Münstedt Rheological and Morphological Properties of Dispersed Polymeric Materials

Filled Polymers and Polymer Blends
1. Auflage 2017
ISBN: 978-1-56990-680-4
Verlag: Hanser Publications
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 474 Seiten

The rheology of polymer melts plays an important role today in industry and academia. Although several textbooks on this subject are available, with very few exceptions they cover homogeneous products only. This book is unique in that it focuses on heterogeneous systems such as particle-filled materials and polymer blends, which are highly important in the world market. It deals with similarities and differences of the flow properties of these two classes of material, providing both a fundamental and a practical understanding.

Key points of the book are the viscous and elastic properties of engineering polymers filled with functional particles and the influence of nanoparticles on rheological properties.

Two key aspects of rheological measurements are discussed: the influence of heterogeneous structures on the flow of materials important for processing and the use of rheological means to get an insight into morphological features. Both approaches are applied to particle-filled melts and to polymer blends. In the latter case it is shown in detail in which way the deformation of droplets formed by the dispersed phase can be affected by outer deformation, particularly in elongation.

Autoren/Hrsg.

Münstedt, Helmut

Leseproben

2 General Rheological Features of Polymeric Materials During processing, polymeric materials can be exposed to various types of deformation. Shear is prevalent in tube flow, for example, while elongation occurs whenever a fluid passes through narrowing ducts. The stresses and strain rates applied during processing can cover a wide range and, therefore, material functions are important for a great number of polymer based systems. They are divided into the linear range, where material properties are not dependent on external parameters like shear rate or stress, and the nonlinear regime in which distinct dependencies exist. The nonlinear behavior is dominant in most processing operations, linear rheological quantities provide relations with the molecular or morphological structure of polymeric materials and compounds. Polymers are viscoelastic, that is, they possess elastic and viscous properties. Therefore, their rheological behavior is time dependent. Detailed knowledge on this matter can be found in various textbooks on rheology, for example, [2.1], [2.2], [2.3], [2.4]. Two important consequences can be drawn from the time dependence. In applications of rheological measurements to processing, comparable time frames have to be assessed and for any definite relation between rheological quantities and structural parameters, time-independent values should be chosen. Moreover, a sometimes pronounced temperature dependence of the rheological behavior should be taken into account. Additionally, the pressure dependence of the viscosity may come into play in a processing operation like injection molding. From this short discussion it is obvious that a comprehensive rheological characterization of polymeric materials requires a lot of effort. Sophisticated experimental tools are needed. 2.1 Experimental Modes 2.1.1 Definitions The principles of rheological experiments are rather obvious. A deformation is applied to a sample and the resulting stress is measured or the other way around. In its general form the stress acting on a sample is described by a symmetrical tensor and the deformation or deformation rate by the corresponding tensors, see [2.4]. In this book, which is concerned with the influence of heterogeneous phases on rheological properties, only results for the simplest types of deformation are presented, namely shear and uniaxial elongation. Therefore, the fundamentals of these two modes are discussed in the following. Shear is defined as (2.1) with a being the shear angle, ?x the relative displacement of one surface of a prismatic body with respect to another in parallel to it and ?y the distance between these surfaces. The shear stress for such a deformation follows as (2.2) where F is the tangential force in the direction of the displacement acting on the surface area A, s stands for the component s12 of the stress tensor. In rheology the time derivative of the shear, the shear rate , plays an important role as the viscosity defined by (2.3) is the quantity describing the viscous behavior. Using Eq. 2.1 it follows (2.4) That means the shear rate is equal to the derivative of the relative velocity v of the surfaces with respect to the local coordinate perpendicular to them. This quantity corresponds to the velocity gradient. In uniaxial elongation of polymer melts the strain increment is defined as and (2.5) The variable eH is called the Hencky strain or natural strain, as the change in length dl is related to the actual length l and not as in the case of the technical or Cauchy strain to the initial sample length l0. ? is the stretching ratio. The elongational rate then follows from Eq. 2.5 as (2.6) with v = dl/dt. The index “H” is omitted as a matter of convenience. The elongational viscosity is defined analogously to that in shear as (2.7) The tensile stress sE, which corresponds to s11 of the stress tensor, follows as (2.8) where F is the time-dependent force acting perpendicular to the cross section A. In contrast to shear, the area the force is attached to changes during extension. It should be mentioned at this point that properties specific to a material such as the viscosity have to be independent of the method by which they were obtained. To determine the viscosity according to Eqs. 2.3 and 2.7, two ways are viable. Either the stress can be set and the deformation rate measured as a function of time or the deformation rate can be chosen and the time dependence of the corresponding stress monitored. As the molecules of a polymeric material react differently under a given stress or strain rate, the time dependencies of the viscosities are not the same even if the steady-state values attained in the two modes are equal. Examples for such behavior can be found in [2.23], for example. In the steady state of deformation the corresponding values of stress and strain rate are the same, of course, and the viscosity becomes time independent. In rheology, time dependencies of the ratio of stress and deformation rate are frequently discussed and they are usually called viscosities. For the purposes of exactness, in those cases the experimental mode applied should be indicated, however. Experiments at a constant deformation rate are commonly called stressing experiments and those at a constant stress are called creep experiments. 2.1.2 Creep and Creep Recovery The principle of creep and subsequent creep-recovery becomes obvious from Fig. 2.1. It is presented for shear, but the same experimental procedure holds for elongation, too. Figure 2.1 Principle of creep and creep recovery A distinct stress is applied to a sample at the time t = 0 and then kept constant. The strain is measured as a function of time. The material function discussed is the compliance defined as (2.9) in shear and (2.10) in elongation. For a subsequent creep recovery, the stress is set to zero at the creep time t0, and the reversible part of the deformation is measured as a function of time. It is designated ?r in shear and er in elongation. The recoverable compliance in shear is defined as (2.11) and that in elongation reads (2.12) The recoverable compliances are clearly defined and represent a direct measurement of the elastic property of a material. As presented in Fig. 2.1, Jr reaches a plateau value after long enough recovery times tr. According to the theory of linear viscoelasticity the creep compliance can be described by (2.13) with J0 being the instantaneous elastic compliance, ?(t) the retarded viscoelastic compliance, and ?0 the zero-shear viscosity (see, for example, [2.4]) As Jr (t) approaches a constant value with time, it follows from Eq. 2.13 that for long enough creep times the approximation (2.14) holds. Consequently, in a linear plot of J(t), from the slope of the creep compliance as a function of the creep time, the zero-shear viscosity can be determined, whereas in the frequently used double-logarithmic plot, J as a function of t approaches a straight line with the slope 1, the intercept of which corresponds to the reciprocal viscosity. It should be mentioned at this point that the steady-state value Je of the recoverable compliance Jr (tr) as a function of the recovery time tr is only reached when the previous creep has been performed long enough to attain the equilibrium state, that is, Je has to be independent of the duration t0 of the creep experiment. In [2.5] and in Section 10.3 it is demonstrated how the experimental parameters for such a state can be determined. The corresponding linear quantity, which is of special importance for the characterization of dispersed polymers as shown later, is called the linear steady-state recoverable shear compliance , that is, (2.15) The time dependence of Jr(tr) in the linear range for t0 ? 8 has some special importance insofar as a discrete retardation spectrum can be calculated according to (2.16) because the instantaneous compliance J0 is generally...