13586
J. Phys. Chem. C 2007, 111, 13586-13594
Pathway-Dependent Electron Transfer for Rod-Shaped Perylene-Derived Molecules Adsorbed in Nanometer-Size TiO2 Cavities L. Gundlach* and R. Ernstorfer Hahn-Meitner-Institute Berlin, Dynamics of Interfacial Reactions, Glienicker Strasse 100, 14109 Berlin, Germany
F. Willig Fritz-Haber-Institut der MPG, Faradayweg 4-6, 14195 Berlin, Germany ReceiVed: October 20, 2006; In Final Form: April 16, 2007
A broad distribution of time constants was found for photoinduced heterogeneous electron transfer (PHET) from the excited-state of a perylene chromophore when the latter was attached via long rigid bridge/anchor groups to the inner walls of nanometer-size cavities formed in a colloidal anatase TiO2 layer. In contrast, in the same environment PHET was dominated by only one short time constant when the perylene chromophore was attached via a short anchor/bridge group. The same results were obtained irrespective of the specific chemical composition of the short or long rigid anchor/bridge groups. To verify that the set of different time constants was caused by different microscopic environments in the nanometer-cavities, PHET was also measured for the same perylene compounds on the (110) surface of TiO2 rutile single crystals, employing here the more sensitive femtosecond two-photon photoemission technique in place of transient absorption. On the surface of the single crystals only one long time constant was measured for PHET also in the case of the long rigid bridge/anchor groups. Thus, the broad distribution of time constants observed in the nanometersize cavities for the long rigid bridge/anchor groups can be attributed to different microscopic environments giving rise to different distances between the chromophore and the nearest TiO2 wall. Consequences of this pathway dependent PHET are discussed for the design of dye molecules and electrodes in dye-sensitized solar cells.
I. Introduction Light-driven electron transfer from a molecule to a semiconductor is fundamental for many photoprocesses. An important example can be found in photovoltaic systems.1 Gra¨tzel showed already 15 years ago2 that such systems can be used for efficient charge-separation. The search for a cheap solar cell made from nontoxic, highly available materials triggered various experimental as well as theoretical studies focusing on the electron transfer (ET) dynamics in dye sensitized solar cells. For different dye molecules and TiO2 layer preparations, the reported ET times range from several 100 fs down to just a few femtoseconds.3-8 The electron acceptor in the Gra¨tzel cell consists of a sponge like structured film made up of TiO2 anatase colloids. This colloidal sponge exhibits a huge concentration of cavities, 50% of the total space, with an average diameter similar to the size of the colloids, i.e., 10 nm. The molecules used for lightsensitization are chemically anchored to TiO2 via acid groups, e.g., carboxylic acid, in these cavities. The structuring of the film is necessary to achieve a sufficient surface enlargement, and thus a dye-sensitized film with a large extinction coefficient. A large extinction coefficient is also necessary for carrying out transient absorption (TA) measurements. The latter technique has been employed in most investigations aiming at the dynamics of ultrafast ET. For TA measurements, the large extinction coefficient has been achieved by investigating either nanometer-structured colloidal films or colloidal suspensions. * To whom correspondence should be addressed. E-mail: larsg@ andromeda.rutgers.edu.
The key parameter for ET dynamics in such systems is the electronic coupling between acceptor and donor states. The Franck-Condon weighted density of states, from which a small fraction contributes to homogeneous ET as in the semiclassical version of the Marcus equation,9 does not enter into the rate of heterogeneous ET, provided the wide band limit is fulfilled.10 Hence, ET times for different molecules anchored on the same substrate are determined mainly by the electronic coupling. Several different dyes, each consisting of the same chromophore, i.e., perylene, and different bridge and anchor groups have been synthesized and investigated by our group.11-14 It has already been shown before for both the homogeneous15,16 and the heterogeneous13,17 ET case, that ET times, and consequently the electronic coupling, can systematically be influenced by the length and the nature of the bridge group inserted between donor and acceptor orbitals. Nanometer-structured films, however, may provide competing pathways for electron injection. Once the donor part of the molecule, i.e., the chromophore perylene, gets close to a wall of the cavity, the electron has the possibility of tunneling directly to the acceptor states in the semiconductor. In this case ET dynamics are not influenced anymore by the length or nature of the bridge group. Thus, the electronic coupling between donor and acceptor states determines the predominant pathway for electron injection. Obviously, the weaker the electronic coupling through the bridge the higher the probability that tunneling along a shortcut to an adjacent wall becomes a relevant ET pathway in the colloidal film. For investigating the influence of surface structuring on ET pathways, TA measurements on nanometer-structured colloidal
10.1021/jp066892s CCC: $37.00 © 2007 American Chemical Society Published on Web 08/21/2007
ET for Rod-Shaped Perylene-Derived Molecules films were compared with time-resolved two-photon photoemission (TR-2PPE) measurements on TiO2 single crystals. TR-2PPE offers higher sensitivity than TA spectroscopy, as far as submonolayer adsorbate layers are concerned. In contrast to TA, TR-2PPE can address a low coverage of molecules on the surface of a single crystal with sufficient sensitivity.18,19 TR-2PPE has frequently been used already for analyzing electron dynamics at metal surfaces, in particular the dynamics of image potential states, adatoms, and small molecules.20-22 Unfortunately, TR-2PPE cannot be used in the case of a colloidal layer. First, the stray-light reflected from the colloidal layer saturates the electron detector. Second, even if the problem with the stray-light can be circumvented, the 2PPE measurement addresses just the topmost layer of a colloidal film because the UV probe light is absorbed by the colloids and the emitted electrons cannot trespass the TiO2 colloids. As a consequence, TA and 2PPE measurements would probe different regions of the colloidal sample. On the other hand, TA spectroscopy is not yet sensitive enough for probing a submonolayer dye coverage on a planar surface. Thus the two different measuring techniques, i.e., TA for the colloidal films and TR-2PPE for the single-crystal surface, had to be employed for measuring photoinduced heterogeneous electron transfer from photoexcited donor molecules into TiO2. On the two different TiO2 substrates, the same perylene derivatives were chemically anchored. Comparing the results obtained with the two methods, we investigate here the influence of the surface structure on the pathways and corresponding dynamics of electron transfer. Colloids made of the anatase phase of TiO223 and of the rutile phase24 can be cast into films with high surface enlargement factors. The Gra¨tzel cell, and most of the model systems made use of anatase TiO2. Unfortunately, there are no techniques known for growing anatase TiO2 single crystals without a high doping level. In addition, cleaning can be carried out much more efficiently and can be monitored by standard surfaces science techniques for the single-crystal surface but not for the colloids. The cleaning procedure involves a heating step that is much more critical for the anatase crystal than for rutile, since anatase undergoes a phase transition to rutile when heated above 775 °C. Therefore, the nanometer-structured colloidal films were prepared for this work from anatase TiO2, whereas rutile single crystals were investigated. For comparison a few measurements were performed with a rutile colloidal film to ensure that the ET dynamics were not influenced by the specific crystal structure of TiO2. A lower signal-to-noise ratio was achieved in the TA measurements with the rutile colloidal films compared to the anatase colloidal films due to the smaller surface enhancement in the former. For the present paper, it is of significance to note that the short time constants measured for PHET from the excited singlet state of the perylene chromophore attached via different short anchor-bridge groups have turned out very similar on the two different surfaces of TiO2, i.e., the nanometer-cavities and at the single-crystal surface.12,13,25 In contrast, the present paper is focusing on the pronounced difference in the PHET time constants measured for the two differently prepared TiO2 surfaces when the perylene chromophore was attached via long rigid, saturated bridge-anchor groups. The latter type of bridgeanchor group is expected to function as an electronic tunneling barrier and should slow-down PHET, thus resulting in a long PHET time constant. This expected effect was indeed observed for the two differently prepared TiO2 surfaces, but PHET showed this ideal behavior only in the case of the single-crystal surface. The same molecules adsorbed in the nanometer-cavities
J. Phys. Chem. C, Vol. 111, No. 36, 2007 13587
Figure 1. Structure of DTB-Pe-tripod (1) and DTB-Pe-rod (2).
