Tuning the HOMO and LUMO Energy Levels of Organic Dyes with N

Apr 10, 2013 - Tuning the HOMO and LUMO Energy Levels of Organic Dyes with N-Carboxomethylpyridinium as Acceptor To Optimize the Efficiency of Dye-Sen...
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Tuning the HOMO and LUMO Energy Levels of Organic Dyes with N‑Carboxomethylpyridinium as Acceptor To Optimize the Efficiency of Dye-Sensitized Solar Cells Ming Cheng,† Xichuan Yang,*,† Fuguo Zhang,† Jianghua Zhao,† and Licheng Sun*,†,‡ †

State Key Laboratory of Fine Chemicals, DUT-KTH Joint Education and Research Centre on Molecular Devices, Dalian University of Technology (DUT), 2 Linggong Road, 116024 Dalian, China ‡ School of Chemical Science and Engineering, Centre of Molecular Devices, Department of Chemistry, KTH Royal Institute of Technology, Teknikringen 30, 10044 Stockholm, Sweden S Supporting Information *

ABSTRACT: Different from traditional D−π−A sensitizers (the traditional design concept of the organic dyes is the donor−π-linker−acceptor structure), a series of organic dyes with pyridinium as acceptor have been synthesized in order to approach the optimal energy level composition in the TiO2−dye− iodide/triiodide system in the dye-sensitized solar cells. HOMO and LUMO energy level tuning is achieved by varying the conjugation units and the donating ability of the donor part. Detailed investigation on the relationship between the dye structure and photophysical, photoelectrochemical properties and performance of DSSCs is described. For TPA-based dyes, by substituting the 3-hexylthiophene group with a carbon−carbon double bond as π-spacer, the bathochromic shift of absorption spectra and higher current density (Jsc) are achieved. When the methoxyl and n-hexoxyl are introduced into CM301 to construct dyes CM302 and CM303, the absorption peak is red-shifted compared with that of CM301 due to the increase of the electron-donating ability. The devices fabricated with sensitizers CM302 and CM303 show higher Jsc and open-circuit voltage (Voc) than those of the device sensitized by CM301, which can be mainly attributed to the wider incident photon-to-current conversion efficiency (IPCE) response and the suppression of electron recombination between TiO2 film and electrolyte, respectively. The effects of different electron donors in DSSCs application are compared, and the results show that sensitizers with a phenothiazine (PTZ) electron-donating unit give a promising efficiency, which is even better than the TPA-based dyes. This is because the PTZ unit displayed a stronger electron-donating ability than the TPA unit (oxidation potential of 0.82 and 1.08 V vs the normal hydrogen electrode (NHE), respectively). For sensitizers CM306 and CM307, the introduction of 1,3- bis(hexyloxy)phenyl increases the donating ability of the donor part. Furthermore, the presence of long alkyl chains decreases the dye adsorption amount on the TiO2 surface, which diminishes dye aggregation and the electron recombination effectively, though, with less adsorption amount of dyes on TiO2, the device sensitized by dye CM307 obtained the best conversion efficiency of 7.1% (Jsc = 13.6 mA·cm−2, Voc = 710 mV, FF = 73.6%) under AM 1.5G irradiation (100 mW·cm−2).

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INTRODUCTION

tional design concept of the organic dyes is the donor−πlinker−acceptor structure, also named D−π−A configuration. Up to now, many kinds of organic dyes based on coumarin,4−7 perylene,8−11 triarylamine (TPA),12−21 carbazole,22−25 indoline,26−28 tetrahydroquinoline,29,30 phenothiazine, and phenoxazine31−36 as donnor and cyanoacetic acid as acceptor have been developed and have shown potential commercial application for DSSCs. In addition, due to the strong electron withdrawing ability, pyridinium has also been successfully utilized in DSSCs application.37 In order to absorb the sunlight as much as possible, a broad absorption spectrum of the dye is

Recently, concern about the usage of classical energy sources, such as fossil fuels, has readily increased due to the environmental and long-term shortage issues.1 Dye-sensitized solar cells (DSSCs) provide a kind of more economical and effective method to carry out the energy conversion from solar light to electricity since O’Regan and Grätzel reported that in 1991.2 A typical DSSC consists of a wide band gap semiconductor photoanode, an anchored molecular sensitizer, a redox electrolyte, and a counter electrode.3 As one of the crucial components in DSSCs, the photosensitizers have always attracted increased interest in the past decades. The organic dyes exhibit a more brilliant future in commercial applications due to low material costs, easy synthesis, high molar extinction coefficients, and environmental friendly materials.3 The tradi© XXXX American Chemical Society

