From charge-discharge current, we can calculate effective surface area around 21 cm
2 of TiO
2 nanoneedles coating on the VCNF array on 1.0 cm
2 of geometric surface. Furthermore, we can calculate the total surface area from transmission electron microscope (TEM) image, as shown in Fig. 6, CNF has the diameter of 100 nm, length of 5 μm, and the needle-shaped TiO
2 nanostructure has the mean diameter of 15 nm and the mean length of 100 nm was deposited onto the surface of CNF. The orientation of the nanoneedles is random. The density of TiO
2 nanoneedle is ~1×10
11 cm
-2 derived from the TEM image. The surface area of a single CNF is
ACNF=2π
RL=1.57×10
-8 cm
2, and the total area of CNF array on 1 cm
2 geometric area is
ACNF, array=
ACNF x (density of CNFs)+1 cm
2=1.57× 10
-8×10
9+1= 16.7 cm
2. Thus the surface enhancement factor is 16.7. By CNF alone, the surface area is not so great. For Gratzel cells, the surface enhancement factor for a 10 m thick TiO
2 NP film is claimed to be ~1000. This is why ZnO NW and TiO
2 NT based solar cell has much lower efficiency than Gratzel cells. After coating with TiO
2 nanoneedles, we can estimate the roughness factor using the similar method. The surface area of a single TiO
2 nanoneedle is
ATiO2=2π
RL=2×3.14×7.5×10
-7×100×10
-7=4.71×10
-11 cm
2, and the total area of TiO
2 nanoneeldes on a single CNF is A
TiO2/CNF = (density of T
iO
2 nanoneedles)×(nanoneedle surface area)×(single CNF surface area) + (CNF surface area)=(10
11 TiO
2/ cm
2)×(4.71×10
-11 cm
2)×(1.57 × 10
-8 cm
2)+(1.57×10
-8 cm
2)=8.96×10
-8 cm
2. So the roughness factor is
ATiO2/CNF/
ACNF= 8.96×10
-8/1.57×10
-8=5.71. The total area of TiO
2-coated CNF array on 1 cm
2 of geometric area is A
TiO2/CNF = (A
TiO2/CNF)×(Density of CNF)+1 cm
2=8.96×10
-8 cm
2×10
9+1=90.6 cm
2. In addition, from redox wave (see in Fig. 5(a) and (b)), we can get charge
Q = 4.96×10
-4 C. Since
Q = neF, the value of n can be calculated as 5.14×10
-9 mol of dye. From Ref. [
20], the dye N-719 molecule occupies an area of about 116-155 Å
2. Therefore, the dye molecules would occupy only about 36 cm
2 if they are closely packed area, namely their surface coverage is only 0.397 monolayer, which is far less than a close-packed monolayer. In order to increase the dye absorption, the surface of TiO
2 nanoneedles on CNFs needs to be chemically activated for stronger dye adsoption.