**3. Conclusion**

On the basis of these parameters, the flow curves of particle-filled PP can be estimated, regardless of the filler type, particle size, and volume fraction. **Figure 16** exemplarily illustrates this on different formulations. The experimental data (symbols) have been excellently fitted (lines),

**Figure 15.** Interaction exponent as a function of consistency index of PP filled with various fillers (T = 200°C).

**Figure 17** comparatively illustrates the influence of the filler volume concentration and the applied shear stress for various fillers in different size fractions on the shift factor B, which has been derived on the basis of (Eq. (6)). On the basis of the shift factor B, the flow behavior of polymer suspensions can be estimated for arbitrary volume concentrations and shear stresses

**Figure 16.** Comparison of experimental data (symbols) to predicted flow curves (lines) for PP filled with various fillers

by using just one parameter set of the interaction function (K\* = 16,706 Pa s<sup>n</sup>, a = 4.076, b = 0.385), (T = 200°C).

using that generally valid parameter set of the interaction function.

or shear rates, respectively.

148 Polymer Rheology

In this chapter, new mathematical models describing interparticle interaction effects in longchain branched and linear polymer matrices have been presented. In the context of studies with variable volumetric filler concentrations, the influence of filler type (morphology and aspect ratio) and particle size on interparticle interactions has been compared.

On the basis of the *generalized interaction function*, the correlation between interaction exponent and consistency index of particle-filled polymer melts can be mathematically described with high accuracy to experimental data. This correlation is characteristic and valid for each individual polymer matrix.

[2] Einstein A. Eine neue Bestimmung der Moleküldimensionen. Annals of Physics.

Interparticle Interaction Effects in Polymer Suspensions http://dx.doi.org/10.5772/intechopen.75207 151

[3] Einstein A. Berichtigung zu meiner Arbeit: Eine neue Bestimmung der Moleküldimensionen. Annals of Physics. 1911;**339**:591-592. DOI: 10.1002/andp.19113390313

[4] Osswald T, Rudolph N. Polymer Rheology – Fundamentals and Applications. Munich:

[5] Mueller S, Llewellin EW, Mader HM. The rheology of suspensions of solid particles.

[6] HJH B. Viscosity of a concentrated suspension of rigid monosized particles. Physical

[7] Hochstein B. Rheologie von Kugel- und Fasersuspensionen mit viskoelastischen MatrixflŸssigkeiten [Ph.D. Thesis]. UniversitŠt Fridericiana Karlsruhe: Karlsruhe; 1997

[8] Tadros TF. Rheology of Dispersions: Principles and Applications. Wiley: Weinheim;

[9] Pasquino R. Rheology of viscoelastic suspensions [Ph.D. thesis]. Napoli: University of

[10] Kitano T, Kataoka T, Shirota T. An empirieal equation of the relative viscosity of polymer melts filled with various inorganic fillers. Rheologica Acta. 1981;**20**:207-209. DOI: https://

[11] Barnes HA. A Review of the Rheology of Filled Viscoelastic Systems. Rheology Reviews.

[12] Hinkelmann B. Zur analytischen Beschreibung des Füllstoffeinflusses auf das Fließverhalten von Kunststoff-Schmelzen. Rheologica Acta. 1982;**21**:491. DOI: https://doi.org/

[13] Pahl M, Gleißle W, Laun H. Praktische Rheologie der Kunststoffe und Elastomere. VDI-

[14] Hansmann H, Laufer N, Kühn S. Investigation on the Flow Behavior of WPC Melts. In: 9th WPC, Natural Fibre and other innovative Composites Congress and Exhibition;

[15] Khodakov GS. On suspension rheology. Theoretical Foundations of Chemical Engineering. 2004;**38**(4):430-439. DOI: https://doi.org/10.1023/B:TFCE.0000036973.95412.a3

