Theoretical insights into the effect of pristine, doped and hole graphene on the overall performance of dye-sensitized solar cells

Abstract

Graphene, a promising two-dimensional carbon material, has been extensively employed in dye-sensitized solar cells (DSSCs) with encouraging results. However, how graphene improves the power conversion efficiency is still unclear. In this research, a series of dyes with pristine, doped and hole graphene based on the dye WS5 were designed and systematically investigated by density functional theory (DFT) and time-dependent DFT (TD-DFT), aimed at revealing the effect of these functionalized graphenes on photophysical properties. The results based on the absorption properties reveal that introducing functionalized graphene not only enhances absorption intensity, but also expands the absorption spectrum, which will lead to a better photocurrent response. According to an analysis of the intermolecular interaction between dye and I₂, all the designed dyes possess a slow electron recombination rate, except WS5-HoS, and then possibly an increasing V_OC. Additionally, J_ph increases steadily as the electronegativity of the doped atoms (C, Si and Ge) in graphene increases. The dyes with the insertion of short functionalized graphene exhibit a superior performance in J_ph to that of long functionalized graphene. Meanwhile, using graphene to decorate the dye WS5 could adjust energy levels to narrow the energy gap. Dyes with short functionalized graphene exhibit the smallest HOMO–LUMO gaps, followed by long functionalized graphene and the dye WS5. With the enhancement in the electronegativity of doped atoms (C, Si and Ge) in graphene, the energy gap decreases steadily. Inserting functionalized graphene facilitates electron transfer properties due to lower aromaticities, especially for dyes with short functionalized graphene. Taken all together, the introduction of short functionalized graphene in a dye is a valid approach to increase overall efficiency, especially for graphene doped with atoms of larger electronegativity, so the photophysical properties of DSSCs could be boosted in the future.

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1. Introduction

The extensive use of fossil fuels has led to serious environmental pollution over the past few decades. With the increasing awareness of environmental protection, sunlight as a green renewable energy source is widely used in various fields, in particular in photovoltaic conversion technologies. In all types of energy devices, the dye-sensitized solar cell (DSSC) is a promising photovoltaic device due to its easy production process, low cost and easily tunable optical properties. Moreover, the conversion efficiency of DSSCs has been reported to be over 14%.¹ A typical DSSC usually includes a semiconductor material (mostly TiO₂), electrolyte, sensitizer, and counter electrode. The sensitizer is regarded as a crucial part among all the components, which shoulders the responsibility for light harvesting, electron transfer and injection. In general, sensitizers can be classified into metal–organic dyes and metal-free organic dyes, and the latter have been extensively investigated because of their flexible molecular design, environmental friendliness and lower cost.

Organic dyes with a D-π–A configuration have been widely studied due to their high molar extinction coefficients, which exhibit a push–pull character. This structure can promote intramolecular charge transfer, and then inject electrons into the semiconductor. However, dyes adopting a D-π–A model usually exhibit narrow absorption spectra in the UV-visible region, leading to poor harvesting of solar energy and great loss of photon conversion efficiency. Therefore, it is necessary to find a reasonable strategy to overcome the above problems. Graphene, a promising two-dimensional carbon material, has been widely researched due to its superior light absorption properties, excellent flexibility, electrochemical stability, strong photoluminescence and high electron mobility. Graphene has been extensively employed in DSSCs with encouraging results. Mihalache et al.² found that graphene quantum dots are beneficial for improving light harvesting efficiency and charge transfer properties. Zhang et al.³ studied the impact of graphene on photoelectric properties using DFT/TD-DFT. The results indicate that dyes with graphene exhibit better performance than other designed dyes due to their enhanced light harvesting capability, and increased absorption bands and coefficients. Graphene and molecules can be linked through covalent functionalization,⁴ which will provide a new way to enhance the photoelectric properties of DSSCs. Hence, the introduction of graphene is a promising strategy to improve efficiency. Additionally, the photoelectric properties of graphene can be effectively tuned by introducing various heteroatoms, such as N, S, O, Si and B.^5–9 This is due to the difference in electronegativity between the atomic dopant and the carbon atom. However, the relationship between atomic electronegativity and photovoltaic properties has not been completely clarified.

