Electrochemistry in Mesoporous Electrodes: Influence of Nanoporosity

C , 2009, 113 (5), pp 2022–2027. DOI: 10.1021/jp808175d. Publication Date (Web): January 9, 2009. Copyright © 2009 American Chemical Society. Cite ...
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J. Phys. Chem. C 2009, 113, 2022–2027

Electrochemistry in Mesoporous Electrodes: Influence of Nanoporosity on the Chemical Potential of the Electrolyte in Dye Sensitized Solar Cells Snir Dor, Larissa Grinis, Sven Ru¨hle, and Arie Zaban* Department of Chemistry, Bar Ilan UniVersity, 52900 Ramat Gan, Israel ReceiVed: September 14, 2008; ReVised Manuscript ReceiVed: NoVember 11, 2008

The illumination of a dye sensitized solar cell (DSSC) shifts the chemical potential of the electrolyte positively with respect to its dark value. This shift is a result of the charge separation process in which electrons are injected into the TiO2 electrode and positive charges are transferred to the electrolyte. In this study, we attempted to measure the electron density in TiO2 under operating conditions by monitoring the hole concentration (chemical potential) in the electrolyte solution. However, the results obtained showed that the chemical potential of the electrolyte in DSSCs is not solely determined by the redox concentrations. The charging of the mesoporous medium alters the electrochemical parameters inside the electrode volume. These changes refer to the ionic strength, the ionic activity, or the standard potential. Consequently, we describe a phenomenon to control the electrochemical potential of an electrolyte solution by altering the nanometric pore size of the TiO2 matrix. While significant for both the analysis and the design of DSSCs, this new phenomenon opens a path for the manipulation of electrochemical processes utilizing mesoporous electrodes. Introduction Dye sensitized solar cells (DSSCs) are low-cost devices to convert solar energy to electric energy. At the hearts of these cells are porous semiconductor electrodes. These electrodes are typically made by the deposition of nanosize TiO2 crystals onto a conducting glass substrate, creating a mesoporous film of several micrometer thickness (Figure 1). The surface of each nanoparticle is coated with a monolayer of sensitizing dye molecules that initiate the photoelectrochemical process upon illumination. An electrolyte redox solution composed of an I-/ I3- redox couple and a counter electrode close the electrical circuit. In practice, the electrolyte is present inside the porous film. In addition, the electrolyte is present in the volume filling the gap between the film and the counter electrode, known as the “bulk electrolyte”.1-3 The electrolyte solution, prepared by a chemical reaction between solid iodine I2(s) and an excess of iodide ions, results in the following equilibrium:

I3- + 2e- T 3IThe chemical potential of the electrolyte solution is determined by the concentration ratio of I-/I3-, and can be calculated using the Nernst equation.4,5 Upon illumination of the cell, I- species reduce the oxidized dye molecules while transforming to I3-. The I3- ions diffuse to the platinized electrode, and are then reduced to I-. This diffusion process is caused by a gradient of ions between the mesoporous TiO2 electrode and the back electrode. Under steady state condition, at open circuit voltage (Voc), the ion concentrations homogenize across the cell and the ion gradient disappears.6,7 The original equilibrium in the redox couple changes, thus forming a new steady state concentration ratio which is expressed by the chemical potential. (The potential shift compared to the dark condition is denoted in this paper as ∆EVoc.) Consequently, using the Nernst equation, one can calculate from ∆EVoc the number of holes transferred to the electrolyte under given conditions. From this calculation, we can determine the

