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J. Phys. Chem. B 2006, 110, 18286-18290
Charge Accumulation and Polarization in Titanium Dioxide Electrodes Carol L. Olson*,† and Ian Ballard Department of Physics, Imperial College, Blackett Laboratory, Prince Consort Road, London SW7 2BZ, United Kingdom ReceiVed: March 17, 2006; In Final Form: July 31, 2006
Nanocrystalline TiO2 electrodes were studied spectroelectrochemically by observing the simultaneous relaxation of the current and absorbance after applying a voltage step. The absorbance behaved differently in two time regimes: (1) ionic polarization in the oxide electrode, in which charged ions, such as Ti3+ sites and/or interstitial Ti4+ sites, move in response to the applied electric field, and (2) the diffusion of Li+ ions into the TiO2. These two behaviors were analyzed with equivalent circuit models. Li+ ions reduce the resistance of the TiO2 by ∼90%, increase the capacitance by ∼350%, and decrease the inductance by ∼30%. Voltage cycling produces a buildup of intercalated Li+ ions, lessening the electrode’s response to the potential step, and causing it to become a more efficient inductor. The potential distribution in the nanoparticles is described by using a dielectric model in which roughly half the applied potential is dropped across the interface with a Li+-ioncontaining electrolyte.
Introduction
Experimental Methods
Porous nanoparticulate films of anatase TiO2 are used in dyesensitized solar cells because the extensive surface area allows for a large dye monolayer, increasing the light harvesting ability of the device. The porous films have a heterogeneous structure with wide particle and pore size distributions, and have been described as “one of the most puzzling components of the DSSC”.1 The multiexponential kinetics of electron injection and recombination have been attributed to this heterogeneity. Benko¨ et al.1 have shown that the crystallinity and particle size influence injection, but cannot address the unanswered questions why electron injection depends on the electrostatic environment provided by the electrolyte2-4 or why diffusive electron transport also depends on the electrostatic condition of the particle.5 In this paper, evidence is presented that shows that ionic polarization occurs in the anatase TiO2 particles in response to the chemical environment and/or an applied potential step. In TiO2, the reduction of a stoichiometric Ti4+ to a charged Ti3+ site may be optically monitored.6-10 With use of equivalent circuit modeling, the current and optical responses to a potential step are analyzed. Lithium is known to intercalate into the TiO2, and nanocrystalline films have been considered to reversibly accommodate Li+ ions for electrochromic devices.11-15 In this work, the role of lithium is quantified in terms of an equivalent circuit model. The behavior of the films after voltage cycling is observed and analyzed with analytical equivalent circuits. The implications for electrochromic and solar cell devices are then discussed. On the basis of these observations, a dielectric model for the potential distribution in the particles is presented, in which a large fraction of the applied potential is dropped across the interface.
Sample Preparation. TiO2 films were prepared by doctorblading the colloidal solutions onto a (TEC-15) fluorine-doped SnO2 conducting glass microscope slide (Hartford glass) using Scotch Magic Tape as spacers placed 1 cm apart as described previously.16 The thickness of the sintered films, measured by using a step profilometer, a Dektak IIA Surface Profile Measuring System (Sloan Technology), were 8 µm films made with 2 layers of scotch tape. The air-dried films were sintered at 450 °C for 20 min. Three-Electrode Cell. A nanoparticulate (unsensitized) TiO2 electrode was placed in a redox inactive electrolyte consisting of 0.1 M tetrabutlyammonium perchlorate (TBAP) in acetonitrile with and without 0.1 M LiClO4. The electrochemistry was performed in a three-electrode cell, with a quartz window, a mesh platinum counter electrode, and a Ag/AgCl reference electrode. All voltages are reported versus Ag/AgCl. Argon was bubbled through the electrolyte to minimize oxygen exposure. Current Measurements. The voltage was applied and the current was recorded with either a custom built system based on a data acquisition card installed in a personal computer and programmed with HPVee or an Autolab PGStat 12 potentiostat. Absorbance Measurements. The transient absorbance in response to a voltage step was recorded simultaneously with the transient current at different applied biases. The reduction of Ti4+ to Ti3+ sites has a broad absorption peak in the visible/ infrared region between ∼650 and >1100 nm, and was observed at 800-900 nm. Optical absorption spectra and time courses, at 800 nm, were obtained with a Shimadzu UV-visible 1601 spectrometer that was interfaced with a dedicated computer enabled with UVPC Personal Spectroscopy Software Version 3.7. The resolution of the optical density (OD) measurements of the Shimadzu spectrometer was on the order of 10-3. The time resolution was limited to 10-1 s and 10 000 data points. A custom-made absorption detector with an LED that emits 850900 nm light enabled collection of higher resolution data. By
* Address correspondence to this author. E-mail: carol.olson@ fotomol.uu.se. † Present address: Department of Physical Chemistry, Uppsala University, Uppsala, Sweden.