Graphene can be classified into pristine and defective kinds. Pristine graphene consists of cir-coronene, which exhibits a planar state.¹⁰ For defective graphene, a single pentagon–heptagon membered ring is embedded in the sheet, which exhibits a warped shape.¹¹ In recent years, various graphene models (such as C₄₂, C₅₄, C₆₆ and C₈₀) have been studied through density functional calculations.^10,11 With the aim of saving computational time, we take cir-coronene C₄₂ with few C atoms as the graphene model to make a reasonable reduction in the computational load, since it is similar to a rectangle, as shown in Fig. 1. This method is widely used in theoretical research.^12–14 Previous works have reported that the length of the conjugate bridge affects the optoelectronic performance.^15,16 Hence, A–B (Short) and C–D (Long) directions were selected to study the effect of graphene distance on the photoelectric properties of DSSCs. Based on the outstanding WS5 dye,¹⁷ a series of graphene-dyes were designed, in which WS5-CS (WS5-CL) represents the introduction of pristine graphene into the dye, WS5-SiS (WS5-SiL) represents the Si-doped graphene, WS5-GeS (WS5-GeL) indicates Ge-doped graphene, WS5-HoS (WS5-HoL) represents hole graphene (see Fig. 1). The total energies of the dyes before and after adsorption on the (TiO₂)₁₆ cluster are listed in Table S1.† Hole graphene is not rare, and can be obtained by synthesis, transfer, and oxidation/reduction processes or even introduced intentionally.¹⁸ Doping Si and Ge into graphene can be achieved using solution exfoliation techniques or the low-energy ion implantation technique.^19–21 From the experimental results, a doped atom directly replaces a carbon atom in graphene, bonding to three C atom neighbours, which is also widely predicted by first-principles calculations.^22–24 The purpose of our work is to theoretically investigate which type of graphene is beneficial for improving the photoelectric conversion efficiency of DSSCs and to reveal structure–property relationships. Herein, some key photovoltaic parameters, including charge transfer (CT) characters, energy gap, light harvesting efficiency, absorption spectra, aromaticity and maximal photon generated current (J_ph) of the dyes were predicted using DFT and TD-DFT methods. According to these quantum chemical calculations, we hope to provide theoretical guidelines for future experimental research.

Fig. 1 Structure of the investigated dyes and graphene.

2. Computational methods

The geometries of the ground-states of all isolated dyes in dichloromethane solution were fully optimized using the B3LYP function with the 6-31G(d,p) basis set. This level of theory has been widely used in related theoretical research due to its stable and comprehensive performance.^25–27 Based on the optimized ground state geometries, the bond lengths, dihedral angles, frontier molecular orbitals (FOMs) and energy levels were obtained. Moreover, the anionic and cationic states of the dyes were optimized at the same level to evaluate the ionization potentials (IP), electron affinities (EA) and chemical reactivity parameters. The time-dependent density functional theory (TD-DFT) method was performed to calculate the optoelectronic properties of the investigated dyes with the optimized molecular structures. To select a proper functional for the TD-DFT calculation, five exchange correlation (XC) functionals, i.e., WB97XD,²⁸ CAM-B3LYP,²⁹ BMK,³⁰ MPW1PW91,³¹ and B3LYP,³² were selected to simulate the absorption spectra of dye WS5 (Fig. 2). The maximum absorption wavelength and absorption shape simulated by the BMK functional together with the 6-31G(d,p) basis set are closest to the experimental results. Therefore, the BMK/6-31G(d,p) method was employed to predict the optical properties, including transition energies (E_g), oscillator strengths (f), and maximum absorption wavelengths (λ_max), in this study. The conductor-like polarizable continuum model (CPCM)³³ was used to consider the effect of solvent environment (dichloromethane). Additionally, the intramolecular charge transfer parameters, heat map and aromaticities were calculated with the Multiwfn program.³⁴ To gain a better understanding of the interface properties between dyes and the TiO₂ surface, the (TiO₂)₁₆(H₂O)₂ cluster model was prepared as the adsorption surface, which was obtained by cutting from the exposed anatase (101) crystal surface. (TiO₂)₁₆ as the smallest TiO₂ anatase (101) cluster can give reasonable results without obvious differences compared with large models.³⁵ This model has been widely used to study dye/TiO₂ interface systems.^36–39 The geometrical optimizations of dyes binding to the TiO₂ cluster were investigated using the same level with the 6-31G(d) basis set for non-metal atoms and the LANL2DZ⁴⁰ basis set for metal atoms. All calculations were performed with the Gaussian 09 program package.⁴¹

