Compression and recovery of carbon nanotube forests described as a phase transition

In this paper we describe experiments and a continuum phase transition model for the compression of carbon nanotube (CNT) forests. Our model is inspired by the observation of one or more moving interfaces across which densified and rarefied phases of the CNT forests co-exist. We use a quasi-static version of the Abeyaratne-Knowles theory of phase transitions for continua with a stick-slip type kinetic law and a nucleation criterion based on the critical stress for buckling of CNT forests to describe the formation and motion of these interfaces in uniaxial compression experiments. We investigate micropillars made from bare CNTs, as well as those coated with different thicknesses of alumina using atomic layer deposition (ALD). The coating thickness affects the moduli of individual CNTs as well as the adhesion energy per contact between CNTs. In order to test the applicability of our model to more complex stress states, we carry out nanoindentation experiments on the CNT pillars and interpret the load-indentation data by incorporating a constitutive law allowing for phase transitions into solutions for the indentation of a linearly elastic half-space. Even though the state of stress in a nanoindentation experiment is more complex than that in a uniaxial compression test, we find that the parameters extracted from the nanoindentation experiments are close to those from uniaxial compression. Our models could therefore aid the design of CNT forests to have engineered mechanical properties, and guide further understanding of their behavior under large deformations.