Received: November 18, 2012 Revised: April 6, 2013

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Figure 1. Molecular structure of the sensitizers.

min. After the film was cooled to room temperature, it was immersed into a 0.2 mM dye bath (CH2Cl2) with 2 mM chenodeoxycholic acid (CDCA) and kept for 16−17 h in the dark at room temperature. The electrode was then rinsed and dried with EtOH. The hermetically sealed cells were fabricated by assembling the dye-loaded film as the working electrode and Pt-coated conducting glass as the counter electrode separated with a hot-melt Surlyn 1702 film (25 μm, Dupont). The redox electrolyte containing 0.04 M I2, 0.06 M LiI, 0.4 M 4-tertbutylpyridine (4-TBP), and 0.6 M 3-propyl-1,2-dimethylimidazolium iodide (DMPII) in MeCN was introduced through a hole drilled in the back of the counter electrode. Finally, the hole was also sealed with the Surlyn film. Adsorption Amount of Dyes on TiO2. The dye-loading on a TiO2 film was estimated from the dye desorption in 0.1 M tetrabutylammonium hydroxide (TBAOH) MeOH solution by means of UV−vis absorption spectroscopy; two pieces of TiO2 films with a total of 1 cm2 (0.5 cm2 per piece) were used. Photocurrent Density−Voltage (J−V) and Electron Lifetime Measurements. The photocurrent−voltage (J−V) properties were measured under AM 1.5G irradiation (100 mW·cm−2) (16S-002, Solar Light Co. Ltd., USA). The incident light intensity was 100 mW·cm−2 calibrated with a standard Si solar cell. The working areas of the cells were masked to 0.159 cm2. The date was collected by an electrochemical workstation (LK9805, Lanlike Co. Ltd., China). The measurement of the incident photon-to-current conversion efficiency (IPCE) was

desirable. Usually, extension of the π-conjugated system (introducing more π units) is a feasible strategy to complete the mission. However, the passive effect is that the large πconjugated system leads to poor photovoltaic properties due to dye aggregation as well as electron recombination issues. To diminish the dye aggregation and the electron recombination, the alkyl chain was often introduced into linker or donor subunits. Consequently, the efficiency can usually be greatly improved. Herein, we further develop this concept to design the cationic dyes (CM301−CM307, see Figure 1), through modifying both donor and linker units with the long alkyl chains, and also investigate the effect of different donors and linkers on the photophysical, photochemical, and photovoltaic properties.

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EXPERIMENT Preparation of DSSCs. A layer of 2 μm TiO2 (18 NR-T, Dyesol) was coated on the F-doped tin oxide conducting glass (TEC15, 15Ω/square, Pilkington, USA) by screen printing and then dried for 5 min at 125 °C. This procedure was repeated 6 times (12 μm) and finally coated with a layer (4 μm) of TiO2 paste (DHS-SLP1, Heptachroma, China) as the scattering layer. The double-layer TiO2 electrodes (area: 6 mm × 6 mm) were heated under an air flow at 520 °C for 60 min and then cooled to room temperature. The sintered film was further treated with a 40 mM TiCl4 aqueous solution at 70 °C for 30 min, then washed with water, and annealed at 520 °C for 60 B

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performed with a Hypermono light (SM-25, Jasco Co. Ltd., Japan). Electron lifetimes for the solar cells were measured using a red-light-emitting diode (1 W) as the light source, and electron lifetime was tested by monitoring transient photovoltage response after a small perturbation of light intensity. Photophysical and Electrochemical Measurements. The absorption spectra were recorded on HP8453 (USA). Electrochemical redox potentials were obtained by cyclic voltammetry (CV) on an electrochemistry workstation (BAS100B, USA). The working electrode was a glass carbon disk electrode; the auxiliary electrode was a Pt wire; and Ag/Ag + was used as the reference electrode. TBAPF6 was used as supporting electrolyte in CH3CN. The ferrocenium/ferrocene (Fc/Fc+) redox couple was used as an internal potential reference. Electrochemical Impedance Spectroscopy (EIS) Tests. Electrochemical impedance spectroscopy (EIS) tests were carried out using an impedance/gain-phase analyzer (PARSTAT 2273, USA) in the frequency range 106 to 10−2 Hz, using 10 mV AC amplitude, under dark conditions with an applied bias voltage −0.75 V.

