Solvent Effect on the Eciency of Triphenylamine-Based Dye-Sensitized Solar Cells, Molecular Approach

In this research, dynamics, and kinetics of some metal-free organic dyes based on triphenylamine having a D- π -A type structure were investigated in the gas phase and solvent (ethanol, dichloromethane, toluene, tetrahydrofuran, chloroform, and dimethylformamide) using the quantum chemistry calculations. These structures consist of triphenylamine as the donor linked to the acceptor units of cyanoacrylic acid and benzoic acid via different π -conjugated systems. The obtained results show that TC601 dye having the ethynyl anthracene phenyl  -conjugated system has the preferred charge/hole transfer properties (  G inj/  G reg ), which in ethanol as the solvent, the lowest values of  G inj and  G reg were evaluated. Molecular spectroscopic properties of the studied dyes reveal that H-P and F-P dyes have favorable molar absorption coefficients in all media. Also, the behaviors of the light-harvesting efficiency (LHE) and incident photon to current efficiency (IPCE) as the functions of the wavelength were analyzed, which show that the presence of solvent increases the values of IPCE and LHE for most studied dyes in comparison with the gas phase. Finally, based on different analyses, TC601 as the dye and ethanol as the solvent are proposed as the preferred candidates to be applied in the DSSCs.

related to DSSC including photon absorption by sensitizer, the formation of an exciton (e-h pair), and transferred to the conduction band (CB) of TiO 2 . Then, injected electron to the counter electrode through the external circuit and finally reduces the electrolyte and regenerates the dye molecule [13,14].
The sensitizer is an essential component that plays a primary role in the sunlight absorption and production of the electric charges and effects on the performance of the DSSC [15,16]. Metal-free organic photosensitizers, which usually have a donor-π spacer-acceptor (D-π-A) architecture, show good performance in DSSC [17]. As an example of these dyes, triphenylamine-based dyes is used as an electron donor in organic structures, due to strong electron-donating nature [18]. In this compound, steric hindrance, and non-planar structure prevent undesirable aggregation of dye on the semiconductor surface. Moreover, the presence of  conjugated linkers, the ability of light-harvesting, and the low cost of triphenylamine-based dyes have made to be used in DSSC extensively [19,20].
In addition to selecting proper and efficient dye, the use of appropriate solvents in the efficiency of solar cells is very important. According to the reports, the interaction of solvent with sensitizer affects the electronic properties, absorption spectrum, and photovoltaic processes of the solar cell and can improve the final efficiency of the cell [21,22].
In 2021, Arslan and co-workers reported photovoltaic properties of three organic dyes having diphenylamine as electron-rich, benzene, benzothiadiazole, and N-ethylhexylbenzotriazole as auxiliary electron-withdrawing groups, quinoline as π-bridge, and cyanoacrylic acid as anchoring group [24]. Theoretical studies on these dyes show that BIM2 dye having benzothiadiazole electron acceptor represents a red shift compared to other dyes (BIM1 and BIM3) due to advanced electron acceptor group ability. Moreover, the photovoltaic properties of these compounds were evaluated in the gas phase and DMSO. According to the results, all three dyes have superior open-circuit voltage, short circuit current density, and higher efficiency in the presence of DMSO solvent in comparison with gas, which can be attributed to the interactions of the solvent-sensitizer.
Han and co-workers examined the application of different solvents such as N, N-dimethylformamide (DMF), methanol (MeOH), and tetrahydrofuran (THF) on the performance of phenothiazine-based metal-free organic dye (WY5) [25]. The results of the calculations reveal that WY5 dye has a longer lifetime, higher opencircuit voltage, short circuit current density, and molar absorption coefficient in methanol in comparison with other solvents and improves the performance of the corresponding DSSCs.
Therefore, based on the above-mentioned reports and achieving better results, the study of solvent effects on the performance of solar cells has been attracting widespread attention in recent years.

