Thermal Characterisation: DSC, TGA, and TMA
The heat transfer calculations in Chapters 1–6 all required material properties: $k$, $\rho$, $c_p$, $T_g$, $T_m$, $\alpha$. This chapter shows where those numbers come from. Three instruments — the differential scanning calorimeter (DSC), the thermogravimetric analyser (TGA), and the thermomechanical analyser (TMA) — are the standard tools for measuring thermal properties of polymers. Every polymer scientist needs to be able to run them, read their output, and extract meaningful numbers.
Close your notes. Try each question from memory, then reveal the answer. The ones you cannot recall are exactly what this chapter reinforces.
RC-1. Write the formula for thermal diffusivity $\alpha$. Identify all three material properties it contains and explain physically what a high $\alpha$ means for how a polymer processes.
RC-2. From memory, give approximate $k$ values (W/mK) for PLA, HDPE, and steel. Which is lowest and why does that matter for polymer processing?
RC-3. In Chapter 6, cooling time for an injection-molded part was proportional to $s^2/\alpha$. If a process engineer replaces a 2 mm HDPE wall with a 2 mm PLA wall, and $\alpha_{\text{HDPE}} = 4\,\alpha_{\text{PLA}}$, by what factor does cycle time change?
7.1 Why Characterise?
You have been given a bag of white pellets labelled “polymer”. Before you can design a mold, set an extruder temperature, or predict how the part will behave in service, you need to know: When does it melt? How much heat does it release when crystallising? Does it absorb moisture? At what temperature does it soften under load? Does it contain fillers?
Thermal characterisation instruments answer all of these questions by measuring what happens to a small sample — typically 5–20 mg — as it is heated and cooled in a controlled way. The results feed directly into the heat transfer calculations you have been doing. DSC gives you $c_p$, $T_g$, $T_m$, and crystallinity. TGA tells you thermal stability and filler content. TMA reveals how dimensions change with temperature. Together, they form the thermal fingerprint of a polymer.
Before reading on — the central equation of this chapter is $c_p = \dot{Q}\,/\,(m\,\beta)$, which is just a rearrangement of $\dot{Q} = m\,c_p\,\beta$ — the same heat-capacity formula you used in every energy balance in Chapters 5 and 6. DSC is simply a measuring instrument for $c_p$, $T_m$, and $\Delta H_m$; the underlying physics has not changed. Similarly, the crystallinity formula $X_c = \Delta H_m/\Delta H_m^\circ$ is a ratio of "heat released by your sample" to "heat released by a perfect crystal" — the same fraction structure as percent yield in chemistry. Once you have $c_p$ from DSC, it feeds directly into $\alpha = k/(\rho\,c_p)$, which feeds into the Ballman–Shusman cooling-time formula from Chapter 6. The chain is: DSC → $c_p$ → $\alpha$ → $t_c$.
7.2 DSC: Differential Scanning Calorimetry
A DSC measures the heat flow into or out of a sample relative to an inert reference as both are heated or cooled at a controlled rate $\beta$ (K/min). The instrument records $dQ/dt$ (mW) vs. temperature (or time).
The governing relationship between heat flow and specific heat is:
$$\frac{dQ}{dt} = m\,c_p\,\frac{dT}{dt} = m\,c_p\,\beta$$
Rearranging, the specific heat can be extracted directly from the measured heat flow:
$$c_p = \frac{dQ/dt}{m\,\beta}$$
where $m$ is the sample mass (kg) and $\beta = dT/dt$ is the heating rate (K/s). In practice, DSC software integrates the heat flow curve over a temperature range to give the total enthalpy change $\Delta H$ (J/g):
$$\Delta H = \frac{1}{m}\int_{T_1}^{T_2} \frac{dQ}{dt}\,dt$$
Each thermal event in the polymer — glass transition, crystallisation, melting — produces a characteristic signature in the heat flow curve.
Measurement equation
$$c_p = \frac{\dot{Q}}{m\,\beta}, \quad \Delta H = \frac{1}{m}\int \dot{Q}\,dt$$
DSC measures heat flow $\dot{Q}$ (mW) vs. temperature; dividing by mass and scan rate extracts $c_p$; integrating a peak gives $\Delta H$.
