Photo-Induced Electron Transfer from Dye or Quantum Dot to TiO 2 Nanoparticles at Single Molecule Level

Dye-sensitized solar cell (DSSC) has attracted wide attention for the potential application to convert sunlight into electricity. Organic dyes blended with TiO2 nanoparticles (NPs) have been recognized as important light harvesting materials especially in the visible spectral range (Hara et al., 2002; Bisquert et al., 2002; Gratzel, 2001; Ferrere & Gregg, 2001; Hagfeldt & Gratzel, 2000; Cahen et al., 2000). The functional materials are assembled in a sandwiched type to undergo photon-induced current process. Following photoexcitation, the embedded dye molecules may lead to electron transfer (ET) to the TiO2 conduction band. The injected electron flows through the semiconductor network and the external load to the counter electrode. At the counter electrode, the oxidized dye is reduced by electron donation from an electrolyte, and then the circuit becomes complete. The electron transfer kinetics in most dye/TiO2 systems is as rapid as in the time regime of femtosecond to several hundred picoseconds. The injected electrons are localized in either subband or surface states of TiO2 semiconductor. A fraction of the electrons, detrapped thermally from the reduced semiconductor, may possibly undergo recombination with the oxidized dye molecules. Such a back ET process takes place slowly from subnanoseconds to several milliseconds. An efficient solar cell deign should control lowering the rate of back electron transfer to prolong the lifetimes of charge-separated states. Therefore, characterizing kinetics of the forward and backward ET may be conducive to facilitating the working efficiency of a solar cell design. Among a variety of DSSC designs, Grätzel and coworkers have applied ruthenium-based dyes adsorbed on the TiO2 thin film, thereby achieving a very high power-conversion efficiency >11% (Gratzel, 2003, 2005). Despite a much lower efficiency in comparison, quantum dots (QDs) adopted recently to substitute for dyes have been popularly investigated including PbS (Plass et al., 2002; Ju et al., 2010), InAs (Yu et al., 2006), CdSe (Lee & Lo, 2009; Fan et al., 2010), CdS (Baker & Kamat, 2009; Lee & Lo, 2009), and PbSe (Luther et al., 2008; Choi et al., 2009). QDs have potential to be an alternative as electron donors (Robel et al., 2006; Kamat, 2008), for their unique properties such as size-dependent tunable energy gap (Yu et al., 2003; Kamat, 2008), a broad absorption band with large absorption cross sections (Yu et al., 2003), and multiple exciton generation (Yu et al., 2003; Luther et al., 2007; Kim et al., 2008; Sambur et al., 2010). When QDs absorb a photon to form an electron-hole


Introduction
Dye-sensitized solar cell (DSSC) has attracted wide attention for the potential application to convert sunlight into electricity.Organic dyes blended with TiO 2 nanoparticles (NPs) have been recognized as important light harvesting materials especially in the visible spectral range (Hara et al., 2002;Bisquert et al., 2002;Gratzel, 2001;Ferrere & Gregg, 2001;Hagfeldt & Gratzel, 2000;Cahen et al., 2000).The functional materials are assembled in a sandwiched type to undergo photon-induced current process.Following photoexcitation, the embedded dye molecules may lead to electron transfer (ET) to the TiO 2 conduction band.The injected electron flows through the semiconductor network and the external load to the counter electrode.At the counter electrode, the oxidized dye is reduced by electron donation from an electrolyte, and then the circuit becomes complete.The electron transfer kinetics in most dye/TiO 2 systems is as rapid as in the time regime of femtosecond to several hundred picoseconds.The injected electrons are localized in either subband or surface states of TiO 2 semiconductor.A fraction of the electrons, detrapped thermally from the reduced semiconductor, may possibly undergo recombination with the oxidized dye molecules.Such a back ET process takes place slowly from subnanoseconds to several milliseconds.An efficient solar cell deign should control lowering the rate of back electron transfer to prolong the lifetimes of charge-separated states.Therefore, characterizing kinetics of the forward and backward ET may be conducive to facilitating the working efficiency of a solar cell design.Among a variety of DSSC designs, Grätzel and coworkers have applied ruthenium-based dyes adsorbed on the TiO 2 thin film, thereby achieving a very high power-conversion efficiency >11% (Gratzel, 2003(Gratzel, , 2005)).Despite a much lower efficiency in comparison, quantum dots (QDs) adopted recently to substitute for dyes have been popularly investigated including PbS (Plass et al., 2002;Ju et al., 2010), InAs (Yu et al., 2006), CdSe (Lee & Lo, 2009;Fan et al., 2010), CdS (Baker & Kamat, 2009;Lee & Lo, 2009), and PbSe (Luther et al., 2008;Choi et al., 2009).QDs have potential to be an alternative as electron donors (Robel et al., 2006;Kamat, 2008), for their unique properties such as size-dependent tunable energy gap (Yu et al., 2003;Kamat, 2008), a broad absorption band with large absorption cross sections (Yu et al., 2003), and multiple exciton generation (Yu et al., 2003;Luther et al., 2007;Kim et al., 2008;Sambur et al., 2010).When QDs absorb a photon to form an electron-hole pair, the electrons may have chance to transfer to an accepting species such as TiO 2 , if the conduction band edge of QDs is tuned higher than the conduction band of TiO 2 (Robel et al., 2006;Yu et al., 2006;Kamat, 2008).Like the DSSC mechanism, kinetic behavior of ET between QDs and TiO 2 is one of the key roles to achieve a high energy-conversion efficiency.The bulk measurements yield ensemble-averaged information and sometimes could mask or overlook specific phenomena occurring at the sensitizer-semiconductor interfaces.For instance, conformation change and reorientation of the adsorbate structure feasibly induce the fluctuation of fluorescence decay times for ET processes, but such detailed dynamical complexity can not be visualized in ensemble experiments (Moerner & Fromm, 2003;Michalet et al., 2006).As a result, single molecule spectroscopy (SMS) has emerged as a powerful tool for investigating the dynamic processes of excited molecules in heterogeneous surrounding (Xie & Dunn, 1994;Garcia-Parajo et al., 2000;Moerner & Fromm, 2003;Michalet et al., 2006;Gaiduk et al., 2007).Analysis of fluorescence intermittency observed in SMS, or called on/off blinking phenomena, has been widely studied to unveil the dynamic behaviors of triplet state (Yip et al., 1998;Veerman et al., 1999;Kohn et al., 2002), molecular reorientation (Ambrose et al., 1994), energy transfer (VandenBout et al., 1997;Cotlet et al., 2005;Flors et al., 2007), spectral diffusions (Xie & Dunn, 1994;Kulzer et al., 1997), and electron transfer (Holman & Adams, 2004;Bell et al., 2006;Wang et al., 2009;Chen et al., 2010).This chapter is confined to understand ET dynamics of either dyes or QDs adsorbed on the TiO 2 NPs thin film at a single molecule level.By taking advantage of the SMS merits, the IFET phenomena of oxazine 1 dye and CdSe/ZnS core/shell QD adsorbed individually on the TiO 2 NPs surface are demonstrated.We acquired fluorescence trajectories of single dye molecule, characteristic of "on" and "off" blinking with time, in which the intensity fluctuation is attributed to the interfacial electron transfer (IFET) behavior.The fluorescent dye molecule lies in an off-blinking state when its electron moves to the TiO 2 NPs conduction band.While the electron transfers back to the oxidized state, the dye molecule blinks on again following photoexcitation.Discrete fluorescence intensity jumps between "on" and "off" level are analyzed by using autocorrelation function.The "on" and "off" lifetimes and the subsequent rate constants of forward and backward ET are then determined.On the other hand, the fluorescence lifetimes of QDs are measured as an alternative determination for the ET rate constants.QDs with different sizes are adopted for demonstration.We apply time-correlated single-photon counting (TCSPC) to measure fluorescence lifetimes among a quantity of QDs for each size.The fluorescence lifetime becomes shorter and the resultant "off" time is prolonged with decreased size of QDs.The off-time and on-time probability densities are then estimated and fitted appropriately.With the aid of Marcus model, theoretical ET rate constants are calculated for comparison and the ET process may thus be gained insight.

