Improved Multiscale Model of Heat Exchange at the Apex of Carbon Nanotube Fiber Cathodes

A multiscale model of field emission (FE) from carbon nanotube fibers (CNFs) is developed which includes a detailed treatment of the heat exchange mechanisms in the array of carbon nanotubes (CNTs) located at the tip of the fiber. The model takes into account Joule heating within the fiber, radiative cooling at the fiber apex, and the transition from Nottingham heating to Henderson cooling in the CNTs in the array at the apex of the fiber as the external electric field is increased. The model uses numerical calculations of the current emitted from each CNT and the energy exchange at their tips. The model predicts the fraction of CNTs being destroyed as a function of the applied external electric field. For the surviving CNTs, the model also predicts the fraction of CNTs either undergoing Henderson cooling or Nottingham heating for both the up and down sweeps of the applied external electrical field. This investigation sheds new light on the FE properties on CNFs.