DFT and TD-DFT study on the structural and

Polymer 97 (2016) 55e62

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Polymer journal homepage: www.elsevier.com/locate/polymer

DFT and TD-DFT study on the structural and optoelectronic characteristics of chemically modified donor-acceptor conjugated oligomers for organic polymer solar cells Francisco C. Franco Jr. a, *, Allan Abraham B. Padama b a b

Chemistry Department, De La Salle University, Taft Avenue, Manila, Philippines ~ os, Laguna, Philippines Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Ban

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 January 2016 Received in revised form 2 May 2016 Accepted 7 May 2016 Available online 8 May 2016

The structural and optoelectronic properties of several substituted poly[N-90 -heptadecanyl-2,7carbazole-alt-5,5-(40 ,70 -di-2-thienyl-20 ,10,30 -benzothiadiazole) (PCDTBT) conjugated oligomers have been investigated by density functional theory (DFT) and time-dependent density functional theory (TDDFT). Various electron-withdrawing and electron-donating groups were attached to the 50 position of the benzothiadiazole unit in the PCDTBT oligomers. HOMO energies (EHOMO), LUMO energies (ELUMO), and the fundamental energy gaps (EGap) were calculated using DFT while the first singlet excited states (EOpt) were calculated using TD-DFT. Results show that the structural properties of the oligomers greatly affect the optoelectronic properties. Results also show that both electron-withdrawing and electron-donating groups are capable of lowering the EGap of PCDTBT. Several properties of substituted PCDTBT, which may affect the solar cell properties, were then calculated and compared with the calculated values for PCDTBT. From the calculated properties, PCDTBT-F showed improvement in the EGap, open-circuit voltage (VOC), and ionization potential (IP), which may lead to solar cells with improved power conversion efficiency (PCE) compared to PCDTBT. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Density functional theory PCDTBT Optoelectronic properties

1. Introduction Organic photovoltaics (OPVs) have attracted a great deal of attention due to their various potential advantages, such as lightweight, easily fabricated, flexible, and low-cost devices [1e5]. Recent developments in organic polymer solar cell devices have led to power conversion efficiencies (PCE) close to 10% [6e8]. However, with Si-based commercial solar cells reaching 25% [9,10], significant improvement in material and device engineering must be made in order for organic polymer solar cells to be commercially attractive. Therefore, in order to synthesize new materials that may eventually lead to higher solar cell device performance, the study of organic polymer material design and intrinsic properties is indispensable. Conversion of light energy to electrical energy in OPVs involves a series of steps as shown in Fig. 1. (1) Bound electron-hole pair (exciton) is generated via absorption of photon in the donor material. (2) The exciton diffuses to the donor-acceptor interface

* Corresponding author. E-mail address: [email protected] (F.C. Franco). http://dx.doi.org/10.1016/j.polymer.2016.05.025 0032-3861/© 2016 Elsevier Ltd. All rights reserved.

(typical diffusion length for organic polymers ~10 nm [11,12]). (3) The bound electron is transferred to the acceptor at the interface. (4) The exciton is dissociated into free charge carriers (i.e., well separated electron and hole) and transported to the electrodes. The amount of light absorbed by the OPV device largely depends on the fundamental energy gap (EGap) and the optical energy gap (EOpt) of the donor material. EGap is the difference between the LUMO (ELUMO) and HOMO (EHOMO) energies for well-separated electrons and holes, i.e., overcoming Coulombic attraction, which can be observed via electrochemical [35,48] and photoemission measurements [47]. On the other hand, EOpt is the minimum energy required for electronic transition to occur, producing bound electron-hole pair (excitons) due to Coulombic attraction, and measured experimentally as the onset of optical absorption, S0 / S1, [35,47]. Due to this, the fundamental energy gap is usually larger than the optical gap. The difference between EGap and EOpt is called the exciton binding energy (EB), the energy required to dissociate excitons into mobile electrons and holes in the donor material [42,43,47]. The driving force for the exciton dissociation in the donor-acceptor interface is the difference in the LUMO energies of the donor (polymer) and acceptor (typically fullerene based)

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F.C. Franco Jr., A.A.B. Padama / Polymer 97 (2016) 55e62

Fig. 1. Schematic diagram of the electron and hole transport mechanism in organic photovoltaic solar cells. Bound electron-hole pairs (excitons) are represented by the shaded regions.

