13744
J. Phys. Chem. C 2008, 112, 13744–13753
A Numerical Simulation and Impedance Study of the Electron Transport and Recombination in Binder-Free TiO2 Film for Flexible Dye-Sensitized Solar Cells Xin Li, Hong Lin,* Jianbao Li, Xiaxi Li, Bai Cui, and Luozheng Zhang State Key Laboratory of New Ceramics & Fine Processing, Department of Material Science and Engineering, Tsinghua UniVersity, Beijing 100084, China ReceiVed: January 2, 2008; ReVised Manuscript ReceiVed: July 1, 2008
A mesoporous TiO2 film consisting of different size nanocrystal particles without any organic binder was prepared on a conductive indium-tin oxide (ITO)-coated polyethylene naphthalate (PEN) plastic sheet by the doctor-blade method to fabricate flexible dye-sensitized photoanodes at 120 °C. It was found that the structure of the film affected the photovoltaic performance of the photoanode greatly. The mechanism of such effects was investigated both by simulation of porosity, surface area, average pore size, and electron diffusion coefficient of the mesoporous TiO2 film, and by impedance study for the electron transport and recombination in a dye-sensitized solar cell (DSC). The results showed that the electron transport and recombination dominated the operation of the DSC with such flexible photoanodes. The optimum photoanode was achieved, and the largest conversion efficiency obtained was 3.93%. 1. Introduction Dye-sensitized solar cells (DSCs) have attracted a lot of attention in scientific research and for practical applications during the past decade.1,2 Their main advantages are high lightto-energy conversion efficiency over a large span of the visible light spectrum under direct sunlight and diffuse light conditions as well as low cost compared to traditional solid-state crystalline silicon solar cells. In particular, a further dramatic cost reduction of DSCs can be realized when its photoanode, such as TiO2 film, is prepared on flexible conductive polymer substrate instead of a conductive glass substrate. However, the treating temperature of the photoanode based on the polymer substrate was limited by the poor melt point of the substrate. Thus, the traditional TiO2 film preparation method by sintering at about 450 °C is not suitable for the preparation of TiO2 film at low temperature, i.e. lower than 150 °C. Several methods have been developed to prepare the nanocrystal TiO2 films at a low temperature, such as chemical deposition,3 mechanical press of nanocrystal particles,4-7 hydrothermal necking,8,9 microwave sintering,10,11 and electrophoretical deposition.12,13 Although good photovoltaic performance can be obtained, all these methods required several steps, beginning with particle deposition and ending with interparticle connections, which are not suited for large-scale modules. In 2007, Miyasaka et al. reported a simple doctor-blade method to prepare nanocrystal TiO2 films at a low temperature.14,15 They obtained a high light-to-energy conversion efficiency of 5.8-6.4% under simulated sunlight of different intensities under optimized conditions. The results made the preparation of flexible DSCs possible for industrial applications. In Miyasaka’s research, a type of small nanoparticles was used as a cement agent instead of organic binder to connect larger particles. Their TiO2 films contained three different size TiO2 nanoparticles. The diameter of the middle size particles in their film was optimized, as well as electrolyte and film thickness. However, they did not investigate the effects of the * Author to whom correspondence should be addressed. E-mail:
[email protected].
