Article pubs.acs.org/JPCC
Anisotropy of Polarizability of Fullerene Higher Adducts for Assessing the Efficiency of Their Use in Organic Solar Cells Denis Sh. Sabirov Institute of Petrochemistry and Catalysis, Russian Academy of Sciences, 450075 Ufa, Russia S Supporting Information *
ABSTRACT: Currently, the purified higher C60 fullerene adducts come into use as electron-acceptor materials in organic solar cells. As known, the number of regioisomeric structures grows up rapidly with the increase of the number of addends in C60 derivatives. To make the computational description of their diversity, an accurate quantum chemical investigation of anisotropy of polarizability of C60 higher adducts has been performed by the modern density functional theory method. The correlation between the calculated dihydronaphthyl-C60 bisadducts anisotropies and the key output parameters of organic solar cells, based on them, has been found. The data on the higher fullerene adducts anisotropy may be useful to search for new fullerene-based electon-acceptor materials for organic solar cells.
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technique.10−15 In the only experimental work,16 the purified derivatives of regioisomeric bis(dihydronaphtho)fullerenes have been used in solar cells separately. The effectiveness of the devices has been found dependent on the positional relationship of functional groups in C60 bisadducts, being maximal for e-, trans-2-, and trans-1-isomers. The search for new fullerene derivatives among the higher adducts of C60 and C70 is continued. Therefore, approaches to estimation of their applicability to photovoltaic devices as an electron acceptor are being developed. In this paper, we focus on anisotropy of polarizability of fullerene higher adducts. Currently, polarizability of C60 fullerene derivatives has been studied in the experimental18 and mainly in the theoretical works.19−27 The interest in polarizability is explained by the opportunities of its application to physical and chemical processes in fullerene-containing systems (chemical reactions,23,28 aggregation,29 the quenching of electronically excited states,30 and formation of donor−acceptor complexes31). Previously,24,25 we have shown that regioisomeric fullerene higher adducts C60O2, C60O3, C60F36, C60F48, and C60Cl30 are characterized by approximately equal mean polarizabilities and differ by anisotropy of polarizability (hereinafter, anisotropy). It means that anisotropy can be an index which describes the otherness of regioisomers. Most of the C60 derivatives, used in photovoltaic applications, are substituted cyclopropa-, aziridino-, pyrrolidino-, and dihydronaphtho[60]fullerenes.2 Therefore, the simplest representatives (without substituents) of the listed classes of C60 bisadducts C60(CH2)2, C60(NH)2, C60pyr2, and C60dhn2 have become the model compounds of primary interest for this study (Figure 1). Their anisotropies have been calculated by the
INTRODUCTION Harvesting energy directly from the sunlight using photovoltaic technology is being recognized as an essential component of future global energy production.1 Diverse monoadducts of fullerenes (mainly C60 derivatives) are widespread as electron acceptor materials in the modern organic solar cells.2 Their use allows achieving power conversion efficiency up to ∼6%. Improvement of the efficiency of fullerene derivatives-based organic solar cells is a rapidly developing interdisciplinary field between the photovoltaics and fullerene materials science. For this purpose, various experimental and theoretical studies have been performed, such as assessing the theoretically possible feasibility of power conversion efficiency and open circuit voltage,2 study on the structure and the frontier orbitals of fullerene derivatives,3 evaluation of order/disorder and charge transfer processes in π-conjugated polymers,4 experimental studies of the effect of solubility of substituted cyclopropafullerenes C60R1R2 and C70R1R2 on solar cells output parameters.5 Higher fullerenes,6 C60 and C70 adducts,7,8 their anions, and low-lying excited states3 became also the objects of theoretical studies. Traditionally, the attention of such works is directed to the frontier orbitals of fullerene derivatives. For example, levels of the frontier orbitals, structural and energetic disorder of bis- and tris-PCBM regioisomers have been estimated in terms of density functional theory (DFT), providing a good orienteer to screen the HOMO and LUMO levels of a candidate fullerene acceptor in a highly automated manner.9 One of the novel and promising ways to enhance PCE and other solar cells output parameters includes the replacement of fullerene monoadducts by the respective bis- and trisadducts of C60 and C70.10−16 Such fullerene derivatives, as known, have multiple regioisomers.17 Currently, the use of the mixtures of C60 and C70 regioisomeric higher adducts (e.g., bis[60]PCBM and bis[70]PCBM) in solar cells have become a common © 2013 American Chemical Society