Fig. 2 Absorption spectra of the dye WS5 in dichloromethane solution under different exchange–correlation functionals with the 6-31G (d) basis set.

3. Results and discussion

3.1 Electronic structures

The reference dye WS5 is composed of phenoxazine (POZ) as a donor, furan as a π-spacer and cyanoacrylic acid (CAA) as an acceptor. For the sake of improving light harvesting ability, a series of dyes were designed by introducing functionalized graphene between the π-spacer and acceptor, based on the dye WS5. The distortion of the π-spacer affects the charge transfer process. The dihedral angles between furan and functionalized graphene are 26.59 (40.97), 25.25 (38.48), 24.66 (38.57) and −24.04° (43.43°) for WS5-CS (WS5-CL), WS5-SiS (WS5-SiL), WS5-GeS (WS5-GeL) and WS5-HoS (WS5-HoL), respectively. It is found that inserting shorter functionalized graphene effectively improves coplanarity, which facilitates electron delocalization and intramolecular charge transfer (ICT) behavior.⁴² As shown in Fig. 3, the lengths of bond 1 to bond 3 are 1.411, 1.428, 1.430 Å for the C₄₂ model; 1.745, 1.759, 1.761 Å for the C₄₁Si model; and 1.828, 1.840, 1.842 Å for the C₄₁Ge model. It is clear that the bond length is increasing steadily with an enhancement in the electronegativity of the doped atoms (C, Si and Ge) in graphene. It can be seen from the side view that Ge and Si are located slightly above the graphene plane due to the increase in bond length.

Fig. 3 Optimized structures of C₄₂, C₄₁Si and C₄₁Ge in top and side view.

The HOMO and LUMO energy levels of the dyes are very important to ensure dye regeneration and electron injection. The HOMO and LUMO energy levels and energy gaps for the studied dyes are shown in Fig. 4. Clearly, the HOMO levels of all dyes are under the redox potential of I⁻/I₃⁻ so that oxidized dyes can be efficiently regenerated.⁴³ In addition, the LUMO levels are above the conduction band edge of TiO₂, which ensures efficient electron injection from the excited state dye into the TiO₂ photo-anode.⁴⁴ Compared with the dye WS5, introducing functionalized graphene between the π-spacer and acceptor leads to the HOMO energy being up-shifted and the LUMO energy being down-shifted. It is interesting that the change in atomic electronegativity (C, Si and Ge) in the graphene and the distance of functionalized graphene have little effect on HOMO energy levels; however, the influence on LUMO energy levels is obvious. An enhancement in the electronegativity of the doped atoms (C, Si and Ge) in graphene and a decrease in the functionalized graphene distance lead to lower LUMO energy levels. The smaller energy gap promotes dye excitation and thus harvests more sunlight. The HOMO–LUMO gaps for the dyes obey the order WS5 > WS5-CL > WS5-HoL > WS5-SiL > WS5-HoS > WS5-CS > WS5-SiS > WS5-GeL > WS5-GeS. The following features are revealed: (i): the introduction of functionalized graphene will reduce the energy gap, which is beneficial to the excitation process; (ii): the dyes with an A–B (Short) direction exhibit a lower energy gap than that of the C–D (Long) direction; (iii): the energy gap decreases steadily with an enhancement in the electronegativity of the doped atoms (C, Si and Ge) in graphene.

Fig. 4 The energy level of HOMO and LUMO for all studied dyes.