of a colloidal anatase layer showed in addition to the long PHET time constant also a distribution of short PHET time constants. The latter contribute significantly to the total signal height and stem from ET channels that do not involve the bridge group. The shortcut ET pathways in nanometer-cavities is the main message of the present paper. II. Experimental Section HET from two different appropriate molecules was investigated, where the bridge-anchor group was formed by the socalled DTB-Pe-tripod and the so-called DTB-Pe-rod. The corresponding molecules are illustrated in Figure 1. Molecule (2) was synthesized in our group. Molecule (1) was synthesized in our group in cooperation with the group of E. Galoppini, Rutgers University. A detailed description of the synthesis of (2,5-di-tertbutyl-perylen-9-yl)phenyl-bicyclooctylbenzyl-phosphonic acid (DTB-Pe-rod) and 2,5-di-tert-butyl-94-[3,5,7-tris-(4-carboxy-phenyl)-adamantan-1-yl]-phenylethynylperylenen (DTB-Pe-tripod) will be given elsewhere. The bridge group at the 9-position forms a rigid link between the perylene chromophore part of the molecule and the rigid bridge/anchor group. Thus, the only degrees of freedom for the anchor/bridge group with respect to the perylene core are rotations around the saturated C-C bonds. The molecules were adsorbed on two different substrates, the planar single crystal (110) surface of rutile TiO2 and the sponge like nanometer-structured colloidal anatase TiO2 film. The surface structure of single crystal (110) rutile and colloidal anatase substrates has been investigated via STM26 and SEM,23 respectively, where the samples had been prepared following the same recipes as those used for the present work. Preparation of the substrates and adsorption of the molecules are described below. Four separate UHV chambers were used for preparing, characterizing, and finally measuring a sample with TR-2PPE or transient absorption. All chambers had a base pressure in the range below 5 × 10-10 mbar. Two of the UHV chambers were tightly screwed to the surface of the laser table and were floating with it. One was equipped with special windows for fs-TA measurements, the other was equipped with a time-offlight (TOF) spectrometer used for the TR-2PPE measurements. The third UHV chamber was equipped with instrumentation for LEED, UPS, and XPS for characterizing the samples. The fourth
13588 J. Phys. Chem. C, Vol. 111, No. 36, 2007 UHV chamber was a small mobile unit, equipped with a battery powered ion getter pump, serving as shuttle for the samples between the other UHV chambers. All of the chambers were equipped with load-lock ports facilitating sample transfer under UHV conditions. One of the UHV chambers was specifically designed for adsorbing molecules from solution on the surface of a solid.13 Many details of the experimental equipment used here for preparing and characterizing the molecule/semiconductor interface have been described before in conjunction with a patented contamination-free MOCVD-UHV sample transfer system.27 The preparation procedure is described in detail in ref 11. A short summary is given below. The XP spectrum of every commercial rutile crystal (CrysTec, Berlin) showed a pronounced carbon peak that was ascribed to organic impurities. Thus, the (110) surface of the rutile crystal was cleaned and ordered by carrying out repeated cycles of Ar+ ion bombardment (700 eV,3 µA, 10 min) and heating (875 K, 10 min) similar to recipes given in the literature.28 At the same time, the C1s peak in the XP spectra disappeared and the well-known clear 1 × 1 LEED image29 appeared. The thus prepared sample showed sufficient conductivity for carrying out photoelectron spectroscopy. The conductivity is mainly due to Ti interstitials.30,31 The Fermi level of the thus treated sample was found just below the conduction band edge. The adsorption procedure started with the already cleaned and ordered rutile crystal. A degassed dye solution was prepared with the well-known Schlenk technique. After the cleaned TiO2 sample was inserted into the preparation chamber under UHV conditions via the load lock port, the chamber was flooded with ultrapure Ar up to about 400 mbar. A small amount of the dye solution was filled into a glass flask that was protected by a closed valve from laboratory air and was connected through a valve and a stainless steel pipe to the UHV chamber. The dye solution was sucked into a cuvette inside the UHV chamber by driving it through the stainless steel pipe with a small pressure gradient. For the next preparation step, the rutile crystal was lowered into the cuvette containing already the dye solution, and after a typical contact time of 20 min, it was removed again from the cuvette. Following the above procedure, the interface with the adsorbed perylene derivatives was rinsed several times with the pure solvent to remove any molecules not bonded to the surface. The solvent was finally sucked out of the UHV chamber and the latter pumped down again to 5 × 10-10 mbar. It is reasonable to expect as the result of the above adsorption procedure a complete coverage of the available adsorption sites with adsorbate molecules. The procedure described above prevented the sample from coming into contact with lab air and allowed at the same time for the formation of strong chemical bonds at the surface with complex molecules that cannot be simply evaporated in vacuum. Several experiments were performed to ensure that the prepared samples were free of contaminants.11 XPS measurements were performed also on samples contacted only with the pure solvents to check on possible carbon impurities introduced by the preparation procedure. Different solvents were used also for adsorbing the molecules. In none of the cases did we find evidence for solvent induced recontamination of the surfaces. The absence of residual solvent molecules after completing the preparation step was confirmed by preparing a sample with methylene chloride as the solvent. No contribution of chlorine to the measured XP spectrum could be detected after the preparation. From the XPS measurements on the differently prepared samples, we conclude that recontamination of the
