Differential Scanning Calorimetry (DSC): Tg, Tm, Hf & Crystallinity Kinetics

Differential Scanning Calorimetry (DSC) is the most widely used thermal analysis technique in polymer science and engineering. It characterizes key thermal transitions ($T_g, T_c, T_m$), heat capacity changes, and phase kinetics. In industrial production (e.g., compounding, blow moulding, film blowing), DSC is essential to check if a semi-crystalline polymer has achieved the target degree of crystallinity. Indian testing labs (e.g., CIPET, SGS India) utilize DSC to identify unknown polymers, evaluate polymer blends, and qualify raw materials.

• Explain the working principle of heat-flux and power-compensated DSC instruments.
• Interpret a DSC thermogram, identifying glass transition ($T_g$), cold crystallization ($T_{cc}$), melting ($T_m$), and crystallization ($T_c$).
• Calculate the degree of crystallinity ($X_c$) from melting peak enthalpy ($\Delta H_m$) data.
• Solve the kinetics of crystallization using the Avrami equation.
• Identify ASTM D3418 (transition temperatures) and ISO 11357 standards.

3.1 Instrument Principles

• Heat-Flux DSC: Sample and reference sit on a common thermoelectric disk in a single furnace. Heat flow is calculated from temperature difference $\Delta T = T_S - T_R$.
• Power-Compensated DSC: Sample and reference sit in separate furnaces with independent heaters. The power required to keep $T_S = T_R$ is measured directly.

3.2 Thermal Transitions on a DSC Curve

A standard heating run plots heat flow (mW/W or W/g) vs. temperature. Transitions include:

1. Glass Transition ($T_g$): Baseline step change (endothermic). Represents a second-order thermodynamic transition (change in heat capacity $\Delta C_p$).
2. Cold Crystallization ($T_{cc}$): Exothermic peak. Occurs when a quenched amorphous phase gains mobility above $T_g$ and packs into crystals.
3. Melting ($T_m$): Endothermic peak. First-order transition (breaking of crystalline structures).

3.3 Calculating Degree of Crystallinity ($X_c$)

Where:

• $\Delta H_m$: Enthalpy of melting (area under the melting peak, J/g)
• $\Delta H_{cc}$: Enthalpy of cold crystallization (if present, J/g)
• $\Delta H_m^\circ$: Enthalpy of melting for a $100\%$ crystalline reference of the same polymer.
  • For PP: $\Delta H_m^\circ = 207$ J/g
  • For PE: $\Delta H_m^\circ = 290$ J/g
  • For PET: $\Delta H_m^\circ = 140$ J/g

Problem: A semi-crystalline Polypropylene (PP) sample is analyzed via DSC. The melting peak shows an enthalpy of melting $\Delta H_m = 92.5$ J/g. No cold crystallization exotherm is observed. If the reference melting enthalpy for 100% crystalline PP is $\Delta H_m^\circ = 207$ J/g, calculate the degree of crystallinity ($X_c$) of this PP sample.

Solution: Since $\Delta H_{cc} = 0$:

Interpretation: The PP sample has a crystalline fraction of 44.69%, which is typical for injection-moulded homopolymer PP. This degree of crystallinity will provide a balance of tensile strength and stiffness.

CIPET (Central Institute of Petrochemicals Engineering & Technology) centres across India use DSC for polymer blend analysis. For example, verifying recycling contamination levels in PP-PE PCR (Post-Consumer Resin) blends by evaluating the distinct melting peaks of PP (165°C) and HDPE (135°C) per ASTM D3418.

• $T_g$ (Glass Transition): Step change in baseline; polymer transitions from glassy to rubbery state.
• $\Delta H_m$: Heat absorbed to melt the crystalline region; area under the endothermic peak.
• $X_c$ (Crystallinity): Percentage of crystalline phase in the semi-crystalline polymer.
• Exothermic: Upward peak in standard DSC convention (releasing heat).
• Endothermic: Downward peak (absorbing heat).

1. ASTM D3418 — Standard Test Method for Transition Temperatures and Enthalpies of Polymers by Thermal Analysis
2. ISO 11357-1 — Plastics — Differential scanning calorimetry (DSC) — Part 1: General principles
3. ISO 11357-3 — Determination of temperature and enthalpy of melting and crystallization

1. Draw a typical DSC heating thermogram for a quenched semi-crystalline PET sample. Clearly label $T_g$, $T_{cc}$, and $T_m$.
2. Why is $T_g$ classified as a second-order transition while $T_m$ is first-order? Reference the behavior of entropy and volume.
3. A PET sample displays $\Delta H_m = 38.0$ J/g and $\Delta H_{cc} = 12.0$ J/g. Calculate $X_c$ if $\Delta H_m^\circ = 140$ J/g.