3.2 IP and EA and chemical reactivity parameters

Ionization potential (IP) and electron affinity (EA) can be used to describe the energy barrier for hole and electron injection. IP denotes the energy change for injecting electrons or adding holes, and EA implies the energy change for injecting holes or absorbing electrons, which can be calculated via the following formulae:

IP = E_cation − E_neutral (1)

EA = E_neutral − E_anion (2)

where E_neutral is the energy of a neutral molecule in the ground state, and E_cation (E_anion) is the energy of a cation (anion) calculated on the basis of the optimized neutral molecule. A smaller IP promotes hole injection, while a larger EA will promote electron injection. As can be seen in Table 1, the results show that all designed dyes have a small IP and larger EA values than that of WS5. Therefore, the insertion of functionalized graphene is beneficial to increasing the electron and hole injection capability.

Table 1 Ionization potential, electron affinity and chemical reactivity (in eV) of dyes

	IP	EA	h	ω ^+	ω
WS5	4.888	2.710	1.089	4.863	6.626
WS5-CS	4.622	3.031	0.796	7.389	9.203
WS5-CL	4.635	2.837	0.899	6.007	7.763
WS5-SiS	4.615	3.052	0.782	7.583	9.402
WS5-SiL	4.638	3.049	0.795	7.474	9.297
WS5-GeS	4.616	3.197	0.710	8.890	10.755
WS5-GeL	4.629	3.215	0.707	9.006	10.878
WS5-HoS	4.624	3.075	0.775	7.739	9.567
WS5-HoL	4.625	2.858	0.884	6.162	7.922

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Chemical hardness (h) represents resistance to intramolecular charge transfer. A dye with a lower h exhibits better charge transfer, thereby emerging with a greater short circuit current density (J_SC). After inserting functionalized graphene, the calculated values of h for all designed dyes are in the range of 0.707–0.899 eV, which are lower than that of WS5 (1.089 eV). Hence, designed dyes will present intramolecular charge transfer and J_SC due to lower h. In addition, the h values decrease from WS5-CS (WS5-CL) to WS5-GeS (WS5-GeL) with an enhancement in electronegativity. This indicates that highly electronegative atom-doped graphene is beneficial for improving J_SC. ω⁺ and ω represent electron-accepting power and electrophilicity index, respectively. Larger values of ω⁺ and ω are preferable. From Table 1, we can see that the ω⁺ and ω of dyes show the same trend, which are in the order WS5-GeL > WS5-GeS > WS5-HoS > WS5-SiS > WS5-SiL > WS5-CS > WS5-HoL > WS5-CL > WS5. Therefore, all the designed dyes exhibit better electron-accepting ability and stabilization energy due to larger ω⁺ and ω values. With an enhancement in the electronegativity of the doped atoms (C, Si and Ge) in graphene, ω⁺ and ω increase gradually from WS5-CS (WS5-CL) to WS5-GeS (WS5-GeL). In conclusion, all the designed dyes will exhibit prominent photoelectrical properties due to a lower h and larger ω⁺ and ω.

3.3 Intramolecular charge transfer (ICT) analysis

Effective charge separation will lead to a better charge transfer (CT) property, which is beneficial for improving conversion efficiency. To visualize the CT characteristics more insightfully, the centroids of the charge for WS5 and the designed dyes are depicted in Fig. 5 and Fig. S1,† in which the blue and green zones correspond to the positive and negative charge distributions. Apparently, all the dyes exhibit a considerable charge separation, except for WS5-SiS, WS5-GeS and WS5-HoL. As can be seen from the heat map, the holes of WS5 mainly localize on the POZ group, while the electrons mainly locate on the furan and CAA groups. The CT originates from POZ to furan and CAA due to the greater contribution of furan for the electrons than for the holes. For WS5-CS, WS5-CL, WS5-SiL, WS5-GeL and WS5-HoS, the CT originates from POZ and furan to CAA. For WS5-SiS, WS5-GeS and WS5-HoL, there is a larger overlap on the functionalized graphene. With the purpose of quantifying the extent of the ICT, the CT indexes are calculated and presented in Table 2. These important parameters include the CT distance (D_CT), which is the difference between the density distribution of the two bary centers upon photo-excitation. The Sr index can be obtained from the integration of electron and hole density over all space, which describes the extent of overlap of the hole–electron distribution. H represents half of the sum of the centroid axis along the electron transfer direction. The t index is the difference between D_CT and H (t = D_CT − H), which can be used to estimate the through-space character with CT excitation. WS5-CL has the largest D_CT (11.46 Å), followed by WS5-CS (9.04 Å), WS5-HoS (7.28 Å), WS5-GeL (7.06 Å) and WS5-SiL (6.50 Å), which are larger than that for WS5 (4.55 Å), implying that those dyes have better ICT properties. Estimated values of H imply that the introduction of functionalized graphene can increase the distance of the centroid axis along the electron transfer direction. The negative charge density of all designed dyes is centered at functionalized graphene (except for WS5-CS/L), which leads to a larger extent of overlap of the hole–electron distribution, which can be confirmed by the Sr values.