Received: February 25, 2013 Revised: April 12, 2013 Published: April 15, 2013 9148
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The mathematical operations on polarizability tensors have been performed by POLARIZ program,41 worked out by us for the fast data processing upon calculations of polarizability. To describe the location of the addends in fullerene bisadducts, we use an auxiliary topological index r, which increases with the increase in the distance between the sites of addition. This index has been conventionally accepted to be zero for e-bisadducts. Accordingly, it takes negative values −1, −2, and −3 for the cis-3, cis-2, and cis-1 isomers with the closer locations of addends, and positive values 1, 2, 3, and 4 for the trans-4, trans-3, trans-2, trans-1 with more remote X fragments (Figure 1). Here, we do not use distances themselves because they can vary depending on the X for the same addition pattern. For trisadducts C60(CH2)3, geometrical parameters become useful, so three distances between the carbon atoms of addends have been used to designate numerically all the isomeric compounds C60(CH2)3. As we found, each of the regioisomers is characterized by the unique combination of the distances (see Supporting Information). To study a correlation between the structure and anisotropy, the average value L of the three mentioned values for each isomer has been calculated.
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RESULTS AND DISCUSSION First of all, anisotropies a2 of [2 + 1]-cycloadducts C60(CH2)2 and C60(NH)2 have been studied. The dependences of their a2 values on the distance between the addends attached, as found,
Figure 1. Structure of biscyclopropa-, bisaziridino-, bispyrrolidino-, and bisdihydronaphthofullerenes C60X2 under study and the designation of addends location for different regioisomers.
modern DFT method with Perdew−Burke−Ernzerhof (PBE) functional. Most importantly, we report the correlation of the calculated anisotropies of regioisomeric bis(dihydronaphtho)fullerenes C60dhn2 with the measured previous output characteristics of solar cells, based on their derivatives.
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COMPUTATIONAL DETAILS PBE/3ζ density functional theory method32 (Priroda program33) has been chosen for the study because it is successfully used for theoretical studies of thermodynamics and kinetics of chemical reactions,34−37 IR and NMR spectra,34,38 and voluminous and mechanical properties39,40 of fullerenes and their derivatives. PBE/3ζ method reproduces the measured mean polarizabilities of C60 and C70 with high accuracy.24,25 Moreover, it was an effective tool to describe the experimentally known phenomenon of polarizability depression of C60 higher fluorides.25 After DFT-optimizations and vibration modes solving (to prove that all the stationary points, respective to the molecules under study, are minima of the potential energy surfaces) by standard techniques, the components of polarizability tensors α have been calculated in terms of the finite field approach as the second order derivatives of the total energy E with respect to the homogeneous external electric field F: αij = −
∂ 2E ∂Fi ∂Fj
(1)
Tensors α have been calculated in the arbitrary coordinate system and then diagonalized. Their eigenvalues allow calculating the anisotropy of polarizability: 1 a 2 = ((αyy − αxx)2 + (αzz − αyy)2 + (αzz − αxx)2 ) 2
Figure 2. Dependence of anisotropy a2 on the distance between the addends in C60(CH2)2, C60(NH)2, C60pyr2, and C60dhn2; Lines correspond to aw2 values calculated by Method II. Numerical data associated with the plot can be found in Supporting Information.
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Figure 5. Dependence of anisotropy a2 of regioisomeric C60(CH2)3 on the average distance between the central atoms of addends. The structural formula of the least anisotropic trisadduct is shown. Numerical data associated with the plot can be found in Supporting Information.