Apparatus
All single molecule experiments were performed with a confocal fluorescence microscope.For the single dye (or QD) experiments, a single-mode pulsed laser at 630 nm (or 375 nm), with a repetition rate of 10 MHz (or 5 MHz) and pulsed duration of 280 ps (or 300 ps), was used as the excitation source.The beam collimated with a pair of lenses was spectrally filtered with an excitation filter before entering an inversed microscope.An oil immersion objective (100x, NA1.40) was used both to focus the laser beam onto the sample, prepared

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on the surface of a glass coverslip, and to collect fluorescence from the sample.The excitation intensity of the pulsed beam was constantly measured to be 40 -210 W/cm 2 right on the top of the bare coverslip throughout the experiments.The fluorescence, after transmitting through a dichroic mirror, was refocused by a tube lens (200 mm focal length) onto an optical fiber (62.5 m diameter) which was coupled to an avalanche photodiode (APD) detector with a 175 m active area.Here the fiber serves as a pinhole to reject out-offocus light.The fluorescence signal may also be reflected simultaneously to a chargecoupled device (CCD) by a beamsplitter.A notch filter (6<OD) or a combination of bandpass filters were positioned in front of the detector to remove excitation background.Given the wide-field images with a CCD detector, each fluorescent single molecule was readily moved to an illuminated position using a x-y positioning stage.The fluorescence lifetime of single molecule was measured by TCSPC with a TimeHarp 200 PCI-board (PicoQuant).The data were stored in a time-tagged time-resolved mode, which allowed recording every detected photon and its individual timing information.By taking into account deconvolution of the instrument response function (SymPhoTime by PicoQuant), the TCSPC curve was analyzed by single exponential tail-fit.

Material preparation
The TiO 2 precursor was prepared by a sol-gel process.72 mL of 98% Titanium(IV) isopropoxide was added to 430 mL of 0.1 M nitric acid solution which was then stirred and heated to 85 o C for 8 h.The colloid, as filtered from the cooled mixture, was heated again in an autoclave at five temperatures of 180, 200, 220, 240, and 260 o C for 12 h to grow TiO 2 NPs.The TiO 2 colloid was concentrated to 13 wt%, followed by addition of a 30 wt% (with respect to TiO 2 ) of polyethylene glycol to prevent from cracking during drying.To prepare for the thin film, 40-50 L of 0.65% TiO 2 NPs aliquot was spin-coated on a cleaned coverslip.The same process was repeated four times to ensure TiO 2 well coated over the coverslip.After drying in the air for 30 min, the film was heated to 450 o C at a rate of 20 o C/min, and remained for 30 min before cooling to the room temperature.The phase and the size of TiO 2 NPs were characterized by using scanning electron microscopy.A drop of 30 L of 0.1 nM oxazine 1 dye in methanol solution or 35 L of 4 -200 pg/L QDs in toluene solution was spin-coated over the TiO 2 NPs surface, and then put on the sample stage of microscope for fluorescence measurement.