materials (ELL). After dissociation, ELL together with the difference between the HOMO energies of the donor and acceptor materials (EHH) prevents the recombination of the dissociated electrons and holes. Therefore, in order for exciton dissociation to be favored and to reduce recombination of electron-hole pairs after dissociation, both ELL and EHH must be greater than the EB of the donor material which is typically ~0.3 eVe0.5 eV [14]. Another important property is the difference between the LUMO energy of the acceptor material and the HOMO energy of the donor material (ELH in Fig. 1). ELH is related to the open-circuit voltage (VOC) of the OPV device. The VOC of the device can be approximated from the empirical equation [5,15]:

VOC ¼

i 1 h DONOR ACCEPTOR EHOMO ELUMO 0:3eV e

(1)

DONOR ACCEPTOR where e is the elementary charge, EHOMO ELUMO ¼ ELH , and 0.3 eV is an empirical factor arising from the quasi Fermi energies of electrons and holes within the EHOMO and ELUMO energies of the acceptor and donor materials, and is subtracted from ELH [41]. VOC together with the short-circuit voltage (ISC), which mainly depends on EGap, are two main factors contributing to the photovoltaic power conversion efficiency (PCE). The PCE of an organic solar cell can be calculated from the equation [14]:

PCEð%Þ ¼

ISC VOC FF 100% Pm

(2)

where FF is called the fill factor which is related to the series and parallel resistances in the device, and Pm is the light intensity. In order to achieve high PCE, several key considerations must be made regarding the intrinsic properties of donor materials: small EGap to have a broader range of absorption in the solar spectrum, and good combinations between the EHOMO and ELUMO of the donor and acceptor materials. poly[N-90 -heptadecanyl-2,7-carbazole-alt-5,5-(40 ,70 -di-2thienyl-20 ,10,30 -benzothiadiazole)] (PCDTBT) replaced poly(3hexylthiophene-2,5-diyl) (P3HT) as the most used organic material for organic solar cells in the recent years due to its superior

properties [16]. PCDTBT has a large VOC vs. PC61BM (0.9 V) [35], low energy gap (1.85 eV), and high stability from oxidation (ionization potential, IP) ¼ 5.45 eV) [50]. One main advantage of organic semiconductor materials over inorganic materials is that the physical properties of organic materials can be easily adjusted by attaching different substituents. The solubility of organic polymers can be enhanced by attaching long chained alkyl substituents; while, the electronic energy levels can be adjusted by doping [13,37,46] and attaching electron-withdrawing or electrondonating substituents [14,17,25,26,56]. With this, it is therefore important to identify and investigate the changes in the properties and performance of this organic material in the presence of these attached substituents. It is worth mentioning that there are other conjugated materials that can be used as alternative for conjugated polymers for solar cells such as 2D-materials: graphene- [61e63], and silicene- [64] based materials. Density functional theory (DFT) based calculations have been significant in understanding electronic properties of different systems in atomic scale [18,19]. It is also commonly used to determine properties of p-conjugated systems [17,29,33,36,59]. Even though DFT calculations have been commonly found to have deviations from experimentally determined values especially for semiconductor systems, the trends for the calculated values are normally the same with the experiments [20,23,44,49]. Moreover, changes on the electronic and geometric properties of modified systems are conveniently addressed using this method. Performing studies using DFT, therefore, will aid experimentalists in the design, prediction and functionalization of different materials necessary for a specific application. In this study, we investigated the effects of substitution of various electron-withdrawing and electron-donating substituents on the structural and optoelectronic properties of poly[N-90 -heptadecanyl-2,7-carbazole-alt-5,5-(40 ,70 -di-2-thienyl-20 ,10,30 -benzothiadiazole) (PCDTBT), a high-performance donor material in OPVs [16], using quantum-mechanical calculations based on DFT and (Time dependentedensity functional theory) TD-DFT. The hydrogen in the 50 position of PCDTBT was replaced with several substituents (-X). The HOMO energy (EHOMO), LUMO energy


(ELUMO), and energy gap (EGap) were calculated from DFT. The first excited singlet state, (EOpt) was calculated by TD-DFT calculations. The solar cell characteristics of the new PCDTBT derivatives (PCDTBT-X) were then predicted and compared with the calculated values for PCDTBT. This study also aims to provide new insights on the structural and optoelectronic properties of modified conjugated polymers, and propose new organic polymer material designs for OPVs with improved solar cell properties.

