Thermal analysis: basic concept of differential scanning calorimetry and thermogravimetry for beginners

Introduction

Thermal analysis consists of techniques used to determine the physical or chemical properties of a substance when it is heated, cooled, or held at a constant temperature. These techniques were first introduced back in 1887 by Henry Le Chatelier, in which is considered as the dawn of present-day thermal analysis. Nevertheless, since the end of the Second World War, it was not easy to perform such experiments. However, the rapid growth of the electronic tools and computer devices observed for the last 30 years, making it relatively easy to find thermal analyzers in an analytical laboratory. The modern thermal analyzers are apparently very easy to be used and it is common to see someone performs a measurement without a clear objective. When questions are asked: why did you perform this differential scanning calorimetry scan? Why did you use this protocol? The answer is: “this is only to see, and I use the standard protocol of the lab”. That is an erroneous statement and it reflects the negligent attitude. Looking at the scientific literature, it is possible to find many books or articles, which focus on thermal analysis methods and the instruments. Nevertheless, looking at many data published in the literature using these techniques, it appears that many mistakes are still made. Hence, the purpose of this paper is to show what are the common mistakes and how to do a good measurement rather than to explain what we can do for the data analysis. We firmly believe that a correct data discussion requires at first a correct data acquisition.

Despite of numerous books and articles published on thermal analysis method (Hatakeyama & Quinn, 1999; Loft, 1975; Saiter, Negahban, Claro, Delabare, & Garda, 2008; Schick, 2009; Wunderlich, 1994; Wunderlich, 2006; Wunderlich, 2007), these publications may be too difficult for course instructors or beginners to follow for their first attempt to the subject or experiment.

Thus, this article may serve as an alternative reference for the mentioned readers. In this article, we will highlight the basic instrumentation of differential scanning calorimetry (DSC) and thermogravimetric (TGA), as well as the step-by-step guides for the estimation of the glass transition temperature (T_g) after DSC. The examples and exercises for the T_g estimation are also provided. Additionally, the step-by-step guides for the determination of the degradation temperature and the activation energy (E_a) of the degradation are provided. The main objective of this article is to provide a basic fundamental of thermal analysis for beginners which is rather easy to follow and can be utilized for educational purposes. TGA is an important analysis which needs to be performed before the DSC measurement in order to avoid any sample degradation during the DSC measurement. Examples of DSC and TGA instruments are presented in Figure 1.

Figure 1:

Instruments of

(a) differential scanning calorimetry and (b) thermogravimetry analysis (Thermal Analysis, n.d.a,b).

For supplementary reading materials, we have listed the related journals and books in Annexe 1. There are also many thermal analysis conferences organized by local and/or international organization each year, and we propose to look for more information from the International Confederation for Thermal Analysis and Calorimetry (ICTAC) website (http://www.ictac.org/).

General consideration

Thermal analysis is the evolution of a physical property of “something” when the temperature changes according to a given time/temperature control. The values of two physical quantities must be known, which means that the equipment consists of at least two sensors, each of them require a calibration procedure. For instance, the determination of the change in the sample’s mass when the temperature is changed will involve two sensors, namely balance and thermometer. Each sensor has its own accuracy, sensitivity, domain of use, etc., which will give the limit of the measurements in terms of the expanded measurement uncertainty and the acceptable number of decimal points of the data. This consideration leads to:

Rule number 1

Before using any equipment, we must know its real performances.

• Name of the equipment

• Nature of the sensors, what is exactly determined, [volume change (ΔV), temperature change (ΔT), pressure change (ΔP), mass change (Δm), …]

• Method of measurements

• Expected measurement accuracy

• Domain of temperature able to be scanned

• Controlled heating rates available

• Controlled cooling rate available (cooling rate of many instrument is not under control)

• Baseline linearity and baseline quality

• Purge gas, nature, flux, how that is under control.

• What kind of samples are accepted by the equipment (solid, bulk, powder, liquid…)

The second point relates to the sample. The expected properties of the sample must be known. Preliminary studies based on published papers on the material or/and similar materials must be done. We can now enunciate:

Rule number 2

Before using any equipment, we must know what we want to know.