Fluorescence lifetimes
As shown in Fig. 1, the TiO 2 NPs thin film was well covered over the coverslip to ensure that the oxazine 1 dye may be fully adsorbed on the TiO 2 surfaces.The enlarged images displayed the NPs size about 20 nm.Fig. 2 shows absorption spectra of oxazine 1 solution in the presence (or absence) of TiO 2 NPs by means of ensemble measurements.The absorption cross section reaches as large as 3.5x10 -16 cm 2 at 630 nm.The fluorescence yield is 0.11 in ethanol as the solvent and increases to 0.19 in ethylene glycol (Sens & Drexhage, 1981).When the dye in methanol solution is diluted from 10 -6 to 10 -8 M, the spectral profile remains the same with a major peak and a minor shoulder.The spectra appear almost the same between the conditions with and without TiO 2 NPs involvement.The results suggest that the dimer contribution should be minor and negligible.A 10 -10 M of oxazine 1 dye solution was spin-coated on a bare or a TiO 2 NPs-coated coverslip.Fig. 3(a) displays the fluorescence images of the single oxazine 1 molecules within a 24 m x 24 m area on the bare coverslip, as excited by a pulsed laser at 630 nm with excitation intensity of 392 W/cm 2 .Each bright spot is attributed to a single molecular fluorescence.The diffraction-limited spot size is about 650 nm.Fig.3(b) shows the background emissions of the TiO 2 NPs surface.Stray light scattered by the TiO 2 NPs causes background noise, which is however dimmer than those fluorescent spots from the dye molecules.Fig. 3(c) shows the single molecular fluorescence images of dye molecules on TiO 2 NPs surface.The maximum fluorescence intensity reaches 650 counts acquired by a CCD within an integration time of 0.5 s.The fluorescent spots have different intensities resulting from variation of molecular orientation and micro-environments.The surface densities of fluorescent oxazine 1 on glass or TiO 2 coverslip are counted to be 0.088 or 0.085 per m 2 , respectively, with an uncertainty of 10%.It is difficult to make a comparison with the surface density prepared initially, since a great amount of dye solution is sputtered away during the spin-coating process.The roughness of the TiO 2 NPs-coated coverslip may reduce the dye molecules from sputtering away to some extents, as compared to a smooth bare glass.Although the surface density of fluorescent spots is similar between them, some molecules in the excitation might be quenched by a faster IFET process before fluorescing and thus fail to be detected.The clefts or interstices in the TiO 2 film are probably ideal sites for effective IFET.As shown in Fig. 4(a), fluorescence decay of a single dye molecule on TiO 2 is obtained for the lifetime measurements by the TCSPC method.The decay curve is fitted to a single exponential function yielding a lifetime of 2.6 ns.In this manner, the lifetimes successively determined among 100 different oxazine 1 molecules are distributed in Fig. 4(b), with an average value of 2.86±0.31ns.The lifetime scattering reveals an inhomogeneous character among the dye molecules measured, because of variation of dipole orientation, transition frequency, and molecular polarization on the surface.In addition, the fluctuation of the lifetime is partially attributed to the power density variation which is about 3%.For comparison, the average lifetimes over 100 oxazine 1 molecules are measured analogously to be 3.02±0.61ns on the bare coverslip.Despite no statistical difference with the uncertainty considered, the average lifetime of the dye on the TiO 2 film is significantly smaller than that on the bare coverslip.While inspecting Fig. 4(b), the asymmetric distribution shows more molecules lying on the side of shorter fluorescence lifetime.It suggests two points.First, some molecules might undergo even faster IFET process such that the excited state lifetimes become too short to be detected.Second, slight difference of the fluorescence lifetimes implies that most IFET processes should be slow and inefficient.The oxazine 1 molecule lacks effective anchoring groups like carboxylate in metal-polypyridine complexes to covalently bind the dye to the semiconductor (Oregan & Gratzel, 1991;Ramakrishna et al., 2005).These dye molecules randomly selected are anticipated to be physisorbed to the TiO 2 NPs surface or loosely trapped at the NPs interstices.However, that does not mean all interactions based on physisorption can not lead to efficient electron transfer.Some organic dyes such as cyanine or xanthene dyes incorporated in Langmuir-Blodgett films deposited on In 2 O 3 or SnO 2 electrodes show very efficient electron transfer even without chemisorptions, due to a large free-energy difference between the lowest unoccupied molecular orbital (LUMO) of the dye and the edge of the conduction band of the semiconductor (Arden & Fromherz, 1980;Biesmans et al., 1991;Biesmans et al., 1992).reported the triplet state lifetime to be 14.5 s for oxazine 1 in acetonitrile solution (Wilkinson et al., 1991), and a significantly longer lifetime is yet expected for the dye adsorbed on the solid film.A constant level of fluorescence intensity in Fig. 5(a) implies that the prolonged lifetimes should be much shorter than the integration time adopted such that the triplet blinking may be smeared out.When 100 single molecules are sampled, about 70% display the trajectories like Fig. 5(a).The remaining show blinks occasionally before photobleaching, in part because of photo-induced electron transfer to impurity sites of the glass coverslip.It is difficult to observe clearly triplet blinking of the single molecule caused by intersystem crossing.Instead, an average intensity of 5 counts/20 ms appears.The triplet state lifetime if assumed to be 14.5 s amounts to 0.003 count, which is too weak to be resolved temporally.

Fluorescence intensity trajectories
As shown in Fig. 6A(a), when the single-molecule fluorescence intensity trajectory of the dye molecules on the bare coverslip is slotted within 1 s-window, the fluorescence decay lifetimes are measured to be 3.63 ns and 3.59 ns for the time period of 54~55s and 266~267s, respectively (Fig. 6A(b)).Alternatively, the lifetime fluctuation trajectory binned in 0.5 swindow gives rise to an average lifetime of 3.440.48ns (Fig. 6A(c)), which is consistent with that averaged over 100 molecules.These facts indicate that the fluorescence intensity fluctuation for oxazine 1 on glass is dominated by the radiative relaxation process from the singlet state.The fluorescence intensity trajectory is slotted within a 500photon binned window to select one "on" intensity and the other "off" intensity (Fig. 6B(a)).
Analyzing the fluorescence decay yields a result of 2.93 and 1.26 ns for the "on" (12.85~13.33s slot) and "off" (29.15~30.20 s slot) lifetime, respectively (Fig. 6B(b)).Given a threshold at 7 counts/20 ms, the fluorescence intensity is divided to higher level and lower level.The lifetime analysis of these two levels yields the results similar to those obtained in the above time slots.The "on" state shows a twofold longer lifetime than the "off" state (Fig. 6B(c)).This fact indicates that the fluorescence intensity fluctuation is caused by both factors of reactivity, i.e., the fraction of IFET occurrence frequency (Wang et al., 2009), and rate of electron transfer.The fluorescence lifetimes analyzed within 0.5s-window fluctuate in a range from 0.6 to 4.8 ns, which is more widely scattered than those acquired on the bare glass (Fig. 6B(d)).This phenomenon suggests existence of additional depopulation pathway which is ascribed to ET between oxazine1 and TiO 2 .However, other contribution such as rotational and translational motion of the dye on the TiO 2 film can not be rule out without information of polarization dependence of the fluorescence.