Fig. 5 The centroids of charge (up) and heat map (down) of WS5.

Table 2 Calculated charge transfer parameters of investigated dyes

	D CT (Å)	Sr	H (Å)	t (Å)
WS5	4.55	0.62	3.51	1.04
WS5-CS	9.04	0.61	6.16	2.88
WS5-CL	11.46	0.51	5.57	5.89
WS5-SiS	2.31	0.81	4.41	−2.10
WS5-SiL	6.50	0.73	6.19	0.31
WS5-GeS	0.75	0.84	4.05	−3.30
WS5-GeL	7.06	0.73	6.68	0.38
WS5-HoS	7.28	0.68	5.97	1.31
WS5-HoL	2.20	0.84	5.48	−3.28

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3.4 Aromaticity

In order to gain a better understanding of the influence of functionalized graphene on the ICT properties, the aromaticities of furan and functionalized graphene in the π-spacer are calculated. A dye with a lower aromaticity will exhibit a better ICT process. The nucleus-independent chemical shift (NICS) is a popular index to measure aromaticity. The NICS(1) value can be calculated at 1 Å above the geometric center of the ring to describe the magnitude of aromaticity.⁴⁵ A larger NICS(1) value corresponds to a smaller aromaticity, which is shown in Fig. 6. In order to achieve greater electronic movement from the donor (POZ) to the anchor group (CAA), the aromaticity of these aromatic rings should be as small as possible. The NICS(1) values of the furan moiety are in the order WS5-GeS (−20.58) > WS5-HoS (−20.60) > WS5-CS (−20.62) > WS5-SiS (−20.80) > WS5-CL (−21.80) > WS5-SiL (−21.21) > WS5-GeL (−21.33) > WS5-HoL (−22.38) > WS5 (−26.87). It is clear that all the designed dyes exhibit more positive NICS(1) values compared to reference dye WS5, implying that inserting functionalized graphene facilitates electron delocalization and ICT. Additionally, the furan near short functionalized graphene will exhibit a predominant electron transfer character compared to that of furan close to long functionalized graphene. The effect of different atom-doped graphenes on ICT was also studied. The results show that NICS(1) values increase steadily as the electronegativity of the doped atoms (C, Si and Ge) in the graphene increases, indicating that dye with Ge-doped graphene will exhibit better photoelectric performance.

Fig. 6 Schematic diagram of electron transfer routes in molecular π-spacer in which the NICS(1) values of the individual heterocyclic rings are indicated.

3.5 Photophysical properties

The light absorption properties of a dye is a vital factor that influences the efficiency of a DSSC, which can be evaluated from UV-vis absorption spectra. A dye with a strong absorption intensity and a wider absorption region usually shows better performance. With the purpose of investigating the effect of functionalized graphene on the light absorption property, the absorption spectra of the studied dyes in dichloromethane which were simulated using the TDDFT/BMK/6-31G(d,p) level are depicted in Fig. 7. Moreover, the corresponding electronic transition properties upon photo-excitation are summarized in Table 3. It is obvious from Fig. 7 that introducing functionalized graphene not only enhances absorption intensity, but also expands the absorption spectrum, which will lead to a better photocurrent response. From Table 3, the maximum absorption peak (λ_max) of prototype dye WS5 is 490 nm, which is assigned to the HOMO to LUMO transition. All designed dyes exhibit a blue shift of 60–111 nm with respect to WS5, implying that the introduction of functionalized graphene would lead to a hypsochromic shift of the absorption spectrum. In addition, the λ_max of WS5-CS, WS5-SiS, WS5-GeS and WS5-HoS show a red shift compared with WS5-CL, WS5-SiL, WS5-GeL and WS5-HoL, indicating that the introduction of shorter functionalized graphene (A–B direction) is beneficial to the bathochromic shift of the absorption spectrum.