• The limit of temperature that a sample can reach before it is thermally degraded

• The melting temperature and the associated enthalpy

• A glass transition temperature

• A Curie temperature

• A secondary relaxation

• A value of heat capacity

• A kinetic of degradation, of crystallization, of curing…

The third point concerns the calibration procedure. As we have two sensors to calibrate, we must have a procedure for each of them. When the temperature changes, we have to consider the problem of heat transfer i.e. convection, conduction and radiation processes. These phenomena are affected by the geometry and the shape of the oven and so on. In other words, the effect of the heating rate on the heat transfer in the oven is fundamental and as a consequence, a calibration procedure will be valuable only for one given heating rate. If the heating rate is changed in the protocol, a new calibration must be done.

Exercise 1

A good exercise is to use the melting signal of a pure element determined by DSC. For instance, indium. The protocol is suggested to be:

• Insert 5 mg of indium in a DSC pan

• Run from 100 to 200 °C with a heating rate of 10 °C min⁻¹ (called C₀)

• Go back to 100 °C with a cooling rate of 10 °C/min

• Run from 100 to 200 °C with a heating rate of 20 °C min⁻¹ (called C₁)

• Go back to 100 °C with a cooling rate of 10 °C/min

• Run from 100 to 200 °C with a heating rate of 100 °C min⁻¹ (called C₂)

• Go back to 100 °C with a cooling rate of 10 °C/min

• Run from 100 to 200 °C with a heating rate of 1 °C min⁻¹ (called C₃)

• Go back to 100 °C with a cooling rate of 10 °C/min

• Run from 100 to 200 °C with a heating rate of 10 °C min⁻¹ (called C₄)

• Go back to room temperature.

Finally, remove the indium sample and keep it for the next calibration procedure. Now by plotting all the signals (except signal C₄) on the same graph, followed by another graph for signal C₀ and C₄ together, we must get something as shown in Figure 2.

Figure 2:

(a) DSC signals of the fusion of a pure element when scanned from low (spectrum C₀) to high heating rate (spectrum C₃) and (b) comparison of the effects of different successive melting/crystallization cycles on the shape of a fusion signal for a pure element.

When the heating rate increases, the comparison of the signals C₀–C₃ show:

• A shift to the higher temperatures of the fusion

• The magnitude of the signal increases

• The width of the signal increases

Nevertheless, by definition the fusion of a pure element does not depend on the heating rate. The energy necessary to melt the indium metal is the same for any heating rate used (Wendlandt, 1986; Wunderlich, 1994). Instead, the heating rate is affecting the instrument resolution and sensitivity. Thus, this observation is not the signature of the material but the signature of the equipment [c.fFigure 2(b)]. We can now write the:

Rule number 3

A calibration procedure is valuable only for one given heating rate, if the heating rate is changed, a new calibration procedure must be done.

The fourth rule is also linked to the calibration procedure. As we need to calibrate two sensors in a temperature domain, it is important to remember that what is true for one temperature is not necessary true for another one. For instance, to calibrate a temperature in a calorimeter, we may use the fusion of indium. We will obtain the temperature shift in order to know the true temperature. For example, the temperature of fusion of indium is 156.6 °C and the measurement with a given heating rate is 157.7 °C. We can deduce that we have to make a correction of 1.1 °C to get a good result. Nevertheless, that is true only for the temperature domain close to the fusion temperature. We may not know if the same temperature shift can be used at 20 °C. That is graphically explained in Figure 3.

Figure 3:

(a) One-standard calibration (b) at least two standards are needed to perform a good calibration.

Rule number 4

We need at least two standard references in the temperature domain investigated to perform a calibration.

One equipment may have the possibility to get simultaneously different quantities, for example heat flux, instantaneous sample’s mass and infrared (IR) spectra. However, this kind of equipment will not be performant for all the quantities measured. Each sensor must be independently calibrated. So, the common idea that we could win time is not true. That leads to:

Rule number 5

The more sensors we have, the more complex is the equipment and generally less sensibility each sensor will have.

Rule 1 – Rule 5 explain on the important steps for DSC users to apply before any measurement of sample is done. Apart from the instrumentation, estimation of the correct data is also crucial in order to obtain a precise and reproducible data.