Autocorrelation analysis
An autocorrelation function based on the fluorescence intensity trajectory is further analyzed.When the dye molecules are adsorbed on the TiO 2 NPs surface, a four-level energy scheme is formed including singlet ground, singlet excited, and triplet states of the dye molecule as well as conduction band of TiO 2 .Upon irradiation with a laser source, the excited population may undergo various deactivation processes.Because the selected dye molecule has a relatively short triplet excursion, the fluorescence in the absence of TiO 2 film becomes a constant average intensity with near shot-noise-limited fluctuation, as displayed in Fig. 5(a) (Haase et al., 2004;Holman & Adams, 2004).As a result, the system can be simplified to a three-level energy scheme.
As the ET process occurs, the fluorescence appears to blink on and off.The transition between the on and off states may be considered as feeding between the singlet and the conduction subspaces (Yip et al., 1998), The on-state rate constant is equivalent to the backward ET rate constant from the conduction band, i.e., while the off-state rate constant corresponds to the excitation rate constant k ex multiplied by the fraction of population relaxing to the conduction band, as expressed by where  is the absorption cross section and h is the photon energy.The average residence times in the on and off states correspond to the reciprocal of the feeding rate in the off and on states, respectively.That is,  on = 1/k off and  off = 1/k on .
The rate constants in on-off transition may then be quantified by analyzing autocorrelation of fluorescence intensities (Holman & Adams, 2004).The normalized autocorrelation function is defined as the rate of detecting pairs of photons separated in time by an interval , relative to the rate when the photons are uncorrelated.It is expressed as where I(t) is the fluorescence intensity at time t and  is the correlation time.The bracketed term denotes the intensity average over time.When the population relaxation is dominated by the singlet decay, the autocorrelation function may be simplified to an exponential decay, i.e., where A is an offset constant, B a pre-exponential factor, and k the decay rate constant.They are determined by fitting to the autocorrelation data.These parameters are explicitly related to the phenomena of on/off blinking due to the ET processes by, If I on >>I off , then the above equation is simplified to The forward and backward ET rate constants in the dye molecule-TiO 2 NPs system can thus be evaluated.According to eq.5, Fig. 7(a) shows that the autocorrelation result based on the fluorescence trajectory of the dye on glass (Fig. 5(a)) appears to be noisy ranging from zero to microseconds.The dynamic information of the triplet state can not be resolved, consistent with the analyzed results of fluorescence decay times.When the dye molecule is on TiO 2 , the fluorescence trajectory given in Fig. 5(c) is adopted as an example for evaluation of the individual "on" and "off" times.As shown in Fig. 7(b), the resulting autocorrelation function is fitted to a single exponential decay, yielding a B/A value of 0.2 and k of 2.17 s -1 .Given the excitation rate constant k ex of 2.2x10 4 s -1 (38.5 W/cm 2 was used) and the fluorescence decay k 21 of 3.28x10 8 s -1 determined in the excited state lifetime measurement, k et and k bet are evaluated to be 5.4x10 3 and 1.8 s -1 , respectively, according to eqs.2,3,7, and 9.The IFET and back ET rate constants with the "on" and "off" times for the examples in Fig. 5(b-d) are listed in Table 1.For comparison, the corresponding lifetime measurements are also listed.A more efficient IFET is apparently accompanied by a shorter excited state lifetime.The process of photo-induced ET involves charge ejection from the oxazine 1 LUMO (~2.38 ev) into a large energetically accessible density of states within the conduction band of TiO 2 (~4.4 ev), while the back ET involves thermal relaxation of electrons from the conduction band or from a local trap (energetically discrete states) back to the singly occupied molecular orbital (SOMO) of the oxazine 1 cation. 37It is interesting to find a linear correlation with a slope of 1.7x10 3 between IFET and back ET rate constants, as shown in Fig. 9. Despite difference of the mechanisms, k bet increases almost in proportion to k et .Such a strong correlation between forward and backward ET rate constants suggests that for different dye molecules the ET energetics remains the same but the electronic coupling between the excited state of the dye molecules and the conduction band of the solid film varies widely (Cotlet et al., 2004).Both forward and backward ET processes are affected similarly by geometric distance and orientation between electron donor and acceptor.