number of electrons that were transferred to the TiO2 electrode when the cell reached Voc (Appendix 1). In this work, we used this method to measure the electron concentration in the TiO2 film (or the number of electrons per TiO2 nanoparticle) as a function of the steady state Voc. The values calculated from measurements of various DSSCs containing TiO2 electrodes of different thicknesses and under different light intensities were approximately 1 order of magnitude higher than the highest electron concentration values reported to date.8-10 This high electron concentration derived from the measured value of ∆EVoc indicates that it is impossible to relate ∆EVoc just to concentration changes caused by the dye injection process. Further investigation showed that the ∆EVocincreased by decreasing the nanometric size of the pores. We propose that this is due to a change in the ion activity inside the mesoporous electrode. Experimental Section Electrode Preparation. All the DSSC electrodes were prepared by the EPD (electrophoretic deposition) method.11 EPD provides a simple preparation of uniform, binder-free films with a controlled thickness and high reproducibility. The TiO2 nanoparticles (P25, Degussa, 25 nm average diameter) were deposited on a conducting FTO glass (TEC-15) with a 15 ohm/ square sheet resistance. After the EPD process was completed, all the prepared electrodes were dried at 150 °C and pressed mechanically. The applied pressure defined the porosity of the TiO2 films. The standard pressure used in this study was 1.6 tons/cm2 for both the series of different film thicknesses and for the light intensity series (17 µm thickness). After the press treatment, the electrodes were sintered at 450 °C for 60 min in air before they were sensitized overnight in an ethanol solution of the dye 5 mM N3, cis-di(isothiocyanato)bis(4,4-dicarboxy2,2-bipyridine) ruthenium(Π) (Solaronix SA). We measured the electrode thickness with a Surftest SV 500 profilometer (Mitutoyo Co). Parameters and Calculations. Based on previous studies, after completion of the EPD, the volume fraction of the particles

10.1021/jp808175d CCC: $40.75  2009 American Chemical Society Published on Web 01/09/2009

Electrochemistry in Mesoporous Electrodes

J. Phys. Chem. C, Vol. 113, No. 5, 2009 2023

Figure 1. Schematic view of redox concentration changes associated with the photoinjection of electrons into TiO2, and the adjacent hole transfer to the electrolyte (a). At Voc, the new steady state redox concentrations homogenize across the cell. In (b) the measurement setup is shown. Two potentials were measured sequentially: the chemical potential of the electrolyte (∆EVoc) and the Voc. ∆EVoc measured from dark to illumination conditions by an automatic shutter shows a staircase graph (c).

is 0.6 in all films.12 The porosity for the pressed electrodes was calculated using the following equation:

Pp )

Lp - 0.4Lnp Lp

where Pp and Lp are the porosity and the thickness of the pressed film, respectively, and Lnp is the thickness of the original, nonpressed film. We calculated the number of particles comprising the DSSC electrode by dividing the volume of the TiO2 in the film; we considered the porosity by the volume of one particle assuming spherical morphology and 25 nm diameter. The “goal seek” function in the Excel program was used to solve eq A.3 (see Appendix 1). The program provides the approximate value of X (M) (added I3- concentration) with an error of 5%. Electrolyte Preparation. The electrolyte solution consisted of 0.5 M TBAI (tetrabutylammonium iodide) and 0.05 M I2 in 1:1 acetonitrile-NMO (3-methyl-2-oxazolidinone). This electrolyte has very low vapor pressure, which keeps its volume fixed after placement in the measurement cell.13,14 A 100 µL volume of solution was used for each measurement. A different concentration redox ratio (see Appendix 2) was prepared to measure a calibration curve using the same amount of TBAI with a different amount of I2. The redox couple is formed by a reaction between I2 and excess of I-, according to the equation

I2 + I- T I3assuming that all I2 converts to I3- based on the high equilibrium constant of this reaction.15-18 All the measurements were performed with AutoLab potentiostat and a Xe lamp calibrated to 1 sun.