Table 1. Optimized Structure and Electron Distribution in HOMO and LUMO Levels of the CM Series Dyes

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RESULTS AND DISCUSSION Synthesis. The structures of triphenylamine (TPA) dyes (CM301−CM305) and phenothiazine (PTZ) dyes (CM306 and CM307) are shown in Figure 1. All of the intermediates and dyes have been prepared according to several classical reactions, and detailed synthetic procedures are described in the Supporting Information. Calculation Study. To understand the geometrical configuration and electron distributions, molecular orbital calculations of dyes CM301−CM307 were performed with the TD−DFT on B3LYP/6-31G(+d), and the isodensity surface plots of CM series dyes are shown in Table 1. All of these dyes have good charge separation. The HOMOs of dyes are delocalized over the donor part. and the LUMO contains the delocalized π* framework, with a sizable electron density distribution on N-(carboxymethyl)pyridinium. Photophysical Properties. Absorption spectra of the dyes CM301−CM307 in a diluted solution of CH2Cl2 and adsorbed onto TiO2 films are shown in Figure 2. The corresponding photophysical data are collected in Table 2. CM304 shows an obvious red-shifted absorption peak (λmax) and higher extinction coefficient compared with CM301 due to the stronger π-conjugated system caused by the smaller twist angle between the TPA unit and carbon−carbon double bonds, which has been proved by the DFT calculation (see Table 1). A similar result was also found between dyes CM302 and CM305. Interestingly, when the methoxyl and n-hexoxyl groups were introduced into CM301 to construct dyes CM302 and CM303, the absorption peak was red-shifted from 455 nm to 481 and 486 nm, respectively. Similarly, compared with CM304, the presence of the methoxyl moiety in CM305 made the absorption spectrum of CM305 red-shift 21 nm. This is mainly because of the increase of donating ability of the electron donor. The dyes CM306 and CM307 with PTZ derivatives as donor show apparent red-shifted absorption peaks (λmax) compared with that of TPA dyes with the same πspacer and acceptor, and this is mainly because of the stronger donating ability of phenothiazine derivatives (see Table 2, 0.82 and 1.08 V vs the normal hydrogen electrode (NHE) for PHZ and TPA, respectively). With the introduction of 1,3bis(hexyloxy)phenyl into the fourth position of phenothiazine

Figure 2. Absorption spectra of CM301−CM307 dyes in CH2Cl2 solution (a) and on TiO2 films (b). C

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Table 2. Photophysical and Electrochemical Properties of CM Series Dye dye

λmaxa in CH2Cl2 (nm)

ε at λmax (M−1·cm−1)

λmaxb on TiO2 (nm)

E0−0c (V)

Eoxd (V) (vs NHE)

ELUMOe (V) (vs NHE)

CM301 CM302 CM303 CM304 CM305 CM306 CM307

455 481 486 483 504 506 520

29400 29900 25900 38400 33400 24100 24000

441 470 466 460 494 489 500

2.21 2.13 2.10 2.17 2.05 2.01 2.00

1.00 0.85 0.83 1.08 0.93 0.82 0.76

−1.21 −1.28 −1.27 −1.09 −1.12 −1.19 −1.24

Absorption spectra were measured in CH2Cl2 solution (2 × 10 −5 M). bAbsorption spectra on TiO2 film were measured with dye-loaded TiO2 films immersed in CH2Cl2 solutions. cE0−0 was determined from intersection of the tangent of absorption on TiO2 film and the X axis by 1240/λ. dThe oxidation potentials of the dyes were measured in CH2Cl2 solutions with TBAPF6 (0.1 M) as electrolyte and ferrocene/ ferrocenium (Fc/Fc+) as an internal reference. eELUMO was calculated by Eox − E0−0. a

Figure 3. Scheme of HOMO and LUMO levels of dyes CM301− CM307.