Fluorescence intermittency and electron transfer by quantum dots 4.1 Fluorescence intermittency and lifetime determination
Three different sizes of CdSe/ZnS core/shell QDs were used.Each size was estimated by averaging over 100 individual QDs images obtained by transmission emission spectroscopy (TEM), yielding the diameters of 3.6±0.6,4.6±0.7,and 6.4±0.8 nm, which are denoted as A, B, and C size, respectively, for convenience.Each kind was then characterized by UV/Vis and fluorescence spectrophotometers to obtain its corresponding absorption and emission spectra.As shown in Fig. 10(a) and (b), a smaller size of QDs leads to emission spectrum shifted to shorter wavelength.From their first exciton absorption bands at 500, 544, and 601 nm, the diameter for the CdSe core size was estimated to be 2.4, 2.9, and 4.6 nm (Yu et al., 2003), respectively, sharing about 25-37% of the whole volume.In addition, given the band gaps determined from the absorption bands and the highest occupied molecular orbital (HOMO) potential of -6.12  -6.15 Ev (Tvrdy et al., 2011), the LUMO potentials of QDs may be estimated to be -4.06,-3.86, and -3.67 eV along the order of decreased size.Each size of QDs was individually spin-coated on bare and TiO 2 coverslip.Fig. 11 shows an example for the photoluminescence (PL) images within a 24 m x 24 m area of the smallest QDs on the glass and TiO 2 NPs thin film, as excited at 375 nm.The surface densities of fluorescent QDs on TiO 2 were less than those on glass.Their difference becomes more significant with the decreased size of QDs.As a single bright spot was focused, the trajectory of fluorescence intensity was acquired until photobleaching.The trajectory is represented as a number of emitting photons collected within a binning time as a function of the arrival time after the experiment starts.Fig. 12 shows the examples for the three sizes of QDs on glass and TiO 2 .The bleaching time of the trajectory appears shorter with the decreased size of QDs, showing an average value of 9.4, 19.6, and 34.1 s on TiO 2 , which are much shorter than those on glass.In addition, QDs on either surface are characterized by intermittent fluorescence.As compared to those on glass coverslip, QDs on TiO 2 endure shorter on-time (or fluorescing time) events but longer off-time events.This trend is followed along a descending order of size.The photons collected within a binning time can be plotted as a function of delay time which is defined as the photon arrival time with respect to the excitation pulse.The fluorescence decay for a single QD is thus obtained.Each acquired curve can be applied to a monoexponential tail-fit, thereby yielding the corresponding lifetime for a selected arrival time slot.For increasing single-to-noise ratio, the on-state lifetime is averaged over the entire trajectory.However, the off-state lifetime cannot be precisely estimated, because its signal is close to the background noise with limited number of photons collected.Fig. 13 shows a single QD lifetime determined for different sizes on glass and TiO 2 .A smaller size of QDs results in a shorter on-state lifetime on either surface.Given the same size of QDs, the lifetime on TiO 2 appears to be shorter than that on glass.Their lifetime difference increases with the decreased size.As reported previously (Jin et al., 2010a), the trajectories of fluorescence intermittency and lifetime fluctuation are closely correlated.A similar trend is also found in this work.Fig. 14 shows the lifetime histograms among 20-90 single QDs for the three sizes on glass and TiO 2 .The corresponding average lifetimes are listed in Table 2.As shown in Fig. 14, the smallest QDs on TiO 2 have much less on-events than those on glass.For clear lifetime comparison of QDs adsorption between glass and TiO 2 , each on-event distribution is normalized to unity.The Gaussian-like lifetime histogram has a wide distribution for both glass and TiO 2 .The lifetime difference for the A type of QDs can be readily differentiated between these two surfaces.As listed in Table 2, their average lifetimes correspond to 19.3 and 14.9 s.In contrast, a tiny lifetime difference between 25.7 and 25.5 s for the C type of QDs is buried in a large uncertainty.Table 2. Size-dependence of on-state lifetimes of quantum dots (QDs) on glass and TiO 2 film which are averaged over a quantity of single QDs.