Results and Discussion Figure 1a shows the processes occurring in the electrolyte solution upon illumination of a DSSC. While electrons are injected into the TiO2 nanocrystals, hole are transferred to the redox electrolyte. This outcome is a measurable quantity, and consequently, we can measure the number of injected electrons that are present in the TiO2 electrode (or per a single TiO2 nanocrystal) in an operating cell (see Appendix 1). Figure 1b presents the system used to measure both the chemical potential of the electrolyte solution and the Voc under given illumination. The system is based on an FTO glass substrate (10 cm2) with half of its surface composing the DSSC and the other half remaining bare. The bare FTO glass was masked from illumination using black tape. A Teflon chamber fitted with an O ring forms the electrolyte compartment above the two parts of the FTO substrate. The Voc of the cell was measured against the Pt counter electrode, while the chemical potential of the electrolyte was recorded using the same Pt wire against an Ag/AgCl reference electrode. The distance between these electrodes were fixed by a Teflon chamber, which also fixed the distance between the electrodes to the DSSC. The electrodes were placed in the masked area to prevent light interference with the Ag/AgCl. The chemical potential of the electrolyte was measured in a cyclic mode to ensure reversibility of the injection/recombination processes. In practice, continuous recording was conducted while illumination was turned on and off using an automatic shutter. Figure 1c shows a schematic illustration of these measurements. To verify that the Nernstian behavior described in eq A.1 (Appendix 1) is valid for the examined electrolyte, we generated the calibration curve shown in Appendix 2. The results show that the electrolyte’s chemical potential is determined by the [I-]3/[I3-] concentration ratios using the Nernst equation. Figure 2 shows the correlation between ∆EVoc and the illumination intensity. Increasing the illumination intensity

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Dor et al. TABLE 2: Correlation between the Number of Electrons per Particle and the Thickness of the TiO2 Film

Figure 2. ∆EVoc measured as a function of illumination intensity. Measurement details are given in Figure 1. Table 1 shows the calculated number of electrons per particle and the measured Voc. The 17 µm thick electrode was pressed at 1.6 tons/cm2. For the unpressed electrode ∆EVoc was within the noise level.

Figure 3. Dependence of ∆EVoc on the film thickness showing higher ∆EVoc with an increasing electrode thickness. Table 2 provides the calculated number of electrons per particle and the measured Voc. The electrodes, prepared with different thicknesses, were pressed at 1.6 tons/ cm2.

TABLE 1: Correlation between the Number of Electrons per Particle and the Illuminated Light Intensity light intensity (%) ∆E (mV) Voc (mV) no. of electrons per particle 100 50 20

1.5 1.2 0.8

811 689 530

834 666 444

results in higher Voc values, due to the higher electron concentration in the TiO2 nanoparticles.18 As expected, ∆EVoc increased with light intensity in correlation with the Voc increase. The calculated values of electrons per particle derived from these ∆EVoc values are approximately 2 orders of magnitude higher than the values previously reported (Table 1).6-9 For example, at 100% illumination intensity (1 sun), when the Voc reaches 811 mV, we measure a ∆EVoc which corresponds to 834 electrons per particle (charge density on the order of 1019 cm-3), using eq A.3. In comparison, values of 1-10 electrons per particle (charge density of 1017-18 cm-3) are commonly reported. Therefore, it is impossible to relate this high ∆EVoc to concentration change caused by the dye injection process. To exclude experimental artifacts, we performed several control experiments. First, the dye sensitized TiO2 electrode was replaced by a mesoporous TiO2 electrode without dye (16 µm, pressure 1.6 tons/cm2). Second, the DSSC was removed entirely and measurements were performed on bare FTO glass. Both experiments did not show any change in redox potential; i.e., ∆EVoc remained 0. Therefore, light interfering with the measurement setup (mainly with the Ag/AgCl reference electrode) or light-induced interaction between the FTO glass and the electrolyte can be ruled out as a cause for the observed ∆EVoc. Furthermore, the electrolyte’s temperature was measured with

thickness (µm)

∆E (mV)