Fig. 7 Simulated absorption spectra of all dyes.

Table 3 The absorption characteristics of the dyes calculated by BMK/6-31G(d) level in dichloromethane

Dye	E g (eV)	λ max (nm)	f	Main configuration
WS5	2.53	490	1.0420	H → L/0.68722
WS5-CS	3.00	414	0.9565	H → L + 1/0.38956
WS5-CL	3.23	384	0.9801	H-2 → L + 1/0.55375
WS5-SiS	3.02	410	1.1437	H-2 → L/0.36583
WS5-SiL	3.18	389	1.0006	H → L + 2/0.43858
WS5-GeS	2.97	417	0.7909	H-4 → L/0.36651
WS5-GeL	3.20	388	1.4290	H → L + 2/0.32353
WS5-HoS	2.88	430	0.9270	H → L + 1/0.50605
WS5-HoL	3.27	379	1.1218	H-1 → L + 2/0.37904

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To investigate the effect of functionalized graphene on the charge-separation process, selected frontier molecular orbitals (FMOs) of the isolated investigated dyes are plotted in Fig. 8. The transition character of prototype dye WS5 arises from HOMO to LUMO. To achieve an effective charge separation, the HOMO should populate on the donor segment and LUMO should localize on the acceptor moiety. As depicted in Fig. 8, the HOMO orbital of WS5 is centered on the whole framework, while the LUMO is populated over the right part of the donor, furan and acceptor. This distributive character is unfavorable for charge transfer and photoinduced electron injection. For designed dyes, introducing shorter functionalized graphene (A–B direction) will lead to better charge separated states except for WS5-GeS. As we know, the –COOH group is used to graft onto TiO₂ and transport electrons. More electrons persisting in the –COOH group for the lowest unoccupied molecular orbitals will lead to a faster electron transfer rate, which is beneficial for improving the performance of DSSCs. The distributive shape of LUMO and LUMO+1 for the dyes with shorter functionalized graphene (A–B direction) is as expected, and the electrons are distributed on the –COOH group. In contrast, the electron density of LUMO+1 and LUMO+2 for the dyes with longer functionalized graphene (C–D direction) are only located at the functionalized graphene group, which will lead to a negative influence on the conversion efficiency of DSSCs. From the FMO distributions of WS5-HoS and WS5-HoL, we can deduce that introducing hole graphene is not favorable to the charge transfer process.

Fig. 8 The selected frontier molecular orbitals (FMOs) of the isolated investigated dyes.

In order to achieve a high photoelectric conversion efficiency, a dye should absorb as much energy from sunlight as possible. η_LHE(λ) represents the light harvesting efficiency at a given wavelength λ. A higher η_LHE(λ) is beneficial for improving the performance of a solar cell, which can be calculated as:^46,47

η_LHE(λ) = 1–10^−Γσ(λ) (3)

where Γ is the surface loading of dye (mol cm⁻²) adsorbed on the semiconductor; σ(λ) is the molecular absorption cross-section (cm² mol⁻¹), which can be obtained from the molar absorption coefficient ε(λ) by multiplication by 1000.^46,48 The values of η_LHE(λ_strong) and [small eta, Greek, macron]_LHE(λ) are calculated and presented in Fig. 9(a). The η_LHE(λ_strong) is calculated at the strongest absorption peak. As can be seen from Fig. 9(a), introducing functionalized graphene into dye WS5 obviously enhances η_LHE(λ_strong). In addition, we also calculate the average light harvesting efficiency [small eta, Greek, macron]_LHE(λ). It is found that all the designed dyes exhibit a higher [small eta, Greek, macron]_LHE(λ) except WS5-CL, WS5-HoS and WS5-HoL.