Process chain scaling
$$c_p \xrightarrow{\,\div\,} \alpha = \frac{k}{\rho\,c_p} \xrightarrow{\,\propto\,} t_c \propto \frac{s^2}{\alpha}$$
Higher $c_p$ → lower $\alpha$ → longer cooling time. One DSC measurement unlocks the entire injection-molding thermal calculation.
7.3 Reading a DSC Curve
A first-heating DSC scan of a semi-crystalline polymer typically shows three events:
Glass transition ($T_g$): A step change in baseline heat flow (no peak). The polymer chains gain mobility at $T_g$; the specific heat $c_p$ jumps upward. $T_g$ is read as the midpoint of the step. Below $T_g$: glassy, stiff. Above $T_g$: rubbery (amorphous regions) or still solid (crystalline regions).
Cold crystallisation ($T_{cc}$): An exothermic peak on heating, appearing only if the sample was quenched (cooled rapidly) from the melt. Rapid cooling trapped the chains in an amorphous state; on reheating they have enough mobility to organise into crystals, releasing heat. Cold crystallisation means the sample was under-crystallised during the original cooling.
Melting ($T_m$): A large endothermic peak. The crystalline regions absorb heat to disorder their chains. The peak area equals the melting enthalpy $\Delta H_m$ (J/g), which is used to calculate crystallinity.
| Feature | Thermal event | Direction | What you extract |
|---|---|---|---|
| Baseline step | Glass transition $T_g$ | Step up in heat flow | $T_g$ (midpoint), $\Delta c_p$ |
| Exothermic peak | Cold crystallisation $T_{cc}$ | Downward peak | $T_{cc}$, $\Delta H_{cc}$ (J/g) |
| Endothermic peak | Melting $T_m$ | Upward peak | $T_m$ (peak), $\Delta H_m$ (J/g) |
| Endothermic baseline rise | Dehydration / moisture loss | Broad upward feature <150 °C | Moisture content (wt%) |
7.4 Degree of Crystallinity from DSC
The degree of crystallinity $X_c$ (dimensionless or %) is calculated from the ratio of the measured melting enthalpy to the reference value for a 100% crystalline sample of the same polymer:
$$X_c = \frac{\Delta H_m - \Delta H_{cc}}{\Delta H_m^\circ} \times 100\%$$
where $\Delta H_m$ is the measured melting peak area (J/g), $\Delta H_{cc}$ is the cold crystallisation peak area (J/g, subtracted because this heat was generated during the DSC scan, not stored from processing), and $\Delta H_m^\circ$ is the reference enthalpy for a perfectly crystalline sample. If no cold crystallisation peak appears, the formula reduces to $X_c = \Delta H_m / \Delta H_m^\circ$.
| Polymer | $\Delta H_m^\circ$ (J/g) | Typical $X_c$ range (%) |
|---|---|---|
| HDPE | 293 | 60–80 |
| LDPE | 293 | 30–50 |
| Nylon 6 | 240 | 25–50 |
| Nylon 6/6 | 196 | 25–50 |
| PLA | 93 | 0–45 |
| PET | 140 | 20–60 |
| ABS | — | 0 (amorphous) |
Crystallinity directly affects thermal conductivity ($k$ increases with $X_c$ because crystalline lamellae conduct better than amorphous regions), density, stiffness, and the heat per shot in injection molding (more crystallinity = more latent heat to remove).
7.5 TGA: Thermogravimetric Analysis
A TGA measures sample mass as a function of temperature (or time at fixed temperature). The sample sits on a precision balance inside a furnace; the instrument records $m(T)$ in milligrams or as a percentage of the initial mass.
Three types of mass loss appear in polymer TGA curves:
Moisture / solvent loss (25–150 °C): Small, early mass loss. Nylons absorb 2–3% moisture; this appears as a broad initial dip. The weight percent moisture equals the mass loss in this region divided by the initial mass.
Decomposition / pyrolysis (300–550 °C for most polymers): The main mass loss event. Polymer backbone scission and volatilisation. The onset temperature $T_{\text{onset}}$ (the temperature at which mass loss begins to accelerate) is a standard thermal stability metric. In air vs. nitrogen, oxidative degradation shifts $T_{\text{onset}}$ lower in air.