Voc (mV)

no. of electrons per particle

3 13 20

0.3 1.3 2

850 826 800

917 899 862

a thermocouple which did not show any change, even if the system was illuminated for several minutes. These control experiments verify that the observed ∆EVoc is the sole result of the DSSC operation. Figure 3 shows the dependence of ∆EVoc on film thickness. Increasing the thickness implies a greater number of particles, which at a given Voc should increase the total number of electrons present in the TiO2. Consequently, this will generate higher ∆EVoc values (provided that the electrolyte volume is similar in all the measurements). Indeed, varying the electrode’s thickness between 3 and 20 µm resulted in a higher ∆EVoc. However, the number of electrons per particle calculation which takes into account the volume of the TiO2 electrode yielded quite similar values in correlation with the minor variation in Voc (Table 2). Here, also, the number of electrons per particle was larger compared to reported values. One of the possible explanations for the excessively high number of electrons per particle (which is derived from the measured value of ∆EVoc) involves changes in the electrochemical environment inside the mesoporous electrode under DSSC working conditions. The electrochemical changes may be related either to the ionic activity or to the standard potential.19 In reference to ionic activity, we note that the Nernst equation is defined for activity (a ) γ[X]), rather than concentrations:

E ) E° -

(γI-[I-])3 (aI-)3 RT RT ) E° log log zF zF aI3γI3-[I3-]

(1)

Consequently, if the activities of the ions present inside the mesoporous film change upon charging of TiO2 by the photoinjected electrons, then eq A.2 (Appendix 1) which assumes γ ) 1 is insufficient. In this case it is required to use the following equation (eq 2) to calculate the electron densities in the TiO2.

(γI3-[I3- + X])[I-]3 RT ∆EVoc ) log zF (γI-[I- - 3X]3)[I3-]

(2)

This understanding implies that γ (of I-, I3-, or both) varies with the Voc. In other words, the high calculated values of electrons per particle imply that the Voc induced activity changes inside the porous electrode. Alternatively, one can relate the observed phenomenon to variations of the standard potential, E°. These variations are induced by the charging of the mesoporous TiO2 matrix in which the electrolyte is present. The theory of the ionic double layer near a charged surface, described by Debye-Hu¨ckel and Gouy-Chapman,20-23 outlines the nanometric-scale decay of the surface potential into the solution. This decay relies on the ion concentration and the surface charge density. In addition, long-range interactions created from the balance between the attractive polarization and repulsive double layer forces, as established by the extended DLVO theory, can change the dielectric properties of the solvent.24-27 Those phenomena can change the electrolyte properties a few tens of nanometers from the electrode-electrolyte interface.21,28

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Figure 4. Illustration that decreasing the size of the pores of the TiO2 film by mechanical pressure increases the association of the electrolyte inside the pores with the interfacial condition. This interaction should lead to higher ∆EVoc values.

In the mesoporous electrode, a large portion of the electrolyte present inside the pores is placed in this critical zone, i.e., within a few tens of nanometers from the TiO2 particle interface. Actually, the diameter of the pores determines the volume ratio between the “bulk” electrolyte and the electrolyte that is exposed to the interfacial conditions. The mesoporous film generates a situation where there is not enough volume inside the pores to allow full decay of the interfacial effects. As the diameters of the pores decrease, the decay length becomes longer than the pore radius. Consequently, controlled decrease of the pore size of the TiO2 film by mechanical pressure during the cell pretreatment should increase this effect and will result in higher ∆EVoc values (Figure 4). To confirm this assumption, a series of mesoporous electrodes with the same initial thicknesses were each pressed to achieve porosity sets prior to the ∆E/Voc measurements (Figure 5). We note that the original electrode thickness, i.e., the number of TiO2 particles in this series, was similar. The only difference among the various electrodes of this set was the porosity. Nevertheless, the results showed a strong correlation between the electrode’s porosity and the measured ∆EVoc, yielding higher apparent electron densities per Voc for the denser electrodes (Table 3). Thus we conclude that ∆EVoc does not solely reflect the electron injection process. On the contrary, the ion concentration changes outside the mesoporous volume (from which we measure ∆EVoc) are mainly the result of a potential-induced deviation of the electrochemical environment inside the mesoporous electrode. Based on the electrochemical measurements, it is impossible to determine which of the proposed mechanisms exists in the mesoporous electrode. The equation involves more variable parameters than the experimental degree of freedom. We are currently trying to gain more insight utilizing local spectroscopy. However, the results clearly show that charging the mesoporous TiO2 electrode results in ion diffusion between the mesoporous volume and the bulk electrolyte, which result in reducing the [I-]3/[I3-] ratio in the bulk electrolyte and lead to measurement of a high value of ∆EVoc. This effect intensifies as we increase the Voc and decrease the porosity. The results presented in this work show that it is possible to modify the electrochemical properties of a solution by physical parameters, i.e., a combination of nanoporosity and charging of the hosting porous medium. In DSSCs, this effect defines an