Interfacial electron transfer
Upon excitation at 375 nm, a QD electron is pumped to the conduction band forming an exciton.The energy gained from recombination of electron and hole will be released radiatively or nonradiatively.However, the excited electron may be feasibly scattered out of its state in the conduction band and be prolonged for recombination.The excited electron probably undergoes resonant tunneling to a trapped state in the shell or nonresonant transition to another trapped state in or outside the QD (Hartmann et al., 2011;Krauss & Peterson, 2010;Jin et al., 2010b;Kuno et al., 2001).The off state of QD is formed, as the charged hole remains.When a second electron-hole pair is generated by a second light pulse or other processes, the energy released from recombination of electron and hole may transfer to the charged hole or trapped electron to cause Auger relaxation.Its relaxation rate is expected to be faster than the PL rate.Given a QD with the core radius of 2 nm, the Auger relaxation rate was estimated to be 100 times larger than the radiative decay rate (Hartmann et al., 2011).The fluorescence fluctuation is obviously affected by the Auger relaxation process that is expected to be <100 ps.
As shown in Fig. 12, the on-time events of fluorescence intermittency for QDs on TiO 2 are more significantly suppressed than those on glass.The shortened on events are expected to be caused by the ET from QDs to the TiO 2 film.The analogous phenomena have been reported elsewhere (Hamada et al., 2010;Jin & Lian, 2009).The more rapid the ET is, the shorter the on-state lifetime becomes.The fluorescence lifetime may be estimated by (Jin & Lian, 2009;Kamat, 2008;Robel et al., 2006) where k r , k A , and k ET denote intrinsic decay rate of radiation, Auger relaxation rate, and ET rate.When QD is adsorbed on glass, the ET rate is assumed to be zero.The fluorescence fluctuation is dominated by the Auger relaxation.Thus, given the lifetime measurements on both glass and TiO 2 and assumption of the same Auger relaxation rate, the ET rate constant from QDs to TiO 2 can be estimated by the reciprocal of the lifetime difference.The resulting ET rate constants are (1.51.4)x10 7and (6.88.1)x10 6s -1 for the QDs A and B, respectively.A large uncertainty is caused by a wide lifetime distribution.The ET rates depend on the QDs size.The smaller QDs have a twice larger rate constant.However, the ET rate constant for www.intechopen.com Photo-Induced Electron Transfer from Dye or Quantum Dot to TiO 2 Nanoparticles at Single Molecule Level 361 the largest size cannot be determined precisely, due to a slight lifetime difference but with large uncertainty.The ET quantum yield  may then be estimated as 22.6 and 13.3% for the A and B sizes, respectively, according to the following equation, The larger QDs result in a smaller quantum yield.
In an analogous experiment, Jin and Lian obtained an average ET rate of 3.2x10 7 s -1 from CdSe/ZnS core/shell QDs with capped carboxylic acid functional groups (Jin & Lian, 2009).Their size was estimated to have core diameter of 4.0 nm based on the first exciton peak at 585 nm.While considering the size dependence, our result is about ten times smaller.It might be caused by the additional carboxylic acid functional groups which can speed up the ET rates.Different from the method of lifetime measurement, autocorrelation of fluorescence intensities can be alternatively used to quantify the kinetic constants in on-off transition, as described in Section III.C (Chen et al., 2010).By analyzing exponential autocorrelation of fluorescence trajectory under a three-level energy system, the forward and back ET rate constants single oxazine dye/TiO 2 film were reported above et al., 2010).As the uncertainty was considered, there was no statistical difference of the lifetime measurements for the single dye adsorption between glass and TiO 2 .Such a small ET activity can be indeed quantified by analyzing the autocorrelation function.Unfortunately, this method cannot be applied effectively to the QDs case, because the kinetic system involves multiple manifolds that make analysis more complicated.The non-exponential fluorescence fluctuation was reported in single semiconductor QDs early in 1996 (Nirmal et al., 1996).To explain such fluorescence intermittency, Efros et al. (Efros & Rosen, 1997) proposed an Auger ionization model, in which an electron (hole) ejection outside the core QDs is caused by nonradiative relaxation of a bi-exciton.However, Auger ionization process would lead to a single exponential probability distribution of 'on' events, which is against the power-law distributions and the large dynamic range of time scale observed experimentally (Kuno et al., 2000(Kuno et al., , 2001)).Nesbitt and coworkers later investigated the detailed kinetics of fluorescence intermittency in colloidal CdSe QDs and evaluated several related models at the single molecule level.They concluded that the kinetics of electron or hole tunneling to trap sites with environmental fluctuation should be more appropriate to account for the blinking phenomena (Kuno et al., 2001).Frantsuzov and Marcus (Frantsuzov & Marcus, 2005) further suggested a model regarding fluctuation of nonradiative recombination rate to account for the unanswered problem for a continuous distribution of relaxation times.
To compare the blinking activity for a single QD, probability density P(t) is defined to indicate the blinking frequency between the on and off states.The probability density P(t) of a QD at on or off states for duration time t may be calculated by (Kuno et al., 2001;Cui et al., 2008;Jin & Lian, 2009;Jin et al., 2010a) , () () where i denotes on or off states, N(t) the number of on or off events of duration time t, N tot the total number of on or off events, and t av the average time between the nearest neighbor events.The threshold fluorescence intensity to separate the on and off states is set at 3.  is the standard deviation of the background fluorescence intensity which can be fitted with a Gaussian function.Fig. 15 shows a fluorescence trajectory with a threshold intensity and its corresponding blinking frequency for a single QD (3.6 nm) on glass and TiO 2 .The subsequent on-state and off-state probability densities accumulated over 10 single QDs for each species are displayed in Fig. 16 and Fig. 17, which show similar behavior as a single QD but with more data points to reduce uncertainty.The P(t) distribution at the on state for each size under either surface condition essentially follows power law statistics at the short time but deviates downward at the long time tails.The bending tail phenomena are similar to those reported (Tang & Marcus, 2005a, b;Cui et al., 2008;Peterson & Nesbitt, 2009;Jin et al., 2010a).These on-state distributions can be fitted by a truncated power law, as expressed by (Tang & Marcus, 2005a, b;Cui et al., 2008;Peterson & Nesbitt, 2009;Jin et al., 2010a) () e x p ( ) where D is the amplitude associated with electronic coupling and other factors, m i the power law exponent for the on state, and  the saturation rate.The truncated power law was developed by Marcus and coworkers for interpreting the blinking behavior of QD which was attributed to the ET process between a QD and its localized surface states (Tang & Marcus, 2005a, b).According to eq.13, the fitting parameters of m on and  on are listed in Table 3.The QDs on TiO 2 apparently result in larger  values than those on glass.In addition, the trend is found that a smaller QD may have a larger .As for m on , the obtained range is from 0.70 to 0.93, smaller than 1.5 as expected by Marcus model (Tang & Marcus, 2005a, b;Cui et al., 2008).Such deviation for m on was also found by the Lian group in a similar experiment (Jin et al., 2010a;Jin et al., 2010b).Note that the power law distribution with a bending tail in the long time region is solely found at the on states.In contrast, the off-state probability density may be fit to a simple power law statistics expressed by, where E is a scaling coefficient and m i is the power law exponent for the off state.A similar trend for both on-and off-state distributions was analogously found elsewhere (Cui et al., 2008;Peterson & Nesbitt, 2009).As listed in Table 3, the obtained m off yields a smaller value when QDs are adsorbed on TiO 2 .They lie in the range of 1.6-2.1, which are consistent with those reported (Kuno et al., 2001;Cui et al., 2008;Peterson & Nesbitt, 2009).
The on-time saturation rate should be associated with the ET rate.According to Marcus model (Tang & Marcus, 2005a, b), the free energy curves of light emitting state and dark state can be represented by an individual parabola along a reaction coordinate, which is assumed to have the same curvature.Then,  on can be related to the free energy change G ET based on the ET process.That is (Tang & Marcus, 2005a, b;Cui et al., 2008), where  is the system reorganization energy, t diff the diffusion correlation time constant for motion on a parabolic energy surface, k B the Boltzmann constant, and T the absolute temperature.Given the conduction band of -4.41 eV for TiO 2 NPs and the LUMO potentials of QDs, -3.67 and -3.86 eV for the A and B sizes, respectively, the corresponding -G ET may    Table 3.The fitting parameters of 10 single quantum dots at the on state in terms of truncated power law distribution and off state in terms of power law distribution.be estimated to be 0.74 and 0.55 eV.The related energy diagram is displayed in Fig. 18.For a smaller QD, the larger conduction band gap between QD and TiO 2 can induce a larger driving force to facilitate the ET process (Tvrdy et al., 2011).If  and t diff remain constant, substituting G ET and  on into eq.15 for different size of QDs yields  to be 636 and -416 meV, of which only the positive value is meaningful.