57

using equation (1). The ionization potentials (IP) were estimated from the negative of EHOMO based from Koopman’s Theorem [31].

3. Results and discussion 3.1. Structural analysis of PCDTBT derivatives

The chemical structures of the PCDTBT derivatives (PCDTBT-X) used in the study are shown in Fig. 2. Various electron-withdrawing (i.e., prefers to gain e): acetyl (eCOCH3), cyano (eCN), fluoro (eF), nitro (eNO2), trifluoromethyl (eCF3); and electron-donating (i.e., prefers to transfer e): amino (eNH2), isopropyl (eCH(CH3)2), dimethylamino (eN(CH3)2), ethenyl (eCH]CH2), hydroxy (eOH), methyl (eCH3), and methoxy (eOCH3), substituents (eX) were attached to the 50 position of the benzothiadiazole unit of the PCDTBT oligomers. The heptadecanyl chain attached to the nitrogen atom of the carbazole unit in PCDTBT was replaced with isopropyl in order to reduce computational costs, but still approximate the electron-withdrawing and steric effects of the heptadecanyl chain. Also, the terminals of the repeating units for all the oligomers were saturated with hydrogen atoms. All calculations were carried out with PC-GAMESS/Firefly QC package which is partially based from GAMESS (US) source code [27,28]. Density functional theory (DFT) and time-dependent density functional theory (TD-DFT) [21e24] were performed to investigate the effects of substitution to the structure and optoelectronic properties of the substituted PCDTBT. Geometry optimizations for PC61BM and substituted PCDTBT oligomers (n ¼ 1e4 units) were performed using the Becke three parameter (exchange), Lee, Yang, and Parr (B3LYP) as the generalized gradient approximation (GGA) functional; and 6-31G(d) as the basis set. B3LYP/6-31G(d) has been successful in predicting trends in conjugated systems without significant computational costs [20,36,54,59]. All geometry optimizations were carried out in gas phase, without any symmetry constraints, and with all atoms allowed to relax. Total energy calculations to obtain the HOMO (EHOMO) and LUMO (ELUMO) energies were performed with 6-311G(d,p) basis set in order to have better accuracy without substantially increasing the computational costs. The fundamental gap (EGap) was calculated from the energy difference between EHOMO and ELUMO. First singlet excited states (EOpt) were calculated using TD-DFT, also at the B3LYP/6-311G(d,p) level. Exciton binding energies (EB) were estimated from the difference between EGap and EOpt [29,30]. The open-circuit voltage (VOC) of the substituted PCDTBT derivatives were evaluated from the calculated values for ELUMO of PC61BM and EHOMO of the PCDTBT derivatives

The dihedral angle (F) and Dr between units in the polymer backbone has significant effects on the conjugation of the polymer, thus, on the optoelectronic properties [17,29,59,60]. It was observed that the structural properties of the optimized oligomer structures showed large dependency on the substituent attached to the benzothidiazole unit. Fig. 3 illustrates the significant dihedral angles and Dr influenced by substitution at the 50 position of the benzothiadiazole unit. Table 1 summarizes the dihedral angles observed for the PCDTBT derivatives studied. It was expected that F1 will have large deviation from coplanarity upon substitution since the presence of any substituent in the 50 position of the benzothiadiazole unit may interact with the sulfur atom of the thiopene unit. The optimized structure for the unsubstituted PCDTBT (-H) was observed to have coplanar thiophene and benzothiadiazole units, similar to previous computational work [55]. Several PCDTBT derivatives also produced coplanar structures: PCDTBT-CN, PCDTBT-F-, PCDTBT-OH, PCDTBT-CH3, and PCDTBTOCH3. On the other hand, the derivatives: PCDTBT-COCH3 (43.6 ), PCDTBT-CH(CH3)2 (72.5 ), PCDTBT-CH]CH2 (41.7 ), PCDTBT-NO2 (44.3 ), and PCDTBT-CF3 (49.1 ), produced structures with large deviations from coplanarity (i.e., F > 40 ). Large deviations were observed due to the steric repulsion of the bulky substituents with the sulfur atom of the adjacent thiophene unit. F2 was mostly unaffected since the substituent in the 50 position doesn’t significantly interact with the other thiophene unit (non-adjacent to substitution). The PCDTBT derivative with the bulky eN(CH3)2, group was observed to have smaller F1 (20.5 ) compared to the less bulky eNH2 group with large F1 (37.1 ). The observed structure is due to the higher p-bonding character for H2NeC(50 ) bond than the (CH3)2NeC(50 ) bond. This can be verified quantitatively by comparing the bond energies (B.E.) of the two NeC bonds using the equation: B.E. ¼ EPCDTB-X Eisolated PCDTBT EX, where EPCDTBT-X corresponds to the total energy of the substituted PCDTBT, Eisolated PCDTBT represents the total energy of isolated PCDTBT, and EX is the total energy of isolated substituent. The B.E. for H2NeC(50 ) and (CH3)2NeC(50 ) were observed to be 4.55 eV and 3.72 eV, respectively. Therefore, the methyl groups of PCDTBT-N(CH3)2 were observed to be out-of-plane from the benzothiadiazole unit resulting to less interaction with sulfur from the adjacent thiophene unit. On the other hand, hydrogens in PCDTBT-NH2 are in plane with the benzothiadiazole ring, and as a result, one of the

