Determination of the Linear Expansion Coefficient

Purpose

To determine the coefficient of thermal expansion (CTE) of a cured coating powder between 50 and 150 °C

Sample

Cured KU600 epoxy resin powder formed as a cylinder, diameter 6 mm, height 1.92 mm.

Conditions

Measuring cell: TMA

Probe: Ball-point probe (quartz glass); diameter 3 mm

Sample preparation: The flat ends of the cylindrical sample were polished with fine sandpaper. Thin quartz glass disks were placed between the sample and probe and between the sample and sample support to distribute the force of the probe evenly over the entire cross-sectional area and so create a low compressive stress. The sample was heated in the TMA once before the measurement to remove relaxation effects.

TMA measurement: Heating from 40 to 160 °C at 5 K/min

Force on the probe: 0.02 N

Atmosphere: Static air

Interpretation

The cylinder had an initial height of 1920 μm and underwent expansion on warming. The expansion up to about 100 °C is relatively small; afterward the slope of the TMA curve is noticeably steeper. The expansion rate, visible as the slope of the curve, is therefore a function of temperature. The change of slope indicates the glass transition, a temperature at which many physical properties change. 

Conclusion

The expansion behavior of a solid material is shown by measuring the sample length/height as a function of temperature. The linear expansion coefficient, α, can be calculated from the slope of the TMA curve. This is usually a function of temperature. A step-like change of α
 indicates that a thermal effect has occurred in the material. 
The determination of low expansion coefficients requires relatively high samples (large L₀). Low heating rates (max: 5 K/min) are therefore used in order to avoid temperature gradients in the large samples. A blank curve should always be subtracted to ensure accurate results.

In the calculation of the numerical values, a distinction must be made between instantaneous and mean coefficients. The mean expansion coefficient shows how much a material expands over a usually large temperature interval, whereas the instantaneous coefficient shows the expansion at a particular temperature. 

^{Determination of the Linear Expansion Coefficient | Thermal Analysis Handbook No.HB18 | Application published in METTLER TOLEDO TA Application Handbook Thermosets, Volume 1}