Fig. 9 (a) The calculated η_LHE(λ_strong) and [small eta, Greek, macron]_LHE(λ) for all dyes; (b) the generated J_ph (mA cm⁻²) for all dyes.

For DSSC as a photoelectric conversion device, the more photons the dyes can get from sunlight, the more electrons can be excited and then injected into TiO₂, which will increase the short-circuit current density (J_SC). J_SC is an important parameter affecting the overall efficiency of the DSSCs, which is related to the integral photon flux density Φ(λ). Hence, the exact part of Φ(λ) generated by the dyes per second per unit area at the given wavelength (λ) can be obtained as follows.⁴⁹ For more details, please refer to these publications.^12,47,50

The maximal photon generated current (J_ph) can be described by the following equation:

According to eqn (5), the calculated J_ph of all the dyes are shown in Fig. 9(b). Among the designed dyes, dyes with Ge-doped graphene (WS5-GeS/WS5-GeL) exhibit the greatest J_ph, followed by Si-doped graphene (WS5-SiS/WS5-SiL), pure graphene (WS5-CS/WS5-CL) and hole graphene (WS5-HoS/WS5-HoL). The following features can be observed: (i): J_ph increases steadily as the electronegativity of the doped atoms (C, Si and Ge) in graphene increases; (ii) Inserting short functionalized graphene will increase the value of J_ph except for WS5-GeS/WS5-GeL; (iii) inserting hole graphene in WS5 has a negative influence on the performance of DSSC due to the lower J_ph. The flow of electric charge across a surface per second per unit area over the whole spectrum equals the short circuit density (J^max_sc).³⁸ Therefore, we can infer that inserting Ge-doped, Si-doped and pure graphene in WS5 is beneficial to improving the performance of DSSCs.

3.6 Electro-optical properties of dye@TiO₂ systems

To better understand the mechanism of electron injection from the excited dye into the semiconductor, the photoelectrical properties of dyes adsorbed on the (TiO₂)₁₆ cluster were systematically studied. Generally, dyes are adsorbed onto TiO₂via three possible adsorption models: monodentate or bidentate bridging and chelating. Previous studies showed that the bidentate binding is the most favorable mode among the three possibilities.^51–53 Therefore, we adopt a bidentate bridging configuration for all dyes absorbed onto the TiO₂ surface in this work, and the corresponding optimized dye/(TiO₂)₁₆ system structures are shown in Fig. S2.† The calculated two Ti–O bonds at all dye/TiO₂ interfaces are in the range of 2.02–2.12 Å, which is similar to the Ti–O bond lengths in bulk TiO₂ (1.934–1.980 Å), implying that the dye is chemisorbed onto the TiO₂ surface. The strong interactions between the dye and TiO₂ will promote electron injection into the semiconductor.⁴⁹ From Fig. S3,† it can clearly be seen that the HOMO levels of all dye/TiO₂ complexes show no obvious change compared to their isolated dyes, while the LUMO decreased from 0.26 eV (WS5-GeS) to 0.62 eV (WS5-CL), indicating that the acceptor group has strong electronic coupling with the TiO₂ surface. The energy gap of WS5/TiO₂ (1.79 eV) is the highest while that of WS5-SiS/TiO₂ (1.42 eV) is the lowest, which are lower than those of isolated dyes due to decreases in the LUMO. The transition energies, absorption peaks, oscillator strengths and major transitions of dyes binding on the TiO₂ surface are tabulated in Table S2.† It is clear that the λ_max of dye/TiO₂ systems exhibits a slight red shift in comparison to isolated dyes. The electron density of FMOs of dyes/TiO₂ in the major transition is shown in Fig. 10. WS5, WS5-CS, WS5-CL and WS5-SiS have similar electron densities of HOMO, HOMO−1 and HOMO−2, which are mainly localized over the whole molecule. The electronic distributions of the HOMO for WS5-SiL, WS5-GeL and WS5-HoS are mainly from the phenoxazine and furan groups. For WS5-GeS and WS5-HoL, the electronic distributions of HOMO−4 and HOMO−1 are centered on functionalized graphene. However, the lowest unoccupied molecular orbitals of all the dyes are completely located on the TiO₂ cluster. This distribution characteristic indicates that all the dyes are promising candidates for DSSCs.