Residue at 600 °C: Non-combustible inorganic filler (glass fibre, carbon black, mineral filler, ash) remains after full pyrolysis. The residue weight percent equals the filler or ash content:
$$\text{Filler wt\%} = \frac{m_{\text{residue}}}{m_{\text{initial}}} \times 100\%$$
| Polymer | $T_{\text{onset}}$ in N&sub2; (°C) | Residue in air at 600°C |
|---|---|---|
| HDPE | 450–490 | <0.1% (no filler) |
| Nylon 6/6 | 410–450 | <1% |
| PLA | 330–360 | <0.1% |
| ABS | 380–420 | <1% |
| 30% glass-filled nylon | 410–450 | ~30% |
7.6 TMA: Thermomechanical Analysis
A TMA measures the change in sample dimension (length or thickness) as a function of temperature under a small, constant applied force. The primary output is the coefficient of thermal expansion (CTE):
$$\alpha_L = \frac{1}{L_0}\frac{dL}{dT} \quad [\text{K}^{-1}\text{ or ppm/K}]$$
Below $T_g$, the glassy polymer has a relatively low, constant CTE. At $T_g$, there is a marked change in slope as the rubbery regions become mobile: the CTE increases significantly. This inflection point is an independent, load-based measurement of $T_g$ that complements the DSC heat flow measurement.
TMA also reveals creep (dimensional change under constant load over time) and softening (the temperature at which the probe penetrates the sample, marking the practical upper use temperature under that specific stress).
| Polymer | CTE below $T_g$ (ppm/K) | CTE above $T_g$ (ppm/K) |
|---|---|---|
| HDPE | 100–200 | 200–400 |
| Nylon 6/6 | 70–100 | 140–200 |
| ABS | 70–90 | 150–200 |
| PLA | 68–80 | 100–150 |
| Steel (comparison) | 10–13 | — |
The large mismatch between polymer CTE (~100 ppm/K) and metal CTE (~10 ppm/K) is why polymer parts bonded to metal substrates are prone to thermally induced stress and delamination when cycled through temperature changes.
7.7 Connecting Characterisation to Heat Transfer Calculations
Every DSC, TGA, and TMA measurement feeds directly into the heat transfer parameters used throughout this course:
| Characterisation result | Where it feeds into heat transfer |
|---|---|
| $c_p$ from DSC baseline | $\alpha = k/(\rho c_p)$; melt energy balance $\dot{Q} = \dot{m}\,c_p\,\Delta T$; cooling time $t \propto s^2/\alpha$ |
| $\Delta H_m$ (melting enthalpy) | Latent heat term in injection molding shot heat: $Q = m(c_p\Delta T + H_c)$ |
| $T_g$ and $T_m$ | Set processing window (above $T_m$ for semi-crystalline; above $T_g$ for amorphous). Set ejection temperature in Chapter 6. |
| $X_c$ (crystallinity) | Affects $k$ (higher $X_c \rightarrow$ higher $k$), density $\rho$, and latent heat per gram. |
| $T_{\text{onset}}$ from TGA | Sets the upper temperature limit for processing; above $T_{\text{onset}}$, the polymer degrades irreversibly. |
| Filler content from TGA residue | Filled polymers have higher $k$, $\rho$, and $\alpha$ than unfilled. Must use composite property values in calculations. |
| CTE from TMA | Thermal stress in bonded or constrained components: $\sigma = E\,\alpha_L\,\Delta T$. |
7.8 Interactive: DSC Curve Explorer
Adjust the polymer parameters to see how the DSC curve changes. The simulated first-heating scan shows $T_g$, cold crystallisation, and melting. Try comparing a rapidly quenched sample (large cold crystallisation peak) with a slowly cooled sample (no cold crystallisation).
7.9 Worked Examples
Example 7.1 — Thermal Diffusivity from DSC Data
A DSC experiment on a polymer film gives $c_p = 2000\ \text{J/kgK}$. A separate hot-disk measurement gives $k = 0.40\ \text{W/mK}$, and the density is $\rho = 1000\ \text{kg/m}^3$. Compute the thermal diffusivity and state its significance for mold cooling.
Solution:
$$\alpha = \frac{k}{\rho\,c_p} = \frac{0.40}{1000 \times 2000} = 2.0 \times 10^{-7}\ \text{m}^2/\text{s}$$
From Chapter 6, cooling time $t_c \propto s^2/\alpha$. For a 2 mm wall ($s = 1\ \text{mm}$): $s^2/\alpha = (10^{-3})^2/(2.0\times10^{-7}) = 5\ \text{s}$. This polymer would require several seconds of mold cooling even with ideal mold contact.