The glass transition

Glass transition is one of the important properties of polymers, which describes the temperature region where the mechanical properties change from hard and brittle to soft and rubbery. This property is crucial in determining which polymers are suitable for particular end-use in any application. Polymers are classified as thermoplastic, thermosets and elastomer which consist of amorphous structure which make most polymers exhibit T_g. Figure 4 shows the classification of polymers which are classified as thermoplastic and thermosets. Both thermoplastic and thermoset polymers exhibit T_g which shows a transition from hard to rubber-like, marking a region of dramatic changes in the physical properties, such as elasticity and hardness. Hence, in this initiative, a good practice on the estimation of T_g will be highlighted. Three supplementary files (i.e.S1−Notes for Course Instructor, S2−Examples to Estimate T_g and S3−Exercise for Students) are provided. S1 describes the step-by-step guide in estimating the T_g using Moynihan’s approach. S2 provides the examples of estimation of T_g with and without Moynihan’s approach using manual graphical method and S3 provides four exercises to estimate the T_g using manual graphical method.

Figure 4:

Classification of polymers.

A good estimation of T_g may yield a T_g value that differs by 3–4 °C as compared to the imprecise estimation technique. For example, in a system of epoxidized natural rubber with 50 mol% epoxidation (ENR-50), a good estimation may give a T_g = −19 °C (Halim, Chan, & Kammer, 2019), and conversely, an imprecise estimation will normally give T_g = −15 °C. This is an example of common mistakes which can be observed in the literature. Consequently, the discussion based on this imprecise estimation may not be correct. Example of a good and imprecise estimation of T_g are presented in Figure 5. In this example, further analysis of the T_g values were done based on linear regression analysis as written in Eq. (1);

where Tgo is the glass transition temperature of neat polymer, Γ is the slope of the linear curve and W_S is the mass fraction of salt (Halim et al., 2019). As presented in Figure 5(a) and (b), good and imprecise estimation of T_g yield different values of Γ. It gives Γ = 0.42 and Γ = 0.38 for good and imprecise estimation of T_g, respectively, where the higher Γ value indicates higher freezing in of polymer chain’s degree of freedom with addition of inorganic salt to the ENR-50. This may suggest that the estimation of T_g is a crucial part before any data interpretation can be made.

Figure 5:

(a) Good and (b) imprecise estimation of T_g for ENR-50 as a function of mass fraction of salt. Dashed lines are the best fit regression of the experimental data with regression coefficient, r² = 0.90 and r² = 0.87 for good and imprecise estimation of T_g, respectively.

This approach that we proposed is easy to be followed for new users. A group of 39 new users of DSC were presented the step-by-step guides on estimation of T_g (refer to S2) and subsequently they tried to estimate the T_g using graphical method as in S3. The T_g values reported for poly(ethylene oxide) (PEO) are PEO = −52.0 ± 0.6 °C and ENR-25 = −45.0 ± 0.3 °C. Consequently, as a rule of thumb, the reported T_g values of PEO and ENR should be −52 and −45 °C, respectively. The guides enable the users to understand the basic working principles for estimation of T_g when they rely on the thermal analysis softwares in subsequent attempt.

We note here, different thermal analysis softwares may have different mathematical algorithms for the estimation of T_g. With the basic understanding as presented as in S2, the users may choose the suitable mathematical algorithm for data extraction based on the “shape” of the glass transition of the DSC scan. Thus, this article may serve as a suitable teaching material for teachers and instructors.

Thermogravimetry

In this section, thermogravimetry will be explained. Thermogravimetric analysis is an important analysis that should be carried out before DSC measurement. This is because, no mass loss or sample decomposition should happen in the DSC. Bad signals as well as damage to the instrument will occur. Thermogravimetry is the determination of the change in the sample mass during heating or time for a given temperature (c.fFigure 6).

Figure 6:

Two ways to perform a thermogravimetric measurement with variation of

(a) temperature and (b) time.

Thus, we need a balance and the best one is the famous Roberval one as shown in Figure 7. In this system the mass is not directly determined, only the mass added to keep the equilibrium is determined. This is an analogue to a constant zero measurement method used in a Wheatstone bridge.

Figure 7:

Roberval balance (left) and Wheatstone bridge circuit diagram (right) which has four arms connected at points a, b, c and d, R_X is the unknown resistance, R₁, R₂ and R₃ are known resistance where R₂ is adjustable and V_G is the measured voltage.