Fig. 2. The chemical structures of the PCDTBT derivatives (PCDTBT-X) used in this study. (-X) represents the attached substituent to PCDTBT.

Fig. 3. Schematic representation of the relevant dihedral angles (F) and Dr determined for various PCDTBT derivatives (PCDTBT-X) in this study. Dr is the difference between the adjacent carbon-carbon double and single bond lengths as shown by bold lines. F1, and F2 are the dihedral angles between thiophene and benzothiadiazole units.

2. Materials and methods


Table 1 Dihedral angles between the substituted benzothiadiazole unit and the adjacent thiophene units of the optimized structures (DFT/B3LYP/6-31G(d)) for n ¼ 4 PCDTBT derivatives (PCDTBT-X). F1, and F2 are the dihedral angles shown in Fig. 3. PCDTBT-X

F1

F2

eH eCOCH3 eNH2 eCH(CH3)2 eCN eN(CH3)2 eCH]CH2 eF eOH eCH3 eNO2 eCF3 eOCH3

0.2 43.6 37.1 72.5 0.1 20.5 41.7 0.1 0.1 0.4 44.3 49.1 0.1

0.3 2.3 1.2 0.2 0.1 3.6 0.4 0.1 0.1 0.2 3.3 0.4 0.1

hydrogens can interact with the sulfur atom of the adjacent thiophene unit, resulting to large dihedral angle. Fig. 4 summarizes the Dr values determined and compared with PCDTBT. The largest Dr were observed for the derivatives: PCDTBTCOCH3, PCDTBT-NH2, PCDTBT-CH(CH3)2, PCDTBT-CH]CH2, PCDTBT-NO2, and PCDTBT-CF3. These derivatives were also the same derivatives with the largest increase in dihedral angles. The increase in Dr values can be attributed to the loss of planarity between the benzothiadiazole and thiophene units which results to less p-conjugation. On the other hand, most coplanar PCDTBT derivatives have similar Dr values with PCDTBT except for PCDTBT-CN which was observed to have significant decrease in Dr (z0.01 Å). One possible reason for the decrease in Dr is the increase of the quinoid character of the ground state of the polymer when substituted with the highly electron withdrawing cyano group [25,26] similar to previous theoretical studies [56]. 3.2. Optoelectronic properties of PCDTBT derivatives Electronic properties: EHOMO, ELUMO, and EGap of PCDTBT of various PCDTBT oligomers were calculated at the DFT/B3LYP/6311G(d,p) level. (The variation of electronic properties with respect to the number of monomer units is shown in Supplementary Material Fig. S1) Various fitting methods were previously used to approximate the polymer energy values