10.1021/jp0616664 CCC: $33.50 © 2006 American Chemical Society Published on Web 08/31/2006
Spectroelectrochemical Study of TiO2 Electrodes
Figure 1. Time course of current and absorbance response to voltage steps: Phase I of the absorbance is due to polarization of the TiO2 electrode and Phase II is due to the diffusion of Li+ ions.
J. Phys. Chem. B, Vol. 110, No. 37, 2006 18287
Figure 3. Typical current response to a 25 mV potential step, after equilibration at various applied biases, of an unsensitized TiO2 electrode in 0.1 M LiClO4 and 0.1 M TBAP in MeCN. The absolute value of the current is shown, with curve fits using a classical equivalent circuit model. The inset shows contributions of the capacitive and Faradaic currents to the curve fit.
diffusion current, due to a concentration gradient, where the current density, i, is a function of the charge, q, the mobility, µ, the potential, φ, the diffusion coefficient, D, and the number of electrons, n.
i ) qµ(∇φ)n + qD(∇n)
Figure 2. Absorbance is proportional to the absolute value of the current in Phase I and proportional to the integral of the current in Phase II.
interfacing this high-resolution absorption detector with the custom built data acquisition system described above, sensitive absorption measurements (∼10-5 OD) could be made on time scales from microseconds to seconds. The high-resolution detector was calibrated against the Shimadzu spectrophotometer. Initially, the absorbance was observed as the applied biases were stepped through from 0 mV to -1 V at -100 mV intervals, with a 25 mV step perturbation applied at each interval. After it was established that absorbance did not saturate, a single bias step (from 0 to -600 mV) was applied and observed over a long time (9000 s), as well as over very short times (0.4 s). The system was also stepped between -0.64 and -1.64 V by using both 0.1 and 1.0 M concentrations of LiClO4 to repeat the work of Hagfeldt.11 The values of the parameters were derived from the best fit of the nonlinear least-squares fitting procedures in Origin 6.1, data analysis software by Origin Lab Corporation. Results and Discussion Two-Phase Response. Figures 1 and 2 show that the current and absorbance response to applied voltage steps, of a TiO2 electrode in 0.1 M LiClO4 and 0.1 M TBAP in MeCN, occurs in two phases. Figure 2 shows in Phase I that the absorbance is proportional to the current and, in Phase II, to the charge. The current density may generally be described, as in eq 1, as the sum of a drift current, due to a gradient in potential, and a
(1)
For a drift current, the absorbance, or number of electrons, is proportional to the current, while for a diffusion current, it is proportional to the integral of the current. The drift current in Phase I is due to polarization of the TiO2 electrode and the diffusion current in Phase II is due to the diffusion of Li+ ions onto and into the TiO2. Diffusion Current (Phase II). The typical response to a 25 mV potential step, of an unsensitized TiO2 electrode, which has already equilibrated at an applied bias in 0.1 M LiClO4 and 0.1 M TBAP in MeCN, is shown in Figure 3. The diffusion of Li ions through the electrolyte onto and into the TiO2 film may be described by a capacitive process, as they accumulate in the Helmholtz layer, and by a Faradaic process, as they cause charge compensating electrons to enter the conduction band of the TiO2.14 The data were fit with an RC circuit model17 where the current is the sum of the capacitive, IC, and Faradaic, IF, currents. IC is given in eq 2, and is as expected for capacitors in parallel.