Figure 5. Correlation between applied pressure and ∆EVoc (a). The initial thickness of all electrodes was 22 µm, and the illumination intensity was calibrated to 1 sun. Decreasing the porosity of the film by mechanical pressing revealed a strong influence on the measured ∆EVoc (b). Consequently, the calculated number of electrons per particle varies despite the similar Voc values (see Table 3).

TABLE 3: Correlation between the Number of Electrons per Particle and Applied Mechanical Pressure pressure (tons/cm2)

thickness (µm)

∆E (mV)

Voc (mV)

no. of electrons per particle

0 1 1.6 2 3 3.4

22 17 15.8 14.9 13.5 12.5

n/aa 0.07 1.8 2.3 2.8 3.6

-850 -870 -886 -885 -878 -860

n/aa 300 774 990 1207 1555

a

The actual ∆EVoc was smaller than the noise level.

unusual interface between the mesoporous electrode volume and the bulk electrolyte. Under operating conditions, the concentrations of the ions must change across this interface to maintain chemical potential continuity. The simplest description of this effect relates to the Voc conditions, where the steady state chemical potential of the electrolyte across the cell is uniform (Figure 6). This uniformity involves a modification of the electrochemical properties (the ion activity change) of the electrolyte present in the porous volume which is compensated by ion motion from the mesoporous volume to the bulk electrolyte or vice versa. In other words, the concentration ratio [I-]3/[I3-] in the bulk needs to be equal to the activity ratio (aI-)3/(aI3-) inside the mesoporous film. The new insight described here calls for reexamination of the DSSC mechanism. Most of the current understanding is based on characterization methods that assume similar ionic concentrations in both the porous volume and the surrounding electrolyte (at Voc steady state condition). The results show a higher than expected positive shift of the bulk electrolyte potential (∆EVoc) upon Voc increase. This positive shift indicates a decrease of the [I-]3/[I3-] ratio in this region and a significant increase of the [I-]3/[I3-] ratio inside the porous region (the latter is expressed as the activity ratio (aI-)3/(aI3-)). Variation of the I3- concentration inside the porous volume following an increase of the cell photovoltage can have a significant variable

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Dor et al.

Figure 7

Figure 6. Schematic presentation of the measurement cell together with the [I-]3/[I3-] concentration ratio throughout the electrolyte at Voc. To maintain uniform chemical potential across the cell, the concentration ratio [I-]3/[I3-] in the bulk needs to be equal to the activity ratio (aI-)3/ (aI3-) inside the mesoporous film. Changes of the ion activity within the mesoporous film cause diffusion such that the [I-]3/[I3-] profile under illumination is not uniform as shown in the lower scheme.

effect on the recombination rates. Unfortunately, quantitative parameters are not yet available. Finally, we note that any electrochemistry that involves mesoporous electrodes should experience the same effect. Specifically, we refer to the possible manipulation of the electrochemical properties of electrolytes utilizing nanoporosity, which may lead to new or more efficient processes. Conclusions The investigation of electron density in DSSCs under illumination shows that the chemical potential of the electrolyte is not solely determined by the redox concentrations. Charging the mesoporous medium alters the electrochemical parameters inside the electrode volume. We can attribute this phenomenon to the ionic strength, the ionic activity, or the standard potential. While significant for both the analysis and design of DSSCs, this new phenomenon opens a path for the manipulation of electrochemical processes utilizing mesoporous electrodes. Acknowledgment. The authors thank the Israeli Ministry of Science for the funding of this research. Appendix 1. Calculations of Electrons per Particle To calculate the number of holes transferred to the electrolyte, we begin with a dark measurement of the cell. In the dark, the chemical potential of the electrolyte (mV) is determined by the concentration ratio of the redox couple I-/I3-, and the potential can be expressed by the Nernst equation (eq A.1):

