Calorimetry & Thermal Metrology

TGA-DSC Thermal Analysis Lab

Q: How is the glass transition temperature (Tg) identified on a DSC curve?

The glass transition (Tg) is a reversible second-order thermodynamic relaxation of amorphous polymer chains. Because it involves no latent heat of transformation, it appears on a DSC heat flux thermogram not as a peak, but as an endothermic baseline step change representing an increase in specific heat capacity (Delta Cp) as rigid glassy chains gain cooperative segmental mobility.

Q: How is polymer percent crystallinity calculated from DSC melting enthalpies?

Percent crystallinity (% Xc) is calculated as the ratio of the net measured heat of fusion (Delta Hm minus any cold crystallization enthalpy Delta Hc) to the theoretical melting enthalpy of a 100% crystalline sample of the same polymer (Delta Hm0): % Xc = ((Delta Hm - Delta Hc) / Delta Hm0) * 100%.

Model Simultaneous Thermal Analysis (STA), Thermogravimetric Analysis (TGA) mass loss %, Derivative Thermogravimetry (DTG), Differential Scanning Calorimetry (DSC) heat flux, polymer glass transitions ($T_g$), melting enthalpy ($\Delta H_m$), and contract testing facility economics.

All Simulations

Glass Transition $T_g$

143.0 °C

$\Delta C_p$ Baseline Step

Melting Point $T_m$

343 °C

Endothermic Peak

Crystallinity $\% X_c$

34.6 %

$\Delta H_m / \Delta H_m^0$ Ratio

Pyrolysis Onset $T_{\text{onset}}$

575 °C

5% Mass Loss Temp

Residual Char / Ash

48.0 %

Mass at 850 °C

10-Yr Project NPV

+$628,000

Discounted Cash Flow

Calorimeter Parameters

Material Specimen Preset

Specimen Mass ($m_0$) 10.5 mg

Microbalance initial loading

Heating Rate ($\beta$) 20 °C/min

Furnace ramp rate (affects kinetic temperature lag)

Glass Transition ($T_g$) 143.0 °C

Polymer amorphous relaxation temperature

Melting Temperature ($T_m$) 343 °C

Crystalline lamellae fusion endotherm

Thermal Degradation ($T_{\text{onset}}$) 575 °C

TGA initial thermal mass loss threshold

Residual Char / Carbon Yield 48.0 %

Non-volatile inorganic filler or graphite char

Analytical Facility Economics

Annual Testing Runs 1,400 runs/yr

Commercial QA/QC & polymer R&D sample throughput

Fee per Sample Run $125 $/sample

Contract analytical lab billing rate per scan

TGA Mass % & DTG Derivative Rate (%/min)

Thermogravimetry

Cyan solid curve represents specimen mass % (left axis); red curve represents derivative DTG mass loss rate (%/min, right axis); yellow dashed marker marks peak decomposition temperature.

DSC Heat Flux Thermogram (mW/mg, Endo DOWN)

Calorimetry

Heat flux plotted with endothermic transitions pointing DOWN. Clearly captures the glass transition ($T_g$) baseline step, cold crystallization exotherms, and melting endotherm peak ($T_m$).

10-Year Contract Thermal Analysis Facility DCF Schedule

Year	Testing Volume	Gross Revenue	OpEx	EBITDA	Free Cash Flow	Cumulative Cash Flow

* Model parameters: Initial CapEx of $145,000 amortized over 10 years straight-line, annual fixed consumables/gas OpEx of $26,000, 21% corporate tax rate, 9% discount rate (WACC).

Engineering & Thermal Metrology Guide

1. Simultaneous Thermal Analysis (STA) Principles

STA pairs a micro-gram precision horizontal beam balance with differential heat flux sensors. By heating a sample in an inert ($\text{N}_2$) or oxidative (Air/$\text{O}_2$) purge gas, thermal mass change ($\Delta m$) and energy exchange ($\Delta H$) are recorded simultaneously. This distinguishes mass-loss events (solvent flashoff, pyrolysis) from pure phase transformations (glass transition $T_g$, melting $T_m$).