calculated from their oligomer values, e.g., linear fit [33,59], exponential fit [32e34], polynomial fit [29]. (The polymer values extrapolated using Meier fit, an exponential fitting method is shown in Supplementary Material, Fig. S2) The energy values calculated in this study seem to converge at n ¼ 4, therefore, we used the n ¼ 4 values to approximate the polymer values. The n ¼ 4 electronic energy values for the PCDTBT are: EHOMO ¼ 4.98 eV, ELUMO ¼ 2.95 eV, and EGap ¼ 2.02 eV. Comparing the calculated values with the experimental values, the calculated values were observed to have large deviations of up to: 8.62%, 18.05%, and 9.19% for the EHOMO, ELUMO, and EGap, respectively, compared to previously determined experimental values: 5.45 eV, 3.60 eV, and 1.85, for the EHOMO, ELUMO, and EGap, respectively [35]. These calculated values at the B3LYP/6-311G(d,p) level are similar with previously calculated values for PCDTBT dimer [57], and PBC-DFT method performed at DFT/B3LYP [58]. The DFT/B3LYP method offers satisfactory results for conjugated polymer systems [29,36e38,56e58] without having significant computational costs. In spite of this, large deviations (up to 10%) were still observed for the EHOMO energies, and up to 1 eV for ELUMO energies [39,40]. However, since we are only interested in the trends of substituted PCDTBT and how their electronic and optical properties compare with PCDTBT, the DFT/B3LYP method is sufficient for this study. In the frontier molecular orbital diagram for PCDTBT, welldelocalized HOMO wavefunctions are observed along the conjugated backbone (i.e., carbazole (CB) - thiophene (T) e benzothiadiazole (BT) e thiophene (T)). On the other hand, the LUMO wavefunctions are generally localized on the thiophene and benzothiadiazole (T-BT-T) units of the PCDTBT. (Frontier molecular orbitals for PCDTBT and its derivatives are shown in Supplementary Material, Figs. S3 and S4) These observations are due to the differences in the HOMO and LUMO energies of the isolated carbazole (CB) and dithienyl-benzothiadiazole (T-BT-T). The EHOMO and ELUMO values for the isolated CB (dotted and dashed lines, respectively), TBT-X-T (black and red segments, respectively) units are shown in Fig. 5. The EHOMO (6.11 eV) and ELUMO (3.51 eV) for PC61BM were also calculated at the DFT/B3LYP/6-311G(d,p) level and included in Fig. 5 (shown as thick black and red segments, respectively). The experimental energy values for PC61BM are: EHOMO ¼ 6.0 eV and ELUMO ¼ 4.3 eV [15] which corresponds to 1.8% and 18.3%

HOMO/LUMO Energy (eV)

58

1.00

CB LUMO T-BT-X-T LUMO

0.00 -1.00

CB HOMO T-BT-X-T HOMO

-2.00

-3.00 -4.00 -5.00 -6.00 -7.00 PC61BM

-CF -CF3 3

-OCH -OCH3 3

-NO 2 -NO2

-OH -OH

-CH -CH3 3

-F-F

-CH=CH -CH=CH2 2

-CN -CN

-N(CH 3)2 -N(CH3)2

-NH 2 -NH2

-CH(CH 3)2 -CH(CH3)2

-HH

-COCH 3 -COCH3

-8.00

PCDTBT-X

Fig. 4. Dr (Å) determined by DFT/B3LYP/6-31G(d) for various PCDTBT derivatives (PCDTBT-X). Dr is the difference between the adjacent carbon-carbon single and double bond lengths as shown by the arrows in Fig. 3. The Dr for PCDTBT is also shown (dotted line).

Fig. 5. Calculated energy values (n ¼ 4) of the PCDTBT derivatives: EHOMO (bottom of rectangular box), ELUMO (top of rectangular box), and EGap (length of rectangular box) using DFT at the B3LYP/6-311G(d,p) level. The EHOMO (dotted line) and ELUMO (dashed line) for an isolated carbazole (CB) unit; and the EHOMO (black segment) and ELUMO (red segment) for the isolated substituted benzothiadiazole (BT-X) units are also shown. The EHOMO (thick black segment) and ELUMO (thick red segment) for PC61BM are included for reference. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


