Rapid Dye Regeneration Mechanism of Dye-Sensitized Solar Cells

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Letter

The Rapid Dye Regeneration Mechanism of Dye-Sensitized Solar Cells Jiwon Jeon, Young Choon Park, Sang Soo Han, William A. Goddard III, Yoon Sup Lee, and Hyungjun Kim J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/jz502197b • Publication Date (Web): 25 Nov 2014 Downloaded from http://pubs.acs.org on November 30, 2014

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The Journal of Physical Chemistry Letters

The Rapid Dye Regeneration Mechanism of DyeSensitized Solar Cells Jiwon Jeon,a Young Choon Park,b Sang Soo Han,c William A. Goddard III,d Yoon Sup Lee,b and Hyungjun Kim*a

a

Graduate School of Energy, Environment, Water, and Sustainability (EEWS), Korea Advanced

Institute of Science and Technology (KAIST), Yuseong-gu, Daejeon 305-701, Korea. b

Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST),

Yuseong-gu, Daejeon 305-701, Korea. c

Center for Computational Science, Korea Institute of Science and Technology, Seoul 136-791,

Republic of Korea. d

Materials and Process Simulation Center, Beckman Institute, California Institute of

Technology, Pasadena, CA 91125, U.S.A.

ACS Paragon Plus Environment

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ABSTRACT. During the light harvesting process of dye-sensitized solar cells (DSSCs), the hole localized on the dye after the charge separation yields an oxidized dye, D+. The fast regeneration of D+ using the redox pair (typically the I-/I3- couple) is critical for the efficient DSSCs. However, the development of kinetic modeling of the dye regeneration process has yet to be fully established and still promote vigorous debates. Here, using comprehensive theoretical calculations, we determined that the inner-sphere electron transfer pathway provide a rapid dye regeneration route of ~4 ps, where the penetration of I- next to D+ to enable an immediate electron transfer forms a kinetic barrier. This explains the recently reported ultrafast dye regeneration rate of a few picoseconds determined experimentally. We expect that our comprehensive understanding of the dye regeneration mechanism will provide a helpful guideline in designing TiO2-dye-electrolyte interfacial systems for better performing DSSCs.

TOC GRAPHICS

KEYWORDS Dye regeneration, Electron transfer, Multiscale simulation, and Dye-sensitized solar cells


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The conversion of sunlight to electricity is one of the most challenging areas for energy generation from renewable natural resources.1 In particular, dye-sensitized solar cells (DSSCs), first proposed by O’Regan and Grätzel,2 are considered most promising due to their low cost and high efficiency, combined with simple conceptual basis for producing photocurrent that mimics nature’s photosynthetic process.3-5 The photo-excited RuII complex dye quickly (< ~100 fs) transfers an electron to the semiconductor nanoparticles, usually TiO2, to produce the DSSC photocurrent, leaving behind the photo-oxidized dye molecule (D+). In order to regenerate the resting dye, the oxidized dye must be reduced by the redox couple, typically iodide/triiodide (I-/I3-), dissolved in the electrolyte. During the course of DSSC operation, we want the kinetics of dye regeneration to occur rapidly to minimize undesirable charge recombination between the hole state of the D+ and the electron state in the conduction band of TiO2, which produces dark current and degrades the energy conversion efficiency. Slow dye regeneration kinetics may also cause stability problems in the dye molecule by increasing the lifetime of the unstable excited or oxidized state. To identify the dye regeneration mechanism and investigate the kinetics of each elementary step, researchers have studied the regeneration process using the flash-photolysis technique coupled with transient absorption (TA) spectroscopic measurements.6-11 However, bleaching experiments invoke many uncertainties; e.g., it is impossible to discern the dye regeneration rate and internal electron-hole recombination rate, and bleaching the system using large enough pulse energy depletes iodides near D+ and thus the observed rate is masked by the diffusion rate of I-. Recently, the most reliable measurement was carried out by Antila et al. using femto- to nano-second TA spectroscopic measurements in 2014.12 In this study, they monitored not only the concentration of D+ but also the electron arrival at the conduction band of


