Evaluation Possibilities for the Glass Transition
Purpose
To describe the various methods for evaluating the glass transition using SBR as an example.
Sample
Uncross-linked SBR
Conditions
Measuring cell: DSC822e with liquid nitrogen cooling option
Pan: Aluminum 40 Pl, with pierced lid
Sample preparation: Elastomer sample of 11.970 mg; The sample was cooled from 10 °C to 50 °C at 0.2 K/min or 20 K/min.
DSC measurement: Heating from –100 °C to 50 °C at 10 K/min
Atmosphere: Nitrogen, 50 ml/min
The figure shows the DSC curves of samples that had been cooled beforehand at 0.2 K/min (black curve) or at 20 K/min
Interpretation
The shape of the glass transition curves depends on the thermal history of the sample. If the heating rate is greater than the rate at which the sample was cooled, then the glass transition is accompanied by an enthalpy relaxation peak. This effect can be seen in the black curve. The red curve was measured after the sample had been cooled rapidly, i.e. the heating rate of the measurement was less than cooling rate. In this case, an enthalpy relaxation peak is not observed. Storage of the sample at temperatures in the range of the glass transition or below can also give rise to an enthalpy relaxation peak.
The characteristic quantities of the glass transition are the glass transition temperature, Tg, and the step height at the glass transition, Δcp. Various standard methods are used to determine these quantities. Several of these methods are incorporated in the STARe software. Besides the STARe method itself, these include the DIN 51007 (DIN), the ASTM E 1356 and IEC 1006 (ASTM, IEC) evaluation methods as well as the determination of the fictive temperature at the glass transition according to Richardson (also described in DIN 51007). As can be seen from the figure, the values obtained for the glass transition temperature and the step height depend on the method of determination used. If the glass transition does not have an enthalpy relaxation peak, the glass transition temperatures determined by the STARe , ASTM and DIN methods are practically the same. The value determined by the Richardson method is slightly lower (about 0.6 K). A comparison of the step heights at the glass transition shows that the Δcp values can be divided into two groups (STARe and DIN methods: 0.466 J/gK; ASTM and Richardson methods: 0.432 J/gK). If an enthalpy relaxation peak occurs, then the differences between the individual Tg and Δcp values obtained from the different evaluation methods increase. The various methods are described below to show how these differences arise and to provide a basis for selecting the most suitable evaluation method for a particular application.
STARe method (+):
The bisector, a1, of the angle between the tangents above and below the glass transition is drawn. The point of intersection of this line with the measured curve is the glass transition temperature (midpoint).
DIN method (Δ):
The glass transition temperature (midpoint DIN) is the temperature at which the measured curve is equidistant between the upper and lower tangents (c1 = c2). c1 is the distance between the measured curve and the tangent below the glass transition. c2 is the distance between the measured curve and the tangent above the glass transition.
ASTM method (♢):
The tangent is drawn at the point of inflection in the region of the glass transition in the measured curve. The glass transition temperature is the midpoint between onset and endset of the inflectional tangent (b1 = b2).
Richardson method (□):
Areas are determined between the extrapolated tangents and the measured curve. The individual areas are drawn in the diagram and labeled A1, A2 and A3. The highest temperature of the area A1 is identical to the lowest temperature of the area A2. When A1 + A3 = A2, this temperature is defined as the glass transition temperature
STARe method:
The tangent at the point of inflection is drawn. This inflectional tangent intersects the two extrapolated tangents drawn above and below the glass transition. The step height, 'cp, is calculated from the difference in heat flow between the points of intersection:
Φu and Φo are the heat flows at the points of intersection of the extrapolated tangents with the inflectional tangent above and below the glass transition temperature, m is the sample mass and β the heating rate.
DIN method:
The step height is determined at the glass transition as in the STARe method, but instead of the inflectional tangent, the tangent of the measured curve at the DIN glass transition temperature is used. The tangent is shown in the diagram as a dashed red line.
ASTM method
The distance between the extrapolated tangents at the ASTM glass transition temperature is calculated.
Richardson Method
The distance between the extrapolated tangents at the Richardson glass transition temperature is calculated.
Comments
The Richardson glass transition temperature describes the actual state of the material before the measurement. It cannot be determined if chemical reactions or physical processes (such as crystallization, evaporation) take place in the glass transition region or if glass transitions overlap. The value of the glass transition temperature obtained with the other methods is also influenced by the shape of the curve, i.e. by the measurement conditions. For comparative measurements, it is therefore important to use the same measurement conditions and evaluation method for the Tg determination. In the ASTM and Richardson methods, the step height, Δcp, at the glass transition temperature is determined. Differences in these values can arise because the two glass transition temperatures differ. The values can be directly related to properties of the materials such as degree of crystallinity or filler content. This is not possible with the other methods for determining Δcp (STARe and DIN) because the step heights determined then depend on the width of the glass transition (slope of the tangents). These values are therefore greater than those from the Richardson and ASTM methods. The ASTM method was therefore used to determine Δcp in the experiments described in this booklet (unless otherwise noted).
Conclusions
When determining quantities at the glass transition, it is important to quote the measurement and evaluation methods used.
Evaluation Possibilities for the Glass Transition | Thermal Analysis Application No. HB401 | Application published in METTLER TOLEDO TA Application Handbook Elastomers Volume 1