Thermomechanical analysis (TMA) predates the use of dynamic mechanical analysis techniques. TMA is used for Tg determination, but is significantly less sensitive than DMA and cannot be used for studying the weaker relaxations, as seen in many polymers. In many respects TMA is the simplest form of thermal analysis equipment. A small sample is mounted in the instrument, which is surrounded by a furnace and the variation of sample length is recorded as a function of time or temperature.

One important application area is the derivation of the coefficient of thermal expansion (CTE). This is usually performed using tension or compression geometries and measuring the expansion; although modern TMAs generally have the same range of deformation geometries as used by DMA.

Another variant of TMAs is the dynamic TMA. These function with half the facilities of a DMA, in that they apply a small constant dynamic load throughout a thermal scan, usually made from low to high temperature. When the sample is glassy, the force is insufficient to cause significant deformation, but as the modulus falls through the glass transition, then the resultant displacement becomes larger and can be seen as an envelope of the TMA signal. Note that the dynamic TMA mode does not measure the phase difference between the force and displacement signals. It just reports the displacement amplitude resulting from the dynamic force.

Calibration of TMAs is relatively straightforward. The displacement (height) signal can be calibrated by inserting accurately measured height samples and noting the instrument output. The offset and gain can then be set to match the true sample size. The temperature is set by the same principle as that used in DSC, namely by melting point standards. Force can usually be calibrated by placing a known weight on the system and noting the force needed to offset it.

For accurate quantitative measurements the effect of the baseline may also need to be taken into account. Normally this only need be carried out when CTE measurements are being made. If the softening point only is required then baseline subtraction is unnecessary. Results of CTE measurements may also be compared to a standard, in a similar manner to specific heat measurements, but provided care is taken with calibration and that scan rates used are fairly low to avoid thermal lag, results obtained should be accurate.

If a film is being measured in extension then the baseline may be measured with a known sample in place. The normal procedure here is to use a well-characterised material with a known CTE. A thermal scan can be performed with quartz or aluminium, for example, using the same sample length and heating rate as will be used in the actual determinations. The known sample expansion can be subtracted from the measured result and this difference is due to the instrument’s baseline, which in turn can be subtracted from future experiments on unknown material. Note that this baseline usually depends on sample length, geometry, heating/cooling rate, thermal conductivity and heat capacity. If any of these parameters change, then the baseline should be remeasured. With respect to the sample’s thermal properties it is best that a material closely resembling the sample under test is used for the calibration.

• Experiment with zero load

Figure 1 shows a classic TMA trace for a polymeric sample being heated through its glass transition. Here the polymer is the amorphous material, poly(carbonate). A 10 mm long bar sample, with a cross-section of approximately 4×4 mm² was mounted in the tension clamps and heated at a rate of 2◦C/min. The ordinate axis shows the sample displacement, with temperature as the abscissa. The indicated temperature in the figure shows the onset calculation, which is the intersection of the glassy sample thermal expansion, from 30 to 130◦C and the rubbery sample expansion from 150 to 170◦C. The intersection can be used as a measure of the glass transition. These data were obtained by mounting a sample in tension clamps and applying zero load. Such an experiment allows free expansion of the sample, which permits the determination of the CTE.

Figure 1 Tg from the onset of thermal expansion plot. The sample in the case is under zero force. A film or fibre may need to be under very slight tension (a few mN) to hold the clamps apart.

• Experiment with constant load

Figure 2 shows thermal expansion data for the same polymer (polycarbonate), tested as a 10 mm long bar sample mounted in the tension clamps, but this time with a compressive load of 1 N. The glassy expansion occurs as before, but when the sample softens at the Tg it is progressively squashed under the compressive load. The onset temperature for the Tg is the same, 145.9◦C. Figure 3 shows the two curves together.

Figure 2 Tg from the onset of thermal expansion plot with the sample under compressive load. At Tg the samples softens and is compressed.

Figure 3 Comparison of the effect of differing applied load to a thermal expansion plot. A range of curves could be produced depending upon the force applied to the sample.

• Coefficient of thermal expansion determination

Figure 4 shows the coefficients of thermal expansion (CTEs) calculated from the slopes of the displacement versus temperature plots, from the above experiments. The CTE is the slope divided by the sample length, i.e. the amount of expansion (mm/mm/◦C). Both glassy CTEs are comparable, but only the data from the no-load experiment have been used to provide the rubbery CTE data. The data under load represent how easily the sample deforms and have nothing to do with the thermal expansion of the sample.

Figure 4 Thermal expansion coefficients for glassy and rubbery states.

• Experiment with constant and dynamic load

Figure 5 shows data from the poly (carbonate) sample run with a compressive load. In addition to the static load, a constant dynamic load at a frequency of 1 Hz was applied throughout the temperature scan. At the start, the sample is very rigid and the dynamic displacement is less than 1 m. After the static Tg determined above, the dynamic displacement is observed to increase over 100-fold. This shows the increased sensitivity that is available from dynamic equipment.

Figure 5 Polycarbonate bar in dynamic TMA mode showing the dynamic amplitude trace in addition to the thermal expansion trace observed under compressive load.

One advantage of performing the dynamic load TMA experiment on a DMA is that we can also view the tan δ values. Figure 6 shows these data. The immediate difference apparent from the two traces is the difference between the Tg as defined by the onset from the displacement measurement and the Tg as defined by tan δ. The onset Tg is essentially obtained from a static or low-frequency test. This difference is due to the frequency dependence of the Tg.

Figure 6 Dynamic TMA mode also showing tan δ plot.

• Baseline measurement example

Figure 7 shows baseline correction data obtained using the method described in above calibration procedures. An aluminium bar sample was used, with a 10 mm length and with a cross section of approximately 3.5×4mm². This was mounted in the tension clamps and heated at a rate of 2◦C/min. A value of 25×10⁻⁶ mm/mm/◦C was used for the CTE of the aluminium sample, which is calculated over the entire ramp by multiplying the temperature difference by this value and the sample length. This value is then subtracted from the observed expansion/contraction values and the resultant curve is the instrument baseline. This has then been fitted to a fourth-order polynomial (or a straight line fit can be used if it is linear) and this polynomial is used in future experiments, the difference between the total displacement and this value being the sample expansion/contraction. As the total data are less than the calculated curve for aluminium, we can conclude that the instrument baseline shows a shrinkage on heating. This is quite normal. Due to various parts of the instrument being at different temperatures, either expansion or contraction is commonly observed. However, sample expansion should always be positive on heating, unless the sample is highly anisotropic.

Figure 7 Instrument baseline determination in extension mode. The upper curve is the theoretical aluminium response, the middle curve the actual data. The subtracted curve shown in bold is the calculated instrumental baseline.