Gundlach et al. samples in the above-described preparation step involving the solvent is negligible. To obtain the TA data, colloidal TiO2 films were prepared with a thickness of about 2 µm on 45 µm thick glass where the recipe followed the procedure described by Nazeeruddin et al.32 Rutile colloidal films were prepared following a procedure described by Park et al.24 Prior to adsorbing the molecules on the anatase film, the latter was heated at 450 °C for 45 min in air. The perylene derivatives were adsorbed onto the colloids from the same solution that was used in the case of the rutile single crystals. The dyecovered nanostructured TiO2 film was rinsed several times with the solvent, dried under argon, and quickly transferred to the UHV chamber designed for carrying out transient absorption measurements. Coating with the dyes and characterization of the samples are described in detail in ref 14. Both, TR-2PPE as well as the TA are pump-probe techniques requiring ultrashort laser pulses. The laser system was based on an ultrafast amplified 150 kHz Ti:sapphire oscillator operating at 800 nm which pumped two noncollinear optical parametric amplifiers (NOPAs).33 Tunable sub-20 fs pulses in the visible and 15 fs pulses from second harmonic generation (SHG) of a nearinfrared output pulse were generated with the first NOPA.34 This setup required 90% of the Ti:sapphire output power, the remaining 10% of the fundamental output was used to generate a white light continuum in a sapphire plate. The 400 nm beam at the exit of the first NOPA was employed again to amplify a broad spectral slice of the above continuum seed in a second NOPA setup. The visible output of this second NOPA was frequency doubled in a 75 µm thick BBO crystal to obtain a sub-20 fs UV pulse centered at 280 nm. The whole experimental procedure has been described in detail in ref 22. Pulse compression was achieved with standard fused silica prism compressors prior to carrying out the SHG processing.35 All measurements were performed with both laser pulses p-polarized and at room temperature. A. Alignment of the Electronic Levels and TR-2PPE Scheme. The energy level of the HOMO ground state of the chromophore perylene attached with an anchor group to the (110) surface of rutile TiO2 was determined from UPS with respect to the band edges of TiO2. The position of the excited singlet state, which functions as an electron donor in the system, was deduced from two-photon photoemission data. A lineup of the energy levels at the interface as derived from such measurements is illustrated in Figure 2for perylene with the tripod anchor/bridge group.36 The lower curve at the left-hand side of Figure 2 shows the HOMO-1 and HOMO peaks obtained from a UPS difference signal between a clean TiO2 and a sample coated with the DTB-Pe-tripod. These are in good agreement with UPS gas-phase spectra measured by Boschi et al.37 that are depicted in gray. The curve shown above the vacuum level EVac is the measured 2PPE spectrum. To measure this spectrum, the perylene chromophore was excited with the pump photon hVpump, and the thus excited electron was emitted with a second photon hVprobe The kinetic energy Ekin of the emitted electron was measured and gives the energetic position of the intermediate state, i.e., the excited-state of perylene. Time dependent measurements were performed by delaying the probe pulse against the pump pulse and collecting the photoelectrons in an appropriate kinetic energy window. The two 0-0 marked lines in Figure 2 indicate the energy of the electronic ground and of the first excited singlet state of the perylene chromophore, respectively. In the actual experiment a vibrational excited-state is formed.
ET for Rod-Shaped Perylene-Derived Molecules
J. Phys. Chem. C, Vol. 111, No. 36, 2007 13589
Figure 2. Alignment of the ground state and excited-state of DTBPe-tripod adsorbed on the (110) TiO2 surface deduced from UPS and 2PPE measurements. The gray curve is a perylene gas-phase spectrum adopted from Boschi et al.37
The alignment of the electronic levels with respect to the conduction band of TiO2 did not change significantly for different bridge/anchor groups. For both the samples, the Fermi level (EFermi) was located just below the conduction band edge. The perylene HOMO position was 2.3 and 2.1 eV below EFermi for DTB-Pe-tripod and DTB-Pe-rod, respectively. UPS measurements on a colloidal anatase sample revealed a value of 1.9 eV below EFermi for the position of the HOMO. III. Results A. TR-2PPE Measurements on the Single-Crystal Surface. DTB-Pe-rod and DTB-Pe-tripod were adsorbed onto rutile single-crystal surfaces from solution as described above. ET times were measured by exciting the chromophore part of the molecules, i.e., perylene, with 440 nm laser pulses of sub-20 fs duration (fwhm). The thus prepared excited-state was probed by a second laser pulse with 280 nm wavelength and sub-30 fs duration for photoemitting the excited electrons. The emitted electrons were detected in the TOF. By delaying the probe pulse against the pump pulse the time dependent population of the excited-state of perylene was probed. Figure 3 shows TR-2PPE measurements of DTB-Pe-rod and DTB-Pe-tripod on the (110) surface of rutile TiO2. Since the signals in Figure 3 (a and b) correspond to the occupancy of excited states, the rise of the signals is given by the instantaneous population of the intermediate state by the pump pulse and resembles the cross correlation of the pulses, whereas the decay of the signal at positive delay times resembles the evolution of the system after excitation. A biexponential fit of the signals decay (not shown here) revealed around 900 fs, and 7 ps for the time constants of DTB-Pe-tripod, and around 200 fs, and 1.6 ps for the time constants of DTB-Pe-rod. However, a biexponential fit is not appropriate for the present system, since it assumes two independent contributions to the signal. This assumption does not hold for the present system, since the TR2PPE signal probes both the excited molecular state and the injected electrons in the TiO2 substrate. The latter contribute only to the signal when they reside within a certain escape depth from the surface.11,38 The respective electrons are not distinguishable in the 2PPE signal as long as they stem from isoenergetic intermediate states (compare Figure 2). As a consequence, the 2PPE signal contains the initial electron injection process of the excited molecular state as well as the consecutive escape
Figure 3. TR-2PPE signals of DTB-Pe-tripod (a) and DTB-Pe-rod (b) on rutile (110). Time trace measured via TR-2PPE in an energy window of 400 meV energy width centered at the excited-state position of the perylene chromophore (dots), and fit curves from the rate model defined by eq 1 are shown. The individual contribution of the molecular intermediate donor state (N1) and the TiO2 acceptor states (N2) are shown as dashed and dotted lines, respectively.