CM305. When phenothiazine derivatives were employed as donors, dyes CM306 and CM307 show more negative HOMO levels than those of TPA dyes CM301−CM303 with the same π-conjugated system and acceptor. The LUMO levels of these dyes are much more negative than the conduction band (CB) of the TiO2 level (−0.5 V vs NHE), which means that the electrons could be efficiently injected into the CB of TiO2 from the excited dyes.38 Furthermore, the large difference between the TiO2 CB and the LUMO levels of the dyes suggests that TBP can be used in the electrolyte to move the CB negatively, yielding higher photovoltage. Photovoltaic and Photoelectrochemical Properties. The photocurrent density−photovoltage (J−V) curves of DSSCs based on dyes CM301−CM307 performed under standard AM 1.5G illumination are shown in Figure S1 of the Supporting Information and in Figure 4. The corresponding

in CM306, the absorption peak of CM307 is red-shifted 14 nm compared with that of CM306. The dyes CM301−CM307 have obvious blue-shifted absorption spectra on the TiO2 surface. To check the effect of long alkyl chains in dyes, the adsorption amount of CM series dyes on a TiO2 film was tested. According to dye adsorption amount measurements (see Table 3), it was found that CM304 dye shows a greater Table 3. Adsorption Amount of CM Series Dyes on TiO2 Film dye

dye-load (mol·cm−2) (×10−8)

CM301 CM303 CM304 CM306 CM307

2.5 2.0 3.1 1.8 1.6

adsorption amount on a TiO2 film (3.1 × 10−8 mol·cm−2) than CM301 (2.5 × 10−8 mol·cm−2), although the CDCA has been added into the dye-bath to diminish the dye aggregation. This is mainly because the dye CM304 with double carbon bonds as πspacer has a good planarity. n-Hexoxyl was introduced in the TPA unit to build dye CM303, and the adsorption amount decrease to 2.0 × 10−8 mol·cm−2, indicating that the introduction of n-hexoxyl can suppress aggregation effectively. Featuring the 1,3-bis(hexyloxy)phenyl in CM306, the dye CM307 has least adsorption amount, just about 1.6 × 10−8 mol·cm−2. Electrochemical Properties. The electrochemical properties of CM301−CM307 are shown in Table 2 and Figure 3. The oxidation potentials (Eox) of these dyes were measured by cyclic voltammetry. The first oxidation potential corresponds to the HOMO level of the dye. The HOMO levels of all the dyes are more positive than the redox potential of I−/I3− (0.42 V vs NHE),38 which means that the oxidized dyes can be regenerated effectively. For dyes CM302 and CM303, the introduction of methoxyl and n-hexoxyl groups in TPA makes the HOMO levels more negative compared with that of CM301 due to the increase of electron donating ability. A similar result was also detected between dyes CM304 and

Figure 4. J−V curves of DSSCs based on CM series dyes.

photovoltaic data are collected in Tables 4 and 5. From the test results, we can see that efficiency values ranging from 2.6% to 6.7% have been obtained for the devices sensitized by CM301, CM303, CM304, and CM307, respectively, without CDCA. Addition of CDCA has a beneficial effect on the overall cell performances: both of the Jsc and Voc of the devices sensitized by these three dyes increase. For CM304, with the addition of CDCA, the Voc increases greatly (from 614 mV without CDCA to 666 mV with saturated CDCA); at the same time, the Jsc is also improved; correspondingly, the η is enhanced. With 2.0 × 10−3 M CDCA, the devices sensitized by CM304 show the highest efficiency, of 4.2%. For CM301, CM303, and CM307, the improvements of Jsc, Voc, and η are much smaller, compared with that of CM304. The results indicate that the dye D

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Table 4. Photovoltaic Performance of DSSCs Based on the CM Series Dyes dye

CDCA (M)

Voc (mV)

Jsc (mA·cm−2)

FF (%)

η (%)

CM301

0 1 × 10 −3 2 × 10 −3 saturated 0 1 × 10 −3 2 × 10 −3 saturated 0 1 × 10 −3 2 × 10 −3 saturated 0 1 × 10 −3 2 × 10 −3 saturated