Theory and computational details
Density functional theory (DFT) [30] and time-dependent density functional theory (TD-DFT) [31] were applied to optimize geometries and obtain the excited state properties of the dyes at the M06-2X/6-311++G(2d,2p) level of theory, respectively. Quantum chemistry descriptors such as the electronic chemical hardness ( e ), electronic chemical potential (μ), electrophilicity (ω), and work function (WF) were calculated through the natural bond orbitals (NBO) analysis [32]. To evaluate the effects of solvents, a conductor-like polarizable continuum (CPCM) model was applied [33,34]. In this study, all computational works were performed by using the Gaussian 09 package [35].
One of the important parameters for describing the performance of DSSC is incident photon to current efficiency (IPCE), which is theoretically calculated by Eq. 1 [36]. IPCE = LHE (). inj . coll (1) where  inj and  coll are the net electron injection efficiency and electron collection efficiency, respectively. LHE is the light-harvesting efficiency that can be obtained from Eq. 2 [37].
where f is the oscillator strength that indicates the probability of electron transfer between the molecular levels. Gibbs energies of electron/hole injection (ΔG inj /ΔG reg ) are determined from Eqs. 3 and 4, respectively [38,39].
where E OX(dye), E OX(dye)* , E CB, and E redox are the oxidation potential of the dye in the ground state, oxidation potential of the dye in the excited state, the energy of the semiconductor conduction band (TiO 2 ), and redox potential of the electrolyte, respectively.
The efficiency of the sunlight-to-electricity conversion in the solar cell ( 0 ) can be expressed by using the open-circuit voltage (V OC ), short circuit current density (J SC ), and fill factor (FF) Eq. 5 [40].
where P in is the incident power of the solar cell, which is under the standard sunlight illumination (air mass 1.5 global). J SC and V OC parameters are theoretically determined by Eqs. 6 and 7 [41,42].
where q, K B , T, n c , and N CB denote the unit charge, the Boltzmann constant, the temperature of the solar cell, the number of electrons in the conduction band, and the accessible density of conduction band (CB) states, respectively. Also, the total current density (J) is calculated from Eq. 8 [43].
where J 0 is the saturation current density and estimated according to Eq. 9 [44].
J 0 is extremely dependent on the bandgap energy of dye (E g ). FF Parameter is calculated according to Eq. 10 [43].
where oc is the normalized V OC that can be obtained by using Eq. 11 [43].
One of the quantum chemistry reactivity indices of the solar cell is work function (WF), which is estimated from NBO data Eq. 12 [45].
where IE (-E HOMO ) and EA (-E LUMO ) are the ionization energy and electron affinity, respectively. E HOMO is the energy of the highest occupied molecular orbital and E LUMO is the energy of the lowest unoccupied molecular orbital.
The rate constant of the electron injection on the dye/TiO 2 interface (k inj ) is one of the main kinetic parameters of the photovoltaic processes in DSSCs, which is evaluated by Eq. 13 [46].
where ℏ is the reduced Planck constant (h/2π),  is the reorganization energy of the system and V RP is the coupling constant between the photosensitizer and TiO 2 surface, which increases in |V RP | leads to enhance in rate constant and improve performance of DSSC. |V RP | can be calculated by Eq. 14 [47].
The rate of photon absorption for a singlet excitation in the dye (R a s ) is estimated by Eq. 15 [48].
where e is the electronic charge, ℏ is the reduced Planck's constant, ε is the dielectric constant of the donor component, k = (4πε o ) −1 = 9 × 10 9 N m 2 C −2 , c is the speed of light and a x is the radius of Bohr's exciton, which can be obtained by Eq. 16 [49].
where α is the material-dependent constant, which indicates the ratio of Coulomb and exchange interactions between the excited electron and hole, a 0 = 5.29  10 -11 m is Bohr radius, μ and μ x are the reduced mass of the electron in the hydrogen atom and the reduced mass of the exciton, respectively.
The singlet exciton dissociation rate (R d s ) can be evaluated through Eq. 17 [50].
where E B is the electron-hole binding energy and ω (c/λ max .) is the frequency of the incident phonon to the dyes. Figure 1 shows the optimized geometry of the studied photosensitizers within corresponding electronic energy in the gas phase, which is performed at the M06-2X/6-311++G(2d,2p) level of theory. To calculate the energy levels of the frontier molecular orbitals (FMO) of the sensitizers, the NBO analysis was applied. As shown in Fig. 2, LUMO energy levels of all dyes are higher than of TiO 2 semiconductor conduction band edge, which demonstrates that the electron transfer from the dye excited state to the semiconductor is efficient. Meanwhile, the HOMO levels of the photosensitizers are adjusted with the redox potential of iodide/triiodide electrolyte, which guarantees that the dye regeneration process is favorable and effective in all media. Therefore, the corresponding properties show that these dyes are suitable sensitizers to be applied in the DSSCs.  Table 1. Table 1 Electronic chemical hardness (ηe), electronic chemical potential (μ), global electrophilicity (ω), work function (WF), Gibbs energy of the electron injection (Ginj), Gibbs energy of the dye regeneration (Greg) and electron-driving force (eVOC) in different media.  TC203 < T-F < F-P < TC202 < H-P < FF-P < TC201 < P1B < TC601