IC(t) ) A1 exp(-t/τ1) + A2 exp(-t/τ2)
(2)
IF(t) ) P erfc(λt1/2) exp(λ2t)
(3)
P ) nFA(kfcO* - kbcR*)
(4)
λ ) kf/DO1/2 + kb/DR1/2
(5)
The Faradaic current, IF, is a function of n, the number of equivalents; F, Faraday’s constant; A, the area of the electrode; kf and kb, the forward and back rate constants; initial concentrations, cO* and cR*, of the oxidized and reduced species; t, time; and DO and DR, the diffusion coefficients of the oxidized and reduced species, respectively. λ is a function of the rate constants and the diffusion coefficients only and is given in eq 5. The inset in Figure 3 illustrates the contributions of the two currents. Figure 4 shows that the absorbance in Phase II may be modeled by integrating the diffusive current. The integral of the diffusion current is given in (6), where t0 is the time at which the potential step occurs.
18288 J. Phys. Chem. B, Vol. 110, No. 37, 2006
Figure 4. Absorbance response to a 600 mV step and curve fit derived from integrating the diffusive current. These data were taken after an equilibration period of about an hour of the TiO2 film in acetonitrile with 0.1 M LiClO4 and 0.1 M TBAP under argon.
absorbancediffusion )
Olson and Ballard
Figure 5. Phase I absorbance response of a TiO2 electrode, in electrolyte containing 0.1 M LiClO4 and 0.1 M TBAP, and curve fit derived from the RCL equivalent circuit. Inset: Absorbance change due to adsorption of Li+ ions.
1(P((1/λ2)(erfc(λ(t- t0)1/2)) exp((λ2)(t - t0)) + 2/((3.14159)1/2λ)(t - t0)1/2)) (6) Polarization Current (Phase I). The polarization response of a TiO2 electrode in electrolyte containing Li+ is shown in Figure 5, where the transition between Phase I and Phase II occurs at ∼300 s. The Phase I polarization current may be modeled, as shown by curve fit in Figure 5, with an RCL equivalent circuit.18,19 This model represents the induction flux as a single averaged constant induction coefficient. It does not imply that all dipoles in the dielectric material have the same relaxation time, but rather that each polarizable element obeys a linear differential equation and follows the principle of superposition.18 Because the migration of ions in an ionic crystal is slower than that of electrons, the large time constant in the dielectric relaxation in Figure 5 is consistent with the movement of polarized ions, such as the observed Ti3+ species, against an applied field. The polarization of the TiO2 electrode, subjected to a voltage step, is more pronounced in Li+-containing electrolyte but can also be seen when Li+ ions are not present (0.1 M TBAP in acetonitrile). In Figure 6, there are two data curves: one (light gray) is transient absorption (800 nm) from a -600 mV voltage step taken with the Shimadzu spectrometer; and the other (gray) is composed of six separate transient absorption (850 nm) responses from -600 mV steps taken with the high-resolution spectrometer. The high-resolution measurements overlay the Shimadzu measurements within the noise. The first highresolution measurement of a short voltage step initiates a decrease in absorption that continues even after the potential step is removed. This suggests that a slow process has been initiated and is not rapidly reversed. When the electrode is initially immersed in the electrolyte, 0 mV is applied across the working and reference electrodes, which is a negative bias relative to the open circuit voltage (which is 0.14 ( 0.02 V for samples in MeCN with 0.1 M TBAP, and 0.23 + 0.03 V for samples in MeCN with 0.1 M TBAP and 0.1 M LiClO4). The Fermi levels in the electrode and solution will match up, creating an electric field at the interface. Mobile ions will then move to compensate that electric field. By fitting both curves to the RCL circuit (Table 1), the effect of lithium on the TiO2 electrode is to increase the capacitance by ∼350%, decrease the resistance by ∼90%, and decrease the inductance by a third. Surface Excess of Li+ Ions. The sharp increase in absorbance shown in the inset of Figure 5 is due to adsorbed Li+ ions, cad,
Figure 6. Phase I absorbance response, measured by two different methods, of a TiO2 electrode, in electrolyte containing 0.1 M TBAP, and curve fit derived from the RCL equivalent circuit.
