Master Thermal Analysis in Just 30 Minutes!

Webinar summary

Thermomechanical analysis, or TMA, is a technique used to measure dimensional changes in a material while the material is subjected to a programmed change in temperature. The resulting TMA curve plots temperature or time on the horizontal axis and dimensional change on the vertical axis, often expressed as length change in micrometers or as a percentage change relative to the initial sample length. An upward shift in the curve indicates expansion, while a downward change indicates shrinkage. From these measurements, thermal expansion ratio, mean coefficient of liner thermal expansion, softening temperature, and dimensional changes associated with transitions or reactions can be evaluated.

The appropriate TMA method depends significantly on the sample shape and the measurement purpose. Compression loading method is used for self- standing solids samples such as blocks or rods, with a constant load applied from above while the sample is heated or cooled. Tensile loading method is used for non-self- standing samples such as films, fibers, or sheets, with the load applied in a way that stretches the sample during measurement. The penetration method is used mainly for plate- or disk-shaped samples and measures dimensional changes in the thickness direction by applying a load through a probe with a pin-shaped tip. Compression and tensile loading methods can determine expansion, shrinkage, and mean coefficient of liner thermal expansion, while the penetration method is especially useful for determining softening temperature under a defined load per unit area.

A TMA instrument consists of a load control mechanism, a differential transformer for detecting dimensional change, and a measurement attachment suited to the sample and method. In a differential expansion configuration, both the sample and the reference material are placed on the support tube attachment. Detection rods contact the surfaces of the sample and the reference, and their movement is transmitted to the core and coil of the differential transformer. The detection system measures the relative displacement between the core and coil, producing the TMA signal.

In a conventional single-rod expansion method, only the sample is measured directly, without a reference. The detected dimensional change includes not only the expansion or shrinkage of the sample, but also dimensional changes in parts of the measuring attachment system, such as the detection rod and support tube. When the sample’s dimensional change is large, changes attributable to the instrument itself may be negligible. However, for small samples or low-expansion materials, these factors can interfere with accurate measurement.

The differential expansion method improves accuracy by measuring the sample alongside a reference material —such as quartz or alumina—whose thermal expansion characteristics are well known from the literatures. Because both the sample and reference sides utilize similar detection rods and share the same support environment, expansion effects originating from the measuring instrument system can be canceled out. The actual sample expansion is then determined from the measured differential signal and the known expansion of the reference. This makes differential expansion measurement particularly useful for materials that undergo extremely small dimensional changes.

TMA curves can be analyzed to determine temperatures associated with changes in mechanical or dimensional behavior. Softening temperature or deformation temperature can be identifying the inflection point where changes from expansion to shrinkage, either by reading a peak top or by finding the intersection of tangent lines. A change in expansion rate resulting from transitions such as phase transitions can also be analyzed as an extrapolated temperature by drawing tangent lines before and after the change and finding their intersection.

Thermal expansion rate is calculated from the change in sample length between the reference temperature and target temperature, divided by the initial sample length and expressed as a percentage. The mean coefficient of linear thermal expansion, or mean CTE, indicates how much the sample expands or shrinks per unit temperature. It is calculated by taking the difference in the expansion rates over a temperature interval and dividing by the difference between the two temperatures. Because CTE depends on the selected reference temperature and target temperature, the temperature interval must be clearly defined.

Several application examples illustrate how TMA can characterize different materials. A glass sample measured by compression loading expanded as it was heated from room temperature, it initially expanded; subsequently, an inflection point marking an increase in the expansion rate appeared, before eventually shrinking. The inflection temperature where the expansion rate changed was analyzed as 290°C, and the softening temperature where expansion changed to shrinkage was 309°C. Expansion rate and mean CTE were then calculated using 50°C as the reference temperature.

Polytetrafluoroethylene, PTFE measured under compression loading method showed thermal expansion over the temperature range from -50°C to 200°C. The obtained CTE was about one order of magnitude larger than that of the glass sample, showing that PTFE undergoes much greater dimensional change in response to temperature. The PTFE curve also showed a rapid increase in expansion rate of about 1% between 20°C and 25°C, attributing a volume change associated with a crystal transition. This indicates that PTFE requires particular care near room temperature, as PTFE can undergo significant changes in shape.

PET film measured under tensile loading showed thermal behavior that was dependent on the measurement direction. The TMA curve for the specimen cut from the original film sheet in the length direction showed expansion, whereas shrinkage was observed starting around 100°C for the specimen cut in the width direction. This difference was attributed to stretching during film production, demonstrating that the thermal expansion behavior of the film can vary depending on the sampling direction.

The penetration method was used to evaluate the softening behavior of amorphous polyethylene terephthalate (PET). The sample began to shrink at around 70°C, followed by the shrinkage increased rapidly as the material softened. The softening temperature determined from the extrapolated temperature at the TMA inflection point was 86°C. Because penetration results depend on the applied load per unit area, the load condition must be specified. In this example, a 500 mN load was applied using a 0.5 mm diameter probe tip, corresponding to about 2.5 MPa.

The TMA8311 can operate from room temperature up to 1500°C as a stand-alone instrument. With cooling accessories, it can cover ranges from -70°C to 600°C using a refrigerated cooling unit or from -150°C to 600°C using an auto-filling type liquid nitrogen unit. It can also perform measurements under humidity-controlled atmosphere conditions from room temperature to 85°C and from 5% to 90% relative humidity.