Coefficient of Thermal Expansion (CTE) for Carbon Nanofibers

Dear iMechanica community,

 One of the biggest difficulties of performing a processing conditions related residual stress analysis and subsequent interfacial fracture assessment for carbon nanofiber containing polymer nanocomposites (especially with aerospace grade epoxies) is the lack of adequate information concerning the range of attainable values of CTEs (Coefficient of Thermal Expansion) for different types of carbon nanofibers. Clearly, the micro-, nanostructure of the nanofiber interior (i.e. orientation of annular graphene layers with respect to the fiber axis, their spacing, defect size/distribution, concentration of synthesis related impurities such as substitutional catalyst particles, the ratio of graphitic/turbostratic contents etc.) and geometric factors such as the extent of the hollow concentric region in case of tubular structures have a combined effect on the resulting CTE range. To circumvent this difficulty I did some first principles based thermomechanical analysis and decided to share the preliminary results with our community to collect your feedback. I think these initial CTE estimates can be implemented with some moderate confidence for predominantly sp2-bonded 1-D carbon nanostructures (nanotubes/nanofibers/nanorods) within the diameter range of 30-500 nm. Also note that a simple sensitivity analysis indicates that the angle between the fiber axis and the inward normal of the basal planes of graphene is the most influential factor in determining the CTE. Let me also note that I set the limits of this orientation angle to 30 and 90 degrees in my analysis and did not consider any periodic/aperiodic waviness of the 1-D structure or localized amorphous carbon presence in the composition. Under these gross assumptions, the values I am getting are the following:

 Coefficient of thermal expansion (CTE) range for carbon nanotubes (CNTs) and carbon nanofibers (CNFs):

 2.7 x 10-6 (1/K) to 4.4 x 10-6 (1/K)

 I looked at the existing literature to see whether these values make any sense and found an experimental paper which mentions a CTE value for the vapor grown carbon nanofibers within the same diameter range as the one in my analysis:

  "Temperature Dependence of Electrical Resistivity in Carbon Nanofiber/Unsaturated Polyester Nanocomposites" by Natsuki, Ni and Wu, published in Polymer Engineering and Science (2008).

 Their value was close to my upper bound with 4 x 10-6 (1/K). If you are aware of CTE values which fall within the above mentioned range or simply want to share your own estimates please reply to this blog. By exchanging ideas and sharing different perspectives on this topic, we can achieve much more in terms of technical and scientific accuracy of these CTE values for carbon nanostructures.

  With my best regards,

  Tanil Ozkan