TABLE 1: Comparison of RCL Circuit Parameters of Systems with and without Li+ Ions
R C L
polarization with 0.1 M Li+
polarization without Li+
% change on addition of Li+
133 3.96 789
1186 0.85 1181
-89 366 -33
on the TiO2 surface due to the applied potential step, and may be used to calculate the surface excess, co*, of Li+ ions. By dividing the change in optical density (0.009 in Figure 5) by the extinction coefficient, (800 M-1 cm-1),6 with Faraday’s constant, the surface charge due to the adsorbed Li+ ions comes out as ∼1 C. This quantity is then added to the bulk concentration, i.e., 0.1 M Li+, to obtain the value of co*, used to obtain the diffusion coefficient. Calculation of Diffusion Coefficient. With the Faradaic current defined in terms of P and λ, it is possible to extract the diffusion coefficient. The rate constants are not functions of time, and depend only on the constant applied potential. Assuming that kf . kb, eq 7 may be extracted.
DO )
(
P λ × 96487 × area × co*
)
2
(7)
The inner area of the electrode is estimated to be 1000 cm2. The diffusion coefficients were found to be 2.4 ( 1 × 10-13 (sample A) and 1.0 ( 0.4 × 10-14 cm2 s-1 (sample B) over a range of applied biases from -600 to -1100 mV. This variation in these two samples is also reflected in the magnitudes of the currents, and suggests that the inner surface and porosity should, in principle, be measured for each sample.
Spectroelectrochemical Study of TiO2 Electrodes
Figure 7. Consecutive measurements of absorbance in response to the applied voltage steps indicated in the lower frame. The measurements are numbered L1 to L18.
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Figure 9. Curve fit using the superposition of two RCL equivalent circuit responses to a voltage step and current transient data after a potential step from -1.64 to -0.64 V in 0.1 M Li+ solution.
TABLE 2: Values Obtained from Curve Fits with the Superposition of Two RCL Circuits slow τ (RCL 1) data L8 L6 L12 L14 L16
Figure 8. Absorbance and current transients for sample in 1 M LiClO4 responding to a voltage step from -1.64 to -0.64 V: these are the positive 1 V potential steps from the dataset in Figure 7.
Estimation of Potential across the Interface. The charge due to adsorbed Li+ ions, cad, may also be used with the value of the capacitance derived from the RCL circuit modeling, given in Table 1, to estimate how much of the applied potential is dropped across the interface. For example, for a -600 mV potential step, q/C is 0.25 V. Roughly half the applied potential is dropped across the Helmholz layer, the rest is taken up by polarization and resistance. This result is consistent with the views of Kang et al.,20 Cao et al.,9 and Lindstro¨m et al.12 Implications for Device Applications. Figures 7 and 8 show data from the same dataset, that is of transient 800 nm absorption and current responses to a 1 V voltage step taken from -0.64 to -1.64 V and back down, in MeCN with 0.1 M TBAP and 1 M LiClO4. The steps between -1.64 and -0.64 V were chosen to repeat the work of Hagfeldt et al.11 Figure 7 shows the complete dataset over time with applied voltage shown below. Figure 8 shows the ones for the potential step from -1.64 to -0.64 V. When the entire dataset is shown together in Figure 7, an upper limit as well as a rising trend in the lower limit of the absorption appears. The upper absorption limit associated with -1.64 V occurs at an optical density of ∼0.28, and is not due to the instrument electronics. With repeated cycling, the lower limit of the absorption change tends to rise, which is clearly seen in curves L14 and L16 of Figure 7. This suggests that as lithium intercalates and causes electrons to occupy Ti3+, fewer sites are available as electron acceptors. Unless enough time has elapsed at a more positive potential so that the Li+ ions can work their way out of the lattice, those Ti3+ sites will not be “turned off” and the absorption will not resume its initial level. The intercalation of Li+ ions and the cycling history of the film influence the amount of charge taken on, which has
R
C
fast τ (RCL 2) L
R
C
L
50
at -1.64 V for 4 min 4 1400 40 4 1600 40 4 2000 40 4 2400 40
0.2 0.2 0.2 0.2
85 85 85 85