process of the injected electrons from the surface of TiO2. The latter contribution to the TR-2PPE signal has been studied separately.11 By taking catechol as a sensitizer for TiO2, we have prepared an ET system where the photoinduced generation of injected electrons is instantaneous, i.e., without finite injection time. These samples showed a long-lived 2PPE signal arising only from photoemission of electrons injected into TiO2. Because the latter system was identical to those discussed in the present section except from the adsorbed molecules, the longlived tail of the signal in Figure 3 (a and b; dotted) is ascribed to the escape of electrons already injected into TiO2. For molecules with relatively slow injection dynamics, the only relevant process contributing to the TR-2PPE signal besides the ET process is a very slowly decaying background.11 This background is easily distinguished from the much faster ET process. The solid lines in Figure 3 represent a fit with the rate equation (eq 1) that describes the level N1 (dashed line in Figure 3) representing the excited-state of the perylene molecule that is populated with the pump pulse Ipump and is depopulated into a second level N2 (dotted line in Figure 3) with the injection rate k1. The population N2 represents the electrons that are injected into acceptor states of TiO2
d N (t) ) -k1N1(t) + Ipump dt 1 d N (t) ) -k2N2(t) + k1N1(t) dt 2 WTR-2PPE(td) )
∫tt
0
(N2 + AN2)Iprobe(t - td) dt
(1)
The population in the second level is decaying with a rate constant k2 that represents relaxation and escape from the surface
13590 J. Phys. Chem. C, Vol. 111, No. 36, 2007
Gundlach et al.
TABLE 1: Comparison between Electron Injection Times Measured via TR-2PPE on DTB-Pe-tripod and DTB-Pe-rod compound name
injection time τ1 [ps]
escape time τ2 [ps]
weight factor, A
DTB-Pe-tripod DTB-Pe-rod
0.97 0.24
10.9 2.4
0.4 0.2
into the bulk of the semiconductor. The latter processes are of course not expected to give rise to a monoexponential behavior.11,39 As a consequence, the monoexponential rate equation for the second level fits the measured data not exactly. However, since we are interested in the ET times (τi ) 1/ki), the latter deviation is of minor importance in the present context. Both contributions are summed up and convoluted with the probe pulse Iprobe resulting in the TR-2PPE yield in dependence of the delay time td. The results of the fits for both molecules are summarized in Table 1. Figure 3 shows that the early dynamics is well reproduced by the model described above. Even more important with respect to the measurements presented below is the fact that short times constants, i.e., shorter 50 fs, are not consistent with the measured data. B. TA Measurements on Colloidal Films. DTB-Pe-rod and DTB-Pe-tripod were adsorbed onto anatase colloidal films from solution as described above. ET times were measured by exciting the chromophore part of the molecules with the same 440 nm laser pulses that have been used for the TR-2PPE measurements. In contrast to the latter method, TA measurements probed the absorption change due to the formation of the perylene cation, i.e., the molecular product state. As a consequence, the decay of the excited molecular state is seen here as the corresponding rise of the signal probing the molecular product state. This is in contrast to the TR-2PPE measurement where only the excited molecular state is contributing to the signal but not the molecular product state. In the TA signal, the decay at positive delay times on the other hand corresponds to the slow recombination of the molecular cation to produce again the ground state. It has already been shown before that ground state absorption, stimulated emission, excited-state absorption, and cation absorption are spectrally well separated, allowing us to address exclusively the time-dependent change of the cation absorption when probed with 560 nm light.4 In the same publication, it has been shown that the decay of the excited state, i.e., the molecular reactant state, matches the rise of the cation, i.e., the ionized molecular product state.4 The decay can be addressed with TR-2PPE as has been discussed in the previous section, whereas the rise can be addressed only with TA and corresponding signals are shown in Figure 4. The latter shows TA of the cationic state of DTB-Pe-rod and DTB-Pe-tripod adsorbed in the colloidal film of TiO2. A biexponential fit of the signals rise has been performed to estimate the dominating time constants (not shown here). The fit revealed around 150 fs, and 1.8 ps for the time constants of DTB-Pe-tripod, and around 30 and 200 fs for the time constants of DTB-Pe-rod. In addition to the time constants obtained from the TR-2PPE measurements there are also much shorter time constants in the TA measurements. Further analysis of the measurements involved a more realistic model discussed in the following. Least-square deviation fits with this model are shown in Figure 4 (a and b) as solid lines. The TA measurements on the anatase colloidal system were fitted with a rate model comprising two contributions. The first represents the subset of molecules where ET occurs via the
Figure 4. Transient absorption signal (dots) of the DTB-Pe-tripod (a) and DTB-Pe-rod (b) cation formation probed at 570 nm when adsorbed on an anatase colloidal film and the fit with a rate model (solid line).
