The effective transfer of phonons, electrons, and load is known to increase with longer carbon nanotubes (CNTs) within CNT agglomerates. For example, in the percolation theory, electron transfer is expected to be achieved with a lesser number of CNTs by the use of longer CNTs in accordance with the relation Nc = 5.71 /Ls2, where Nc and Ls are percolation threshold and CNT length, respectively [1–4]. For example, higher electrical conductivity was observed for transparent conductive films using network thin films of longer CNTs [5, 6]. In addition, Miyata el al. reported a field effect transistor (FET) with high mobility using long single-walled CNTs (SWCNTs) . Further, in CNT/polymer composites, the beneficial effect of CNT length on the efficiency of phonon/electron transport and interfacial load transfer has been reported [8–11]. Such superiority in properties from long CNTs originates from the fewer CNT junctions, which interrupt phonon, electron, and load transfer, in a network structure of CNTs required to span the material.
Although these reports suggest the advantages of long CNTs on electron, thermal, and mechanical properties of a CNT assembly, this point has not been explicitly demonstrated experimentally. In other words, almost all the above experiments have employed only short CNTs, on the order of micrometers, with only one exceptional report by Zhu et al., who reported on the properties of composite of multiwalled CNTs with thick diameters (approximately 40 to 70 nm) and bismaleimide (BMI) . Particularly, there has been no report on the effect of length on the properties of SWCNTs exceeding 1 mm.
There are three reasons why research on the CNT length dependence of various properties of CNT assemblies has been difficult. First, the synthesis of long CNTs with uniform length in a large quantity is difficult. For example, Wang et al. reported the synthesis of long single-wall CNTs with a maximum length of 18.5 cm, but there were substantial variations in CNT length . Cao et al. reported an interesting approach for length-tunable CNT growth, but the length did not reach to millimeter scale . Furthermore, several groups reported the methods for classifying long/short CNTs, but this was not applied to CNTs that were longer than 10 μm in length [14–17]. Secondly, due to the tight entanglement among CNTs, the dispersion of CNTs without CNT scission is difficult. Ultrasonic agitation, which has been typically employed as a dispersion method, is known to shorten CNTs as it disentangles them . Finally, there is no available method to measure the lengths of individual CNTs longer than 100 μm. CNTs with lengths of several micrometers have been evaluated by atomic force microscopy (AFM) [8–11, 14–17], but this method encounters extreme difficultly when obtaining statistically significant data for long CNTs.
Using water-assisted chemical vapor deposition (CVD), we reported the synthesis of a vertically aligned SWCNT array (SWCNT forest) with height exceeding a millimeter . The SWCNT forests possessed several excellent structural properties, such as long length, high purity, and high specific surface area. This development opened up the potential for various new applications of CNTs, such as high-performance super-capacitors [20–23] and highly durable conductive rubbers [24, 25]. Subsequently, many groups reported the growth of long SWCNTs. For example, Zhong et al. reported the growth of SWCNT forests reaching 0.5 cm in length . Hasegawa et al. reported growth of SWCNT forests of several millimeters in length without an etching agent (water) . Numerous studies have also reported the synthesis of multiwalled CNT forests [28–30]. However, the following points remain unclear at present: the correlations between forest height and (1) the actual CNT length and (2) the electrical, thermal, and mechanical properties after formation of CNT assemblies.
In this research, we report the effect of the length of long CNTs on the electrical, thermal, and mechanical properties. Our results demonstrated a strong dependence of the SWCNT aggregate properties on the length. Specifically, buckypaper produced from 1,500 μm SWCNT forests exhibited approximately twice the electrical conductivity (52 vs. 27 S/m) and twice the tensile strength (45 vs. 19 MPa) of a buckypaper produced using 350 μm SWCNT forests. The use of an automated synthetic system equipped with height monitoring and dispersion strategy recently reported by Kobashi et al.  allowed overcoming the first two of the aforementioned issues, namely the required large quantity of long CNTs and CNT dispersion method to preserve length.