Determination of solubility parameters of single-walled and double-walled carbon nanotubes using a finite-length model

Carbon nanotube (CNT) dispersions have been prepared using a variety of surface modification methods; however, these methods frequently have a negative effect on the intrinsic properties of CNTs or need to remove the surface modifiers. The Flory-Huggins theory suggests that such problems can be alleviated or eliminated, if ideally, when the solubility parameters of CNTs and a given medium are very similar or equal to each other. Since the earlier reported solubility parameters of CNTs were determined by indirect methods and varied in wide ranges, we suggested herein a possible way of directly determining the solubility parameter of various types of CNTs by using a finite-length model, and reported the determined solubility parameters of pristine single-walled carbon nanotubes (SWCNTs) and pristine double-walled carbon nanotubes (DWCNTs). Through the validity test of the suggested model it was found that a 2 nm finite-length of CNTs can represent the longer CNTs for the study of the solubility parameters. In addition, the pristine DWCNTs were found to have higher solubility parameters than the pristine SWCNTs, and within the given type of CNTs, the solubility parameters varied inversely with the diameter of the CNTs. Based on the obtained results, it was expected that the solubility parameters for pristine multi-walled carbon nanotubes (MWCNTs) should be similar to or slightly higher than the values for DWCNTs.