[16] Laufer N, Koch M, Hansmann H, Boss C, Ofe S. Effects of Interparticle Interactions on the Flow Behaviour of Low Density Polyethylene Filled with Various Fillers. In: Europe Africa Conference 2017 of the Polymer Processing Society (PPS); 26-29 June 2017;

Verlag GmbH: Düsseldorf; 1995. 448 p. ISBN: 3-18-234192-8

19-20 June 2012; Hanser, München: 2012. pp. A6-1–A6-11

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Naples Federico II; 2008

doi.org/10.1007/BF01513064

2003:1-36

Dresden

10.1007/BF01534327

Carl Hanser Verlag; 2015. 225 p. ISBN: 978-1-56990-517-3

**Figure 18.** Flow functions of LDPE filled with varying volume fractions of glass beads (d50 = 60 μm), (T = 190°C); (a) measured values; (b) comparison of experimental data (symbols) to predicted flow curves (lines).

Based on the *generalized interaction function*, the shear thinning flow behavior of polymer suspensions can be estimated with high accuracy, regardless of filler type, particle size and volume fraction. The procedure for this is illustrated below using the example of LDPE filled with glass beads (d50 = 60 μm):


#### **Author details**

Nico Laufer<sup>1</sup> \*, Harald Hansmann2 , Christian Boss<sup>1</sup> and Stefan Ofe<sup>1</sup>

\*Address all correspondence to: laufer@ipt-wismar.de

1 Institute for Polymer Technologies e. V., Wismar, Germany

2 Department of Mechanical Engineering, Hochschule Wismar University of Applied Sciences, Technology, Business and Design, Wismar, Germany

#### **References**

[1] Shenoy A. Rheology of Filled Polymer Systems. Dordrecht: Kluwer Academic Publishers; 1999 475 p. ISBN: 0-412-83100-7


Based on the *generalized interaction function*, the shear thinning flow behavior of polymer suspensions can be estimated with high accuracy, regardless of filler type, particle size and volume fraction. The procedure for this is illustrated below using the example of LDPE filled

**Figure 18.** Flow functions of LDPE filled with varying volume fractions of glass beads (d50 = 60 μm), (T = 190°C);

**2.** determination of the functional relationship between consistency index and volumetric

**3.** determination of the functional parameters of the generalizes interaction function (Eq. (8))

**5.** estimation of the flow functions for arbitrary volumetric filler concentrations (Eq. (9); **Figure 18b**)

and Stefan Ofe<sup>1</sup>

, Christian Boss<sup>1</sup>

2 Department of Mechanical Engineering, Hochschule Wismar University of Applied

[1] Shenoy A. Rheology of Filled Polymer Systems. Dordrecht: Kluwer Academic Publishers;

**1.** analysis of the flow functions for different filler concentrations (**Figure 18a**)

(a) measured values; (b) comparison of experimental data (symbols) to predicted flow curves (lines).

with glass beads (d50 = 60 μm):

filler concentration (Eq. (7))

**Author details**

Nico Laufer<sup>1</sup>

150 Polymer Rheology

**References**

**4.** derivation of the shift factor B (Eq. (6))

\*, Harald Hansmann2

1999 475 p. ISBN: 0-412-83100-7

\*Address all correspondence to: laufer@ipt-wismar.de

1 Institute for Polymer Technologies e. V., Wismar, Germany

Sciences, Technology, Business and Design, Wismar, Germany


[17] Laufer N, Hansmann H, Koch M, Boss C, Ofe S, Düngen M. Influence of interparticle interaction effects on the rheological properties of low density polyethylene filled with glass beads. Polymer Testing. 2017;**62**:440-446. DOI: https://doi.org/10.1016/j. polymertesting.2017.07.019

