# Temperature-Modulated Differential Scanning Calorimetry (TM-DSC) at High-Temperatures

Temperature modulated DSC, abbreviated TM-DSC, is an extension of the conventional DSC technique. It was introduced by Reading et al. in the early 1990s when they went public with a software modification allowing the superimposition of a sinusoidal temperature fluctuation onto an underlying heating or cooling rate. Since then, use of the method has become widespread, especially in the low-temperature field in the areas of polymers and pharmaceuticals.

With the launch of the new 400 series instruments in 2008, NETZSCH has expanded the application range of this technique to higher temperatures for the first time. This allows TM-DSC to now also be applied to inorganic materials like metals, alloys, minerals or glasses.

## Theoretical Background of TM-DSC

The benefit of the method is the separation of complex overlapped effects. In order to realize this, the heating rate used is not constant but superimposed by a sinusoidal wave.

T(t) = T0 + HR.t + A.sin(? t) --> dT/dt=HR+A ? cos(? t)

where:

T0: starting temperature
HR: underlying heating rate
? : angular frequency
t: period
A: amplitude

Figure 1. Modulated heating rate with a period of 60 s and amplitudes of 0.1, 0.3 and 0.5 K (underlying heating rate: 2 K/min).

## Dynamic Measuring Modes

Depending on the selected parameters for period, amplitude, and underlying heating rate, various dynamic measuring modes can be executed, namely: heat only (A? < HR), heat-cool (A? > HR) and heat-iso (A? = HR). As a result, the sample will either be heated only, heated and cooled, or heated and alternately held at a constant level for a while.

The heat-only mode is preferred for eliminating reversible melting and crystallization.

Additionally, the quasi isothermal mode can be used to determine heat capacity.

As a consequence of the perturbation (modulated heating rate), the sample temperature oscillates in a sinusoidal manner as well, resulting in a fluctuating heat flow signal (Fig. 2).

Figure 2. TM-DSC measurement of a glass sample, carried out with an STA 449 F1 Jupiter® system in synthetic air at a heating rate of 3 K/min, for a period of 60 s and with an amplitude of 0.5 K

There is normally a phase shift (delay) between the perturbation and the response. TM-DSC mathematically deconvolutes this response by means of Fourier analysis into two types of signals, a reversing and a non-reversing one. In addition, it calculates an average heat flow (total heat flow) which is analogous to the DSC signal using a linear heating rate.

## What Kind of Signals Can Be Separated?

Specific heat changes are always visible in the reversing DSC curve. In contrast, time-dependent processes like relaxation, re-crystallization, curing, decomposition, or evaporation are always apparent in the non-reversing DSC curve.

Therefore, it should be possible to easily separate glass transitions from relaxation or re-crystallization effects (as can be seen in Fig. 2 and 3). Melting processes, however, as well as fast chemical reactions, are visible in both the reversing and non-reversing DSC signals. In this context, the experimental parameters have a decisive impact on the test result. For specific parameter sets, it may be feasible to achieve a good separation between, for example, melting and the decomposition process; for other sets it may not.

Figure 3. Measurement curve of fig. 2 split into the reversing and the non-reversing signal. The glass transition is clearly visible in the reversing signal (green curve); the non-reversing signal (red curve) shows the relaxation as well as two crystallization effects. The blue curve is the total heat flow curve, equivalent with the curve of a conventional DSC instrument.

The reversing (or alternating) heat flow is heat capacity-dependent and represents the thermodynamic component. The non-reversing (or non-alternating) heat flow represents the kinetic component.

## Examples

The following test runs (1) and (2) were carried out with an STA 449 F1 Jupiter® system equipped with a steel furnace, a type S sample carrier and Pt/Rh crucibles with lids. The corresponding modulation was performed by using liquid nitrogen cooling in the manual mode (35% basic power).

## Steel

According to the iron-carbon phase diagram, the alpha-beta transition of iron will take place at around 700°C to 800°C, mainly depending on the carbon content of the sample. In the same temperature range, the Curie transition from the ferromagnetic to the paramagnetic state of iron occurs, sometimes leading to an overlapping of the two effects (see Fig. 4).

Figure 4. STA measurement on steel (heating rate: 5 K/min)

The result of the corresponding TM-DSC experiment can be seen in Fig. 5. The magnetic change as a second-order transition appears in the reversing part (black dashed curve), whereas the structural change becomes evident in the non-reversing part (red dashed curve), with an extrapolated onset temperature of 756°C.

Figure 5. TM-DSC measurement on steel (heating rate: 5 K/min, period: 60 s, amplitude: 0.5 K) blue: total heat flow, red: non-reversing curve, black: reversing curve

## Isothermal cp Determination

At the moment, the ASTM International Technical Committee is working on a new standard (ASTM E 37; 3rd draft was published in August 2008) for determining specific heat capacity by sinusoidal modulated temperature differential scanning calorimetry. The operating range of tests is defined to be between -100°C and 600°C.

In order to find out if this method can also be applied to higher temperatures, a measurement on sapphire was performed with isothermal steps (30 minutes each) at 600°C, 700°C, 800°C and 900°C (see Fig. 6).

Figure 6. TM-DSC measurement on sapphire (heating rate: 5 K/min, period: 60 s, amplitude: 0.5 K) blue: sapphire as sample, red: sapphire as standard

The evaluation procedure for such tests is already included in the NETZSCH Proteus software. The calculated results are depicted in Fig. 7 together with the theoretical cp curve for sapphire, already stored in the software.

Figure 7. Specific heat determination on sapphire - comparison between experimental (colored symbols) and theoretical data (violet curve)

The difference between the experimental and the nominal values is within the given temperature range less than 2% and therefore in the same range of accuracy what can be achieved with the DSC 404 or STA 449 systems by using the dynamic ratio method or the method according to ASTM E 1269.

## Conclusion

TM-DSC as a method does indeed meet its requirement of being able to separate superimposed effects in various cases. Glass transitions can be separated well from decomposition, relaxation, evaporation, or cold-crystallization processes. Additionally, it is a suitable tool for determining cp in the quasi-isothermal mode within tight tolerances. But if melting is involved, the choice of the modulation parameters has to be taken into consideration. Under certain circumstances, these can have a decisive influence on the measurement results for the reversing and non-reversing part.

This information has been sourced, reviewed and adapted from materials provided by NETZSCH-Gerätebau GmbH.