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Although many researches for developing photochemical energy conversion systems have been carried out during the last two decades by utilizing a Langmuir-Blodgett film [5 - 7], SAM [8], a polymer film with dispersed functional molecules [9 - 11] and so on, no efficient system has been developed except semiconductor systems as mentioned above. It is now important to know if an efficient system can be constructed without semiconductor.

The calculation speed of a personal computer is getting faster, and its main memory and a storage device are becoming larger every year. Numerical simulation on a small scale can be done with the computer. Virtual devices on the computer are used for developing actual new devices in various industrial fields. Such a device on the computer would be also useful in the chemistry field.

In the present study, we have developed a virtual device of a bipolar photogalvanic cell which consists of two layers with dispersed functional molecules, and studied whether such a device is able to function as an efficient photo-energy conversion system.

Figure 1. Schematic representation of the bipolar photogalvanic cell to indicate the electron energy level in the different phases.

Figure 1 shows a schematic illustration of the energy levels of a bipolar photogalvanic cell. The cell consists of two layers of different nature with dispersed functional molecules; i.e., polyanion and polycation polymer layers, polyanion polymer and solution layers, and polycation polymer and solution layers. The mediator layer involves vacancies or cracks to which sensitizer molecules are accessible to form a charge separation region. It is assumed that the sensitizer cannot penetrate the mediator layer beyond the charge separation layer. The mediator cannot also penetrate the sensitizer layer.

where

Assuming that incident photons are absorbed by a micro volume (1cm × 1cm × Dz), the decrease in the number of photons follows the Lambert-Beer law:

where

where

where

where

where

In the same manner of M

where

I) In the case of

II) In the case of

Figure 2. Configuration of a bipolar photogalvanic cell.

Figure 3. Photocurrent changes induced by switching on and off the irradiation using a virtual photogalvanic cell. -, *k*_{d} = 5 mol^{-1}cm^{3}s^{-1}, *k*_{r} = 1 × 10^{5 }mol^{-1}cm^{3}s^{-1}; ---, *k*_{d} = 50 mol^{-1}cm^{3}s^{-1}, *k*_{r} = 1 × 10^{7} mol^{-1}cm^{3}s^{-1}; ..., *k*_{d} = 500 mol^{-1}cm^{3}s^{-1}, *k*_{r} = 1.5 × 10^{9} mol^{-1}cm^{3}s^{-1}.

Table 1. Parameters for the simulation.

D_{M} /10^{-11}cm^{2}s^{-1} | 5.0 |

C_{M} /10^{-3}mol cm^{-3} | 6.2 |

D_{S} /10^{-7}cm^{2}s^{-1} | 1.0 |

C_{S} /10^{-5}mol cm^{-3} | 1.0 |

l_{1} /10^{-5}cm | 2.5 |

l_{2} /10^{-5}cm | 10.0 |

l_{3} /10^{-5}cm | 2.0 |

Intensity /mW | 30.0 |

Wavelength /nm | 450.0 |

k_{P} /10^{5}s^{-1} | 7.0 |

k_{nr} /10^{6}s^{-1} | 1.0 |

Figure 4. Photocurrent changes induced by switching on and off the irradiation using a virtual photogalvanic cell. -, Cell A;---, Cell B; ..., Cell C. The parameters for the simulation are the same as those in Table 1 except for the thickness of layers. *k*_{d} = 50 mol^{-1}cm^{3}s^{-1}, *k*_{r} = 1 ×10^{7} mol^{-1}cm^{3}s^{-1}.

On the other hand, when the sensitizer cannot penetrate into the internal region of the mediator layer, the increase in the mediator layer thickness decreases the steady-state photocurrent, and it takes a longer time to reach the steady-state photocurrent (Cell A and C). This means that the thickness of the charge separation layer can be estimated by measuring photocurrent responses at various thicknesses of the mediator layer using an actual device.

Figure 5. Dependence of the short-circuit photocurrent on the diffusion coefficient of the mediator () and dependence of the fraction of oxidized sensitizer on the apparent diffusion coefficient ().

Figure 5 shows the simulated dependence of the short-circuit photocurrent (*J*_{SC}) in a steady state on the diffusion coefficient of the mediator (*D*_{M}) under the conditions where the sensitizer-side is not the rate-determining step. Table 2 shows the parameters for the simulation. *J*_{SC} increases with the diffusion coefficient, reaching a plateau above *D*_{M} = 1 × 10^{-7}cm^{2}s^{-1}, whereas the fraction of the oxidized sensitizer increased with the *D*_{M} at low diffusion coefficients, a maximum value was exhibited around 1 × 10^{-9}cm^{2}s^{-1} and then it decreased with the diffusion coefficient. It is indicated that not only the diffusion coefficient but also the charge separation efficiency must be improved to advance the performance of the device.