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TiO2, which allows more clear-cut definition of the beginning time of the dye regeneration process (t = 0). Surprisingly, this revealed that the existence of the I-/I3- redox couple within the electrolyte phase enables ultrafast reduction of D+ within only a few picoseconds, which is in stark contrast to the previous reports based on bleaching experiments where the dye regeneration rate is ranging from nanoseconds to microseconds.6-10 Accordingly, to provide mechanistic understanding of the recently observed ultrafast dye regeneration process, we here performed comprehensive theoretical studies to calculate all relevant kinetic constants. One can consider two possible dye regeneration mechanisms3,13,14; single iodide process (SIP): [D++I-] + I- → [D0+I•] + I-

(S1)

[D0+I•] + I- → D0 + I2-•

(S2)

where I- solely transfers an electron to the dye to yield I•, which then eventually yields I2-• by encountering another I- after the diffusion of I• away from the dye (ET precedes the I-I bond formation), and two iodide process (TIP): [D++I-] + I- → [D+…I-…I-]

(T1)

[D+…I-…I-] → D0 + I2-•

(T2)


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where I- awaits the approach of a second I- to form an I-I bond and then transfers an electron to the dye, yielding I2-• (ET is after I-I bond formation). The characteristic difference between SIP and TIP is which step between ET and I-I bond formation will precede the other one. The thermodynamic driving force of TIP is higher than SIP (the standard reduction potential (E0) of (I•/I-) is 0.1 V higher than the E0 of (D+/D0), whereas the E0 of (I2-•/2I-) is 0.3 V lower than the E0 of (D+/D0))19,20,29; however, in TIP, the I-I bond formation process between two iodides, which requires the collision of two negatively charged Iwithin the same solvation shell, should be kinetically disfavoured. Although theoretical investigations have been performed to reveal which mechanism will dominate,15-18 they were mostly focused on investigating the thermodynamic stability and atomistic structures of [D++I-] complex,15,16 which was inappropriate since both mechanisms can start from [D++I-] complex as shown in (S1) and (T1). More recently, Asaduzzaman et al. and Liu et al. performed DFT calculations coupled with implicit solvation to compare the free energy barrier for SIP and TIP;17,18 however, no decisive conclusion has been drawn. The former group claimed the dominance of TIP, but the latter group claimed that SIP can have the lower kinetic barrier than TIP for certain geometry. Based on the recent experimental result, however, we note that TIP can hardly explain the ultrafast dye regeneration kinetics of a few picoseconds since the coulomb repulsion between two iodides within the same solvation shell is estimated as enormous (it is already > 1.4 eV at ~10 Å distance). Thus, if there exists a sufficiently fast ET pathway based on SIP explaining the recent experiment, the more straightforward SIP is ought to be dominant over the course of dye regeneration process.


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To grasp an atomistic level of understanding, we first performed the molecular dynamics (MD) simulation to include full atomistic details of solvent molecules (i.e., explicit solvents) since the solvation structure and dynamics should be important in understanding ET kinetics.19 Our MD simulation system consists of anatase TiO2 with bilayers, N3 dye (cis[RuII(dcb)2(NCS)2], dcb = 4,4’-dicarboxy-2,2’-bipyridine), and an AN based electrolyte with ionic salts.20 (See section 3 of supporting information (SI) for the detailed descriptions of simulation system, and force-field validations are in Figures S1-S4.) Although we investigated two different dye configurations on the TiO2 surface, ‘upright’ and ‘sideways’ in Figure 1a, we found only a marginal difference in those two configurations, and thus we discuss mostly about the ‘upright’ configuration case while the other case is shown in SI. From the last 10 ns of our 22 ns MD simulation trajectories, we calculated the radial distribution function of Ru and I-, gRu-I(r) and found two peaks as shown in Figure 2a (see Figure S5a for the ‘sideways’ dye orientation): one located at ~6 Å from Ru, which is within the same solvation shell as D+ (innersphere), but with a very low intensity (0.03 average occupation) so that it can be referred as a trapped state with a short life-time, the other located at ~10 Å with a high intensity (1.31 average occupation), where each of D+ and I- is fully solvated with AN (outer-sphere). We referred this state as a [(D+)+(I-)] complex in the mechanism of (S1) or (T1) with a substantial life-time (parentheses were introduced to clarify that D+ and I- have their own solvation shells). As a first possibility, we considered a direct ET pathway from I- located at the outersphere position to D+, i.e., outer-sphere electron transfer (OSET). The driving force for this ET is


