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All teaching chapters stay open. Choose a direct route to the relevant explanation, or follow the full sequence from first principles.
Understand the reader problem
Chapters 1–2. Start this reading route.
Define the model and numbers
Chapters 3–5. Start this reading route.
Work the essential calculation
Chapters 6–7. Start this reading route.
Change the setting and examine evidence
Chapters 8–10. Start this reading route.
Practise and read further
Chapters 11–12. Start this reading route.
For polymer crystallinity measured by differential scanning calorimetry (DSC), the first heating run can retain evidence of the sample’s manufacturing and storage history. A second run after melting and controlled cooling describes the new thermal history created inside the instrument, not a second independent reading of the original specimen.
Work through an illustrative polymer blend with melting enthalpy 48 J/g, cold-crystallisation enthalpy 12 J/g and polymer fraction 0.80. Its corrected first-run crystallinity is 30% with the stated reference enthalpy. We will show every denominator, then change the heating history and re-evaluate.
Chapter index
Understand the reader problem · Chapters 1–2
1. Two heating curves can tell two different stories
2. Define what differential scanning calorimetry measures
Define the model and numbers · Chapters 3–5
3. Separate initial crystals from crystals grown during heating
4. Specify the sample basis before using any formula
5. Write the crystallinity estimator and identify its denominator
Work the essential calculation · Chapters 6–7
6. Calculate the first-heating estimate from start to finish
7. See what goes wrong if one correction is omitted
Change the setting and examine evidence · Chapters 8–10
8. Second heating describes a deliberately changed history
9. Change the cooling rate and expect the trace to change
10. Audit the measurement before trusting the percent
Practise and read further · Chapters 11–12
11. Try the exercise and repair the recurring errors
12. Connect the material to the measurement literature
CHAPTER 1 OF 12 · Understand the reader problem
1. Two heating curves can tell two different stories
A polymer component arrives with moulding, drawing, annealing or cooling history already built into its microstructure. The first DSC heating may capture transitions that reflect this history. After the specimen has melted, cooled by a deliberate programme and reheated, those original structures may have changed.
A comparison of first and second runs can be valuable, but only when the question is clear. Are we describing the part as received, or asking how the formulation behaves after a standardised thermal cycle?
Treating the two traces as interchangeable can erase the very processing evidence the first run was intended to measure.
CHAPTER 2 OF 12 · Understand the reader problem
2. Define what differential scanning calorimetry measures
DSC measures a differential heat-flow response during a controlled temperature programme. It is not a direct camera showing polymer crystals. Thermal transitions and reactions must be inferred from their heat-flow signatures, with instrument calibration and baseline processing.
Melting usually produces an endothermic signal. Crystallisation can produce an exothermic signal. A glass transition typically appears as a step in heat capacity rather than a melting peak.
The sign plotted upward or downward for an endotherm varies by instrument or plotting convention. Record positive magnitudes for our enthalpy calculation instead of accidentally subtracting a negative number twice.
CHAPTER 3 OF 12 · Define the model and numbers
3. Separate initial crystals from crystals grown during heating
Some initially amorphous polymer can reorganise and crystallise while the DSC ramp is heating it. This is called cold crystallisation and appears as an exothermic process between the relevant transitions under suitable conditions.
If the same crystals later melt on that scan, the melting enthalpy includes crystals created after the experiment began. Subtracting the cold-crystallisation magnitude avoids mistakenly attributing all melted crystals to the initial specimen.
Not every material shows a clean separable cold-crystallisation peak. Competing reactions, overlapping melting and recrystallisation or incomplete transition coverage require a more specialised analysis.
CHAPTER 4 OF 12 · Define the model and numbers
4. Specify the sample basis before using any formula
Imagine a 10 mg specimen containing 8 mg of the crystallisable polymer and 2 mg of inert filler. The polymer mass fraction is w=0.80. We assume the enthalpies have been divided by the full 10 mg specimen mass.
Let ΔHm=48 J per gram of total specimen, ΔHcc=12 J per gram of total specimen and ΔH0=150 J per gram of fully crystalline polymer. The last quantity is an illustrative reference parameter, not a universal constant for real polymers.
We assume no overlapping reaction or degradation, appropriate baselines, complete relevant melting in the scanned range and a defensible choice of polymer reference enthalpy.
| Input | Illustrative value | Mass basis |
|---|---|---|
| Total specimen mass | 10 mg | Whole specimen |
| Crystallisable polymer mass | 8 mg | Polymer only |
| Polymer fraction w | 0.80 | Whole specimen |
| Melting enthalpy ΔHm | 48 J/g | Whole specimen |
| Cold-crystallisation enthalpy ΔHcc | 12 J/g | Whole specimen |
| Reference ΔH0 | 150 J/g | 100% crystalline polymer |
CHAPTER 5 OF 12 · Define the model and numbers
5. Write the crystallinity estimator and identify its denominator
Using positive peak-area magnitudes, the simplified mass-based crystallinity estimate is Xc=(ΔHm−ΔHcc)/(w ΔH0), expressed as a fraction of the crystallisable polymer mass.