643 662 670 673 670 686 690 697 614 642 660 666 706 708 710 715

6.6 7.9 7.6 7.2 11.9 12.5 12.3 11.3 5.9 7.4 8.6 8.1 13.1 13.7 13.6 12.4

73.8 72.8 75.1 74.9 74.1 73.1 73.8 74.2 72.6 73.1 72.7 73.1 72.3 72.4 73.6 74.1

3.1 3.8 3.8 3.6 5.9 6.2 6.3 5.8 2.6 3.4 4.2 3.9 6.7 7.0 7.1 6.6

CM303

CM304

CM307

Figure 5. IPCE spectra of DSSCs based on CM series dyes.

the TPA units, sensitizers CM302 and CM303 show a higher and wider spectral response resulting in a higher Jsc value. Similar results can also be detected between dyes CM304 and CM305, CM306 and CM307, respectively. In order to reveal the reasons for the increased photovoltage, the lifetime of some dyes based DSSCs and band-edge shifts for different dyes were measured and the test results were shown in Figures 6 and 7. As shown in Figure 6, the measurement of the

Table 5. Photovoltaic Performance of DSSCs Based on the CM Series Dyes dye

Voc (mV)

Jsc (mA·cm−2)

FF (%)

η (%)

CM301 CM302 CM303 CM304 CM305 CM306 CM307

670 681 690 660 672 702 710

7.6 11.3 12.3 8.6 11.9 13.1 13.6

75.1 73.2 73.8 72.7 73.1 74.8 73.6

3.8 5.6 6.3 4.2 5.9 6.9 7.1

aggregation is diminished to some extent with the introduction of long alkyl chains on the donor part and 3-hexyl thiophene. Under optimized conditions, the device sensitized by CM301 gave an efficiency of 3.8% with a short-circuit photocurrent density (Jsc) of 7.6 mA·cm−2, an open-circuit photovoltage (Voc) of 0.67 V, and a fill factor (FF) of 75.1%. Replacing the 3hexylthiophene group with a carbon−carbon double bond to construct the dye CM304, the Voc value was slightly decreased to 0.66 V but with some increase of photocurrent and yielding a higher efficiency of 4.2% under the same light illumination. The increase of Jsc can be mainly attributed to the higher IPCE between 450 and 650 nm. Similar results were also observed between CM302 and CM305. Featuring the methoxyl and nhexoxyl groups in the TPA units, the dyes CM302 and CM303 rendered a higher Jsc and Voc value. The increase of Jsc can be mainly attributed to the enhancement of the donating ability of the donor part. With the enhancement of the donating ability, a red-shifted absorption spectrum of dye and much higher IPCE spectrum were obtained. Similarly, the device sensitized by CM305, which is built by introducing methoxyl into the TPA unit in dye CM304, also showed a higher Jsc and Voc value, corresponding to a much higher efficiency. When phenothiazine derivatives were employed as donor part to construct the dyes CM306 and CM307, both the Voc and Jsc values were improved compared with the TPA dyes, hence yielding an ideal efficiency of 6.9−7.1% under the same conditions. From the IPCE spectra of DSSCs (Figure 5) based on CM series dyes one can see that increasing the donating ability of the donor part is beneficial to improve the efficiency of DSSCs. For example, by featuring the methoxyl or n-hexoxyl groups in

Figure 6. Electron lifetimes as a function of open-circuit voltage for DSSCs based on CM series dyes.

Figure 7. Evolution of cell capacitance as a function of photovoltage for films with different sensitizers (CM301, CM303, CM304, and CM307).

injected electron lifetime(s) of DSSCs based on different CM dyes presents an interesting result. The τe values of DSSCs based on CM series dyes are in the order CM305 < CM302 < CM303 < CM306 < CM307. This result implies that the introduction of methoxyl, n-hexoxyl, or 1,3-bis(hexyloxy)phenyl units can greatly suppress the electron recombination between the injected electron and electrolyte or oxidized dye. The conduct bands (CB) of TiO2 sensitized by these dyes (CM301, E

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21.8 ohm, which is a little bit higher than that of CM304. This is mainly because the introduction of 3-hexylthiophene as bridge effectively suppressed the electron recombination between the TiO2 film and electrolyte compared with the carbon−carbon double bond. Featuring the methoxyl and nhexoxyl groups in the TPA units, the dyes CM302 and CM303 rendered a higher Rrec and higher Voc. The dye CM307 gives the highest Rrec value of 41.8 ohm among these dyes; correspondingly, the highest Voc was obtained. These results suggest that the electron recombination between the TiO2 film and electrolyte is indeed suppressed by introduction of the long alkyl chains in electron donor groups and thiophene units efficiently.