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the fluctuations in the solvation shell (i.e., the change in the polarization of the media). This long-range ET across the solvation shell is often non-adiabatic due to the weak long-ranged interactions between the fully solvated donor (I-) and the fully solvated accepter (D+). Once the I௅ோ approaches D+ (while preserving its solvation shell), the rate constant for long-range ET (݇ா் ) ௅ோ determines the overall rate constant for OSET (kOSET), ݇ைௌா் = ݇ா் (Figure 2b).

௅ோ using Marcus theory, we first considered the free energy for the To estimate the ݇ா்

reduction of I- (Gred,I) and that for the reduction of D+ (Gred,D), which are defined as Gred,I = G(I-|I-) – G(I•|I•)

(1)

Gred,D = G(D0|D0) – G(D+|D+)

(2)

where G(A|B) denotes the free energy of the A state associated with the equilibrium configuration of the B state. The Nernst equation leads to ∆G = Gred,D – Gred,I = -nF∆E0, where ∆E0 is the difference between the E0 of (I•/I-) and the E0 of (D+/D0). In our previous work,21 we demonstrated that DFT coupled with Poisson Boltzmann Implicit Solvation (PBIS) leads to a result in reasonable agreement with the experimental E0 values of iodine-related species, after adding an additional correction for the spin-orbit coupling (SOC) effect that we computed from separate spin-orbit DFT (SODFT) calculations (Figure S6S7).21 Using the same procedure, we obtained Gred,I = -5.517 eV and Gred,D = -5.444 eV, resulting in E0 = 0.072 V, which is consistent with the experimental value of ~0.1 V.22 We then defined the reorganization energy for iodide (λI) and that for dye (λD) as follows:

λI = G(I•|I-) – G(I•|I•)

(3)


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λD = G(D0|D+) – G(D0|D0)

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(4)

We considered that most of λD is due to the reorganization of the ligands coordinating the Ru center (dcb’s and NCS’s); therefore, we calculated λD using the difference of the single-point DFT energy of D0 at the optimized geometry of D+ and the energy of D0 at the optimized geometry of D0 in solvent (Figure 3a). Because we performed all of the calculations within PBIS, the relaxation of the outside implicit solvent molecules was artificially included in our calculations. However, we expect that the contribution of the outside solvent molecules to be marginal. These calculations yield λD = 0.263 eV. For the estimation of λI, we defined the vertical excitation energy (Gvert,I) of the Iaccompanying the unrelaxed state of the first solvation shell of AN, i.e., the instantaneous binding energy of an electron to the cluster of I- solvated by the first coordination shell, as follows: Gvert,I = G(I•|I-) – G(I-|I-)

(5)

Under the assumption that the relaxation process near I- is dominated by the relaxation of the first coordination shell, we sampled 11 clusters of I- coordinated with the first solvation shell of AN from our MD simulations (see Figure S8), which represent I- states dissolved in AN solvent. We then computed Gvert,I as the average of the ionization energies of these clusters, which were calculated from single-point DFT calculations of the sampled clusters within PBIS with and without a negative charge. The average among the 11 sampled clusters leads to 6.328 eV, and the SOC adjustment (which is estimated from the difference between the gas phase energies of I- and


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I• from the SODFT considering that no quenching of the SOC occurs by the solvation) finally yields Gvert,I = 6.038 eV. Substituting Eqs. (1) and (5) into Eq. (3) leads to

•

λI = Gvert,I + Gred,I = 0.522 eV, and

•

a total reorganization energy, λ (=λD+λI) = 0.784 eV.