2. Glass Transition ($T_g$) & Heat Capacity Step ($\Delta C_p$)

The glass transition is an amorphous relaxation where immobilized polymer chains gain cooperative conformational degrees of freedom. In DSC, $T_g$ exhibits no latent heat; it appears as a characteristic sigmoidal baseline shift: $$\Delta \Phi = \beta \cdot m \cdot \Delta C_p$$ where $\beta$ is heating rate, $m$ is sample mass, and $\Delta C_p$ is the differential heat capacity increase ($0.2\text{–}0.5\ \text{J}/(\text{g}\cdot\text{K})$).

3. Enthalpy of Fusion & Percent Crystallinity

During melting, ordered crystalline lamellae disrupt into random coils, absorbing endothermic latent heat ($\Delta H_m$). By integrating the peak area under the DSC heat flux curve, absolute degree of crystallinity is determined: $$\% X_c = \frac{\Delta H_m - \Delta H_c}{\Delta H_m^\circ} \times 100\%$$ where $\Delta H_c$ is cold crystallization enthalpy and $\Delta H_m^\circ$ is the reference enthalpy for a 100% crystalline sample ($130\ \text{J/g}$ for PEEK, $104.7\ \text{J/g}$ for PVDF).

4. Pyrolysis Kinetics & Derivative Thermogravimetry (DTG)

Thermogravimetric decomposition follows Arrhenius kinetics: $d\alpha / dt = A \exp(-E_a / RT) f(\alpha)$. The first derivative ($dm/dT$) curve pinpoints the peak decomposition temperature ($T_{\text{peak}}$). Residual mass at $850^\circ\text{C}$ quantifies inorganic fillers, flame retardant chars, or aerospace carbon fiber content in polymer composites.

Frequently Asked Questions

Simultaneous Thermal Analysis (STA) measures both mass change (TGA) and heat flow (DSC) on the exact same specimen simultaneously under identical temperature and gas atmospheres. This eliminates sample inhomogeneity and experimental variance, allowing unambiguous differentiation between physical phase transitions without mass loss (such as melting, crystallization, and glass transitions) and chemical decomposition reactions with mass loss (such as dehydration, desolvation, oxidation, and pyrolysis).

The glass transition ($T_g$) is a reversible second-order thermodynamic relaxation of amorphous polymer chains. Because it involves no latent heat of transformation, it appears on a DSC heat flux thermogram not as a peak, but as an endothermic baseline step change representing an increase in specific heat capacity ($\Delta C_p$) as rigid glassy chains gain cooperative segmental mobility.

The DTG curve represents the rate of mass loss with respect to temperature ($dm/dT$) or time ($dm/dt$). Peaks in the DTG curve identify the inflection points where thermal decomposition, vaporization, or volatilization occurs most rapidly, allowing precise deconvolution of overlapping multi-step pyrolysis reactions.

Percent crystallinity ($\% X_c$) is calculated as the ratio of the net measured heat of fusion ($\Delta H_m$ minus any cold crystallization enthalpy $\Delta H_c$) to the theoretical melting enthalpy of a 100% crystalline sample of the same polymer ($\Delta H_m^\circ$): $\% X_c = ((\Delta H_m - \Delta H_c) / \Delta H_m^\circ) \times 100\%$.

A standard simultaneous TGA-DSC instrument with autosampler, purge gas controller, and circulating chiller requires approximately $130,000 to $160,000 in capital expenditure (CapEx) and $26,000 in annual consumables (platinum/alumina pans, high-purity nitrogen/oxygen, furnace thermocouple calibrations). At an annual volume of 1,400 contract testing runs priced at $125 per sample, the facility generates $175,000 in annual revenue, delivering payback in under 2.5 years.