The Rheology Handbook. Thomas Mezger

[3.21] [3.22].

3.5Temperature-dependent flow behavior and viscosity function

      This section informs about the temperature-dependence of viscosity. Here, the degree of the shear load is kept at a constant value for each single test interval.

3.5.1Test description

      Preset

      1 With controlled shear rate (CSR): γ ̇ = const (see Figure 3.34), and time-dependent temperature profile T(t), e. g. as an upward or downward ramp

      2 With controlled shear stress (CSS): τ = const (similar to Figure 3.34), and time-dependent temperature profile T(t), e. g. as an upward or downward ramp

      Result

      Function of τ (or γ ̇ , respectively) and η dependent on the temperature (as in Figures 3.35 to 3.37, if time t is replaced by temperature T on the x-axis; see also Figures 3.46 and 3.47).

      The shape of the curves of τ(T) and η(T) are similar because τ and η are proportional since

      τ = η ⋅ γ ̇ (here with γ ̇ = const). However, the curves of the functions of γ ̇ (T) and η(T) show an

      inverse shape since γ ̇ and η are inversely proportional (since η = τ/ γ ̇ , here with τ = const).

       Figure 3.46: Temperature-dependent viscosity curve

3.5.2Temperature-dependent flow behavior of samples showing no hardening

      Viscosity values always depend on the measuring temperature. In almost all cases, viscosity decreases if the sample is heated. Users mostly are interested in the softening or melting tempera­ture . Highly viscous materials usually show greater temperature dependence compared to low- viscosity ones.

      When cooling, the solidification temperature is determined. The term crystallization temperature is used for crystal-forming materials and freezing point for water, and sometimes, congealing temperature for gel-forming materials.

      Usually, the temperature is presented on the x-axis of the η(T)-diagram on a linear scale, and viscosity on the y-axis, either on a linear scale, as shown in Figure 3.46, or on a logarithmic scale, if the values are covering a wide range.

      Due to the strong dependence of all rheological parameters on the temperature, for the test protocol it is recommended to specify the measuring temperature exactly for each measuring point. It is therefore essential to control the temperature carefully. For information on “freeze-thaw-cycle tests” in order to evaluate temperature stability of emulsions, see Chapter 8.6.2.2b: oscillatory tests.

      Note: High-temperature test on a glass melt

      Viscosity tests were performed on a standard glass sample DGG1 from PTB (Physikalisch-Tech­nische Bundesanstalt, Braunschweig, Germany), using a concentric cylinder measuring geometry made of aluminum oxide (bob diameter 15 mm, cup internal diameter 30 mm), as rotational tests in the shear rate range of 0.1 s-1 to 10 s-1. After exceeding the softening point at T = 930 °C, in each case occurred ideal-viscous flow behavior, showing the following values of the shear viscosity η (see Table 3.4) [3.77].

Table 3.4: Viscosity values of a glass sample
measuring temperature	1000 °C	1050 °C	1100 °C	1200 °C	1250 °C	1350 °C	1400 °C
viscosity of the glass melt	760 Pas	310 Pas	150 Pas	40 Pas	30 Pas	12 Pas	7 Pas

      Values of the complex viscosity obtained with oscillatory tests on the same measuring sample resulted in similar results (see Note 3 in Chapter 8.6.2.2).

       Figure 3.47: Temperature-dependent viscosity curve of a material showing gel formation,

      hardening or curing

3.5.3Temperature-dependent flow behavior of samples showing hardening

      In order to enable an undestroyed curing process, shear loading should be low, for example at the shear rate of γ ̇ = 1 s-1. Figure 3.47 presents a temperature-dependent viscosity function of a material showing gel formation, hardening or curing.

      Minimum viscosity , gelation temperature or gel temperature, gel point or gelation point

      Mostly, the viscosity curve shows a minimum value ηmin. This point is sometimes called the softening or melting temperature. Evaluating coatings such as paints or powder coatings, the following information my be important for practical users: At this point a wet coating layer may show optimum flow, spreading and leveling behavior. However, if the value of ηmin is too low, a wet layer may be too thin, and it may show sagging and edge creep, giving not enough edge protection finally. On the other hand, if ηmin is too high, a layer may not level out smoothly enough, and de-aeration may be not sufficient to obtain a surface without so-called pinholes, craters or air bubbles finally. All these effects may reduce the gloss of the surface after all.

      Often, as a definition is taken: The gel temperature or gel point is reached if the viscosity has increased to a certain upper limiting value which was pre-defined by the user. The terms gelation temperature and gel temperature are often used with the same meaning.

      Information given in Chapter 3.4.3 on the test conditions and on the possible differences arising when using the different test modes controlled shear rate (CSR) or controlled shear stress (CSS) also applies here. Among others, one of the advantages of oscillatory tests is the accurate determination of the sol/gel transition temperature after the onset of gel formation (see Chapter 8.6.3b).

      Example 1: Testing epoxy resins

      1 Temperature at the viscosity minimum: at T = +165 °C (e. g. showing ηmin = 10 Pas)

      2 Gel temperature (when reaching the pre-defined value of η = 100 Pas): at T = +175 °C

      Example 2: Gelation point when cooling mineral oils (acc. to ASTM D5133 and D7110)

      Here, oils are cooled down in the range of T = -5 to -40 °C, at a constant cooling rate of

      ΔT/Δt = 1 K/h, which corresponds to one degree Celsius per hour (according to D7110 with 3 K/h). The gelation point is defined as the temperature value at which the oil viscosity is reaching

      η = 40,000 mPas = 40 Pas. Note: Here, a Brookfield viscosity is usually measured at the rotational speed of n = 0.3 min-1, and the shear rate is assumed to be γ ̇ = 0.2 s-1. In order to evaluate this relative viscosity values: see Chapter 10.6.2.

      Example 3: Gelation temperature of reaction resins when reaching the thousendfold viscosity value

      Gelation temperature Tgel is reached when ηgel = 1000 ⋅ ηmin with ηmin as minimum viscosity. Measuring via a temperature ramp with a gradient of ΔT/Δt = 2 K/min in the range of T = 50 °C until (Tgel + 10 K) , e. g. using a PP-geometry (gap 0.5 mm) at a constant shear rate of 10 s-1.

      Note 1: Gelation index GI, and GI temperature (according to ASTM D341 and D7110)

      When cooling oils, the gelation index GI is determined in temperature steps of ΔT = 1K (Kelvin; acc. to ASTM D5133 in the range of T = -5 to -50 °C) or of ΔT = 3 K (acc. to ASTM D7110 in the range of T = -5 to -40 °C) between two measuring points. Calculation of the GI after each step as