus G" is larger than G' after the preshear condition. It ensures a correct leveling. Then, after a finite time, the paint should show a crossover of G' and G" moduli, with the G' part dominating after this crossover. This behavior is associated with a sol-to-gel transition. After the sol-to-gel transition, the liquid formulation becomes more viscous and stops flowing. It means that after a specific timescale, the mechanical behavior of the paint becomes elastically dominated.

Sagging is mainly governed by gravitational loads. The gravitational load that triggers the flow of the applied formulation can be easily calculated. The liquid layer formulation can be considered as spread over an inclined plane (Figure 7.8), and the shear stress distribution profile results in a maximum value at the interface with the substrate, while it is null at the free coating/air interface.

Gravitational effects increase with formulation density, film thickness, and inclination angle. The maximum shear rate, at the substrate/coating interface, increases with a decreasing viscosity. Formulation flow can be minimized by increasing the viscosity at the typical shear stress of the coating/substrate system until the colloidal solution is dried.

Under the value of the apparent yield stress of the system, an optimized formulation behaves like a solid, forming a sort of network given by molecular interactions. An external load larger than the apparent yield stress of the formulation (e.g., the load applied during brushing) can break the network microstructure and can activate the fluid flow. A formulation with this characteristic can prevent sagging but, at the same time, can be easily spread over the substrate.

Thickeners as Rheology Modifiers

Paints and coatings formulations also contain some additives called thickeners. Such additives, also known as rheology modifiers, are used to tailor the viscosity of the final product, to make it more suitable for production, spreading, leveling, and sag resistance.

Schematization of paint layer and maximum stress and shear rate acting at the substrate/paint interface

FIGURE 7.8 Schematization of paint layer and maximum stress and shear rate acting at the substrate/paint interface.

Thickeners are commonly added in formulation production to improve the grinding process. During the grinding phase, inorganic fillers and pigments are added to the liquid formulation and mixed at high shear stress to maximize their dispersion. Thickeners are added to decrease the size of particle aggregates in the dispersion medium, improving product uniformity and pigment yield.

Thickeners are also used in several mixing phases, in which liquid components are injected or poured in other preparations. In this step, thickeners are useful to facilitate the transfer of liquids from one container to another.

Finally, thickeners are widely used to adapt the product viscosity to the final application procedure. Paints and coatings applied via spraying should be less viscous than those applied by brush or roller. The optimization of formulation viscosity allows optimizing the surface coverage, avoiding using too much material or the formation of uneven coatings.

On the other hand, a too-much use of thickeners can lead to some drawbacks, such as flocculation, “fish-eye” formation, and other film defects.


Rheology is the science of fluid flow. Industrial coatings and paints are governed by rheological parameters, and a deep knowledge of formulation rheometry allows optimizing production, storage, and stability of the final products, also providing important information on their application and final properties of coatings, in terms of surface smoothness and homogeneity.

Generally, paints and coatings formulations behave like non-Newtonian fluids, showing different rheological parameters to tune and to be tailored for each specific use. Their complex mechanical behavior can be studied by rheometry, developing ad hoc continuous and oscillatory tests to calculate parameters of interest.

Several empirical models can be used to fit experimental data, starting from more complex mathematical models involving stress and strain tensors, and time-depen- dent viscosity laws.

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