small particles as cement on photovoltaic performance of the flexible DSCs, and the electron transport and recombination in such a film for the flexible DSCs was still uncertain. In the opinion of Graetzel et al.,16 the electron transport and recombination processes govern the operation of the flexible DSCs. Thus, scrutinizing the influence of the components of the structure having particles with two different sizes on the DSCs by studying the electron transport and recombination in the film should be necessary and be helpful to improve the photovoltaic performance of the flexible DSCs. Electrochemical Impedance Spectroscopy (EIS) is a steady state method measuring the current response to the application of an ac voltage as a function of the frequency. EIS was widely employed to study the kinetics of electrochemical and photoelectrochemical processes including the electron transport and recombination processes occurring in the DSCs over the past decade.17-19 An important advantage of EIS over other techniques is the possibility of using tiny ac voltage amplitudes exerting a very small perturbation on the system. Therefore, EIS was taken into the present research to study the electron behavior in this research. On the other hand, EIS responses are always attributed to the effect of mesoporous film structure on the electron movement. Thus, the investigation of the mesoporous film structure should help to explain the results of EIS. The characterization of the mesoporous structure is usually conducted by nitrogen or argon adsorption isotherms at liquid nitrogen temperature.20 However, such methods would be inconvenient for researchers to characterize the porous structure when the components of the structure vary continuously in a great range. Numerical simulation of this structure by computer, based on a theory of particle mixtures, would be helpful and convenient for the characterizations of the structure. In the present research, a mesoporous TiO2 film consisting of two different size nanocrystal particles, where the smaller particles synthesized by hydrothermal method were used as binder,21 was prepared on a conductive indium-tin oxide (ITO)coated polyethylene naphthalate (PEN) polymer sheet by the doctor-blade method. Simulation of the TiO2 film by computer
10.1021/jp800023z CCC: $40.75 2008 American Chemical Society Published on Web 08/07/2008
Electron Transport and Recombination in Binder-Free TiO2 Film
J. Phys. Chem. C, Vol. 112, No. 35, 2008 13745
Figure 1. Modeling of the structures formed by particles: (a) particle and associated pore; (b) numerical simplification of particle and associated pore; (c) the dilated structure of the larger particles when mixed with the smaller particles; and (d) the “wall and barrier” effects of the larger particles. The dark gray area represents particles and the light gray area represents pores.
with the Matlab program was conducted and verified by the results of nitrogen adsorption methods. The photovoltaic performance of the flexible photoanodes with varying the components of the low-temperature sintering film, i.e. the content of the smaller particles and the size of the larger particles, was studied. The electron transport and recombination in the TiO2 film were measured by the EIS method. The effect of the content of the smaller particles and the effect of the diameter of the larger particles on the electron movement in the film was analyzed combined with the simulative and EIS results. The effect of the structure of the mesoporous film on its electron behavior was confirmed. What is more, the simulative particle mixtures model is proved to be helpful to predict the nanostructure made up of different size particles, which could be applied in other nanostructure fields besides the DSCs. 2. Modeling 2.1. Numerical Modeling of the Porous Structure of TiO2 Film. Generally, a porous structure with single-size particles is made up of two components, particles and pores. In fact, each solid particle shares pores with other particles and the pores are effectively continuous. However, for analytical purposes, the net effects can be modeled as an equal number of finite pores and particles. Here, each particle in the structure is assumed to be associated with a single corresponding pore as shown in Figure 1a. In addition, for easy comprehension, a particle and its relative pore are modeled as a cube having a
mean size of D0 and a cube pore having a mean size of X0, respectively, as shown in Figure 1b. Therefore, the pore ratio of the structure, U0, is
U0 )
X03
(1)
D03
When particles with a smaller size, having a mean size of D1, are added into the structure above, the newly added particles would attempt to fill the pores in the structure and form a new structure. The mixing of the smaller particles would dilate the structure of the larger particles due to the interference between different size particles. This is modeled by assuming that the larger particles move apart to occupy the centers of spaces which have the same geometric relationship with the structure formed by the larger particles alone before dilation as shown in Figure 1c. The pore ratio of the larger particles after dilation should be U0′′ )
(X0′′)3 + (D0 + mD1)3 - D03 D03
) (1 + mr)3 +
(X0′′)3 D03
-1
(2)
where mD1 represents the distance between two neighbor larger particles after dilation and r ()D1/D0) is the diameter ratio of the smaller particles versus the larger particles. Before dilation, the smaller particles have their own pore ratio, U1, which has an expression similar to eq 1. When filling the pores in the dilated structure, the smaller particles would be
13746 J. Phys. Chem. C, Vol. 112, No. 35, 2008
Li et al.