Model prediction of electron transfer
In the following is the Marcus model which has been successfully used to describe the ET kinetics for the systems of organic dyes coupled to various metal oxides (She et al., 2005;Tvrdy et al., 2011), where H(E) is the overlap matrix element, (E) the density of electron accepting states, h the Planck's constant, and G the free energy change of the system, which is composed of three factors.They are (1) the energy change between initial and final electronic states, equivalent to G ET mentioned in eq.15, (2) the free energy difference between nonneutral donating and accepting species in the ET process, and (3) the free energy of coulombic interaction for electron and hole separation (Tvrdy et al., 2011).Among them, only G ET can be measured experimentally.Because of similarity as the work by the Kamat group (Tvrdy et al., 2011), the contributions of the second and third factors are referred to their work.That is, where e is the elementary charge, R QD and  QD are the radius and dielectric permittivity of the QD,  TiO2 is the dielectric permittivity of TiO 2 , and s is the separation distance between QD and TiO 2 .Given s, assumed to be the same as reported (Tvrdy et al., 2011), and the data of G ET , R QD ,  QD and  TiO2 , G is estimated to be -0.22,-0.143, and -0.054 eV for the A, B, and C sizes of QDs, respectively.As compared to G ET , the driving force for moving electron from QD to TiO 2 is suppressed after taking into account the additional contributions in eq.17.
In a perfect semiconductor crystal, the density of unoccupied states (E) is given as (She et al., 2005;Tvrdy et al., 2011) where V o is the effective volume, known to be 34.9Å 3 for TiO 2 crystal, m e * the electron effective mass, equivalent to 10 m 0 (m 0 is the mass of free electron) (She et al., 2005), and ħ is h/2.For a TiO 2 nanoparticle with high surface to volume ratio, the density of states in eq.18 requires modification by considering the defect states which are treated as a Gaussian distribution of width . (She et al., 2005;Tvrdy et al., 2011) The modified density of states  D (E) is then expressed as Given a constant H(E), substituting eqs.18 and 19 into eq.16yields an explicit relation between k ET and G.As reported (She et al., 2005), when the dye/metal oxide system was surrounded by a buffer layer, the reorganization energy  increases to 100-500 meV, because additional energy is required for system rearrangement.In this work, CdSe/ZnS QDs are spin-coated on the TiO 2 NPs film which is exposed to the air.The requirement of reorganization energy should be small.Therefore, the  value of 636 meV in the estimate (eq.15) seems to be unreasonable.When G ET is replaced by G,  is obtained to be 178 and -248 meV based on eq.15.The selected  of 178 meV is more acceptable than the one obtained with G ET substituted.The width  of defect states for the TiO 2 NPs is insensitive in the k ET calculation by eq.16.We adopt the same  of 50 meV as reported (Tvrdy et al., 2011).Given H(E) assumed to have 0.83 cm -1 and the data of G, , and , k ET is optimized to be 1.42x10 7 , 6.80x10 6 , and 1.86x10 6 s -1 for three increased sizes of QDs.The first two results agree very well with the experimental findings.The ET rate constant for the C type of QDs cannot be precisely determined experimentally, but may be estimated with the aid of model prediction.For our system, CdSe/ZnS core/shell QDs are spin-coated on the TiO 2 thin film.Unlike this preparation procedure, Kamat and coworkers immersed TiO 2 film in the colloidal CdSe QDs solution to make a tight contact between donor and acceptor and then measured the electron transfer rates under a vacuum condition (Tvrdy et al., 2011).Therefore, the overlap matrix elements, H(E), which is associated with the coupling between electron donating and accepting states, must make difference.In our work, the core CdSe QD and TiO 2 have a loose contact and thus a smaller H(E) of 0.83 cm -1 is obtained.In contrast, a much larger value of 57 cm -1 was adopted by the Kamat group (Tvrdy et al., 2011).That is why the ET rates obtained herein are relatively slower by a factor of 10 4 .

Concluding remarks
This chapter describes IFET induced by a single dye molecule or a single QD which is individually adsorbed on the TiO 2 NPs film.The fluorescence lifetimes determined among different single oxazine 1 dye molecules are widely spread, because of micro-environmental influence.These lifetimes are in proximity to those measured on the bare coverslip, indicative of the IFET inefficiency for those dye molecules sampled in this work.However, some molecules may proceed via very efficient IFET process, but fail to be detected.Due to a shorter triplet excursion, oxazine 1-TiO 2 NPs system is treated effectively as a three-level system upon irradiation.The exponential autocorrelation function may thus be analyzed to quantify the related kinetic rate constants in an on-off transition.The IFET processes are found to be inhomogeneous, with a rate constant varying from molecule to molecule.The reactivity and rate of ET fluctuation of the same single molecule are the main source to result in fluorescence intensity fluctuation.These phenomena, which are obscured in the ensemble-averaged system, are attributed to micro-environment variation for each single molecule.The oxazine 1 dye is apparently unsuitable for application to the DSSC design, because of its lower ET rates.Nevertheless, the single molecule spectroscopy provides a potential tool looking into the microscopic ET behaviors for different dye molecules to facilitate the working efficiency for the cell design.In addition, it is capable of detecting a low ET quantum yield, which is difficult to measure with conventional ensemble-averaged methods.
Photo-Induced Electron Transfer from Dye or Quantum Dot to TiO 2 Nanoparticles at Single Molecule Level 367 The second part of this chapter describes the ET from QDs to TiO 2 NPs film.The ET kinetics depends on the size of CdSe/ZnS QDs.The trajectories of fluorescence intermittency of three different sizes of QDs on glass and TiO 2 are acquired and the subsequent fluorescence lifetimes are determined.While assuming the lack of electron transfer for the QD on glass, the ET rates from QD to TiO 2 may be inferred in terms of reciprocal of the lifetime difference.The following trend is found: the smaller the size of QDs, the larger the ET rate constants.The distribution of off-time probability density versus the arrival time is fit to a simple power law statistics.However, the plot of on-time probability density can be characterized by a truncated power law distribution.Marcus's electron transfer model is employed to fit the bending tail behavior and to further calculate the ET rate constants, which show consistency with our experimental findings.

Fig. 1 .
Fig. 1.Images of TiO 2 NPs thin film by using scanning electron microscopy.The average sizes of TiO 2 NP are about 20 nm for both films.

Fig. 3 .
Photo-Induced Electron Transfer from Dye or Quantum Dot to TiO 2 Nanoparticles at Single Molecule Level Fig. 4. (a) Fluorescence decay of single oxazine 1 molecule in the presence of TiO 2 NPs measured by using time-correlated single photon counting.The instrument response function gives a faster decay estimated to be 550 ps.(b) Distribution of excited state lifetimes among 100 single oxazine 1 molecules on the TiO 2 NPs surface, yielding an average lifetime of about 2.86 ns.

