The Rheology Handbook. Thomas Mezger

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       Figure 3.21: Flow curve showing a yield point

      (on a linear scale)

       Figure 3.22: Flow curve showing a yield point

      (on a logarithmic scale)

      Summary: Using the flow curve analysis methods mentioned above, the resulting yield point is dependent on the speed resolution of the viscometer or rheometer used. An instrument which can detect lower rotational speeds (e. g. nmin = 10-4 min-1) will display a lower yield point value compared to a device which cannot detect such low minimum speeds (e. g. displaying nmin = 0.5 min-1 only). Of course, the latter device cannot detect any motion below its measuring limits, therefore still evaluating any speed in this range as n = 0. As a result, a lower value of the yield point will be obtained by the more sensitive instrument. This can be illustrated clearly when presenting flow curves on a logarithmic scale (see Figure 3.22): The lower the smallest shear rate which can be detected, the lower is the corresponding shear stress. Therefore counts the following: A yield point is not a material constant since this value is always dependent on the options of the measuring instrument used.

      For this reason, the two methods (a and b) mentioned before should only be taken for simple quality assurance tests, thus, just for a rough estimation of a yield point.

      Note: Yield point and flow point

      For users in R & D, however, more modern methods are recommended compared to the simple methods as explained above, using flow curves. See Chapter 4.4 for analysis of yield points by a logarithmic shear stress/deformation diagram; or even better, see Chapter 8.3.4 to determine both yield point and flow point (oscillatory tests, amplitude sweeps). An overview on even further methods which might be used for yield point determination is given in [3.25].

       3.3.4.2Further information on yield points

      3.3.4.2.1a) Time-dependence of the yield point

      Yield point values depend on the duration of the test. With each new measuring point at the beginning of each new step on the stress ramp, the structure of the sample is stretched at first under the applied constant shear load. As a consequence, a constant, steady-state measuring value is resulting (e. g. in the form of the shear rate γ ̇ ) but only after a certain delay. To avoid this time-

      dependent start-up effect which is also called transient effect, the user should wait sufficiently long at each measuring point (see also Chapter 3.3.1b and Figure 2.9: no. 5). For samples showing clearly time-dependent behavior, differing measuring times for an otherwise identical preset test profile may result in different yield point values. A yield value also depends on the sample preparation before the test (e. g. concerning shear load, time effects, temperature) [3.26].

      Summary: A yield point is not a material constant. Since it is time-dependent, it depends on the conditions during the preparation of the sample as well as on the test conditions.

      Note: Structural strength at rest and frequency sweeps

      When determining structural strength or consistency-at-rest, frequency sweeps (oscillatory tests) are the better way of testing in principle since they take best into account the influence of time. Here, when presetting frequencies, time-dependent results are obtained since a frequency is an inversed time (see also Chapter 8.4.4a).

      For “Mr. and Ms. Cleverly“

      3.3.4.2.2b) Interaction forces and network of forces

      Dispersions and gels are showing yield points due to intermolecular forces (van-der-Waals forces). This includes dipole-dipole interactions between particles, and between particles and the surrounding dispersion agent. There are different kinds of interaction forces (with specification of the typical bonding energy per mol): Electrostatic interactions between permanent dipoles (Keesom forces; < 30 kJ/mol), interactions due to induction between permanent and induced dipoles (Debye forces; < 2 kJ/mol), and dispersion forces between mutually induced dipoles (London forces; < 40 kJ/mol) [3.22] [3.27] [3.64] [3.82]. They are all based on physical-chemical bonds (secondary bonds) between the molecules and have a considerably lower bonding energy, usually below 20 kJ/mol, compared to the chemical primary valency bonds which are acting within the molecules. These primary bonds are covalent electron-pair bonds, ionic or metallic “electron gas” bonds which are usually showing energy values of 50 to 400 kJ/mol, and maximum values of 1000 kJ/mol [3.20] [3.28]. Bonds via intermolecular hydrogen bridges (< 50 kJ/mol) are an exceptional type of physical-chemical secondary bonds. In large numbers, however, they can have a great effect on rheological behavior.

      Interactions may build up a three-dimensional network of forces. In the low-deformation range, this network occurs as a stable and solid-like structure resulting in elastic behavior (gel-like character, or gel-like state, see also Chapter 8.3.2a).

      3.3.4.2.3c) Plastic behavior

      DIN 1342-1 and -3 states the following: “For a plastic material, rheological behavior is characterized by a yield point.” And: “Plasticity is the ability of a material to show remaining deformation (and flow) only if the yield point is exceeded. Below the yield point occurs no or only elastic deformation.” Further: “A deformable material is called plastic if it behaves in the range of low shear stresses as a rigid, elastic or viscoelastic solid, in a higher shear stress range however, as a liquid. The shear stress value at which the transition takes place is called the yield point (or yield stress).” Sometimes further terms can be found in literature such as “plastic deformation”, “plastic creep”, or “plastic flow”.

      In 1916, Eugen C. Bingham (1878 to 1945) described the behavior of dispersions showing a yield point СКАЧАТЬ