pushed away from the larger particles by a distance of ZD0 as shown in Figure 1d, i.e. “wall and barrier” effects22a of the larger particles. While the pore ratio of the smaller particles after dilation, U1′′, would be different from U1. An analysis of the geometric and algebraic relationships of the two particles and their pores ratio in Figure 1d would yield the following equation
U0′′ 1 + U0′′ ) 1 + U1 (1 + U0′′) - (1 + z)3
(3)
Z is a function of the size ratio and the pore ratio of the larger particles alone, which should be22b
Z ) kinf + [(1 + U0)1⁄3 - 1 - kint]rkp
(4)
where kint and kp are empirical constants. As the pore ratio of the small particles and the larger particles is known after mixing, the overall pores ratio of the new structure can be calculated as
Un )
U0′′U1′′
(5)
1 + U0′′ + U1′′
The porosity Vn, and the total surface area Sn of the structure would be
Vn )
Un 1 + Un
and
Sn ) Sn,0 + Sn,1 )
(6)
(
nx (1 - nx) 6 Vtotal + 1 + Un D1 D0
)
(7)
where Sn,oand Sn,1 are the surface areas of the larger particles and that of the small particles, and nx and Vtotal are the weight content of the smaller particles and the total volume of the mixture structure, respectively. In this structure model, the average distance between two sizes of particles is regarded as the average pore size. To determine the average pore size, it is assumed that each particle is surrounded by a pore with a uniform thickness, d, as shown in Figure 1e. Thus, the average pore size would be 2d, which could be obtained by
(1 - nx) D03
[(D0 + 2d)3 - D03] +
nx D13
[(D1 + 2d)3 - D13] )
Figure 2. (a) Transmission line impedance model for a typical DSC. (b) Simplified equivalent circuit for a DSC at a high bias potential.
transfer resistance of the charge recombination process between electrons in TiO2 film and I3- in electrolyte, respectively. Besides, Cµ ()cµL) is the chemical capacitance of the TiO2 film that accounts for the change of electron density as a function of the Fermi level.24 RTCO and CTCO are the charge-transfer resistance and double-layer capacitance at the uncovered TCO/ electrolyte interface, respectively. Zd(El) represents the Warburg impedance relative to the Nernst diffusion of I3- in electrolyte. RPt and CPt are the charge-transfer resistance and double-layer capacitance at the counter electrode, respectively. When changing applied potentials, the completed model shown in Figure 2a would be reduced to several other models.25 At small applied potentials, the TiO2 film is regarded as an insulator, so only the circuit elements of RTCO, CTCO, Zd, RPt, and CPt remain in the model. At intermediate applied potentials, the resistance of the TiO2 film decreases exponentially as the Fermi level of the film is shifted by the applied potential, whose model is shown in Figure 2a. In this situation, the resistance of the film and the recombination resistance between TiO2 surface and I3- in electrolyte could not be ignored. The impedance of the photoanode is given by Kern et al.,26 which is similar to Bisquert’s equation24 as
UnVsolid (8) where Vsolid represents the total volume of the smaller particles and the larger particles. Among the above equations, the values of U0 and U1 were obtained based on a BJH (Barrett-Joyner-Halenda) method, the values of m, kint, and kp were referred from the literature.22b All calculations were performed with use of a Matlab program running on a PC computer. Porosity diagrams, surface area diagrams, and average pore size diagrams were obtained. 2.2. Electrochemical Modeling of the DSC with the Flexible Photoanode. Many theoretical models were proposed to interpret the complex system of the DSC under different conditions. An equivalent circuit for a complete DSC is represented by a transmission line model as shown in Figure 2a.23 Rs is a series resistance standing for the transport resistance of the two TCOs of electrodes. If the thickness of the TiO2 film as L, the Rw ()rtL) and the Rk ()rct/L) are the electron transport resistance in the mesoporous film and the charge-
((
Z ) Rw where
)(
1
k i 1+ d k
)
)
1⁄2
d ) Dcb/L2,
[( ) ( ) ]
coth
k d
1⁄2
1+
k ) k ) 1/τ
i k
1⁄2
(9)
(10)