deviations for the calculated EHOMO, and ELUMO values, respectively. The EHOMO and ELUMO for the isolated unsubstituted T-BT-T unit are: 5.53 eV and 2.85 eV, respectively, similar to previously calculated values in Ref. [20]. As shown in Fig. 5, the differences between the HOMO energies of CB and T-BT-X-T units ranges from 0.01 eV up to 0.56 eV, and results to good orbital mixing. On the other hand, the differences between the LUMO energies of CB and T-BT-X-T ranges from 1.5 to 2.4 eV which results to less orbital mixing of the LUMO wavefunctions, resulting to LUMO wavefunctions closer to the LUMO of T-BT-X-T. From the isolated T-BT-X-T derivatives, it can be observed that the derivatives with electron withdrawing substituents have lower EHOMO and ELUMO than PCDTBT. This observation can be attributed to the stabilization of the HOMO and LUMO of the isolated fragments due to withdrawal of e charge by the substituent [14], which results to lower energy values. On the other hand, lower EHOMO but higher ELUMO values were observed for isolated fragments with large dihedral angles (i.e., F > 40 ) and electron donating substituents. This observation can be attributed to the loss of p-conjugation in the fragment as observed from Dr values. The bond energy between the eCH(CH3)2 and eCH]CH2 substituted benzothiadiazole unit and adjacent thiophene unit was observed to decrease to 4.97 eV and 5.06 eV, respectively, compared to the bond energy for the unsubstituted benzothiadiazole which is 5.40 eV. Electron donating substituents with dihedral angles less than 40 have EHOMO and ELUMO values greater than the isolated unsubstituted T-BT-X-T. This is attributed to the destabilization of the HOMO and LUMO, owing to the release of e charge of the substituent leading to higher energy values [14,17]. From the n ¼ 4 energy values, PCDTBT derivatives with electronwithdrawing substituents: PCDTBT-COCH3, PCDTBT-CN, PCDTBT-F, PCDTBT-NO2, and PCDTBT-CF3 have lower EHOMO and ELUMO levels. On the other hand, PCDTBT derivatives with electron-donating substituents: PCDTBT-CH3, PCDTBT-NH2, PCDTBT-OH, and PCDTBT-OCH3 have higher EHOMO and ELUMO levels. The EGap values were observed to be in the range between 1.85 eV and 2.47 eV. Several derivatives with electron-withdrawing and electrondonating substituents have lower EGap compared to PCDTBT: PCDTBT-COCH3, PCDTBT-N(CH3)2, PCDTBT-NO2, PCDTBT-CN, PCDTBT-F, PCDTBT-OH, and PCDTBT-OCH3. For electronwithdrawing substituents, ELUMO decreases more than EHOMO, while for electron-donating substituents, EHOMO increases more than ELUMO. Larger EGap values were observed for several PCDTBT derivatives compared to PCDTBT: PCDTBT-NH2, PCDTBT-CH(CH3)2, PCDTBT-CH]CH2, PCDTBT-CH3, and PCDTBT-CF3. With the exception of PCDTBT-CH3, these PCDTBT derivatives were also observed to have the largest dihedral angles. Deviation from planarity reduces the p-conjugation in the polymer thus widening the EGap. For PCDTBT-CH3, it was observed that the electron-donating effect resulted to slightly larger increase in ELUMO than EHOMO resulting slight to increase in EGap. Table 2 summarizes the calculated n ¼ 4 electronic and optical properties at the DFT and TD-DFT at the B3LYP/6-311G(d,p) level. The EHOMO, ELUMO, and EGap values are listed as mentioned in Fig. 5. According to previous calculations for P3HT, increase in dihedral angles to about 16 from planarity does not have significant effects on the energy values, EHOMO, ELUMO, and EGap [65]. The first singlet excitation energy, EOpt value for PCDTBT was 1.69 eV, a 10.1% deviation from the experimentally determined value of 1.88 eV, measured from the onset of absorption in solution [51]. (The evolution of the excitation energies and oscillator strengths for n ¼ 1 to n ¼ 4 oligomers with their corresponding configurations are shown in Supplementary Material, Table S1) The EOpt values were observed to have the same trends with EGap, that is, PCDTBT derivatives with large dihedral angles have larger EOpt values. It must be noted that

59

Table 2 Calculated energy values EHOMO, ELUMO, and EGap of the PCDTBT derivatives using the n ¼ 4 oligomer values with DFT at the B3LYP/6-311G(d,p) level. EOPT was calculated from the n ¼ 4 oligomer values of the PCDTBT derivatives with TD-DFT at the B3LYP/ 6-311G(d,p) level. EB values were calculated from the difference between EGap and EOpt. PCDTBT-X

EHOMO (eV)

ELUMO (eV)

EGap (eV)

EOpt (eV)