CM303, CM304, and CM307) are slightly different, ranging from −0.45 V to −0.50 V. The TiO2 film sensitized by CM307 shows the most negative CB while the film sensitized by CM304 shows the most positive CB. Correspondingly, different Voc values were obtained with different sensitizers. Electrochemical Impedance Spectroscopy (EIS). In addition, electrochemical impedance spectroscopy (EIS) also was employed to study the electron recombination and electrolyte reduction process in DSSCs based on these dyes CM301−CM307 under −0.75 V bias applied voltage under dark conditions. The Nyquist and Bode phase plots are shown in Figure 8. Some important parameters can be obtained by

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CONCLUSION By changing the different π-spacers and electron donor, a series of TPA and PTZ dyes were designed and synthesized as photosensitizers for the application of dye-sensitized solar cells. For TPA-based dyes, by substituting the 3-hexyl-thiophene group with a carbon−carbon double bond as π-spacer, a bathochromic shift of absorption spectra and a higher current density (Jsc) are achieved, but the Voc is a little decreased. Also, the significant differences in the redox potential of these dyes are caused by small structure changes. The introduction of methoxyl and n-hexoxyl groups in TPA shifts the HOMO and LUMO levels negatively. In addition, the dyes with alkoxyl groups in the donor part show wider incident photon-tocurrent conversion efficiency (IPCE) response and inferior electron recombination between the TiO2 film and electrolyte; hence, higher Jsc, Voc, and efficiency are achieved. Sensitizers with a phenothiazine (PTZ) electron-donating unit gave a promising efficiency (7.1%), which is even better than the case of TPA-based dyes. This is because the PTZ unit displayed a stronger electron-donating ability than the TPA unit (oxidation potential of 0.82 and 1.08 V vs the normal hydrogen electrode (NHE), respectively). Tuning the HOMO and LUMO energy levels of organic dyes has big effects on the performance of DSSCs, and this strategy of structural modification will pave a road to develop more efficient organic dyes in the future.

Figure 8. Nyquist (a) and Bode plots (b) of DSSCs based on CM series dyes.

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fitting the EIS spectra to an electrochemical model. RS, Rrec, and RCE represent the series resistance, the charge-transfer resistance at the dye/TiO2/electrolyte interface, and the charge-transfer resistance at the counter electrode (CE), respectively. The Rrec obtained by EIS is on the order of CM304 < CM301 < CM305 < CM303 < CM302 < CM306 < CM307 (see Table 6). This trend is in accordance with the electron lifetime measurement results stated above. The dye CM304 gives the lowest Rrec value of 20.1 ohm among these dyes, corresponding to the lowest Voc. Rrec of the CM301 dye is

Detailed synthesis routes of triphenylamine (TPA) dyes (CM301−CM305) and phenothiazine (PTZ) dyes (CM306 and CM307), and J−V curves of DSSCs. This material is available free of charge via the Internet at http://pubs.acs.org.

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RS (ohm)

Rrec (ohm)

RCE (ohm)

CM301 CM302 CM303 CM304 CM305 CM306 CM307

19.4 16.3 17.6 18.1 17.3 17.7 18.4

21.8 34.2 34.0 20.1 27.8 39.1 41.8

3.39 3.96 3.89 3.25 3.24 4.04 3.76

AUTHOR INFORMATION

Corresponding Author

*X.Y.: e-mail, [email protected]; fax, +86 411 84986250; phone, +86 411 84986247. L.S.: e-mail, [email protected]; fax, +46-8-791-2333.

Table 6. Parameters Obtained by Fitting the EIS Spectra to an Electrochemical Model dye

ASSOCIATED CONTENT

S Supporting Information *

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the financial support of this work from China Natural Science Foundation (Grant 21076039, F

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Grant 21276044, and Grants 21120102036 and 20923006), the National Basic Research Program of China (Grant No. 2009CB220009), the Swedish Energy Agency, K&A Wallenberg Foundation, the State Key Laboratory of Fine Chemicals (KF0805), and the Program for Innovative Research Team of Liaoning Province (Grant No. LS2010042).

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