bridge/anchor group. This subset is assumed to contribute with a single time constant to the signal and is compatible with the ET time measured via TR-2PPE on the rutile single-crystal surface. The second subset represents all other molecules that are bound at sites where the chromophore-part is located close to an adjacent TiO2 wall. The latter subset contributes a set of short time constants to the fit arising from the distribution of different distances l from the chromophore to the respective TiO2 wall. To our knowledge, a distribution function for the latter distances was not yet reported in the literature. Many different configurations with different distances between the rim of the chromophore and the adjacent TiO2 walls can be expected for the nanometer-cavities of the colloidal layer. The colloidal layer is certainly not a good system for studying the influence of different adsorption configurations of the chromophore with respect to the surface of the substrate. The latter type of study is much better defined on the surface of a single-crystal.40 Since it does not appear meaningful to interpret details of different configurations in the colloidal layer we have adopted the simplest distribution by assuming a linear distribution of distances for the chromophores from the nearest TiO2 wall. Of course, also other distributions are plausible, but the data will anyhow not allow for a meaningful distinction. The important point to demonstrate here is that short distances between chromophore and nearest TiO2 wall are contributing to the measured time-dependent TA signals. Since the fit was sufficiently good already with the linear distance distribution, we decided to use the latter for fitting all of the measurements presented here. The injection time τTS was connected to the distance by τTS ) 1/(k0 exp(-βl)) since this is expected for a tunneling process, where k0 was set to 1/fs and the factor β was set to 1/Å. The latter value has been reported for saturated hydrocarbon bridges15,41 and appears reasonable for the bridge groups. In the model, we assumed that the shortest time constant for the shortest distance lshort was in the same range as for a molecule directly physisorbed on a solid surface. Keller et al.42
ET for Rod-Shaped Perylene-Derived Molecules
J. Phys. Chem. C, Vol. 111, No. 36, 2007 13591
TABLE 2: Comparison between Electron Injection Times Measured with TA for the DTB-Pe-tripod and the DTB-Pe-rod lower upper injection limit limit time recombination weight time factor τTS τTS τTB compound name [fs] [ps] [ps] 1/krec A DTB-Pe-tripod DTB-Pe-rod
5 5
1.3 0.08
1.8 0.21
2 ns 20 ps
1.1 3.5
and Krichmann et al.43 have reported time constants between 1 and 7 fs for physisorbed C6F6 on Cu(111). Here, we used a value for lshort that corresponds to an injection time of 5 fs. The shortest time constant is identified with an adsorption site where the TiO2 surface comes close to the rim of the perylene chromophore that is not protected by the bulky tertiary butyl group. The rate model used to fit the data is given by
d e N (t,l) ) -N eTS(t,l) kTS(l) + Ipump dt TS d c N (t,l) ) N eTS(t,l) kTS(l) - N cTS(t,l) krec dt TS kTS(l) ) k0e-βl d e N (t) ) -N eTB(t) kTB + Ipump dt TB d c N (t) ) N eTB(t) kTB - N cTB(t) krec dt TB WTS ) WTA(td) )
∫l
llong
short
N cTS dl
∫t t (N cTB + AWTS)Iprobe(t - td) dt 0
Here, Ipump is again the pump pulse, N cTS is the cation signal of the first subset that injects in a direction different from the bridge group (through short-cut(TS)), N cTB is the cation signal of the second subset that injects along the bridge group (through bridge(TB)), kTS(l) is the distance dependent tunneling-rate and A the weight factor (amplitude ratio) for the first subset. N eTS and N eTB are the population of the excited-state for the first and second subset, respectively. The upper integration limit llong, the amplitude ratio A, the laser intensities Ipump,probe, the recombination rate krec, as well as the regular injection time τTB ) 1/kTB are fit parameters. Due to the linear distribution of l, τTS will always be smaller than τTB as long as A gets neither too large nor too small. In the latter two cases, one of the two contributions could be neglected. The values for both fits are given in Table 2. The values for the recombination times are not reliable because of the limited time range of the measurement addressing the injection rate. They are given for completeness only. It should be noted that due to the exponential relationship between l and τTS and due to the integration over l, WTS puts the emphasis on the short time constants. For example, a least-square fit where the integral over all of the short injection times is replaced by just one short time constant results in 30 fs for the latter with a weight factor A ) 2.9.12,55 The fast injecting subset was not found for the two long, rigid molecules on the single-crystal surface. In contrast, for the
Figure 5. Comparison between cation transient absorption of DTBPe-tripod on a rutile colloidal film (open circles) and on an anatase colloidal film (filled circles).
nanometer-structured colloidal film it showed a large contribution of the additional short-cut injection pathways. C. Control Measurements with Rutile Colloidal Films. To check whether the injection times were depending significantly on details of the crystal structure, DTB-Pe-tripod was measured also on a rutile colloidal film that was deposited on a 500 µm thick glass plate. The latter had been prepared primarily for use in a solar cell where thicker glass is preferred. Unfortunately, the thick glass gives rise to a strong nonlinear response of the sample, the so-called coherent artifact,44 i.e., the initial spike in Figure 5. The anatase films were specifically prepared for ultrafast spectroscopic measurements on 50 µm thick glass in order to reduce the contributions of the coherent artifact in the measurement. Figure 5 shows the transient absorption signal of the DTB-Pe-tripod cation on rutile and anatase colloidal films. Both samples produce very similar multiexponential injection dynamics. Based on this result, the comparison of TA signals measured on anatase colloidal films with TR-2PPE measurements performed on rutile crystals appears meaningful. IV. Discussion A. Increasing PHET Times by Inserting Long Rigid Bridge/Anchor Groups. For the perylene chromophore covalently bonded directly to an anchor group and the latter bonded to surface atoms of TiO2, ultrashort PHET times have been measured employing femtosecond 2PPE on the (110) surface of the rutile TiO2 single crystal, i.e., 9 fs in the case of the carboxylic anchor group and 24 fs in the case of the phosphonic anchor group.12 It is interesting to note that very similar PHET time constants, i.e., 13 and 28 fs, respectively, were obtained from transient absorption measurements of the latter two compounds adsorbed in nanometer-cavities of a colloidal anatase TiO2 layer.17 Instantaneous PHET without any finite PHET time was achieved by adsorbing catechol molecules on the surface of a TiO2 single crystal, where direct optical charge-transfer takes place from the molecular ground state to electronic acceptor states of the semiconductor.11,45 For certain device applications, PHET is not required to occur on an ultrafast time scale. A slow-down of PHET is in certain cases even helpful since the same spacer groups that slow-down PHET can also slow-down the recombination reaction between electrons on the semiconductor surface and the ionized chromophore to form again the molecular ground state. It is wellestablished that saturated -CH2-CH2- bonds inserted between the molecular donor and the semiconductor can slow down
