Modulated Temperature Thermomechanical Analysis (MT-TMA) is a way of separating the thermally reversing nature of linear expansion from irreversible changes in dimensions that accompany creep under load or relaxation of imposed stresses (such as orientation during manufacture).
Where a material is heated, it usually expands. On cooling, it will contract to the same original length. This is reversible thermal expansion and the rate of change of length with respect to temperature is the thermal expansion coefficient of the material. However, if the material softens as it is heated and (as is usual in the case of TMA) it is subjected to a mechanical load then it will flow and creep. This deformation is permanent and the specimen will not recover its original length on cooling. Alternatively, if the material was stretched when soft and then cooled before the experiment, residual stresses will have been left in the sample. On heating these will relax and the specimen will shrink. It can only be made to return to its original length by the original drawing process. The length changes measured by conventional TMA are therefore a convolution of these effects unless the specimen is completely isotropic and measurements are made under zero load (thermodilatometry).
If, however, a modulated temperature program (such as those used in MT-DSC) is employed rather than the conventional linear temperature ramp then it is possible to separate the temperature dependent thermal expansion from the time (& temperature) dependent creep or stress relaxation behaviour. An example of the typical raw data from such a measurement is shown below for a sample of epoxy resin run, as received, in a TMA at a heating rate of 0.2°C/min with a 600 s period, 1°C amplitude sinusoidal temperature modulation.
The conventional TMA curve (L) is simply a moving average of the length change over one period. The reversing thermal expansivity (alpha) is derived from the ratio of the amplitudes of the length change and temperature change using a discrete Fourrier transform. The total rate of length change (dL/dT) is simply the derivative of the average length with respect to temperature. As with MT-DSC there is a time lag between the temperature change and the sample response (delta). These four signals (shown below) are the fundamental data obtained from a MT-TMA experiment.
From this, it is readily apparent that the sample appears to show a large change in length as it goes through the glass-rubber transition. This effect is not sustained and the average rate of change of length passes through a maximum before decreasing again. This would be the typical finding from a conventional TMA experiment. The reversing thermal expansivity (alpha) shows a characteristic step change around 60°C which clearly identifies the Tg. The phase lag (delta) also shows a peak in this region. Both the thermal expansivity and phase lag show high temperature "tails" - this was investigated further by re-heating the sample under the same conditions:
The data for the "re-run" sample shows that it has increased in glass transtion temperature over the "as received" specimen. This is presumably as a result of post-cure of the sample during the initial measurement. The "tails" on the thermal expansivity and phase lag curves of the initial material around the Tg are presumably a consequence of this process occuring.
MT-TMA measurements can also be made on cooling. This has the advantage that the thermal history of the sample can be better defined (no residual stresses, etc.). In this way the effect of the temperature modulation can be investigated. Measurements on the same sample at two different modulation periods are shown below. This demonstrates that the thermal expansivity is dependent on the timescale of the measurement in a similar way to MT-DSC and DMA.
- D. M. Price, "Modulated-Temperature Thermomechanical Analysis" Journal of Thermal Analysis 51 (1998) 231-236
- D. M. Price, "Novel methods of Modulated-Temperature Thermal Analysis" Thermochimica Acta 315 (1998) 11-18
- D. M. Price, "Modulated-Temperature Thermomechanical Analysis" Proc. 26th NATAS Sept 13-15 (1998) Cleveland, Ohio, pp. 27-32 [available as PDF (66kB)]
- D. M. Price, G. M. Foster, "Modulated temperature thermomechanical analysis of fibres" Journal of Thermal Analysis & Calorimetry 56 (1999) 649-654