Photovoltaic properties and electron injection processes
Also, based on the data in Table 1, a decrement in the dye electrophilicity and less ability to electron acceptance is in agreement with increment in eV OC parameter.
The solvent improves the eV OC character in TC201, TC202, TC203, and TC601 dyes, which can be due to the proper interaction of the dye and solvent.
Linear correlations between the global electrophilicity index, the electronic chemical potential, and work function with eV OC in different media are illustrated in

Kinetics of photovoltaic processes
Theoretical values of the exciton radius (a x ), electron-hole binding energy (E B ), the coupling constant of photosensitizers/TiO 2 , (V RP ), charge transfer rate constant between the dye and TiO 2 surface, (k inj ), and the rate of the exciton formation/dissociation (R a / R d ) in different media were calculated and represented in Table 2. Also, their possible correlation was analyzed.
According to the obtained data, TC601 dye is the preferred photosensitizer from the kinetic viewpoint in all media, due to the faster exciton formation/dissociation rate in comparison with other dyes, which may be related to the grater electron injection rate constant, and more prominent coupling constant between the dye and TiO 2 surface. Also, all studied dyes have better kinetic properties in the gas phase in comparison with other solvents. Ethanol is the preferred solvent from these points of view. The obtained theoretical R a /R d trend of the photosensitizers in all media are respectively according to: T-F < TC203 < F-P ≅ H-P ≅ TC202 < FF-P ≅ P1B < TC201 < TC601 and T-F < P1B < TC203 < H-P ≅ F-P < FF-P < TC202 < TC201 < TC601  Theoretical correlations of the rate of exciton formation and exciton binding energy, as well as the rate of the exciton dissociation with the exciton binding energy and exciton radius, are shown in Figs. 5a and 5b, respectively.
Based on Fig. 5a, the lower required energy to separate the electron-hole leads to faster and more favorable exciton formation. Also, according to Fig. 5b, the dyes having less exciton binding energy and higher exciton radius show the efficient exciton dissociation that results in a greater ability of the electron transfer toward semiconductor. The theoretical trend of IPCE and ΔG inj in different solvents is depicted in Fig.   6. According to this figure, IPCE is highly dependent on ΔG inj changes and TC601 dye has a higher incident photon to current conversion efficiency and lower Gibbs energy of the electron injection in comparison with other dyes in all solvents, which is due to the presence of the extended -conjugated system in this dye.

Absorption spectra and the efficiencies of the DSSCs
To evaluate the performance of the DSSCs, spectroscopic properties including the oscillator strengths (f), vertical excitation energy (E 0-0 ), maximum wavelength ( max ), light-harvesting efficiency (LHE), incident photon to current conversion efficiency (IPCE), and major transition configurations of the excited dyes in different media were calculated using the TD-DFT method and listed in Table S1. Considering Table S1 and simulated absorption spectra in Fig

Photocurrent-voltage characteristics of the DSSCs
The DSSC performance parameters of dyes such as open-circuit voltage (V OC ), short circuit current density (J SC ), fill factor (FF) and solar cell efficiency ( 0 ) in different media were calculated and represented in Table 3 and the corresponding current-voltage (J-V) curves are depicted in Fig. 11.

Fig. 11
The simulated diagram of the voltage-current studied dyes in different media.
Theoretical data in Table 3 and Figure 11 demonstrate that P1B and TC601 dyes have the highest open-circuit voltage and short circuit current density in all media, respectively. This behavior can be explained by the stronger ability of the electron-withdrawing of the benzoic acid in P1B dye and the presence of an extended -conjugated system in TC601 dye. Moreover, the obtained theoretical data in Table   3 reveal that the solar cell based on P1B dye is superior in terms of the fill factor and solar cell efficiency in comparison with other dyes. Also, the obtained results show that H-P, F-P, FF-P, T-F, and P1B dyes have the highest values of V OC , J SC, and  0 in the gas phase in comparison with the solvents.
The possible correlation of the solar cell efficiency and short circuit current density with IPCE in Fig. 12 in various phases shows that the increase in conversion efficiency is according to the short circuit current density enhancement, which improves the final efficiency of the studied DSSCs.

Conclusion
In this work, photovoltaic, kinetics, and electrical features of some metal-free triphenylamine-based dyes, containing electron-rich triphenylamine, electron-deficit cyanoacrylic acid, and benzoic acid, and disparate π-conjugated systems were analyzed in the gas and solvent media for highly efficient DSSCs by density