Thermal analysis

Why it matters

Thermal analysis answers practical questions fast. Is this polymer batch the same as the last one? What is its glass transition? How crystalline is it? How much filler or moisture does it contain, and at what temperature does it start to decompose? Two instruments do most of this work: DSC (differential scanning calorimetry) and TGA (thermogravimetric analysis).

DSC: heat flow

A DSC heats a small sample (typically 2 to 10 mg in a crimped pan) and an empty reference pan at a controlled rate, often 10 K/min, and records the difference in heat flow needed to keep both on the same temperature program. Events show up as features on that curve:

• Glass transition (Tg): a step in the baseline, because heat capacity increases when an amorphous region becomes rubbery. Report the midpoint and the method you used.
• Melting (Tm): an endothermic peak. Its area is the enthalpy of fusion.
• Crystallization (Tc) and cold crystallization: exothermic peaks on cooling or heating.
• Curing of thermosets: a broad exotherm; residual cure shows up as a smaller exotherm in a second run.

Check your instrument's sign convention: some software plots endotherms up, others down. Always label the axis "endo up" or "exo up".

Peak area to enthalpy

DSC software integrates the peak above a baseline. Doing it yourself makes the units clear. If heat flow q is in mW and you integrate over temperature in K, you get mW·K. Divide by the heating rate in K/s to get mW·s, which is mJ:

energy (mJ) = area (mW*K) * 60 / rate (K/min)
enthalpy (J/g) = energy (mJ) / mass (mg)

Worked example. A 5.0 mg polyethylene sample at 10 K/min shows a melting peak with an area of 125 mW·K above the baseline. Energy = 125 × 60 / 10 = 750 mJ, so dH_m = 750 / 5.0 = 150 J/g. Using about 293 J/g for 100% crystalline polyethylene (a literature value; sources vary by a few percent), crystallinity is 150 / 293 = 51%.

The first and second heat

The first heating run reflects the sample's thermal history (how it was processed and stored). A standard approach is heat, cool at a controlled rate, then heat again: the second heat compares materials on an equal footing. Report both when processing history matters.

TGA: mass

A TGA weighs a sample continuously while heating it, in nitrogen (to see decomposition) or air (to burn off organics). The curve shows mass percent vs temperature; steps are mass losses. The derivative curve (DTG) turns each step into a peak, which makes overlapping steps easier to separate.

Typical uses:

• Moisture and volatile content (loss below about 150 °C).
• Polymer decomposition temperature (often reported as the temperature at 5% loss).
• Filler or ash content: the residue after burning off the polymer in air, for example glass fiber content in a composite.

Worked example: calcium oxalate monohydrate

Calcium oxalate monohydrate (CaC2O4·H2O, 146.11 g/mol) is a common TGA check standard because it loses mass in three clean steps:

The residue is CaO, about 38.4% of the starting mass. If your instrument measures 12.0% for the first step, the 0.3% difference is something to explain: calibration, buoyancy, or a partly dehydrated standard. Exact step temperatures shift with heating rate and atmosphere.

Reading curves in Python

Exported data are just columns of temperature and signal. With numpy, np.interp reads the mass at any temperature, np.argmax finds a peak, and a trapezoid sum integrates a peak above a straight baseline drawn between two chosen temperatures. The baseline choice matters: report the limits you integrated between.

Common mistakes

• Mixing up endo up and exo down, and calling a melt a crystallization.
• Comparing first-heat curves of samples with different processing histories.
• Forgetting units: integrating over time vs temperature without converting by the heating rate.
• Too heavy or poorly contacting samples, which smear peaks and lag the temperature.
• Ignoring atmosphere in TGA: the same polymer decomposes differently in air and nitrogen.

Safety and training

These instruments run to hundreds of degrees (TGA furnaces to 1000 °C or more), use purge gases, and decomposition can release toxic products that must be vented. Run samples only after your lab's training, following its procedures and safety data sheets. In this course you work with data.

Recap

• DSC measures heat flow: Tg is a step, melting is an endotherm, and peak area gives enthalpy and crystallinity.
• TGA measures mass: each step is a loss you can match to chemistry, and the residue gives filler or ash content.
• Integrate with a clear baseline, mind units and sign conventions, and record thermal history.

Try it

Open the Do tab to compute TGA mass-loss steps and a DSC melting enthalpy and crystallinity from synthetic curves with numpy.