Fig. 10 Distribution patterns of the FMOs for dye/TiO₂ clusters in the major transition.

The collected electrons in the TiO₂ conduction band can recombine with the electrolyte, which is the main charge recombination process and leads to a negative effect for DSSCs. The high concentration of iodine electrolyte close to the TiO₂ surface would reduce the electron lifetime in TiO₂ and accelerate the charge recombination. Previous simulations showed that using I₂ to study electron recombination for dye-electrolyte is more realistic.^54,55 Therefore, we consider only I₂ as the electron acceptor in the charge recombination process. The optimized molecular structures of the dye/TiO₂-I₂ complex and corresponding binding energies are exhibited in Fig. 11. A more negative binding energy corresponds to a stronger interaction, which will lead to a higher iodine concentration around the TiO₂ surface. WS5-HoS has the most negative binding energy, and other designed dyes possess smaller binding energies than that of WS5, indicating that using functionalized graphene to decorate the dye WS5 might result in an inhibitory effect on charge recombination except for WS5-HoS, possibly increasing V_OC.

Fig. 11 The optimized structures of the dye/TiO₂-I₂ complex and corresponding binding energies (unit in kcal mol⁻¹).

4. Conclusion

To sum up, we performed a comprehensive theoretical investigation of how functionalized graphene affects the photovoltaic performance of a dye sensitizer in DSSCs. The ground- and excited-state properties of all the dyes were calculated via DFT and TD-DFT methodologies. Based on an analysis of electronic structures, intramolecular as well as interface charge transfer processes, and absorption properties, the main conclusions can be itemized as follows:

• The introduction of functionalized graphene in dye WS5 could decrease ionization potentials (IP) as well as chemical hardness (h), and increase electron affinities (EA), electron-accepting power (ω⁺) and electrophilicity index (ω), meaning that all the designed dyes will exhibit better photoelectrical properties. Among all the designed dyes, the prominent optical and electrical properties of dyes with short functionalized graphene over those of long functionalized graphene are due to smaller IP and h, and larger EA, ω⁺ and ω.

• Using graphene to decorate the dye WS5 could adjust the energy levels to narrow the energy gap. Dyes with short functionalized graphene exhibit the smallest HOMO–LUMO gaps, followed by long functionalized graphene and dye WS5. In addition, the energy gap decreases steadily with an enhancement in the electronegativity of doped atoms (C, Si and Ge) (such as WS5-CS/L > WS5-SiS/L > WS5-GeS/L).

• According to analysis of the intermolecular interaction between dye and I₂, all the designed dyes possess a slow electron recombination rate except WS5-HoS, possibly increasing V_OC.

• J_ph increases steadily with an increase in the electronegativity of doped atoms (C, Si and Ge) in graphene. Moreover, the dyes with insertion of short functionalized graphene exhibit a superior performance in J_ph to that of long functionalized graphene.

• All the designed dyes exhibit lower aromaticities compared to dye WS5, especially for dyes with short functionalized graphene, implying that inserting functionalized graphene facilitates electron ICT properties. Additionally, the aromaticities around the doped atoms decrease steadily with an increase in the electronegativity of doped atoms (C, Si and Ge) in graphene.

• For the absorption property, introducing functionalized graphene not only enhances absorption intensity, but also expands the absorption spectrum, which will lead to a better photocurrent response. The absorption spectrum of dyes with short functionalized graphene exhibits a bathochromic shift compared to long functionalized graphene.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We are grateful for the financial support of this research from the National Natural Science Foundation of China (51779065 and 51579057) and the State Key Laboratory of Urban Water Resource and Environment, Harbin Institute of Technology (2019DX11).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9qi01264h

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