Here Dcb, τ, k, kB, T, q, A, and ns represent effective diffusion coefficient of an electron in the TiO2 nanoparticle, lifetime of an electron in the film, reaction rate constant for the recombination of an electron, Boltzmann constant, absolute temperature, charge of a proton, the electrode area, and the electron density at the steady state in the conduction band, respectively. According to Kern25 and Adachi,27 electrons in the trap state are regarded as diffusing charges with the diffusion constant Deff ) Dcb(Rw/Rk). Thus, Rw and Rk are defined as
R )
kBT
L , D q Ans eff 2
Rk )
kBT
1 Lk q Ans eff 2
(11)
And electrons in the trap state also react with I3- with a pseudo-first-order reaction rate with reaction rate constant keff,
Electron Transport and Recombination in Binder-Free TiO2 Film
J. Phys. Chem. C, Vol. 112, No. 35, 2008 13747
which is equal to 2nsk. When keff, Rk, and Rw were obtained from EIS, the effective diffusion of an electron in TiO2 film would be determined. At high applied potentials, the resistance of the TiO2 film is so small that it could be ignored and the model of the DSC could be simplified as Figure 2b. In this situation, the recombination resistance between the film and I3- in electrolyte can be easily obtained by EIS. In the present study, the influence of particle size on the electron transport in the structure film for the flexible DSC and on the recombination with I3- at the TiO2/electrolyte interface was scrutinized. Hence, intermediate and high bias potentials were applied in the DSCs when EIS measurements were conducted. 3. Experimental Section 3.1. Preparation of the Flexible Photoanodes and Fabrication of the DSC. The low-temperature sintering TiO2 film prepared in the present study is composed of two nanocrystalline particles: smaller particles as cement and larger particles as the main body. As mentioned above, the smaller particles acted as a binder to chemically connect the larger particles. It was prepared following the procedure as described in the literature:28 hydrolyzing titanium tetraisobutoxide in the presence of nitric acid (pH 1), the hydrolysis slurry being heated to 80 °C and stirred vigorously for 8 h followed by autoclaving at 180 °C for 12 h. After hydrothermal treatment, an 8 wt % nanocrystalline anatase TiO2 colloid solution, named precursor here, was obtained. The prepared TiO2 particles have a mean diameter of 9 nm, which depends on the hydrothermal temperature. The larger particles were supplied from Showa Titanium Co. Ltd., and were prepared by gas phase pyrolysis from titanium tetrachloride. Five kinds of TiO2 particles with different sizes determined by X-ray diffraction, used as the larger particles here,werestudied.Table1showsthesize,BET(Brunauer-EmmettTeller) surface area, and rutile content of the large particles used in the study. To compare, P25 particles (anatase:rutile ) 7:3, Degussa, German) with an average diameter of 23 nm were also accepted as the larger particles here. The larger particles were mixed with precursor in various weight ratios by continuous stirring for 24 h to form a homogeneous viscous paste. The resulting binder-free paste was spread on ITO-coated polymer (ITO/PEN, 13-15 Ω/0, Tobi, Japan) by the doctor-blade method and dried at 150 °C for 5 min. Finally, low-termperature sintering films composed of the larger particles and the smaller particles were obtained. The thickness of the films heat-treated at 150 °C was about 5-6 µm, measured with a scanning electron microscope (SEM, LEO 1530, German). The mesoporous TiO2 films were immersed overnight in a dry ethanol solution of 5 mM ruthenium (2,2′-bipyridyl-4,4′dicarboxilate)2(NCS)2 (K-N719 dye, Kojima Chemicals Corporation, Japan) and then dried at room temperature to form photoanodes. One drop of an iodine-based electrolyte solution was deposited onto the surface of a dye-adsorbed TiO2 film. The electrolyte solution was composed of 50 mM iodine (I2), 500 mM lithium iodide (LiI), and 500 mM tert-butylpyridine TABLE 1: TiO2 Particles with Various Average Diameters Used in the Present Research sample 1 (P25) sample 2 sample 3 sample 4 sample 5 ave diameter (nm) 23 BET area (m2g-1) 50-60 rutile content (%) 30
30 35-60