13592 J. Phys. Chem. C, Vol. 111, No. 36, 2007 electron transfer (an example for the present system can be found in ref 36). It should be noted that corresponding results for molecular donor-acceptor pairs covalently linked via molecular bridge groups have been established already two decades earlier.15,16 For several reasons, it is advantageous to use rigid bridge groups instead of flexible molecular chains. For the present work, we have employed bicyclooctane in the molecular DTB-Pe-rod and adamantane in the DTB-Pe-tripod structure (Figure 1). These two rigid saturated spacers function as an electronic tunneling barrier since the reaction distance and thus also the electron-transfer time is increased.25 For a well defined adsorption geometry, PHET always shows exponential time behavior irrespective of the strength of the electronic interaction, provided the energy levels at the interface match the wide band limit criterion.46 The latter is fulfilled on the surface of TiO2 for all of the perylene compounds mentioned in the present paper.12,13 It is obvious that the above rigid spacer groups can only function as tunneling barriers for electron-transfer if the distance from the perylene donor to the surface of TiO2 is increased compared to the absence of the spacer group. To know this, one has to measure for each compound the orientation and distance of the molecular donor perylene with respect to the crystal surface. The adsorption geometry for the perylen compounds discussed in this paper has been determined recently on the (110) surface of rutile single crystals from angle and polarization dependent 2PPE measurements.36,40 In accordance with earlier work, we have found in the case of the carboxyl anchor group a perpendicular orientation of the long axis of a long rigid molecule with respect to the crystal surface. In contrast, with the phosphonic acid anchor group, the axis of the rod-shape molecule is tilted by 66° with respect to the surface normal. The latter adsorption geometry is in accordance with the type of adsorption bonds predicted for this anchor group on the TiO2 surface by recent theoretical work of Perssons’s group.47 Both, the molecular DTB-Pe-rod and the DTB-Pe-tripod are increasing the distance between the perylene chromophore (Figure 1) and the planar TiO2 surface. The resulting electronic tunneling barrier slows down PHET and realizes a time constant of 240 fs in the case of the DTB-Pe-rod and 970 fs in the case of the molecular DTB-Pe-tripod. It is clear that fundamental questions regarding through space versus through bonds electron transfer can be studied very well on the surface of a singlecrystal provided the adsorption geometries are well-characterized. The situation becomes particularly simple if the wide band limit is realized at the interface,46,48 since this avoids corrections for the often not precisely known change in the magnitude of Franck-Condon factors. The latter diminish the electron-transfer rate if the wide band limit is not fulfilled, e.g., in the case of electron transfer in a donor-acceptor molecule. B. Short PHET Times that Arise for Long Rod-Shaped Dye Molecules in Nanometer-Cavities. Since the PHET time of the perylene chromophores covalently bonded directly to an anchor group, i.e., carboxylic and phosphonic acid, has a very similar value on the (110) surface of rutile single crystals and in the nanometer-cavities of the colloidal anatase layer,12 one could perhaps expect a similar result also for long rod-shaped molecules. The latter expectation is only partially supported by the experimental data shown in Figures 3 and 4. There is indeed again the long injection time with a value similar to the one measured for the rod-shaped compound on the surface of the rutile single crystal, i.e., around 240 fs for the DTB-Pe-rod and between 0.9 ps for the DTB-Pe-tripod. The longest time constant obtained for the latter compound from TA measurements on
Gundlach et al. the anatase surface in the nanometer-cavities was even 1.8 ps. Similar time constants measured in the nanometer-cavities as observed on the single-crystal surface can be attributed to similar adsorption configurations in the two systems, where ET occurs from the perylene chromophore in the direction of the bridgeanchor group to TiO2. The initial fast rise of the transient absorption signals measured for the DTB-Pe-rod and the DTB-Pe-tripod in the nanometer-cavities (Figure 4) shows the occurrence of a broad distribution of much shorter injection time constants between 5 and 80 fs for the DTB-Pe-rod (between 5 fs and 1.3 ps for DTB-Pe-tripod) that are absent on the surface of a single crystal. Fast electron transfer is attributed to short-cuts that arise for chromophores attached to long rigid anchor/bridge groups in the nanometer cavities. Considering the average diameter of 10 to 20 nm and the fairly wide size distribution of the nanometercavities in the anatase layer,49 it is at hand to attribute the short time constants to geometric configurations, where the perylene chromophore is positioned closer to another TiO2 wall than the one onto which the anchor group is attached. Such configurations will arise at edge or corner sites in the nanometer cavities. At the latter sites, electron transfer can proceed from the perylene chromophore to the nearest TiO2 wall and thereby ignore the much longer electron-transfer path in the direction of the TiO2 surface where the anchor group is attached. Even though details of the corresponding adsorption geometries are not known, the occurrence of the short electron-transfer times provides unambiguous evidence for the existence of these nonideal adsorption sites and the corresponding short-cut electron-transfer pathways. The large weight factor for the contribution of the shorter ET times suggests that long rodshaped molecules adsorb even preferentially at corner- or edgesides. It appears at first surprising that also longer ET times have been found in the nanometer-cavities compared to the single-crystal surfaces for the DTB-Pe-tripod, i.e., 1.8 ps compared to 0.97 ps. The latter result is tentatively ascribed here to residual impurities in the nanometer-structured film, e.g., remaining in the form of microdeposits that cannot be removed from the walls of the nanometer cavities and can lead to a decreased electron tunneling probability compared to vacuum if the electron affinity is repulsive, i.e., higher than the vacuum level. It should be noted here that nonideal adsorption geometries that give rise to short-cut ET lead not only to faster PHET but also to faster recombination reactions in the nanometer-cavities compared to a single-crystal surface. The latter effect can be detrimental for the efficiency of a dye-sensitized solar cell or any other device where fast recombination has to be avoided. C. Shape and Electronic Structure of Dye Molecules and Nanometer-Geometry of the Electrodes. Our final remarks address the design of a dye-sensitized solar cell considering the above results. It is sufficient to consider here a one-gap cell. The point of interest is here to slow-down recombination in an all solid-state dye-sensitized cell aiming at about 10% solar conversion efficiency. One could at first think perhaps of introducing a tunneling barrier by depositing another suitable material in the nanometer cavities. There are, however, stringent rules for building a barrier layer with a suitable band offset via heteroepitaxial growth.50 They involve lattice matching and the choice of elements that do not give rise to a gradual chemical intermixing at the interface. To our knowledge, successful heteroepitaxial growth of a barrier layer has not yet been demonstrated for a device that forms a corner geometry and even less so for nanostructured materials. Since the interface of interest involves in the present system an organic molecule