EB (eV)

eH eCOCH3 eNH2 eCH(CH3)2 eCN eN(CH3)2 eCH]CH2 eF eOH eCH3 eNO2 eCF3 eOCH3

4.98 5.10 4.93 5.19 5.18 4.88 5.05 5.02 4.86 4.94 5.28 5.19 4.82

2.95 3.11 2.68 2.72 3.32 2.87 2.87 3.02 2.88 2.88 3.37 3.13 2.86

2.02 1.99 2.25 2.47 1.86 2.01 2.18 1.99 1.97 2.07 1.91 2.06 1.96

1.71 1.69 1.91 2.12 1.56 1.69 1.84 1.69 1.69 1.75 1.58 1.73 1.67

0.32 0.30 0.34 0.36 0.30 0.32 0.34 0.30 0.28 0.32 0.33 0.33 0.29

the EGap values are all greater than the EOpt values since it takes additional energy to fully separate electrons and holes into free carriers. The difference in EGap and EOpt is called the exciton binding energy (EB), also shown in Table 2. EB values were observed to be in the range between 0.29 eV and 0.35 eV, consistent with exciton binding energies for conjugated polymers [14]. The largest increases in EB, i.e., 0.02 eVe0.04 eV from PCDTBT, were observed for the PCDTBT derivatives with large deviation from planarity, i.e., F > 40 similar to previous observations for P3HT. It was observed previously that less than 30 increase in the dihedral angles does not have significant effects on the binding energy of P3HT [45]. Fig. 6 shows the evolution of the oscillator strengths for all substituted PCDTBT oligomers; an important property related to the absorption coefficient of materials, thus, also an important parameter for OPVs. Coplanar oligomer PCDTBT derivatives generally have large oscillator strengths, which result from highly extended p-conjugation due to good spacial overlap of the wavefunctions [20]. Conversely, the derivatives that have the lowest oscillator strengths are the PCDTBT derivatives with large dihedral angles (F > 40 ), which result to less spacial overlap of the wavefunctions.

3.3. Solar cell characteristics Fig. 7 summarizes the trends in the predicted solar cell

Fig. 6. Oscillator strengths for the first singlet excitation transitions, S0 / S1, of the n ¼ 4 oligomers used in this study calculated at the TD-DFT/B3LYP/6-311G(d,p).

60


Fig. 7. Summary of the predicted solar cell characteristics of the polymers in this study: (a) ability of the polymer to dissociate excitons and prevent recombination, ED-R, (b) open circuit voltage, VOC, (c) energy gap, EGap, and (d) ionization potential, IP. The dashed lines in (b), (c), and (d) represents the calculated values for PCDTBT. Filled circles and cross marks represent positive and negative values for ED-R, respectively, in (a); while the filled circles and cross marks represent better and worse predicted properties than PCDTBT, respectively, in (b), (c), and (d).

properties: ED-R, IP, VOC, and EGap values. Fig. 7(a) shows the ability of the polymer to dissociate excitons and prevent recombination, ED-R, calculated using the difference between the ELL (from Fig. 1) and EB. It can be observed that there are two polymers with negative values: PCDTBT-CN and PCDTBT-NO2. This will negatively impact the dissociation of excitons to charge carriers and will favor electron-hole recombinations. The rest of the polymers show positive ED-R which will drive the dissociation of excitons and prevent electron-hole recombinations. From the calculated values, PCDTBT derivatives that will result to higher VOC, from equation (1), and IP, calculated from the negative of EHOMO, compared to PCDTBT are the electron-withdrawing substituted polymers with stabilized EHOMO: PCDTBT-COCH3, PCDTBT-F, PCDTBT-CN, PCDTBT-NO2, and PCDTBT-CF3. The calculated VOC for PCDTBT/PCB61M was 1.16 V, compared to the experimentally determined VOC for PCDTBT/PC61BM solar cells which was