Figure 3. Two possible structures arising for trans-1-C60dhn2 due the different mutual orientation of nonplanar dihydronaphthalene fragments of the molecule.
have the minimum at r = 0 corresponding to e-bisadducts (Figure 2). In the case of C60(NH)2, the difference in anisotropies for cis-3, e-, and trans-4 isomers are very small (less than 1.6 Å6). The largest a2 values are typical for trans-1 adducts, which have functional groups placed on the opposite poles of the carbon framework. The more complicated situation is observed for [2 + 3]- and [2 + 4]-cycloadducts with pyrrolidine and dihydronaphthalene moieties, respectively. In these cases, for each bisadducts positions, designated in Figure 1, two or three unique structures can be found, due to the nonplanarity of the mentioned moieties. It is demonstrated for two isomeric trans-1bis(dihydronaphtho)fullerenes as an example (Figure 3). The emerged diversity has not been discussed in the synthetic and photovoltaic works. However, the anisotropic properties of such isomers may differ. Therefore, we have estimated a2 of bispyrrolidino- and bis(dihydronaphtho)fullerenes in two ways. According to Method I, we have found all possible isomers for each of eight positions, compared their total energies (taking into account zero-point vibration energies), screened out energetically unfavorable structures, and used anisotropies of the most stable isomers (see Supporting Information). The second way (Method II) consists in the calculation of the weighted anisotropies aw2, using the values ai2 and relative energies for each of the found isomers, having a similar addition pattern: n
a w2 =
∑ i=1
ai2 exp(−ΔEi /(RT )) n ∑i = 1 exp(−ΔEi /(RT ))
(3)
where ΔEi = Ei − E0 are the differences in total energies (including zero-point vibration energies) of the considered structure and the most stable one. The dependences of a2 on r, obtained in terms of the described approaches, are presented in Figure 2. Method I gives the greater variation of a2 values, whereas Method II leads to the smoothed differences between anisotropies of bisadducts with eight possible variants of addition. Nevertheless, both of the methods predict very large difference in anisotropies of bis(dihydronaphtho)fullerenes (in
Figure 4. Correlation between the output parameters of organic solar cells, based on bis(dihydronaphtho)fullerene derivatives, and anisotropies of regioisomeric C60dhn2. Output parameters PCE, VOC, FF, and JSC values are taken from the recent experimental work.16.
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Figure 6. Structures of hexakiscyclopropafullerenes with uniform (a), focal (b), and compact (c) distributions of addends.
These compounds, as it turned out, are characterized by the lowest values of anisotropy. On the contrary, the devices, utilizing highly anisotropic adducts, show the lowest values of the output parameters. Slight discrepancy of data for cis-2- and cis-3-bisadducts with the discussed relationship can be explained by the fact that their mixture was used in devices because of the failed separation. As known, VOC values can be accurately predicted with the use of LUMO energies of acceptors.7,9 However, in the case of C60dhn2, we can find a more precise correlation with the anisotropy values than with LUMO levels (see Supporting Information). Strict ordering of the donor and acceptor phases is necessary for the transport of charge carriers to the electrodes in solar cells. It would seem that the high anisotropy of polarizability should facilitate the ordering. However, the correlation between the efficiency and anisotropy is reversed (Figure 4). Thus, the role of disorder in the charge transport process should be reconsidered. Though the physical meaning of the found correlation requires the further theoretical and experimental studies, anisotropy can be used for choosing the fullerene higher adducts for acceptor materials in photovoltaic applications. Taking into account the recent application of triscyclopropafullerene derivatives to organic solar cells,11,12 dependence of anisotropy on the average distance between the addends for 47 possible regioisomers C60(CH2)3 have been investigated (Figure 5). According to calculations, C3-symmetry isomer has the lowest anisotropy. This isomer is characterized with equidistance of CH2 and their uniform distribution on the fullerene core (Figure 5). In addition, calculations of a2 values of three C60(CH2)6 with uniform, focal, and compact distributions of CH2 fragments have been performed (Figure 6). Effective routes to the substituted hexakiscyclopropafullerenes are worked out43 (these compounds seem to be promising compounds for materials science in general and photovoltaic applications in particular). According to DFT calculations, the isomers C60(CH2)6 with uniform distribution of addends is the least anisotropic: its a2 value is zero in contrast to foc-C60(CH2)6 and comp-C60(CH2)6. The analogous situation is observed for their NH counterparts C60(NH)6 (Table 1). Using anisotropy values, we can assume that C3-C60(CH2)3, uni-C60(CH2)6/C60(NH)6 and their derivatives should demonstrate higher efficiency applied to organic solar cells than their positional isomers.