Using Marcus theory for the OSET, we predict that the barrier for ET, ∆G‡= (λ+∆G)2/(4λ) = 0.234 eV

(6)

௅ோ This result yields a rate for the long-range ET of >

400 ps, which is too slow to explain the experimentally observed rate constant of a few picoseconds.12 As an alternative, we considered another ET pathway consisting of two steps; (1) Ilocated at the outer-sphere position (~10 Å from Ru) is desolvated and drawn near to D+ (to the inner-sphere position; ~6 Å from Ru) to form a trapped state (penetration process), and then (2) I- transfers an electron to D+ through an orbital-orbital interaction (short-range ET). This ET process is denoted as an inner-sphere ET (ISET), where kinetic constants for the penetration and ௌோ short-range ET are respectively denoted as kp and ݇ா் (Figure 2b).

ௌோ Our previous DFT studies21 found that nearly instantaneous kinetics of ET (1/݇ா் ~

order of femtoseconds) is available when I- locates near RuIII within 5-6 Å and the p-orbital of S


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(of NCS ligand) mediates the p-orbital of I- and the empty t2g d-orbital of RuIII, which is also in consistent with other previous theoretical studies17,18. This implies that the penetration processes to certain sites where the short-range ET is possible are only responsible for the fast dye regeneration kinetics. In this respect, we considered three different penetration pathways:

•

the penetration to the bottom site of D+ forming (D++I-)B, where the short-range ET is unaffordable,

•

the penetration to the side of D+ to form (D++I-)S, and

•

the penetration to the top site of D+ to form (D++I-)T. In the latter two pathways, shortrange ET occurs.

(refer Figure S9a-b for the atomistic structure of each site.) In these penetration processes, the electrostatic attraction of I- and D+ provides a driving force, while the partial loss of the strong solvation shell of the small I- ion (Figure S10) retards the dynamics. As a result, the overall kinetics of ISET (kISET) should be dominated by the penetration ௌோ ≈ 1/kp). kinetics for the latter two pathways (1/kISET = 1/kp + 1/݇ா்

From MD simulation, penetration events were detected with a faint peak at inner-sphere regime (~6 Å) of gRu-I(r) (Figure 2a). However, the number of penetration events sampled from our MD simulations was not sufficient to perform a statistically meaningful analysis to compute the kp. To better sample the rare penetration events, we performed MD simulations in the constrained reaction coordinate dynamics ensemble by adopting ‘Bluemoon’ ensemble sampling (detailed procedure is in section 4 of SI).23 Here, the simulation was constrained to sample states


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along the reaction path, thus enabling sufficient sampling for states with low equilibrium populations (e.g., transition states). Figure 4 shows the entire free energy profile of A(r), where the free energy barrier for the penetration, ∆A‡p, was calculated as 0.098 eV. We also separately estimated the rates for the three different penetration pathways into the side site (kps), the top site (kpT), and the bottom site (kpB) (see Figure S9b). By measuring the dwell time at each site (Figure S11), we separate the rdependent free energy quantity, A(r), into the distance (r) and orientation-dependent free energy quantities: AS(r), AT(r), and AB(r) (mathematical details are given in section 4 of SI). This leads the free energy barriers for the penetration into the side, top, and bottom sites to ∆A‡pS = 0.099 eV, ∆A‡pT = 0.097 eV, and ∆A‡pB ≫ kBT, respectively (Table. S1). Under the assumption that ௌோ ݇ா் ≫ kp and the steady-state approximation, these results lead to an overall rate for the ISET,

kISET ≈ kpS + kpT = 2.5 × 1011 s-1 (kISET ≈ kpS + kpT + kpB = 2.3 × 1011 s-1 for the sideways dye orientation). We note that there is no penetration into the bottom site for the upright dye orientation due to the blocking bottom site by the TiO2 surface. These predictions lead to a reduction time scale of ~4 ps, which is at least 100 times faster than the time scale for the OSET (>> 400 ps), and in agreement with the experimental data of a few picoseconds. Thus, we conclude that the ISET pathway is kinetically much more favorable than the OSET pathway. In our simulations based on classical force fields, we note that the electron relaxation effect between D+ and I- at the transition state is not taken into consideration. If we consider such an effect, the barrier is expected to be even more lowered, thus the time scale for ISET becomes < 4 ps. Therefore, we conclude that ISET is the dominant dye regeneration pathway which is responsible for the ultrafast dye regeneration route.12