The numerator removes crystals generated during the heating run. The denominator converts the per-gram-of-whole-specimen enthalpy to a per-gram-of-polymer basis and compares it with the assumed fully crystalline reference.
If filler content has already been accounted for by the DSC software, applying w a second time would be an error. Confirm the exact mass basis of the reported enthalpies.
CHAPTER 6 OF 12 · Work the essential calculation
6. Calculate the first-heating estimate from start to finish
The net first-heating enthalpy is ΔHm−ΔHcc=48−12=36 J/g specimen. The reference enthalpy on a full-specimen basis is wΔH0=0.80×150=120 J/g specimen.
Therefore Xc=36/120=0.30, or 30% of the crystallisable polymer. This number is an estimate under the conditions and assumptions of this example.
The value is not a claim that 30% of every polymer component is crystalline. Its meaning is specific to our defined hypothetical material, reference enthalpy, pan mass and integration method.
CHAPTER 7 OF 12 · Work the essential calculation
7. See what goes wrong if one correction is omitted
If cold crystallisation is ignored, the apparent result is 48/120=40%. That is ten percentage points above the corrected illustration because crystals grown in the heating ramp are counted as if present initially.
If the filler fraction is ignored while the cold-crystallisation correction is retained, the result is 36/150=24% on an incompatible denominator. Both 40% and 24% answer a different calculation from the one intended.
If neither correction is used, 48/150=32% may look plausible by coincidence. A reasonable-looking number is not evidence that the physical basis is correct.
CHAPTER 8 OF 12 · Change the setting and examine evidence
8. Second heating describes a deliberately changed history
Suppose the specimen is fully melted without degradation, cooled under a controlled protocol and reheated. On this second scan, imagine ΔHm,2=45 J/g specimen with no measurable cold-crystallisation enthalpy.
Using the same illustrative w=0.80 and ΔH0=150 J/g polymer gives Xc,2=45/(0.80×150)=0.375, or 37.5%.
This higher number need not mean the first DSC run was wrong. It can simply mean that the controlled cooling created a different crystal population from the original manufacture or storage conditions.
| Calculation | Value | What it represents |
|---|---|---|
| Corrected first heat | (48−12)/(0.8×150)=30% | Estimated as-received polymer crystallinity |
| Ignore cold crystallisation | 48/(0.8×150)=40% | Overattributes new crystals to original |
| Ignore filler fraction | (48−12)/150=24% | Wrong mass basis |
| Second heat after controlled cooling | 45/(0.8×150)=37.5% | Estimate after changed thermal history |
CHAPTER 9 OF 12 · Change the setting and examine evidence
9. Change the cooling rate and expect the trace to change
Fast cooling can leave some semicrystalline polymers more amorphous, so a subsequent heating ramp may display a pronounced cold-crystallisation exotherm. Slower cooling can allow more crystallisation before the next run begins.
The direction and extent depend on polymer chemistry, molecular architecture, nucleating agents, thickness, cooling programme and thermal degradation. Do not transplant one polyethylene or PET result to every material.
When reporting a comparison, include the actual temperature limits, heating and cooling rates, atmosphere, specimen preparation and whether results are first heat or second heat.
CHAPTER 10 OF 12 · Change the setting and examine evidence
10. Audit the measurement before trusting the percent
Peak integration requires a defensible baseline, temperature range and mass calibration. Overlapping thermal events or prior decomposition can invalidate the simplified net-enthalpy estimate.
Document the DSC instrument, calibrated heat-flow response, sample-pan type, purge environment, specimen mass, pan sealing, conditioning, scanning rate and enthalpy reference. The chosen ΔH0 value must come from material-appropriate literature or validated reference data.
The relative crystallinity information can be useful even where a claimed absolute percentage is too uncertain. Explain the scope rather than decorating a shaky estimate with extra decimal places.
CHAPTER 11 OF 12 · Practise and read further
11. Try the exercise and repair the recurring errors
Exercise: for a different hypothetical polymer blend, let ΔHm=36 J/g specimen, ΔHcc=6 J/g specimen, w=0.75 and ΔH0=160 J/g polymer. Then Xc=(36−6)/(0.75×160)=30/120=25%.
FAQ: Does a second heat recover the original processing history? No. Is cold crystallisation the same as melting? No, they are different heat-flow events. Is 150 J/g a safe ΔH0 for any polymer? No, it was an example parameter.
The errors to avoid are inconsistent specimen/polymer denominators, sign-convention double negatives and drawing production conclusions from a trace whose thermal treatment is not recorded.
CHAPTER 12 OF 12 · Practise and read further
12. Connect the material to the measurement literature
Explore the Polymer Science subject root, then branching and network formation for a different structural property that DSC enthalpy alone cannot settle.
Read TA Instruments’ crystallinity application note, its first-heating and cold-crystallisation explanation and the interpretation of unexpected DSC transitions.
The transferable habit is to read the experiment’s history and denominator together. A number without its measurement context is not yet a material property.
Continue through Polymer Science, The Gold Standard of Education and How X Works. Original worked examples use their stated assumptions; source references checked 22 October 2026.