Hierarchical Nanostructures for Photo-Electro-Chemical Cells - Hierarchical Nanostructures for Energy Devices - page 191

d n 3 r 4 n g | 4

Figure 8.13 Simplified model to calculate the roughness factor of a hierarchical

structure.

are attached to the surface of each backbone, the RF is approximately cal-
culated as the following equation:

roughness factor R ðÞ N pDH þ 0 : 25pD 2

Þ þ nN pdh þ 0 : 25pd 2

ð ð Þ

.

(8 : 5)

ab

For the high aspect ratio backbone and branch nanowires (D { H, d { h), the
RF can be further simplified as follows:

roughness factor R ðÞ Np DH þ ndh

ð Þ

(8 : 6)

ab

Usually, nanowires do not have circular cross sections and are often tapered
rather than having straight edges. However, the above expression can be
employed to provide an estimate without incurring significant errors. Also,
when the hierarchical structure has multi-generation branches, the above
equation is readily adjustable.
Lee et al. 10 synthesized TiO 2 photoanodes of different RFs for DSSCs and
verified that the DSSC eciency ratio is in quite good agreement with the RF
ratio as displayed in Figure 8.14. Many other studies also adopted the RF as
an important parameter for PEC cell performance. 9,72-74 It is worth noting
that a higher RF does not necessarily mean higher cell performance. For
example, a 2 mm thick film consisting of 30 nm size nanoparticles has a
roughness factor of about 210, which is much higher than that of a film of
the same thickness comprising hierarchical nanowire structures (around