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To complete the mechanism, after the I- transfers its electron to D+, the product I• reacts with another I- to form an I-I chemical bond, yielding I2-•, i.e., (S2). To estimate the rate for I2-• production after ISET, we instantaneously changed the charge distribution of D+ and I- at the trapped state (r = ~6 Å) into D0 and I• during MD simulations to mimic instantaneous ET process. We used a Morse potential to describe the pair potential between I- and I•, the parameters of which were optimized to reproduce the bond energy and vibrational frequency of I2-•. The overall time scales for the I2-• formation were calculated to be in the range of 100 to 300 ps from three independent simulation sets (Figure S12). Considering that our MD simulation results in a slightly slower diffusion of I- (DI-sim. = 0.9 × 10-9 m2s-1 (see Figure S13) versus DI-exp. = 1.7 × 10-9 m2 s-1.24), we expect that the actual time scale for I2-• formation may be faster by a factor of 2. Although 3 data points is not sufficient to provide a statistical treatment, the computed time scale for I2-• formation agrees fairly well with the experimental measurement of the rate constant, (2.4 ± 0.2) × 1010 M-1s-1,8 which yield a time constant of ~70 ps for a Iconcentration is 0.6 M, as determined in our simulations. In summary, we here presented that the ISET-SIP mechanism is responsible for the experimentally reported rapid dye regeneration based on our comprehensive set of simulation studies. Figure 5 shows the overall dye regeneration mechanism and the calculated relevant time scales. Our full set of theoretical characterizations of the rates of various ET pathways provides information to help resolve many controversies regarding the dye regeneration mechanism. Now that the reduction mechanism is understood to involve the ultrafast ISET involving a single iodide, one can start considering how to enhance the dye regeneration kinetics by redesigning the ligands to maximize the interaction of iodide with the dye molecule.


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We further note that our current estimation on the ET rate using transition state theory (TST) is based on quasi-equilibrium approximation. However, when the kinetics becomes extremely fast, contribution of non-equilibrium non-adiabatic process could be substantial. For the example of the charge separation and recombination process in DSSC with femtoseconds order, previous studies have unveiled that non-equilibrium non-adiabatic effect becomes substantial.25-27 Considering the 4 ps time scale of dye regeneration, non-equilibrium nonadiabatic effect is thought not to be significant as the charge separation and recombination dynamics; however, more in-depth investigation and clarification of the contribution of nonequilibrium non-adiabatic effect on dye regeneration kinetics should be of great interest for future study. We also anticipate that our current detailed understanding of the reduction kinetics may be relevant for other photoelectrochemical devices involving charge transfer processes.


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Figure 1. Final structures of TiO2-dye-electrolyte interfacial systems taken after 22 ns of NVT MD simulations. Two different dye configurations are considered: (a) the ‘upright’ configuration and (b) the ‘sideways’ configuration. The electrolyte phase consists of 30 I-, 5 I3-, and 34 Li+ within 957 acetonitrile solvent molecules. The simulation cell size is 39.09 Å × 39.13 Å × 64.42 Å and contains 6840 atoms in total.


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Figure 2. Radial distribution function of Ru and I-, gRu-I(r), and schematic showing the competition between the OSET pathway and the ISET pathway. (a) gRu-I(r) is obtained from the last 10 ns of the NVT MD simulations with the upright dye configuration (gRu-I(r) for the sideways dye configuration is shown in Figure S5a). There are two peaks at ~6 Å (with integrated population of 0.03) and ~10 Å (with integrated population of 1.31). As representatively in the figure inset , at r = ~6 Å, the solvation shell of I- is merged with that of D+, yielding partial desolvation, whereas at r = ~10 Å, both I- and D+ separately develop their own solvation shells (the first coordination shell of I- is colored in purple). Thus, we define r = ~6 Å as the inner-sphere regime which is comparable to the Ru-I distance from DFT-optimized structures within the implicit solvents (~5 Å) and r = ~10 Å as the outer-sphere regime. (b) Schematic showing the competition between the OSET pathway and the ISET pathway. The


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iodide located at the outer-sphere regime can either transfer an electron to D+ across ~10 Å (OSET, red color) or it can penetrate into the inner-sphere regime while partially losing the solvation shell to inject an electron directly into D+ (ISET, blue color).