ET for Rod-Shaped Perylene-Derived Molecules and an inorganic oxide, it appears to be a more promising route if the barrier is directly introduced by way of synthesis of suitable organic compounds. It is known that anchor groups like carboxylic acid and phosphonic acid are forming strong bonds at the surface of TiO2. Therefore, it is at hand to introduce the barrier in the form of a suitable bridge group between the anchor group and the actual chromophore. Slowing-down electron transfer by inserting suitable molecular bridge groups is a well-known technique for molecular donor-acceptor pairs.15,16 The experimental results presented in this paper show that such an approach is indeed successful with linear rod shaped molecules at the planar surface of a single crystal of TiO2. However, the many edge and corner sites in the nanostructured TiO2 layer make the distance between the chromophore and the adjacent TiO2 wall ill defined, and fast electron transfer arises due to short-cut pathways. Thus, a molecular solution to forming an electronic tunneling barrier appears still feasible but has to be sought in the shape of a spherically shaped molecule where the distance between the chromophore part of the molecules and the adjacent TiO2 walls is well-defined even at an edge or corner site. In the latter case, the actual chromophore is surrounded on all sides by spacer groups with the anchor groups attached at the other side. Most of the Ru compounds that have been employed by the Gra¨tzel group in the dye-sensitized electrochemical solar cell (N3 dye) fulfill the requirement of an at least partially spherical shape. One could slow down PHET in the latter type of molecules if one would insert long rigid saturated spacer groups between the bipyridyl ligands and the carboxylic anchor groups. Of course, the resulting molecules would be bulky and would most likely not be able to occupy all the sites in the nanometer cavities where the smaller Ru compounds can be accommodated. Consequently, less solar light would be absorbed in a nanometerstructured TiO2 layer of a given thickness. This would make the diameter of the light-absorbing layer an even more critical issue for the competition between the escape of the injected electrons to the collector electrode of the solar cell and the recombination losses than it is already with the present Ru compounds. Slowing down the electron injection step in the Ru-bipyridyl type molecules would lead to the virtually complete conversion of all of the population from the higher to the lower lying more triplet-like excited-state of this dye. The corresponding intersystem crossing occurs, e.g., with a time constant of about 50 fs.51 At present, the consequences for the efficiency of the dyesensitized solar cell are not clear since there are different assumptions about the position of this lower excited-state with respect to the conduction band of the colloidal anatase layer.56 Another way of avoiding short-cut electron-transfer pathways for long rod-shaped molecules is a cylindrical geometry of the nanometer electrodes instead of nanometer-diameter cavities with the rod-shaped molecules oriented perpendicular to the long axis of the cylinders. The spacing between neighboring cylindrical nanometer electrodes must be sufficiently wide to accommodate at least two times the length of the rod-shaped molecules and an additional hole transport layer. On the other hand, the spacing between neighboring electrode cylinders should not be too large since a maximum number of dye molecules is to be packed into a given thickness of the electrode layer. It is obvious that there will be an optimized design with respect to diameter, and length of the cylinder and the distance between the cylindrical electrodes for a solid-state dye sensitized solar cell. Hitherto, a cheap practical procedure has not yet been found for preparing with TiO2 such an electrode where the above
J. Phys. Chem. C, Vol. 111, No. 36, 2007 13593 parameters for the nanometer cylinders can be varied. Instead, the above scenarios are currently being explored with the recently developed nanometer-diameter cylindrical-shaped ZnO electrodes.52 The latter, however, have an additional difficulty since a suitable method has to be found for anchoring the rodshaped dye molecules with the required perpendicular orientation on the surface of the ZnO cylinders. It is well-known that the ZnO lattice dissolves in the presence of even weak acids, i.e., the currently used anchor groups, releasing the corresponding salts into the adjacent solvent space.53 Anticipating a solution to these material problems our present work shows that cylindershaped nanometer-electrodes where adjacent planar surfaces are separated by a sufficient distance appear to be a better choice than nanometer-cavities if electron injection and thus also recombination is to be slowed-down by inserting a long rodshaped saturated bridge molecule between chromophore and anchor group as electronic tunneling barrier. Acknowledgment. We are grateful for financial support of the German Science foundation, L.G. (SPP1093) and R.E. (SFB450), and to Prof. Elena Galoppini and Dr. Silke Felber for the synthesis of the rod-shaped perylene-derived molecules. References and Notes (1) Brabec, C.; Zerza, G.; Sariciftci, N.; Cerullo, G.; Lanzani, G.; Silvestri, S. D.; Hummelen, J. Ultrafast Phenomena XII : Proceedings of the 12th International Conference, Charleston. Elsaesser, T., Mukamel, S., Murnane, M. M., Scherer, N. F., Eds.; In Springer Series in Chemical Physics; Springer: New York, 2000; pp 589-592, Vol. 66. (2) O’Regan, B.; Gra¨tzel, M. Nature 1991, 353, 737. (3) Ghosh, H. N.; Asbury, J. B.; Lian, T. J. Phys. Chem. B 1998, 102, 6482. (4) Burfeindt, B.; Hannappel, T.; Storck, W.; Willig, F. J. Phys. Chem. 1996, 100, 16463. (5) Hannappel, T.; Burfeindt, B.; Storck, W.; Willig, F. J. Phys. Chem. B 1997, 101, 6799. (6) Huber, R.; Moser, J.-E.; Gra¨tzel, M.; Wachtveitl, J. J. Phys. Chem. B 2002, 106, 6494-6499. (7) Schnadt, J.; Bru¨hwiler, B.; Patthey, L.; O’Shea, J.; So¨dergren, S.; Odelius, M.; Ahuja, R.; Karis, O.; Baessler, M.; Persson, P.; Siegbahn, H.; Lunell, S.; Martensson, N. Nature 2002, 418, 620. (8) Piotrowiak, P.; Galoppini, E.; Wei, Q.; Meyer, G. J.; Wiewio`r, P. J. Am. Chem. Soc. 2003, 125, 5276-5279. (9) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 322, 811, 265. (10) Ramakrishna, S.; Willig, F.; May, V. J. Chem. Phys. 2001, 115, 2743-2756. (11) Gundlach, L.; Ernstorfer, R.; Willig, F. Phys. ReV. B 2006, 74, 035324. (12) Gundlach, L. Surface Electron-transfer Dynamics in the Presence of Organic Chromophores. Ph.D. Thesis; Freie Universita¨t: Berlin, 2005. (13) Ernstorfer, R. Spectroscopic investigation of photoinduced heterogeneous electron transfer. Ph.D. Thesis; Freie Universita¨t: Berlin, 2004. (14) Zimmermann, C.; Willig, F.; Ramakrishna, S.; Burfeindt, B.; Pettinger, B.; Eichberger, R.; Storck, W. J. Phys. Chem. B 2001, 105, 9245. (15) Oevering, H.; Paddon-Row, M. N.; Heppener, M.; Oliver, A. M.; Cotsaris, E.; Verhoeven, J. W.; Hush, N. S. J. Am. Chem. Soc. 1987, 109, 3258. (16) Paddon-Row, M. N.; Oliver, A. M.; Warman, J. M.; Smit, K. J.; M. P. de Haas, H. O.; Verhoeven, J. W. J. Phys. Chem. 1988, 92, 6958. (17) Ernstorfer, R.; Gundlach, L.; Felber, S.; Storck, W.; Eichberger, R.; Willig, F. J. Phys. Chem. B 2006, 110, 25383-25391. (18) Zhao, W.; Wei, W.; White, J. M. Surf. Sci. 2003, 547, 374-384. (19) Zhong, Q.; Gahl, C.; Wolf, M. Surf. Sci. 2002, 496, 21. (20) Boger, K.; Weinelt, M.; Fauster, T. Phys. ReV. Lett. 2004, 92, 126803. (21) Shumay, I. L.; Ho¨fer, U.; Reuss, C.; Thomann, U.; Wallauer, W.; Fauster, T. Phys. ReV. B 1998, 58, 13974. (22) Gundlach, L.; Ernstorfer, R.; Riedle, E.; Eichberger, R.; Willig, F. Appl. Phys. B 2005, 80, 727-731. (23) Gra¨tzel, M. Prog. PhotoVoltaic Res. Appl. 2000, 8, 171-185. (24) Park, N.-G.; Schlichtho¨rl, G.; van de Lagemaat, J.; Cheong, H. M.; Mascarenhas, A.; Frank, A. J. J. Phys. Chem. B 1999, 103, 3308-3314. (25) Persson, P.; Lundqvist, M. J.; Ernstorfer, R.; Goddard, W. A., III; Willig, F. J. Chem. Theory Comp. 2006, 2, 441. (26) Diebold, U. Surf. Sci. Rep. 2003, 48, 53-229. (27) Hannappel, T.; Visbeck, S.; To¨ben, L.; Willig, F. ReV. Sci. Instrum. 2004, 75, 1297-1304.