Table 2. Parameters for the simulation.

C_{M} /10^{-3}mol cm^{-3} | 6.2 |

D_{S} /10^{-7}cm^{2}s^{-1} | 1.0 |

C_{S} /10^{-5}mol cm^{-3} | 1.0 |

l_{1} /10^{-5}cm | 2.5 |

l_{2} /10^{-5}cm | 10.0 |

l_{3} /10^{-5}cm | 0.0 |

k_{d} /mol^{-1}cm^{3}s^{-1} | 50.0 |

k_{r} / 10^{7}mol^{-1}cm^{3}s^{-1} | 1.0 |

Intensity /mW | 30.0 |

Wavelength /nm | 450.0 |

k_{P} /10^{5}s^{-1} | 7.0 |

k_{nr} /10^{6}s^{-1} | 1.0 |

The action spectrum for the short-circuit photocurrent is shown in Figure 7. The action spectrum agreed with the absorption spectrum of [Ru(bpy)

PB has the two redox couples shown below [15, 16]:

The injected electrons have a potential of around 0.17V vs. Ag|AgCl as estimated from the formal potential of eq. 19. Possible reactions at the cathode are either eq. 21 or 22:

Figure 6. Current changes induced by switching on and off the irradiation on the cell (0.25cm^{2}).

However, eq. 22 is negligible because dioxygen was reduced below -0.2V vs. Ag|AgCl under this condition (Figure 8). Since the open-circuit voltage was small (0.15V vs. Ag|AgCl), a possible mechanism for the present photogalvanic cell would be expressed as:

Figure 7. Action spectrum for the short-circuit photocurrent and absorption spectra of Ru(bpy)_{3}^{2+} (-) and Prussian Blue (---).

Figure 8. Cyclic voltammogram of ITO electrode in 0.1M KNO_{3} (pH2) using three electrodes system. Scan rate is 5 mV/s. -, under air; ---, under Ar.

Table 3. Properties of the ITO|PB|Ru(bpy)_{3}^{2+}|ITO.

D_{M} /10^{-11}cm^{2}s^{-1} | 4.0 |

C_{M} /10^{-3}mol cm^{-3} | 6.2 |

D_{S} /10^{-6}cm^{2}s^{-1} | 6.0 |

C_{S} /10^{-5}mol cm^{-3} | 1.0 |

l_{1} /10^{-5}cm | 0.4 |

l_{2} /10^{-5}cm | 0.4 |

l_{3} /10^{-4}cm | 65.0 |

k_{P} /10^{5}s^{-1} | 7.0 |

k_{nr} /10^{6}s^{-1} | 1.0 |

V_{OC} /mV | 118.0 |

J_{SC} /mAcm^{-2} | 2.3 |

Fill Factor /% | 20.5 |

Table 3 shows the properties of the photogalvanic cell as obtained from the experimental results and the simulation. The apparent diffusion coefficients were estimated using Cottrell's equation, and the phosphorescence rate constant (*k*_{p}) and non-radiative rate constant (*k*_{nr}) were calculated using the quantum efficiency of the phosphorescence (f = 0.042)[17]. The charge separation and the recombination rate constants were estimated from the current response induced by switching on and off using the virtual device, as 5 × 10^{2} mol^{-1}cm^{3}s^{-1} and 6 × 10^{9} mol^{-1}cm^{3}s^{-1}, respectively.

This work was partly supported by a Sasakawa Scientific Research Grant from the Japan Science Society.

[ 2] A. Hagfeldt, M. Gratzel,

[ 3] T. Yoshida, K. Yamaguchi, T. Kazitani, T. Sugiura, H. Minoura,

[ 4] P. Peumans, V. Bulovic, and S. R. Forrest,

[ 5] A. Desormeaux, R. M. Leblanc,

[ 6] M. Yoneyama, A. Fujii, S. Maeda, T. Murayama,

[ 7] M. Fujihira, K. Nishiyama, H. Yamada,

[ 8] H. Imahori, T. Azuma, Y. Sakata,

[ 9] G.-J. Yao, T. Onikubo, M. Kaneko,

[10] K. Yamada, N. Kobayashi, K. Ikeda, R. Hirohashi, M. Kaneko,

[11] X.-Y. Yi, L.-Z. Wu, C.-H. Tung,

[12] A. Fujishima, M. Aizawa, T. Inoue,

[13] T. Abe, H. Shiroishi, K. Kinoshita, M. Kaneko,

[14] M. Kaneko, S. Teratani, K. Harashima,

[15] K. Itaya, T. Ataka, S. Toshima, and T. Shinohara,

[16] K. Itaya, I. Uchida, V.D. Neff,

[17] J.V-. Houten, R.J. Watts,

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