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Figure 3. Schematics showing the (a) dye reduction process and (b) iodide oxidation process. Here the (A|B) notation denotes the A state associated with the environments accommodated for the B state. The overall free energy changes (Gred,D or -Gred,I) can be partitioned into a combination of the vertical excitation energy that is required for adding/subtracting an electron to the redox center without involving geometric relaxation (Gvert,D or Gvert,I) and the reorganization energy required for the geometric relaxations of environments surrounding the redox center (λD and λI). We show the Ru center before ET (RuIII) in green, the Ru center after ET (RuII) in orange, the I center before ET (I-) in magenta, and the I center after ET (I•) in green. Using Marcus theory for the outer-sphere electron transfer (OSET), we determined the electron transfer (ET) rate by the free energy difference between the states before and after ET, ∆G = Gred,D - Gred,I, and the reorganization energy, λ = λD + λI. To evaluate the ET rate using Marcus theory, we computed ∆G using separate density functional theory (DFT) calculations of the dye


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molecule and of the single I atom in conjunction with the Poisson Boltzmann implicit solvation (PBIS) method. We then computed λD by comparing the DFT self-consistent field energies (SCFE) while fixing and relaxing the geometry of the ligands of the dye molecule. Rather than directly evaluating λI, we instead computed Gvert,I from the DFT SCFEs using clusters of iodide surrounded by acetonitrile solvent molecules in the first-coordination shell that were sampled from the classical MD simulation trajectories (Figure S8).


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Figure 4. Calculated free energy profile, A(r) as a function of the Ru…I- distance (r). We show a representative case for the upright configuration (the sideways configuration case is shown in Figure S5b). For the regime where the sampling quality of the radial distribution function between Ru and I- (gRu-I(r); Figure 3) is high (r > 10.5 Å), we computed A(r) by directly converting gRu-I(r). For r < 10.5 Å, we sampled intensively the penetration events by using constrained MD simulations. From a series of MD simulations performed while constraining r at various distances, we obtained the r-dependent mean force (MF) profile, shown as a blue dotted curve. The integration of the blue curve leads to the potential of mean force (PMF), which is equivalent to the free energy profile. we determined The energy barrier for the penetration of I-, to be ∆A‡P, = 0.098 eV, leading to a rate constant for penetration (kp) of 2.5 × 1011 s-1 and a time scale of ~4 ps.


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Figure 5. Overall dye regeneration mechanism. After electron injection from the photoexcited dye (RuII*) to TiO2, a hole remains at the Ru center of the oxidized dye, D+ (left bottom figure). Next, I- located ~10.5 Å from the Ru center penetrates to a location within ~6 Å of D+ over a period of ~4 ps and immediately transfers an electron to the Ru center to reduce D+ (top figure, short-range electron transfer). After the inner-sphere electron transfer (ISET) proceeds, the electrostatic interaction between the dye molecule and iodine atom abruptly changes, allowing the product I• to diffuses away from D0. After 100-300 ps of diffusion, I• encounters another I- to form I2-•.


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ASSOCIATED CONTENT Supporting Information. Section 1 includes additional figures. Section 2 includes table and optimized DSSC force field parameters. Section 3 provides computational details. Mathematical details for the free energy profile and barriers are in section 4. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *Email: [email protected] Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was mostly supported by the Global Frontier R&D Program (2013M3A6B1078884) on Center for Hybrid Interface Materials (HIM) funded by the Ministry of Science, ICT & Future Planning. S.S.H. thanks the financial support from the Korea Institute of Science and Technology (Grant No. 2E24630). W.A.G. received support from the Joint Center for Artificial Photosynthesis, a DOE Energy Innovation Hub, supported through the Office of Science of the U.S. Department of Energy under Award Number DE-SC0004993.


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Rapid Dye Regeneration Mechanism of Dye-Sensitized Solar Cells

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