I3- + 2e- T 3IE ) E° -

RT [I-]3 log zF [I3 ]

(A.1)

where E° is the standard potential, R is the gas constant (R ) 8.314 J/K · mol), T is the absolute temperature in Kelvin, F is the Faraday constant (F ) 9.648 × 104 C/mol), and z is the number of electrons transferred in the reaction Upon illumination, the equilibrium in the electrolyte solution is disturbed; the concentration of I3- increases and the concentration of I- ions decreases, until the DSSC reaches Voc. As a

consequence, a positive shift (∆EVoc) in the chemical potential of the electrolyte solution is created. When the DSSC reaches Voc (steady state), each TiO2 particle accumulates the maximum number of sustainable electrons and each additional injected electron recombines with an I3- ion to re-form the I- ion. In other words, at Voc, the dynamic injection/recombination equilibrium maintains both the number of electrons in the TiO2 and the electrolyte composition constant. At this point, the electrolyte solution contains new constant concentrations of the redox couple, homogenized across the cell. If we interrupt this steady state condition, by extinguishing the light, the chemical potential of the electrolyte will return to its original value accompanied by the original redox concentrations. This process occurs due to the recombination process, in which all the injected electrons accumulated in the mesoporous film react with the I3- species generated upon illumination. Therefore, at Voc (steady state conditions), the chemical potential of electrolyte may be expressed by the following Nernst equation. Here, the variable X (M) represents the concentration of the I3- added to the electrolyte solution upon illumination: I3[I3-] [I3-] + X

dark concn: concn under Voc condition:

+

2e-

T

2X

3I[I-] [I-] - 3X

-

E ) E° -

RT [I - 3X]3 log zF [I3- + X]

(A.2)

Subtracting eq A.1 from eq A.2 (∆EVoc ) Edark - Elight) results in eq A.3. This equation defines the correlation between X (M) and ∆EVoc. ∆EVoc is a measurable parameter.

∆EVoc ) -

[I3- + X][I-]3 RT log zF [I - 3X]3[I3-]

(A.3)

Having X (M) and the volume of electrolyte in the cell (L), we can determined the number of I3- ions added to the electrolyte solution when the cell reaches Voc. By applying the stochiometric ratio between the added I3- ions and the number of electrons transferred to the TiO2 (a ratio of 1:2), the apparent number of the electrons accumulated in the mesoporous TiO2 film is known. Finally, dividing this number by the number of particles comprising the TiO2 film (see the Experimental Section) provides the number of electrons present in each TiO2 nanocrystal at a given Voc (in an operating cell). Appendix 2. Nernstian Behavior of the Electrolyte Electrolyte solutions of different concentration ratios were prepared (see the Experimental Section) and measured for their chemical potentials at room temperature (298 K). The Nernst equation, in Figure 7, is written by placing the constant of RT/ F, which is equal to 59 mV and z ) 2 in eq A.1. Plotting these measured potentials as a function of log [I-]3/[I3-] shows a linear