0.9 V [35]. The deviation resulted from the large deviations observed from the calculated (more positive) ELUMO values, i.e., 18.3% for PC61BM. The estimated VOC values for the PCDTBT derivatives are shown in Fig. 7(b). Other PCDTBT derivatives with large F: PCDTBT-CH(CH3)2, and PCDTBT-CH]CH2, also produced higher VOC and IP due to stabilized HOMO energies. Higher VOC suggest that these PCDTBT derivatives may have improved power conversion efficiency compared to PCDTBT, i.e., PCE proportional to VOC. Since IP is approximated to be equal to the negative of the EHOMO, the lower is the EHOMO (more negative), the higher is the IP (shown in Fig. 7(d)). Larger IP may result to a polymer material more stable to oxidation and which may result to higher device lifetime. Several PCDTBT derivatives will result to a lower EGap (Fig. 7(c)) compared to PCDTBT namely: PCDTBT-COCH3, PCDTBT-N(CH3)2, PCDTBT-CN, PCDTBT-F, PCDTBT-OH, PCDTBT-CF3, and PCDTBTOCH3. Electron-withdrawing substituents: -COCH3, -CN, -F, and eCF3, lower the EGap by mainly lowering the ELUMO. Electrondonating substituents: -OH, -N(CH3)2, and eOCH3 lower the EGap by mainly increasing the EHOMO. The results suggest that these PCDTBT derivatives may increase the short-circuit density (ISC) of the solar cell compared to PCDTBT since lower EGap will result to a broader absorption range for the polymer which will increase the amount of charge carriers generated, thus, leading to higher PCE. Table 3 presents a comparison of the predicted solar cell properties of substituted PCDTBT (PCDTBT-X) with the calculated values for PCDTBT. It is observed that two PCDTBT derivatives have better solar cell properties than PCDTBT: PCDTBT-F and PCDTBT-COCH3 (labelled “o”) in all calculated properties from Table 3. However, from the structural analysis of the derivatives, it was observed that PCDTBT-COCH3 had dihedral angles as large as 43.6 as shown in Table 1. This resulted to a great decrease in the oscillator strength of the material (i.e., low absorption coefficient), which may reduce the photocurrent density of the material for a certain thickness of the active layer (typically ~1 mm [53]). The non-planar structure may also lead to problems in the morphology of the active layer when the polymer-acceptor blend is prepared which has a great impact on the solar cell electrical properties: ISC, VOC and fill-factor FF [52]. Therefore, PCDTBT-F derivative may have overall better solar cell properties than PCDTBT. PCDTBT-F showed improvements in the calculated values of some important solar cell properties, i.e., EGap, VOC, and IP compared to PCDTBT.

4. Conclusions The structural and optoelectronic properties of various substituted poly[N-90 -heptadecanyl-2,7-carbazole-alt-5,5-(40 ,70 -

Table 3 Comparison of the calculated solar cell properties for the various PCDTBT derivatives vs. PCDTBT in this study: ability to dissociate and prevent recombination (ED-R), open-circuit voltage (VOC), energy gap (EGap), and ionization potential (IP). PCDTBT-X

ED-R (eV)

VOC (eV)

EGap(V)

IP (eV)

eCOCH3 eNH2 eCH(CH3)2 eCN eN(CH3)2 eCH]CH2 eF eOH eCH3 eNO2 eCF3 eOCH3

o o o x o o o o o x o o

o x o o x o o x x o o x

o x x o o x o o x o x o

o x o o x o o x x o o x


di-2-thienyl-20 ,10,30 -benzothiadiazole) (PCDTBT) conjugated oligomers were studied by density functional theory (DFT) and timedependent density functional theory (TD-DFT). Results show that structural effects, such as large increase in F and Dr negatively affect the EGap and EOpt which will lead to lower amount of light absorbed in solar cells. Results also suggest that several electronwithdrawing and electron-donating substituents are capable of reducing the EGap of PCDTBT, which may lead to higher ISC. Coplanar thiophene and substituted benzothiadiazole units in PCDTBT derivatives lead to higher oscillator strengths, which may lead to higher light absorption. Electron-withdrawing substituents with lowered EHOMO level may also lead to higher VOC and more stable polymer due to higher ionization potential, IP. However, for the case of PCDTBT-CN, the decrease in frontier orbitals is too great which may negatively impact the solar cell characteristics. From the PCDTBT derivatives investigated, PCDTBT-F showed higher VOC and IP, and smaller EGap compared to PCDTBT. These results suggest that PCDTBT-F may have better solar cell power conversion efficiency since PCE is proportional to both VOC and ISC. PCDTBT-F is also expected to have improved oxidation stability due to the higher IP. While discrepancies in the calculated values exist in reference to existing experimental data, the conclusions and predictions based from the obtained trends for the substituted PCDBT study can aid in future designs of organic materials based on PCDTBT for solar cell application. Acknowledgements FFJr. acknowledges funding from the University Research Coordination Office (URCO) of De La Salle University e Manila under Project No. 35N1TAY14-3TAY14. Appendix A. Supplementary data

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