*3.2.1 TiO2 nanoparticle*

The highly crystalline anatase TiO2 nanoparticles (NPs) was synthesized by 2-step autoclaving technique (**Figure 4(a)**). A pH controlled TiO2 suspension was prepared by commercial TiO2 power. (P25, Degussa) The TiO2 suspension is placed in a total volume of 60 mL in a Teflon-lined stainless steel autoclave (125 mL

*A New Generation of Energy Harvesting Devices DOI: http://dx.doi.org/10.5772/intechopen.94291*

#### **Figure 3.**

*<sup>γ</sup>*<sup>2</sup> <sup>¼</sup> *<sup>k</sup>*eff *D*eff þ *iω D*eff

*x* ¼ *L*,

*qA*

*<sup>S</sup>* <sup>¼</sup> *KBT qns*

*<sup>L</sup>*<sup>2</sup> , *<sup>ω</sup>*<sup>k</sup> <sup>¼</sup> *<sup>k</sup>*eff and *<sup>γ</sup><sup>L</sup>* <sup>¼</sup>

The equivalent impedance Z2 of Bisquert [39] is obtained as follows:

<sup>¼</sup> *Con <sup>L</sup> D*eff

transport resistance, and *R***<sup>k</sup>** is the charge transfer resistance related to recombination of electrons at the TiO2/electrolyte interface. The relation can be expressed by

The total impedance (*Z***s**) of the DSSC can be calculated by the summation of *Z*1,

From experimental (*L*, *A*, *δ*) and EIS data (the maxima values of *ω*Z1, *ω*Z2, *ω*Z3 of the semi-circle diameters along the *Z*' axis), necessary information on charge

The highly crystalline anatase TiO2 nanoparticles (NPs) was synthesized by 2-step autoclaving technique (**Figure 4(a)**). A pH controlled TiO2 suspension was prepared by commercial TiO2 power. (P25, Degussa) The TiO2 suspension is placed in a total volume of 60 mL in a Teflon-lined stainless steel autoclave (125 mL

*∂*Δ*n ∂x* � �

*∂*Δ*n*

1

ffiffiffiffiffi 1 *k*eff q

> ffiffiffiffiffiffiffi 1 *k*eff

s

<sup>1</sup> <sup>þ</sup> *<sup>e</sup>*2*γ<sup>L</sup>*

*D*eff *γ*

<sup>¼</sup> <sup>Δ</sup>*<sup>I</sup>*

*<sup>A</sup>* <sup>¼</sup> <sup>Δ</sup>*<sup>J</sup>* (24)

<sup>1</sup> � *<sup>e</sup>*2*γ<sup>L</sup>* (26)

*<sup>∂</sup><sup>x</sup>* <sup>¼</sup> <sup>0</sup> (25)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *ω*k *ω*d þ *iω ω*d

� *<sup>R</sup>*<sup>ω</sup> <sup>¼</sup> *Con* <sup>1</sup>

) (with *ω*<sup>k</sup> *= k*eff), *R***<sup>w</sup>** is the electron

*Zs* ¼ *Z*<sup>0</sup> þ *Z*<sup>1</sup> þ *Z*<sup>2</sup> þ *Z*3*:* (31)

*Lk*eff

s

coth½ð Þ *ω*k*=ω*<sup>d</sup> ð Þ� 1 þ i*ω=ω*<sup>k</sup>

, *Rk* <sup>¼</sup> *<sup>ω</sup>*<sup>d</sup> *ω*k

and using the following boundary conditions at

*Solar Cells - Theory, Materials and Recent Advances*

the impedance *Z*<sup>2</sup> is obtained by Kern et al. as [39].

*<sup>ω</sup>*<sup>d</sup> <sup>¼</sup> *<sup>D</sup>*eff

1 ð Þ *ω*k*=ω*<sup>d</sup> ð Þ 1 þ *iω=ω*<sup>k</sup> � �<sup>1</sup>*=*<sup>2</sup>

> *L D*eff

*Rw* <sup>¼</sup> *kBT q*<sup>2</sup>*Ans*

*Z*2, *Z*3, and the external resistance, *Z*0,

**3.2 Materials preparation**

*3.2.1 TiO2 nanoparticle*

**194**

Here, *ω* is modulation frequency (s�<sup>1</sup>

transport kinetics can be determined (**Figure 3**).

By defining

*Z*<sup>2</sup> ¼ *R*<sup>ω</sup>

*R*<sup>k</sup> = (*ω*d/*ω*k)� *R*w.

*x* ¼ 0, *qD*eff

*<sup>Z</sup>* ¼ �*<sup>S</sup>* <sup>1</sup>

(23)

(27)

(28)

(30)

<sup>1</sup>*=*<sup>2</sup> (29)

*(a) A electrical equivalent and (b) an illustrative Nyquist plot of a DSSC with R0, R1, R2, and R3, and each peak frequency maxima of* ω*Z1,* ω*Z2, and* ω*Z3, respectively. Reprinted from [26, 51].*

volume, Parr Instrument Co.) and heated at 240°C for 12 h. The resulting powders are dried at �80°C in a conventional drying oven for 24 hour (**Figure 4(b)**). The pure Anatase colloidal TiO2 nanoparticle was obtained by autoclaving the low-pH titanate suspension at 240°C for 12h (**Figure (4c)**) [45].