Example 7.2 — Crystallinity and Latent Heat Correction
A nylon DSC curve shows a melting peak with $\Delta H_m = 120\ \text{J/g}$ and no cold crystallisation peak. The reference value for 100% crystalline nylon is $\Delta H_m^\circ = 240\ \text{J/g}$. Find $X_c$ and the latent heat contribution to the shot heat for a 0.10 kg part.
Solution:
$$X_c = \frac{120}{240} \times 100 = 50\%$$
Latent heat per gram: $\Delta H_m = 120\ \text{J/g} = 120{,}000\ \text{J/kg}$. For 0.10 kg: $Q_{\text{latent}} = 0.10 \times 120{,}000 = 12{,}000\ \text{J} = 12\ \text{kJ}$. This is additional to the sensible heat and must be removed by the mold cooling system.
7.10 Concept Questions
A DSC scan of a PLA film shows a large cold crystallisation peak before the melting peak. What does this tell you about how the film was originally cooled? What processing change would eliminate the cold crystallisation peak?
A TGA experiment runs a 20 mg sample of glass-fibre-reinforced nylon in air to 600 °C. The residue is 6 mg. What is the glass fibre weight fraction?
Two samples of the same HDPE resin are DSC-tested: Sample A was slowly cooled from the melt (2 K/min); Sample B was quenched in ice water. Sketch qualitatively how their DSC first-heating curves would differ. Which sample has higher crystallinity? Which has a cold crystallisation peak?
A process engineer receives a batch of nylon pellets labelled “dry” but suspects moisture contamination. Describe a TGA experiment that would confirm or rule out moisture, and explain what feature of the TGA curve to look for. If 2.4 mg of water is found in a 30 mg sample, what is the moisture content?
From a DSC report to a cooling-time prediction.
A DSC report on an unknown semi-crystalline polymer gives: $c_p = 1800\ \text{J/kgK}$ (melt), $T_m = 180\,°\text{C}$, $T_g = 55\,°\text{C}$, $\Delta H_m = 60\ \text{J/g}$, $\Delta H_m^\circ = 93\ \text{J/g}$. A separate measurement gives $k = 0.16\ \text{W/mK}$, $\rho = 1240\ \text{kg/m}^3$.
(a) Identify whether this polymer is likely PLA, nylon, or HDPE, using the values of $T_g$, $T_m$, and $\Delta H_m^\circ$ as clues. Calculate the degree of crystallinity $X_c$.
(b) Calculate the thermal diffusivity $\alpha$ from the DSC $c_p$ and the given $k$, $\rho$. Express in m²/s.
(c) The polymer is injection-molded into a part with half-wall thickness $s = 1.5\ \text{mm}$. Mold temperature $T_w = 30\,°\text{C}$, ejection temperature $T_e = 70\,°\text{C}$. Use the Ballman–Shusman formula $$t_c = \frac{s^2}{\pi^2\alpha}\ln\!\left(\frac{4}{\pi}\cdot\frac{T_m-T_w}{T_e-T_w}\right)$$ to calculate $t_c$ (s).
(d) A competitor material has $c_p = 2400\ \text{J/kgK}$ and the same $k$ and $\rho$. Without calculating, predict whether its $t_c$ will be longer or shorter, and by roughly what factor. Explain the physical reason.
7.11 Problem Set
DSC analysis of a polymer gives $c_p = 2000\ \text{J/kgK}$. A separate thermal conductivity measurement gives $k = 0.40\ \text{W/mK}$. The polymer density is $\rho = 1000\ \text{kg/m}^3$. Calculate the thermal diffusivity $\alpha$ in m²/s.
$\alpha = k\,/\,(\rho\,c_p)$
diffusivity bundles all three material properties into one number; the $c_p$ from DSC is the key input that connects characterisation to process design
A nylon DSC scan shows a melting peak with area $\Delta H_m = 120\ \text{J/g}$. There is no cold crystallisation peak. The reference enthalpy for 100% crystalline nylon is $\Delta H_m^\circ = 240\ \text{J/g}$. Calculate the degree of crystallinity $X_c$ (%).
$X_c = (\Delta H_m\,/\,\Delta H_m^\circ)\times 100\%$
crystallinity is the fraction of the maximum possible melting energy — higher $X_c$ means more latent heat to remove in injection molding
A DSC experiment heats a 10 mg polymer sample from 25 °C to 125 °C (a range of 100 °C). The software integrates the heat flow curve over this range and reports a total heat input of 2.0 J. Calculate $c_p$ in J/kgK.