Table 1. Anisotropy of Polarizability of C60 Higher Adducts with Different Distributions of Added Groups (Å6) a2 type of distribution
C60(CH2)6
C60(NH)6
uniform focal compact
0.00 600.87 169.38
0.99 368.65 109.68
some cases, more than 1000 Å6) that is enough to be distinguishable by experimental techniques. Similar to [2 + 1]cycloadducts, regioisomers with r close to zero are the least anisotropic: these are e-C60pyr2, trans-4-C60dhn2, and eC60dhn2, demonstrating a2 values 196.3, 570.1, and 767.7 Å6, respectively (Method I). Here we should note that the minimal anisotropy for C60dhn2 can be found for cis-1-bisadduct. However, it is energetically unfavorable due to the steric hindrances and, in contrast to the other regioisomers, cis-1C60dhn2 derivatives has not been identified among the products of addition to C60.16 Method II indicates e-C60pyr2 and eC60dhn2 (with r = 0) to be the minima on the aw2 versus r plot. Both approaches predict the highest anisotropy of polarizability for trans-1-isomers. As we found, bisadducts with the diverse attached moieties demonstrate almost similar dependences of anisotropy on the distance between the addends. We propose that analogous dependences take place for respective substituted bisadducts. This proposition based also on the recent experimental findings42 that pyrrolidinofullerene-based dendrimers display similar polar and electrooptical characteristics independent of their dendrimer generation, that is, independent of the molecular size of substituent with the same chemical quality. Thus, the series of the substituted cycloadducts should inherit the ratio of anisotropies of the respective parent compounds. The effect of fullerene bisadduct structure on the solar cell performance have been examined experimentally for the substituted bisdihydronaphtho[60]fullerenes. We have weighed the output parameters, measured recently,16 with a2 values of the simplest regioisomeric bis(dihydronaphtho)fullerenes, calculated in the present work. The devices with the derivatives of e-, trans-4-, and trans-2-C60dhn2 as an electron-acceptor material show the highest output solar cells parameters (power conversion efficiency PCE, open circuit voltage VOC, filling factor FF, and short-circuit current density JSC; Figure 4). 9151
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CONCLUSIONS The anisotropies of polarizability of C60 higher adducts with the attached cyclopropane, aziridine, pyrrolidine, and dihydronaphthalene moieties have been calculated by PBE/3ζ density functional theory method. The correlation between the calculated dihydronaphthyl-C60 bisadducts anisotropies and the output parameters of organic solar cells (VOC, PCE, JSC, and FF) has been found. According to the found correlation, the most efficient fullerene-based electron-acceptors are characterized by the lowest anisotropy. The screening of the isomeric tris- and hexakis-adducts allowed the elicitation of their least anisotropic isomers (C3-C60(CH2)3 and uni-C60(CH2)6/ C60(NH)6), whose derivatives are proposed to be the most effective in organic cells application. The anisotropy of polarizability can be useful not only for analysis of the suitability of fullerene derivatives in photovoltaic applications. It may also be an effective tool to study the interactions of fullerene derivatives with active sites of enzymes, processes of ordering in fullerene-containing systems and their transport properties.
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ASSOCIATED CONTENT
S Supporting Information *
Numerical data associated with the Figures 2 and 5; auxiliary LUMO calculations. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Presidium of the Russian Academy of Sciences (Program No. 24 “Foundations of Basic Research of Nanotechnologies and Nanomaterials”).
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