13594 J. Phys. Chem. C, Vol. 111, No. 36, 2007 (28) Li, M.; Hebenstreit, W.; Gross, L.; Diebold, U.; Henderson, M. A.; Jennison, D. R.; Schultz, P. A.; Sears, M. P. Surf. Sci. 1999, 437, 173190. (29) Reiβ, S.; Krumm, H.; Niklewski, A.; Staemmler, V.; Wo¨ll, C. J. Chem. Phys. 2002, 116, 7704-7713. (30) Henderson, M. A.; Epling, W. S.; Perkins, C. L.; Peden, C. H. F. J. Phys. Chem. B 1999, 103, 5328. (31) Henderson, M. A. Surf. Sci. 1999, 419, 174. (32) Nazeeruddin, M. K.; Kay, A.; Rodicio, I.; Humphry-Baker, R.; Mueller, E.; Liska, P.; Vlachopoulus, N.; Gra¨tzel, M. J. Am. Chem. Soc. 1993, 115, 6382. (33) Ernstorfer, R.; Gundlach, L.; Zimmermann, C.; Willig, F.; Eichberger, R.; Riedle, E. Ultrafast Optics IV: Selected Contributions to the fourth International Conference on Ultrafast Optics; Krausz, F., Korn, G., Corkum, P., Walmsley, I. A., Eds.; 2004; Vol. 95, pp 393-398. (34) Piel, J.; Riedle, E.; Gundlach, L.; Ernstorfer, R.; Eichberger, R. Opt. Lett. 2006, 31, 1289-1291. (35) Kozma, I. Z.; Baum, P.; Lochbrunner, S.; Riedle, E. Opt. Exp. 2003, 11, 3110. (36) Gundlach, L.; Felber, S.; Storck, W.; Galoppini, E.; Wei, Q.; Willig, F. Res. Chem. Intermed. 2005, 31, 39-46. (37) Boschi, R.; Murrell, J. N.; Schmidt, W. Faraday Discuss. Chem. Soc. 1972, 54, 116. (38) Gundlach, L.; Ernstorfer, R.; Willig, F. Prog. Surf. Sci. 2007, 82, 355-377. (39) Duncan, W. R.; Stier, W. M.; Prezhdo, O. V. J. Am. Chem. Soc. 2005, 127, 7941-7951. (40) Gundlach, L.; Szarko, J.; Socaciu-Siebert, L. D.; Neubauer, A.; Ernstorfer, R.; Willig, F. Phys. ReV. B 2007, 75, 125320. (41) Johnson, M. D.; Miller, J. R.; Green, N. S.; Closs, G. L. J. Phys. Chem. 1989, 93, 1173-1176.
Gundlach et al. (42) Keller, C.; Stichler, M.; Fink, A.; Feulner, P.; Menzel, D.; Fo¨hlisch, A.; Hennies, F.; Wurth, W. Appl. Phys. A 2004, 78, 125-129. (43) Kirchmann, P. S.; Loukakos, P. A.; Bovensiepen, U.; Wolf, M. New J. Phys. 2005, 7, 113. (44) Lorenc, M.; Ziolek, M.; Naskrecki, R.; Karolczak, J.; Kubicki, J.; Maciejewski, A. Appl. Phys. B 2002, 74, 19-27. (45) Moser, J.; Punchihewa, S.; Infelta, P. P.; Gra¨tzel, M. Langmuir 1991, 7, 3012. (46) Ramakrishna, S.; Willig, F.; May, V.; Knorr, A. J. Phys. Chem. B 2003, 107, 607. (47) Nilsing, M.; Lunell, S.; Persson, P.; Ojama¨e, L. Surf. Sci. 2005, 582, 49-60. (48) Willig, F.; Zimmermann, C.; Ramakrishna, S.; Storck, W. Electrochim. Acta 2000, 45, 4565. (49) Shklover, V.; Nazeeruddin, M.; Zakeeruddin, S. M.; Barbe, C.; Kay, A.; Haibach, T.; Steurer, W.; Hermann, R.; Nissen, H.-U.; Gra¨tzel, M. Chem. Mater. 1997, 9, 430-439. (50) Capasso, F., Margaritondo, G., Eds. Heterojunction Band Discontinuities: Physics and DeVice Applications; North-Holland: Amsterdam, 1987. (51) Kallioinen, J.; Benko¨, G.; Sundstro¨m, V.; Korppi-Tommola, J. E. I.; Yartsev, A. P. J. Phys. Chem. B 2002, 106, 4396-4404. (52) Law, M.; Greene, L. E.; Johnson, J. C.; Saykally, R.; Yang, P. Nat. Mater. 2005, 4, 455. (53) Bauer, C.; Boschloo, G.; Mukhtar, E.; Hagfeldt, A. J. Phys. Chem. B 2001, 105, 5585. (54) Dinkel, C.; Morbach, G.; Willig, F. 2006, in preparation. (55) The other fit-parameter were τTB ) 235 fs, 1/krec ) 15 ps (56) Electronic level with lowest energy that gives rise to current flow across the whole width of the colloidal layer.
