When designing new products, engineers have a wide variety of materials to choose from. Correctly analyzing all material properties while placing them in the context of the final product or application is an extremely challenging task. In material selection, two thermal properties play a significant role: the thermal conductivity and the coefficient of thermal expansion.
In any thermodynamic application, the thermal conductivity and the coefficient of thermal expansion of materials should be carefully considered, especially in applications where these properties affect the final performance and service life. Choosing materials with the appropriate thermal conductivity can improve efficiency and performance. Due to their unique thermal properties, carbon fibers can be used in many new application areas.
Thermal Conductivity
Thermal conductivity, also known as thermal diffusivity, in the simplest terms, is a measure of how effectively heat flows through a given material. Materials with a simple molecular structure typically also have higher thermal conductivity. When materials are heated, particles gain energy and vibrate. This vibration causes molecules to collide with other particles and transfer energy to them. The more heat applied, the more vibration and energy transfer occur.
The mathematical representation of thermal conductivity is as follows:
K = Thermal conductivity (W/(mK)) or (Btu/(hr ft °F))
Q =Heat transfer (W) or (Btu)
d = Distance between two isothermal planes (m) or (ft)
A = Surface area (m²) or (ft²)
Delta T = Temperature difference (K) or (°F)
Thermal conductivity varies with materials. Since carbon fibers come in different types, each with its unique properties, they differ from other materials like water. The table below shows the different thermal conductivities of various materials.
Manufacturers and researchers have developed carbon fiber composites with high or low thermal conductivity for different applications. The method of measuring thermal conductivity also affects the final measurement result. If the thermal conductivity is measured along the fibers, it is usually higher than when measured across the fibers (perpendicular direction).
Carbon fibers with high thermal conductivity can be used in various applications. For example, a Japanese company has developed carbon fibers to suppress battery degradation in mobile applications for electronic devices. The final application should determine whether engineers need carbon fibers with low or high thermal conductivity.
Coefficient of Thermal Expansion
Another key thermodynamic property that engineers should consider is the coefficient of thermal expansion. The coefficient of thermal expansion is a measure of how the dimensions of an object change when exposed to temperature changes. There are three types of coefficients of thermal expansion: volumetric, areal, and linear.
Since carbon fibers are typically solid in most applications, engineers should focus most on the areal and linear coefficients of thermal expansion.
The mathematical representation of the linear coefficient of thermal expansion is as follows:
alpha = Linear coefficient of thermal expansion (K^{-1} or 1/K) or (°F^{-1} or 1/°F)
L = {Original length (m) or (ft)
Delta L = Length change (m) or (ft)
Delta T = Temperature change (K) or (°F)
The mathematical representation of the areal coefficient of thermal expansion is as follows:
alpha = Areal coefficient of thermal expansion (K^{-1} or 1/K) or (°F^{-1} or 1/°F)
A = {Original area (m²) or (ft²)
delta A = {Area change (m²) or (ft²)
delta T = Temperature change (K) or (°F)
Like thermal conductivity, the coefficient of thermal expansion of carbon fibers can also vary greatly. This coefficient largely depends on the direction of the carbon fibers in the matrix. The typical range of the coefficient of thermal expansion is between -1 K^{-1} to +8 K^{-1}. The table below shows the different coefficients of thermal expansion for various materials.
Carbon fibers have a negative coefficient of thermal expansion. When the material is heated, it contracts. Carbon fiber atoms are typically fixed along the x and y axes. The planar bonds that fix the fibers along the x and y axes are covalent bonds. This makes the z direction not fixed and held together by weaker van der Waals forces.
When carbon fibers are heated, the atoms begin to vibrate, mainly in the z direction. As this occurs, the vibrating atoms pull on adjacent atoms. The entire phenomenon causes the atoms to bind more tightly together and contract the material in the x and y directions. As the heat increases and the atoms begin to vibrate, the material continues to contract.
In some applications, the negative thermal expansion property can produce some interesting results. Carbon fibers can be combined with a resin matrix that has a positive coefficient of thermal expansion, where the resulting matrix's coefficient of thermal expansion is close to zero. This can be crucial for some small devices such as measuring equipment.