Different configurations of balance are shown in Figure 8, but whatever the shape of the oven, a good thermo-balance must be able:

1. To detect a mass variation of one micro gram in the full domain of temperature available.

2. To scan a domain of temperature from 10 °C to 1500 °C. 1000 °C can be enough for organic components and the lower temperature is required if the evaporation of water needs to be evaluated. This low temperature is also needed because the time lag between the temperature for which the measurement begins and the temperature for which the stability of the balance is obtained depends upon the heating rate and may need a long time for the water evaporation process to occur.

3. To control the nature and the flux of the gas (oxygen, air, nitrogen, argon) during experiment.

Figure 8:

Schematic of the position of the furnace with respect to the balance

(a) below the balance (b) above the balance and (c) beside the balance.

Assuming a constant pressure during all the experimental duration, equilibrium is obtained when the summation of all the forces applied is nil as written in Eq. (2).

If we applied this very simple relationship to our system, we have Eq. (3)

where P is the instantaneous force of gravity, P_a is the Archimedes reaction according to the fact that the system is in a fluid ambiance and has achieved its hydrostatic equilibrium, where the buoyant force is equal to its weight, and P_e is the force of gravity measured to get the equilibrium as shown in Figure 9.

Figure 9:

Forces engaged to get the equilibrium of the balance.

This is the value of m (T) that we want to know, and this one is determined by Eq. (4)

thus, we need to know the quantity ρ (T) V or at least its effect on the accuracy of our measurement. One way to observe the effect of Archimedes reaction consists to perform a measurement with an inert sample or with no sample, which is equivalent to determine the behavior and quality of the base line of the thermogravimetry. As Figure 10 shows, the baseline obtained can be different from the expected one because in addition to the Archimedes effect, the sensors will also give its own contribution (there is no reason that the sensor exhibits identical accuracy, identical linearity, for all the temperatures scanned).

Figure 10:

Example of a baseline obtained during a thermogravimetric measurement.

The first step using a thermobalance is to know what the baseline is, when the experimental conditions are changed. For that, we propose Exercise 2.

Exercise 2

A good training is to make different baselines by changing the experimental conditions, for example;

• Base line one (BL₁)

  • Nitrogen gas with a low value of the flux (F₁)

  • Empty oven

  • Heating rate of 10 °C min⁻¹

  • Domain of temperature scan from 50 to 800 °C (or 1000 °C if possible)

• Base line two (BL₂)

  • Nitrogen gas with a low value of the flux (F₁)

  • Empty oven

  • Heating rate of 50 °C min⁻¹

  • Domain of temperature scan from 50 to 800 °C (or 1000 °C if possible)

• Base line three (BL₃)

  • Nitrogen gas with a high value of the flux (F₂)

  • Empty oven

  • Heating rate of 10 °C min⁻¹

  • Domain of temperature scan from 50 to 800 °C (or 1000 °C if possible)

• Base line four (BL₄)

  • Nitrogen gas with a high value of the flux (F₂)

  • Empty oven

  • Heating rate of 50 °C min⁻¹

  • Domain of temperature scan from 50 to 800 °C (or 1000 °C if possible)

The next step is to superimpose these curves and to analyze the differences observed and conclude the effect of the heating rate and gas flux. Due to the different of the geometry and sensors of the equipment, the results obtained can be different. Nevertheless, by this way it is possible for each apparatus to determine what are the optimized values for the heating rate and the gas flux. We may now write:

Rule number 6

It is of prime importance to make a baseline and to analyze its shape before any new series of measurement with the same experimental conditions that we will use for the sample data acquisition.

After the quality of the baseline is determined, the calibration procedure has to be performed. As previously explained, the calibration procedure requires the true mass and the true temperature. Hence, we need to calibrate the two sensors.

For the mass sensor, it is relatively easy to get the reference of the mass as it is generally given by the balance supplier. Conversely, it is more difficult for temperature sensor as the standard material with a degradation process (mass loss) occurring exactly at one given temperature does not exist. A procedure using magnetic materials with different Curie temperatures may be used, but this method requires specific equipment and is difficult to bring into play. An alternative method is to get a certificate of calibration from equipment supplier, then choose a material for instance a poly(vinylchloride) (PVC) (plastic which exhibits a very simple signal of degradation which can be easily quantified, if of course the sample composition is well known), similarly, cellulosic materials can be used. The only problem is to have enough amount of sample to be able to recalibrate during many years and to be sure that the secondary reference is stable enough during storage. The signals expected on a thermogravimetric curve are summarized in Figure 11.

