Читать книгу The Rheology Handbook - Thomas Mezger - Страница 175

An approximation model for kinetic activity in chemistry was developed in the general form by Svante A. Arrhenius (1859 to 1927) who introduced an activation constant (see also Chapter 14.2: 1884) [3.74]. The Arrhenius relation in the form of a η(T) fitting function describes the change in viscosity for both increasing and decreasing temperatures:

Equation 3.6

η(T) = c1 ⋅ exp (-c2 / T) = c1 ⋅ exp [(EA / RG) / T]

with the temperature T in [K], (i. e. using the unit Kelvin), and the material constants c1 [Pas] and c2 [K] of the sample (where c2 = EA / RG), the flow activation energy EA [kJ/mol], and the gas constant RG = 8.314 ⋅ 10-3 kJ / (mol ⋅ K)

Conversion between the temperature units:

Equation 3.7

T [K] = T [°C] + 273.15 K

At a certain temperature, the flow activation energy E A characterizes the energy needed by the molecules to be set in motion against the frictional forces of the neighboring molecules. This requires exceeding the internal flow resistance, with other words, a material-specific energy barrier, the so-called potential barrier [3.27].

The exponential curve function (Equation 3.6) occurs in a semi-logarithmic diagram as a straight line showing a constant curve slope if (1/T) is plotted on a linear scale on the x-axis (with the unit: 1/K), and η on a logarithmic scale on the y-axis. In this lg η / (1/T) diagram, the so-called Arrhenius curve, temperature-dependent behavior occurs as a downwardly or upwardly sloping straight line for a heating or a cooling process, respectively.

Note : Recommended temperature range for fitting functions (Arrhenius and WLF)

The Arrhenius relation is useful for low-viscosity liquids and polymer melts in the range of T > Tg + 100K (with the glass-transition temperature Tg, see Chapter 8.6.2.1a) [3.10] [3.34]. For analysis of polymer behavior at temperatures closer to Tg, it is better to use the WLF relation. For more information on this time/temperature shift method TTS, see Chapter 8.7.1.