even higher current densities might be expected that would lead to failure. In carbon
nanotubes, current densities in the range of 10
13 A m
À2 were observed. For
comparison it must be mentioned that, in electrical machines, a current density
of maximal 10 A mm
À2 ¼ 10
7 A m
À2 is used as reference value.
In this context, the Hall effect must be discussed, as this phenomenon is of special
interest in connection to two-dimensional nanomaterials. Classically, the Hall effect
describes a voltage that is, in the presence of an external magnetic field, measured
perpendicularly to the direction of the transport of the electrical current. The basis
principle is shown in Figure 10.10.
Figure 10.8 I–V characteristics of a 50-nm diameter, 5-mm long silver nanowire measured at 4.2 K
[4]. The current offset in the original data was removed.
Figure 10.9 Current density to failure for gold nanowires of different diameters, determined
at room temperature. Note the increasing maximum current density with decreasing wire
diameter [5].
10.1 Fundamentals of Electrical Conductivity in Nanotubes and Nanorods j275