$c_p = Q\,/\,(m\,\Delta T)$, with $m$ in kg
specific heat = energy deposited per unit mass per degree — this is exactly what the DSC baseline slope is measuring in every scan
A polymer sample has a known degree of crystallinity $X_c = 35\%$. The reference melting enthalpy for this polymer at 100% crystallinity is $\Delta H_m^\circ = 200\ \text{J/g}$. What melting peak area (J/g) will the DSC show, assuming no cold crystallisation?
$\Delta H_m = X_c \times \Delta H_m^\circ$ (rearranged from the crystallinity formula)
the DSC melting peak area is proportional to the crystalline fraction — use this to predict what the scan will look like before running the experiment
A TGA experiment on a composite polymer sample starts with 50 mg. After complete pyrolysis at 600 °C in air, a residue of 15 mg remains (glass fibre, which does not combust). What is the glass fibre weight fraction (wt%)?
Filler wt% $= (m_{\text{residue}}\,/\,m_{\text{initial}}) \times 100\%$
TGA weighs what survives full combustion — only inorganic filler remains, giving a direct gravimetric measure of composite loading
In your polymer characterisation lab, you receive an opaque white film labelled only “Sample X.” A DSC first-heating scan gives the following features:
- A broad moisture endotherm from 50–100 °C (mass loss confirmed by TGA: 2.5%)
- A glass transition step at $T_g = 47\,°\text{C}$
- A cold crystallisation exotherm at $T_{cc} = 95\,°\text{C}$ with $\Delta H_{cc} = 22\ \text{J/g}$
- A melting endotherm at $T_m = 178\,°\text{C}$ with $\Delta H_m = 44\ \text{J/g}$ (peak area)
The TGA in nitrogen shows $T_{\text{onset}} = 340\,°\text{C}$ and essentially zero residue at 600 °C.
(a) Is Sample X amorphous or semi-crystalline? Justify.
(b) Calculate the degree of crystallinity using $\Delta H_m^\circ = 93\ \text{J/g}$.
(c) Based on $T_g \approx 47\,°\text{C}$, $T_m \approx 178\,°\text{C}$, the presence of crystallinity, and the moisture sensitivity, identify the most likely polymer. Justify each clue.
(d) The film will be injection-molded. What drying protocol do you recommend before processing, and what maximum barrel temperature would you set?
7.12 Chapter Summary
Key Equations
| Quantity | Formula | Source |
|---|---|---|
| Specific heat from DSC | $c_p = Q\,/\,(m\,\Delta T)$ | DSC enthalpy integration |
| Heat flow at constant rate | $dQ/dt = m\,c_p\,\beta$ | DSC baseline region |
| Degree of crystallinity | $X_c = (\Delta H_m - \Delta H_{cc})\,/\,\Delta H_m^\circ \times 100\%$ | DSC melting peak |
| Filler / ash content | Filler wt% $= m_{\text{residue}}/m_{\text{initial}} \times 100\%$ | TGA at 600 °C in air |
| Coefficient of thermal expansion | $\alpha_L = (1/L_0)\,dL/dT$ (ppm/K) | TMA expansion mode |
| Thermal diffusivity (links to processing) | $\alpha = k\,/\,(\rho\,c_p)$ (m²/s) | Combines DSC $c_p$ with $k$, $\rho$ |
Key Ideas
- DSC gives $T_g$, $T_m$, $c_p$, $\Delta H_m$, and crystallinity. It is the most information-dense thermal characterisation tool for polymers.
- The degree of crystallinity $X_c = \Delta H_m / \Delta H_m^\circ$ sets latent heat per gram, thermal conductivity, and density.
- A cold crystallisation peak means the sample was quenched; the true processing crystallinity uses $(\Delta H_m - \Delta H_{cc})$.
- TGA reveals thermal stability ($T_{\text{onset}}$), moisture content (loss <150 °C), and filler/ash fraction (residue at 600 °C).
- TMA measures CTE and gives a load-based $T_g$ that complements the DSC value.
- All three instruments feed directly into heat transfer calculations: $c_p \rightarrow \alpha$; $\Delta H_m \rightarrow Q_{\text{shot}}$; $T_g$, $T_m \rightarrow$ processing window and ejection temperature.