Electrochemistry in Mesoporous Electrodes correlation with a 32 mV slope. We expected this correlation from a Nernst equation that describes an electrochemical equilibrium involving a transfer of two electrons (theoretical value 29.5 mV). Consequently, under normal conditions, the chemical potential of the electrolyte is determined by the ion concentration ratio and the Nernst equation may be used to calculate the value of the parameter X in eq A.3, using the measured value of ∆EVoc. References and Notes (1) O’Regan, B.; Gra¨tzel, M. Nature 1991, 353, 737. (2) Barde´, C. J.; Arendse, F.; Comte, P.; Jirousek, M.; Lenzmann, F.; Shklover, V.; Gra¨tzel, M. J. Am. Ceram. Soc. 1997, 80, 3157. (3) Chou, T. P.; Zhang, Q.; Cao, G. Z. J. Phys. Chem. C 2007, 111, 18804. (4) Nazeeruddin, M. K.; Kay, A.; Rodicio, I.; Humphry-Baker, R.; Muller, E.; Liska, P.; Vlachopoulos, N.; Gra¨tzel, M. J. Am. Chem. Soc. 1993, 115, 6382. (5) Fukui, A.; Komiya, R.; Yamanaka, R.; Islam, A.; Han, L. Sol. Energy Mater. Sol. Cells 2006, 90, 649. (6) Schlichtho¨rl, G.; Huang, S. Y.; Sprague, J.; Frank, A. J. J. Phys. Chem. B 1997, 101, 8141. (7) Fisher, A. C.; Peter, L. M.; Ponomarev, E. A.; Walker, A. B.; Wijayantha, K. G. U. J. Phys. Chem. B 2000, 104, 949. (8) Kytin, V. G.; Bisquert, J.; Abayev, I.; Zaban, A. Phys. ReV. B 2004, 70, 193304. (9) Kopidakis, N.; Benkstein, K. D.; van de Lagemaat, J.; Frank, A. J. Phys. ReV. B 2006, 73, 45326. (10) Bailes, M.; Cameron, P. J.; Lobato, K.; Peter, L. M. J. Phys. Chem. B 2005, 109, 15429.

J. Phys. Chem. C, Vol. 113, No. 5, 2009 2027 (11) Grinis, L.; Dor, S.; Ofir, A.; Zaban, A. J. Photochem. Photobiol., A 2008, 198, 52. (12) Ofir, A.; Dittrich, Th.; Thirosh, S.; Grinis, L.; Zaban, A. J. Appl. Phys. 2006, 100, 74317. (13) Zaban, A.; Greenshtein, M.; Bisquert, J. ChemPhysChem 2003, 4, 860. (14) Bisquert, J.; Zaban, A.; Greenshtein, M.; Mora-Sero, I. J. Am. Chem. Soc. 2004, 126, 13550. (15) Kebede, Z.; Lindquist, S. E. Sol. Energy Mater. Sol. Cells 1999, 57, 259. (16) Liu, Y.; Hagfeldt, A.; Xiao, X. R.; Lindquist, S. E. Sol. Energy Mater. Sol. Cells 1998, 55, 267. (17) Rensmo, H.; Lindstorm, H.; Sodergren, S.; Willstedt, A. K.; Solbrand, A.; Hagfeldt, A.; Lindquist, S. E. J. Electrochem. Soc. 1996, 143, 3173. (18) Bisquert, J.; Zaban, A.; Salvador, P. J. Phys. Chem. B 2002, 106, 8774. (19) Maccarty, C.; Vitz, E. J. Chem. Educ. 2006, 83, 757. (20) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamental and Applications, 2nd ed.; Wiley: Hoboken, NJ, 2001. (21) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991. (22) Wong, I.; Fotter, M.; Melosh, N. Soft Matter 2007, 3, 267. (23) Lewis, T. J. IEEE Trans. DEI 2003, 10, 769. (24) Huang, H.; Ruckenstein, E. J. Colloid Interface Sci. 2004, 273, 181. (25) Brant, A.; Childress, E. EnViron. Eng. Sci. 2002, 413 No 6, 19. (26) Bostro¨m, M.; Deniz, V.; Franks, G. V.; Ninham, B. W. AdV. Colloid Interface Sci. 2006, 123-126, 5–15. (27) Hoek, M. V.; Agarwal, K. J. Colloid Interface Sci. 2006, 298, 50. (28) Gregg, B. A. Coord. Chem. ReV. 2004, 248, 1215.

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