Fig. 5
(a) displays fluorescence intensity as a function of running time of a single oxazine 1 molecule on the bare coverslip with a 20 ms binning time to record the photon counts of emission.These time scales average out any faster fluorescence fluctuation or blinking of the dye molecules.The single-molecule trace shows a constant level of fluorescence intensity which then drops to the background in one step when photobleaching occurs.Wilkinson et al.
Photo-Induced Electron Transfer from Dye or Quantum Dot to TiO 2 Nanoparticles at Single Molecule Level

Fig. 6 .
Fig. 6. (A) Single-molecule fluorescence decay profile of oxazine1 on bare glass.(a) The fluorescence intensity fluctuation slotted at 1 and 2 positions each within 1-s window.(b) Fluorescence decay profile for the 1 and 2 slots gives rise to the decay time of 3.63 ns and 3.59 ns, respectively.(c) The lifetime (binning window 0.5s) fluctuation trajectory (left), and the histogram for the lifetime trajectory from 0 to 50 s before photobleaching.The average lifetime is 3.440.48ns.

Fig. 6 .
Fig. 6. (B) Single-molecule fluorescence decay profile of oxazine1 on TiO 2 NPs film.(a) The fluorescence intensity fluctuation slotted at one "on" position and the other "off" position.(b)Fluorescence decay profile for the "on" and "off" slots gives rise to the decay time of 2.93 and 1.26 ns, respectively.(c) Given a threshold set at 7 photocounts/20 ms, the emission trajectory is separated to higher level and lower level.Fluorescence decay profiles for high and low intensity have similar results as the "on" and "off" slots in (b).(d) The lifetime (binning window 0.5s) fluctuation in a range from 0.6 to 4.8 ns (left), and the histogram for the lifetime trajectory from 0 to 50 s before photobleaching.On the other hand, Fig.5(b-d) show the fluorescence trajectories of individual dye molecules in the presence of TiO 2 NPs thin film ranging from several microseconds to seconds before photobleaching.These trajectories are classified into three types among 100 single dye molecules as sampled.About 20% of molecules yield the traces as inFig.5(b), in which the interaction with TiO 2 NPs is weak such that the molecule fluoresces at most time.A 60% majority show the traces as in Fig.5(c), in which a stronger interaction is found and the "off" time becomes longer.The remaining 20% give the traces as inFig.5(d), in which the

Fig. 7 .
Fig. 7. Autocorrelation function of fluorescence intensity from single oxazine 1 molecules (a) on bare coverslip, (b) on TiO 2 NPs-coated coverslip.The inset in (a) is the enlarged trace within the range of 1 ms.

Fig. 6 .Fig. 8 .
Photo-Induced Electron Transfer from Dye or Quantum Dot to TiO 2 Nanoparticles at Single Molecule Level

Fig. 9 .
Fig. 9.A linear correlation between photo-induced electron transfer and back electron transfer rate constant.
Fig. 10.(a) Absorption and (b) fluorescence spectra of QDs in toluene solution with excitation wavelength fixed at 375 nm.The maximum intensities for both spectra have been normalized.A, B, and C species have the diameters of 3.6, 4.6, and 6.4 nm, respectively.

Fig. 12 .
Photo-Induced Electron Transfer from Dye or Quantum Dot to TiO 2 Nanoparticles at Single Molecule Level

Fig. 13 .
Fig. 13.The fluorescence decay, detected by the TCSPC method, for three types of QDs spincoated on (a) glass and (b) TiO 2 film.The number of counts is normalized to unity.

Fig. 14 .
Fig. 14.The distributions of fluorescence lifetime for (a,b) QDs A and (c,d) QDs B and C. (a) comparison of on-event occurrence for QDs A between glass and TiO 2 .(b,c,d) each area of distribution is normalized to unity.The lifetime distributions of QDs on glass and TiO 2 are displayed in red and blue, respectively.

Fig. 15 .
Fig. 15.The fluorescence trajectory and corresponding on/off blinking frequency distribution of single QD A on (a,b) glass and (c,d) TiO 2 film.The black lines denote the intensity thresholds to separate the on and off state which are set at a level 3σ above the background noise.σ is the standard deviation of background noise.

Fig. 16 .
Fig. 16.The on-state probability density of 10 single QDs with A, B, and C size on (a,b,c) glass and (d,e,f) TiO 2 film.The order of increased size is followed from a to c and from d to f.The spots denote experimental data and lines denote simulation by truncated power law distribution.

Fig. 17
Fig. 17.The off-state probability density of 10 single QDs with A, B, and C size on (a,b,c) glass and (d,e,f) TiO 2 film.The order of increased size is followed from a to c and from d to f.The spots denote experimental data and lines denote simulation by power law distribution.
Fig. 17.The off-state probability density of 10 single QDs with A, B, and C size on (a,b,c) glass and (d,e,f) TiO 2 film.The order of increased size is followed from a to c and from d to f.The spots denote experimental data and lines denote simulation by power law distribution.

Fig. 18 .
Fig. 18.The energy diagram of TiO 2 and QDs with A, B, and C size.
Photo-Induced Electron Transfer from Dye or Quantum Dot to TiO 2 Nanoparticles at Single Molecule Level Photo-Induced Electron Transfer from Dye or Quantum Dot to TiO 2 Nanoparticles at Single Molecule Level www.intechopen.com Photo-Induced Electron Transfer from Dye or Quantum Dot to TiO 2 Nanoparticles at Single Molecule Level353Here, k 21 is the relaxation rate constant from the excited singlet to ground state containing the radiative and non-radiative processes and k et is the forward ET rate constant.k ex is related to the excitation intensity I o (units of erg/cm 2 s) by )www.intechopen.com

Table 1 .
The excited state lifetimes and kinetic data for the single-molecule traces shown in