**Chapter 8**

**Provisional chapter**

**Rheology of Highly Filled Polymers**

**Rheology of Highly Filled Polymers**

DOI: 10.5772/intechopen.75656

In many applications and/or manufacturing processes, highly filled polymers are necessary. One of these fields is powder metallurgy, where polymers or polymer mixtures are used to enable the shaping process within the production of the parts. Metal and also ceramic powders are mixed with different polymeric substances with a powder content of more than 50 vol%. Within the production, this mixture, called feedstock, has to flow into the final shape. Thus, for a proper understanding of the production processes, fundamental knowledge on the flow behavior of the feedstocks is required. For the rheology of polymers, several techniques together with the proper equipment are available. In the case of high viscosities, rotational and high-pressure capillary rheometers (HPCRs) are used. To gain reliable data, a proper measurement procedure is essential, which means that the operator has to have a deeper physical understanding of the material and the effects arising during the measurements. Therefore, this chapter gives an insight into rotational and high-pressure capillary rheometry with special emphasis on the behavior of polymers highly filled with stiff particles. Based thereon important remarks on the measurement equipment, procedure and evaluation of the measured data are provided.

**Keywords:** rheology, polymer, highly filled, feedstock, plate-plate rheometer, high-pressure capillary rheometer, yield stress, powder loading, Bagley correction

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.

Joamin Gonzalez-Gutierrez and Clemens Holzer

Joamin Gonzalez-Gutierrez and Clemens Holzer

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Christian Kukla, Ivica Duretek,

Christian Kukla, Ivica Duretek,

http://dx.doi.org/10.5772/intechopen.75656

**Abstract**

**1. Introduction**

[18] Laufer N, Hansmann H, Boss C, Ofe S. Effects of Volume Fraction, Size and Geometry of Different Fillers on Interparticle Interactions in LDPE Melts. In: 3rd International Conference on Rheology and Modeling of Materials; 02-06 October 2017; Miskolc-Lillafüred

#### **Rheology of Highly Filled Polymers Rheology of Highly Filled Polymers**

Christian Kukla, Ivica Duretek, Joamin Gonzalez-Gutierrez and Clemens Holzer Christian Kukla, Ivica Duretek, Joamin Gonzalez-Gutierrez and Clemens Holzer

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.75656

#### **Abstract**

[17] Laufer N, Hansmann H, Koch M, Boss C, Ofe S, Düngen M. Influence of interparticle interaction effects on the rheological properties of low density polyethylene filled with glass beads. Polymer Testing. 2017;**62**:440-446. DOI: https://doi.org/10.1016/j.

[18] Laufer N, Hansmann H, Boss C, Ofe S. Effects of Volume Fraction, Size and Geometry of Different Fillers on Interparticle Interactions in LDPE Melts. In: 3rd International Conference on Rheology and Modeling of Materials; 02-06 October 2017; Miskolc-Lillafüred

polymertesting.2017.07.019

152 Polymer Rheology

In many applications and/or manufacturing processes, highly filled polymers are necessary. One of these fields is powder metallurgy, where polymers or polymer mixtures are used to enable the shaping process within the production of the parts. Metal and also ceramic powders are mixed with different polymeric substances with a powder content of more than 50 vol%. Within the production, this mixture, called feedstock, has to flow into the final shape. Thus, for a proper understanding of the production processes, fundamental knowledge on the flow behavior of the feedstocks is required. For the rheology of polymers, several techniques together with the proper equipment are available. In the case of high viscosities, rotational and high-pressure capillary rheometers (HPCRs) are used. To gain reliable data, a proper measurement procedure is essential, which means that the operator has to have a deeper physical understanding of the material and the effects arising during the measurements. Therefore, this chapter gives an insight into rotational and high-pressure capillary rheometry with special emphasis on the behavior of polymers highly filled with stiff particles. Based thereon important remarks on the measurement equipment, procedure and evaluation of the measured data are provided.

DOI: 10.5772/intechopen.75656

**Keywords:** rheology, polymer, highly filled, feedstock, plate-plate rheometer, high-pressure capillary rheometer, yield stress, powder loading, Bagley correction
