Contact mechanics and thermal conductance of carbon nanotube array interfaces

A model is developed in this work to predict the thermal contact resistance of carbon nanotube (CNT) array interfaces with CNT arrays synthesized directly on substrate surfaces. An analytical model for contact mechanics is first developed in conjunction with prior data from load–displacement experiments to predict the real contact area established in CNT array interfaces as a function of applied pressure. The contact mechanics model is utilized to develop a detailed thermal model that treats the multitude of individual CNT–substrate contacts as parallel resistors and considers the effects on phonon transport of the confined geometry that exist at such contacts. The influence of CNT array properties, e.g. diameter and density, are explicitly incorporated into the thermal model, which agrees well with experimental measurements of thermal resistances as a function of pressure for different types of interfaces. The model reveals that: (1) ballistic thermal resistance dominates at the CNT array interface; (2) the overall performance of CNT array interfaces is most strongly influenced by the thermal resistance at the contacts between free CNT ends and the opposing substrate surface (one-sided interface) or the opposing CNT array (two-sided interface); and (3) dense arrays with high mechanical compliance reduce the thermal contact resistance of CNT array interfaces by increasing the real contact area in the interface.