**1. Introduction**

The addition of inorganic or organic fillers into polymeric materials is an effective way to attain certain desirable properties for different applications [1].The rheological behavior is dependent on the amount of fillers in the liquid polymer. Other factors influencing the viscosity of the highly filled polymers are the particle size and shape, the particle size distribution,

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

the nature of the filler and the polymer matrix, as well as the use of coupling agents or compatibilizers. A detailed description of these influencing factors is given in [1].

through a channel, cylindrical pipe, or slit by means of pressure (like high-pressure capillary rheometers (HPCRs)) [2]. In this section, the specific details of performing rheometry on highly filled polymers with both types of rheometers are presented. It is important to remember that in order to have a complete rheological characterization of highly filled polymers both rheometers are needed to cover the range of shear rates that could occur during different

Rheology of Highly Filled Polymers

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A rotational rheometer consists of a rotating or oscillating geometry and a fixed geometry; between these two geometries, the sample is sheared by a known torque when using a controlled shear stress (CSS) rheometer or a known deformation rate when using a controlled strain rate (CSR) rheometer. Several measuring geometries are available for rotational rheometers of polymeric materials; the most common examples are concentric cylinders (Couette or Searle Type), cone plates, and parallel plates (or disks) [2]. For highly filled polymers, parallel plates are the preferred measuring geometry (**Figure 1**). The main reason for using parallel plates is that the measuring gap can be adjusted. The high content of solid rigid particles in highly filled polymers could prevent reaching gaps smaller than 0.5 mm, which are required when using truncated cone-plate geometries and certain types of concentric cylinders. It is recommended that the measuring gap be at least 10 times larger but not larger than 50 times

In order to satisfactorily measure rheological data in a rotational rheometer, two conditions

For highly filled polymers, adhesion to the plate surface can be complicated since the filler particles may be in direct contact with the plate surface and thus reduce the friction. Over time also particle migration or sedimentation might contribute to the formation of a lowviscosity depleted layer between the plate surface and the bulk of the fluid. Both conditions could lead to slip effects. In order to prevent slip from happening, it is recommended to use serrated plates (instead of smooth plates), as shown in **Figure 2**. The serrated plates provide enough grip between the sample and the measuring plates; thus, the sample is

processing operations [16].

**2.1. Rotational rheometer**

need to be satisfied:

**ii.** the flow must be laminar.

than the largest particle inside a suspension [2].

**Figure 1.** Schematic drawing of the parallel plate rheometer.

**i.** the sample must adhere to the plate surface and

For very dilute systems, the fillers are sufficiently apart that the interaction between them is negligible, and their rheological behavior is drastically changed when the concentration increases beyond 15 vol%, approaching a solid-like behavior [2]. However, the critical volume fraction, at which the solid-like behavior is observed, is a function of the particle shape and size distribution [1]. In this chapter, we discuss the flow behavior of filled polymers with a particle concentration well above 15 vol%, where the interparticle interaction cannot be ignored; these materials are referred at as highly filled polymers. Highly filled polymers have found applications in many industries including the adhesive, dental, battery, ceramic, metallurgy, electronics packaging, and solid propellant industries; therefore, understanding their flow behavior is crucial for many industrial applications [1].

In the literature, a wide variety of models to describe the dependence of the viscosity of mainly the volume concentration of the filler φP is available [3–12]. Other parameters like shape factors or interactions between the particles are also taken into account [1, 13]. Einstein was the first to address the suspension behavior in the dilute limit theoretically ([4], corrected 1911 [5]). Later on, further models have been developed. Regarding the concentration of the filler as the main parameter, these models can be structured into two groups [13]:


In addition to [1, 13], we show in this chapter some models with a flow behavior integrating a yield strength.

Particular applications of highly filled polymers in the ceramic and metallurgy industries are ceramic injection molding (CIM), metal injection molding (MIM), and fused filament fabrication (FFF) [14, 15]. FFF is a special variant of material extrusion (ME) additive manufacturing (AM). In CIM, MIM, and FFF, a polymeric blend is used as a carrier or binder material for stiff powders during the fabrication of ceramic and metallic parts with complex geometry. Since the final part obtained at the end of these processes must be metal or ceramic, the filler content should be larger or equal to 50 vol% [15]. Measuring the rheological behavior of these materials is crucial to ensure that the correct processing conditions (e.g., for injection molding or extrusion) are used. Thus, it is one of the main motivations and backgrounds for preparing this chapter.

In this chapter, the methods used to measure the rheological properties of highly filled polymers with stiff fillers together with special issues or features of the rheological behavior of highly filled polymers are discussed in Section 2, and models used to describe the viscosity of highly filled polymers are explained in Section 3.