implications for the reversibility and responsiveness of electrochromic devices. For a responsive device, an internal buildup of lithium would have to be avoided. In Figure 8, the sample is stepped from -1.64 to -0.64 V, after an equilibration period at -1.64 V of greater than 4 min, except the curves labeled L2 and L8. These two datasets were taken after the system had remained at -0.64 V for more than 4 min, then rested at -1.64 V for only about 8 s, and then stepped to -0.64 V. Curves L2 and L8 show the same behavior as those published by Hagfeldt et al.11 for nanocrystalline films responding to a voltage change from -0.64 to -1.64 to -0.64 V. They concluded that nanocrystalline films exhibited reversible Li+ insertion behavior desirable for electrochromic applications. However, the other datasets, in which the system equilibrated at the more negative potential, do not show this reversibility. The absorbance does not reflect the removal of the potential step until between 60 and 125 s later. Furthermore, this relaxation time increases with more voltage cycling as shown by curves L12, L14, and L16 in Figure 8. The data presented here suggest that the reversibility depends on the history of the film. These curves may also be examined in more detail by using an RCL equivalent circuit. The values of R, C, and L vary due to the various relaxation times of different kinds of dipoles, and also to the interaction between dipoles. It is possible to work out a distribution function for the relaxation times from these data.18,20 Here, a model20 has been applied in which a fast and a slow RCL circuit response are superimposed, with the curve fits shown in Figure 9. The slow behavior is reproduced better than the fast, suggesting that the slow response is due to a single species while the fast response may include electronic polarization as well as an ionic contribution. Table 2 shows that there is a trend in the values of the inductor in the equivalent circuit for the slow response. At fast times when there is mixed conduction, the resistance is lower and the inductance is less. As the dipoles become aligned, and
18290 J. Phys. Chem. B, Vol. 110, No. 37, 2006 local polarized orbitals dovetail, and the material becomes a more efficient inductor. Dielectric Potential Model. The observed “infrared” polarization indicates that ionic defects in the TiO2 solid are moving to oppose the field caused by the presence of charged ions in the Helmholtz layer and/or an applied electric field. Therefore, the electrostatics of the TiO2 particle are best described with a dielectric potential model. Ions in the electrolyte will realign to oppose the electric field and cancel the electric field in solution. Likewise, defects, such as Ti3+, and intercalated Li+ will segregate to the surface under the influence of an applied field, as has been shown with atomistic simulations21 of Li+ at the anatase TiO2 (101) surface, to minimize the field in the solid. An electric field is only sustained at the interface. This is consistent with the conclusion of Zaban et al.10 that electrons move through the film by diffusion because of ionic screening of an applied electric field, and with the ideas that a large fraction of the potential is dropped across the Helmholtz layer,9,22 and that traps are located at the surface.23 Conclusions The response of a nanocrystalline TiO2 electrode to a potential step occurs in two phases. Initially, polarization occurs, in which mobile ions in the TiO2, such as Ti4+ interstitials, Ti3+, and intercalated Li+ ions, move to oppose the applied electric field, producing a drift current, which may be modeled as an RCL equivalent circuit. In the second phase, Li+ ions in the electrolyte adsorb onto and insert into the TiO2, creating a diffusion current, modeled as an RC circuit. The values of the RCL circuit elements yielded by the curve fits for electrolyte with and without Li+ show that Li+ ions reduce the resistance by about 90%, increase the capacitance by about 350%, and decrease the initial inductance by about 30%. Using the equivalent circuit parameters, the diffusion coefficient is calculated to be on the order of 10-14 and 10-13 cm2/s for two different samples. A rough calculation of the potential drop across the interface shows that nearly half of the potential is dropped across the Helmholtz layer. The reversibility of Li+ insertion in nanoparticulate films reported by Hagfeldt is due to surface adsorption. Intercalation is also occurring but not reported within the scope of his measurements, and this will affect the cycling capability of electrochromic devices. An RCL model may be used to explain the current response due to a potential step from -0.64 to -1.64 V. The inductance increases significantly with voltage cycling.