Figure 11:

Five different themogravimetric curves.

Using the example of Signal 1, it is possible to extract the information reported in Table 1 and which are also indicated in Figure 12.

Figure 12:

Quantities available from a thermogravimetric curve.

It is possible to obtain the eight parameters for each degradation step. The determination of quantities m_i, m_f and Δm are rather easy, but relatively not too easy for quantities T₁, T₂, T₃ and T₄ as these quantities depend greatly on the quality of the signal. Alternatively, it is better to use the derivative dm/dT curve to estimate the characteristic temperatures of the degradation process at its extremum, known as inflection point (T_{d, inflection}). The derivative curve obtained from a single step decomposition process is displayed in Figure 13. Example of TGA analysis where T_{d, inflection} and the temperature onset beginning of mass loss (T_{d, onset}) for poly(ethylene oxide)/natural rubber-graft-poly(methyl methacrylate) (PEO/NR-g-PMMA) binary blends (Zainal, Chan, & Ali, 2017) are listed in Table 2.

Figure 13:

Shape of a derivative thermogravimetric analysis (DTGA) curve.

Example of bad baselines are presented in Figure 14. In Figure 14(a), the first baseline shows a typical effect of a gas purge problem (e.g. the chimney of the evacuated gas is more or less obtruded). The second baseline is due to the gas, which is firstly quasi blocked in the chimney, and at a certain temperature the chimney is suddenly open. Cleaning procedures of the gas purge and gas evacuation equipment are needed to solve these problems. Baseline 3 happens when there is a defect in the thermocouple welding or the sensor. In this case, the measurement has to stop immediately, and repair is needed.

Figure 14:

Examples of (a) bad base lines and (b) bad sample signals.

Example 1 in Figure 14(b) shows a typical bad sample signal when the sample is a small size powder form which makes the particles easily to be extracted from the oven and then drop back into the oven during heating. Whereas Example 2 is observed when the powder drops outside of the oven.

Knowledge of thermal stability and degradation mechanism of material is important. For example, data of thermal stability and degradation mechanism of conducting polymers must be required in order to know the optimum performance of the polymers to be used in specific application at certain temperature as well as to avoid any polymer degradation. This is because, due to the loss of dopant and conductivity at high temperature, the use of conducting polymers in electronic devices, solid state batteries, chemical sensors, etc., has been restricted (Chen, Dong, Li, & Gao, 2009). Analysis from TGA should not only be restricted to different T_d values as in Table 2, but other important kinetic quantities, for example the E_a, pre-exponential factor (A) and order of degradation can be extracted. Many works have been reported on methods to determine these quantities (Carrasco, 1993; Freeman & Carroll, 1958; Friedman, 1969; Kissinger, 1957; Yang, Fang, Liu, Liu, & Zhou, 2000). These methods which are classified as integral, differential and special methods may involve a lot of experiments with tedious procedures and calculations. Hence, in this part, we discuss an alternative approach to determine the E_a quantity using the temperature-dependent of the rate of thermal degradation in terms of Hoffman’s Arrhenius-like relationship (the step-by-step guides are provided in S4−Estimation of E_a). In this relationship, the first derivatives of the mass retained (%) versus reciprocal of temperature is used as written in Eq. (5);

where R is the gas constant. The estimation of E_a quantity can be extracted from the slope of the semi-logarithmic plots of Eq. (5) as shown in the linear region in Figure 15.

Figure 15:

Plot of ln(|deriv. mass retained|) against 1/T₁. Solid regression curve is after Eq. (5). Data is retrieved from (Zainal et al., 2017).

Table 3 lists the E_a quantities for different systems estimated using the Hoffman’s Arrhenius-like relationship, retrieved from (Halim, Chan, & Sim, 2016; Zainal et al., 2017).

Conclusions

The basic overview of thermal analysis was presented, which covers the instrumentation of DSC and TGA, step-by-step guides for the estimation of T_g value, explanation on the estimation of quantity E_a based on Hoffman’s Arrhenius-like relationship as well as exercises for the estimation of T_g value. This initiative will enhance the understanding and suitable for teachers and course instructors to coach the university students on how to perform good measurements together with correct data acquisition.