Carbon nanotubes(CNTs)have been used as nanoscale fillers to tune the transport properties of nanocomposites.While up to seven orders of magnitude enhancement has been achieved for the electrical conductivity of CNT-polymer composites,thermal conductivity enhancement is still far below the theoretical prediction based on the particle mixing theory.This has been attributed to the contact thermal resistance between CNTs and between CNTs and various host materials such as different polymers.However,compared to the extensive studies of thermal transport through individual CNTs of different morphologies,the research on thermal transport through contacts between CNTs is still very limited.As such,a good understanding of the contact thermal conductance at CNT-CNT junctions is still lacking.Here we report on experimental measurements of contact thermal conductance between individual multi-walled CNTs.Results show that the contact thermal conductance between CNTs increases with the tube diameter with an exponent of~2.4.The normalized contact thermal conductance per unit area linearly depends on the tube diameter,which is intriguing because it is commonly expected that the normalized conductance should be size-independent.Semi-quantitative analyses indicate that this surprising observation can be attributed to three coupled underlying mechanisms:(1)an unexpectedly long phonon mean free path along the c-axis of graphite of more than 100 nm,(2)phonon reflection from free surfaces nearby the contact,and(3)the phonon focusing effects in highly anisotropic graphitic materials.