Olson and Ballard The observation of polarization in the TiO2 is the basis for a dielectric model for the electrostatics of the nanoparticle. Acknowledgment. The authors would like to gratefully acknowledge the indispensable guidance of Jenny Nelson and wish also to thank Greenpeace Environmental Trust and Overseas Research Scholarships for financial support. References and Notes (1) Benko¨, G.; Skårman, B.; Wallenberg, R.; Hagfeldt, A.; Sundstro¨m, V.; Yartsev, A. P. J. Phys. Chem. B 2003, 107, 1370. (2) Kelly, C. A.; Farzad, F.; Thompson, D. W.; Stipkala, J. M.; Meyer, G. J. Langmuir 1999, 15, 7047. (3) Tachibana, Y.; Haque, S. A.; Mercer, I. P.; Klug, D. R.; Durrant, J. R. J. Phys. Chem. B 2000, 104, 1198. (4) Tachibana, Y.; Haque, S. A.; Mercer, I. P.; Moser, J.; Klug, D. R.; Durrant, J. R. J. Phys. Chem. B 2001, 2001, 7424. (5) Nakade, S.; Kambe, S.; Kitamura, T.; Wada, Y.; Yanagida, S. J. Phys. Chem. B 2001, 105, 9150. (6) Kolle, U.; Moser, J.; Gratzel, M. Inorg. Chem. 1985, 24, 2253. (7) Howe, R.; Gratzel, M. J. Phys. Chem. 1985, 89, 4495. (8) Rothenberger, G.; Fitzmaurice, D.; Gratzel, M. J. Phys. Chem. 1992, 96, 5983. (9) Cao, F.; Oskam, G.; Searson, P. C.; Stipkala, J. M.; Heimer, T. A.; Farzad, F.; Meyer, G. J. J. Phys. Chem. 1995, 99, 11974. (10) Zaban, A.; Meier, A.; Gregg, B. A. J. Phys. Chem. B 1997, 101, 7985. (11) Hagfeldt, A.; Vlachopoulos, N.; Gratzel, M. J. Electrochem. Soc. 1994, 141, L82. (12) Lindstro¨m, H.; So¨dergren, S.; Solbrand, A.; Rensmo, H.; Hjelm, J.; Hagfeldt, A.; Lindquist, S.-E. J. Phys. Chem. B 1997, 101, 7717. (13) Lindstro¨m, H.; So¨dergren, S.; Solbrand, A.; Rensmo, H.; Hjelm, J.; Hagfeldt, A.; Lindquist, S.-E. J. Phys. Chem. B 1997, 101, 7710. (14) So¨dergren, S.; Siegbahn, H.; Rensmo, H.; Lindstrom, H.; Hagfeldt, A.; Lindquist, S.-E. J. Phys. Chem. B 1997, 101, 3087. (15) Van de Krol, R.; Goossens, A.; Schoonman, J. J. Phys. Chem. B 1999, 103, 7151. (16) Nazeeruddin, M. K.; Kay, A.; Rodicio, I.; Humphrey-Baker, R.; Muller, E.; Liska, P.; Vlachopoulos, N.; Gratzel, M. J. Am. Chem. Soc. 1993, 115, 6382. (17) ComprehensiVe Treatise of Electrochemistry; Plenum Press: New York, 1984; Vol. 9 (Electrodics). (18) Daniel, V. V. Dielectric Relaxation; Academic Press: London, UK, 1967. (19) Maier, J.; Jamnik, J.; Leonhardt, M. Solid State Ionics 2000, 129, 25. (20) Bottcher, C. J. F.; Bordewijk, P. Theory of Electric Polarization; Elsevier Scientific: Amsterdam, The Netherlands, 1978; Vol. 2. (21) Olson, C. L.; Islam, M. S.; Nelson, J. J. Phys. Chem. B 2006, 110, 9995. (22) Kavan, L.; Kratochvilova, K.; Gratzel, M. J. Electroanal. Chem. 1995, 394, 93. (23) Wang, H.; He, J.; Boschloo, G.; Lindstrom, H.; Hagfeldt, A.; Lindquist, S.-E. J. Phys. Chem. B 2000.
