// Blog July 31, 2023

Measuring Coefficient of Thermal Expansion (CTE) of Polymers by Thermomechanical Analysis (TMA)

Thermomechanical analysis (TMA) is a critical tool for measuring a material’s expansion over a temperature range, providing key insights into its integrity and reliability.

TMA measures a material’s expansion or contraction when subject to a temperature change. It involves applying a controlled force to a sample while it is heated or cooled and measuring the resulting deformation or movement. TMA is used to study the properties of metals, polymers, ceramics, and composites. It can provide insights into their behavior under different conditions, such as in high-temperature environments or under mechanical load.


Figure 1: Rigaku Thermo Plus EVO2 TMA

1. Coefficient of Thermal Expansion

A critical parameter TMA characterizes is the coefficient of thermal expansion (CTE). The CTE or average linear expansion % represents the amount of expansion that will occur per unit of length or volume within a specific temperature range. For example, if a material has a CTE of 5 ppm/°C, it will expand by 5 parts per million (ppm) of its original size for every degree Celsius increase in temperature. The CTE can vary depending on the material’s composition and structure and thus is an important material property to characterize. If the sample length is  at room temperature and at T°C, the average CTE from room temperature to T°C is

An equation defining the coefficient of thermal expansion (CTE). CTE = 1/l * (change in l)/(change in T)


α represents the instantaneous coefficient of linear expansion at temperature T°C and sometimes called the coefficient of derivative linear expansion:

An equation defining the coefficient of derivative linear thermal expansion, symbolized by a Greek letter alpha. 

Alpha = 1/l * (the first derivative of l by T at constant time)In the case of polymers, CTE should be considered as it can predict the material’s behavior under varying conditions of stress and/or temperature fluctuations over areas such as:

  1. Design: The CTE of a material can affect its dimensional stability and the fit of parts. Polymers with high CTEs can expand extensively with temperature change, which can cause components made from them to distort. This is important in areas such as electronics, where precision is crucial.
  2. Manufacturing: Understanding the CTE of polymers is vital during material manufacturing since it can impact the shrinkage and warpage of the material during cooling or curing, influencing the quality and consistency of the final product.
  3. Reliability: The CTE of a polymer can also impact its durability and reliability. Polymers with high CTEs may be more prone to cracking or delamination when exposed to temperature changes or mechanical stress, which can compromise the integrity of the material and its performance over time.

Crack growth - tire - metravib

Figure 2: An example of fatigue cracking in a rubbery polymer. 

2. Measuring CTE of Polyethylene Terephthalate  

For example, Rigaku measured the CTE of polyethylene terephthalate (PET), a plastic commonly used in packaging.
An image showing Overlayed TMA, TG, DSC, and DTA curves of PET sample

Figure 3: Overlayed TMA, TG, DSC, and DTA curves of PET sample

As seen in Figure 3, the PET sample is stable until about 77°C where it begins shrinking rapidly until it reaches 136°C. Over the temperature range, it shrinks by almost 1 millimeter. Since PET is used for various applications, from clothing to food packaging, this would be an essential consideration for manufacturing optimization and product quality.

Pairing the analysis with TGA, DSC, and/or DTA can complement the TMA results by providing more insight into the thermal events over the temperature range. There is a glass transition temperature at about 82.4°C, followed shortly by a dilatometric softening temperature (1 mm contraction), and the cold crystallization is evident at 161°C. The glass transition was also observed on the DTA and DSC curves, in good agreement with the TMA result.

These properties help inform design and processing decisions. For example, glass transition temperature will determine the flexible or rigid application of a material. If a polymer is heated above its glass transition temperature, it will become more flexible, whereas keeping it below the glass transition temperature will enable a rigid format.




TAL: TMA Expertise for Polymers and Composites Testing

Thermal Analysis Labs has a Rigaku TMA that can run the measurements to identify sample CTE and glass transition. Furthermore, our Rigaku DSC Vesta can run DSC tests to provide vital heat flow measurements that can be coupled with TMA results to understand material properties better. For a full overview of our services, consult our 2023 contract testing catalog. Have a question? Reach out to one of our thermal analysis experts to start the discussion.



About the Author

Lauren works in the Thermal Analysis Labs division of C-Therm Technologies. She holds a Bachelor of Science in Chemical Engineering with the Nuclear Power Option from the University of New Brunswick.



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