Does the Donor-Ï-Acceptor Character of Dyes Improve the Efficiency

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Letter

Does the Donor-#-acceptor Character of Dyes Improve the Efficiency of Dye-sensitized Solar Cells? Chung Man Ip, and Alessandro Troisi J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b01149 • Publication Date (Web): 19 Jul 2016 Downloaded from http://pubs.acs.org on July 21, 2016

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The Journal of Physical Chemistry Letters

Does the Donor-π-Acceptor Character of Dyes Improve the Efficiency of Dye-Sensitized Solar Cells? Chung Man Ip† and Alessandro Troisi†,* †

Department of Chemistry and Centre for Scientific Computing, University of Warwick, UK

Abstract We quantified the donor-π-acceptor (D-π-A) character of a large number of dyes (116) used in dye-sensitized solar cells (DSSC) and correlate them with the power conversion efficiency of the corresponding cell. The result indicates that there is no correlation between different measures of D-π-A strength and efficiency, i.e. the effect of the D-π-A character is completely washed out by other effects. We propose that other design rules should be identified by statistically testing them against the now rich set of experimentally available data.

TOC graphics

Keywords Electron Transfer; Statistics; Quantum Chemistry; QSAR

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The development of new organic dyes for dye sensitized solar cells (DSSCs) has been dominated by virtually a single design rule.1–3 It has been postulated that a good dye should contain an electron acceptor (A) portion (where the LUMO is localized) close to the semiconducting surface and an electron donor (D) portion (where the HOMO is localized) close to the solution. The two should be connected by a π-conjugated bridge and the overall design is then known as the D-π-A structure (Fig. 1).1,3,4 In theory such design scheme should be effective for facilitating charge injection from the dye to the semiconductor (the dye’s LUMO interacts strongly with the conduction band states of the semiconductor), and increasing the efficiency of charge neutralization by the electrolyte with respect to charge recombination (the HOMO should accept more readily an electron from the electrolyte than from the semiconductor). It is well-known that D-π-A scheme provides not only the advantage of creating long-lived charge separated state, but also great flexibility to modify the chemical structure of dyes. This in turn leads to myriad of possibilities to idealize dye’s performance, such as adjusting the amount of π conjugation to refine a dye’s ability to absorb solar radiation,1 and insert alkyl side chain to avoid dye aggregation.5 As such, there has been an extraordinarily large volume of work devoted to the widely adopted D-π-A scheme for metal-free organic dyes,1,3,6 with almost 1000 papers returned by Web of Science (WoS) for a search containing ‘dye-sensitized’, ‘solar’ and D-π-A related keywords limited to the past 5 years.30 Despite this effort, the power conversion efficiency based on these dyes has seen little improvement in recent years, in which the pinnacle achieved has remained at around 9%1,3 over some time. It has also been suggested that D-π-A character will supposedly lead to a dye with high reorganization energy, which will negatively impact its performance.3 All in all this leads to the question of whether D-π-A character can truly paves the way to DSSC with higher power conversion efficiency. In this study we assess the influence of D-π-A character on power conversion efficiency. We have devised a quantitative measure for D-π-A character, computed this measure for 116 metal-free organic dyes, and examined the correlation between the D-π-A character and power conversion efficiency of these dyes. In the field of DSSCs, models are typically constructed based on physical principles, and the application of statistical analysis is relatively rare. Statistical modeling becomes useful when a large set of homogeneous experimental results become available and one can seek correlations between experimental properties and a number of predictors of the same property. It is widely used for example in drug discovery, where many quantitative structure-activity relationship (QSAR) studies7–9 have been conducted to identify chemicals that can provide certain medicinal 2


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functions under specified conditions. In material discovery, while perhaps the same level of usage is not seen, precedents are not in short. For examples, various scaling relations between adsorption energies have been examined for computational screening of catalysts,10 and different properties of ionic liquids have been predicted using QSAR models.11 Thanks to the increasing quality and quantity of data on dyes in DSSC in recent years, it is now possible to conduct statistical studies to understand their structure-property relationships, and generate tools for predicting the performance of new dyes. A group of such models were built for coumarin and phenothiazine dyes, with the objectives of revealing structure-photovoltaic performance relationships and designing new molecular structures with optimal properties for these families of dyes, using descriptors relating to properties such as vibrational normal modes and topology of dyes, among other predictors.12–15 The use of molecular interaction fields has also been proposed.16 We have recently explored the ability of several predictors to help modelling the efficiency of new dyes and we concluded that a useful prediction of the efficiency can be built as a function of the (computed) oxidation free energy and the reorganization energy of the dye.17 It is equally interesting to determine properties that do not correlate with the measured efficiency and, in ref. 17, we have seen for example that the molecular dipole moment, even when scaled by the molecular size, does not correlate with the efficiency. In this paper we address specifically the question in the title given its importance in the current research. The critical pre-requisite for any statistical analysis is the availability of an unbiased and sufficiently large set of experimental data, which has not been available for DSSC. A strategy to develop such set is therefore pivotal for our analysis. The following properties would be essential for the data set: (i) it should represent a good sampling of historical data but also account for more recent progresses in the field; (ii) it should refer to data collected under similar experimental condition with sufficient chemical similarity between the dyes; (iii) the data set, which will be unavoidably a subset of all those available, should be collected without being handpicked by the analyst, to exclude any type of bias and, in particular, confirmation bias18 in the dataset. In order to satisfy these criteria, we collect our data in accordance with the following strategy. We initially consider, as done in ref. 17, the neutral metal-free organic dyes reported in Mishra et.al.’s review in 20091 to sample work precedent to the publication of this review. To sample more recent work but maintain uniformity in the data set we collect data on the efficiency of new dyes subject to the following constraints: (i) dyes contain only a single carboxylic anchoring group; (ii) the measurement of power conversion efficiency is performed under AM1.5G 3



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illumination; (iii) the redox shuttle was iodide/triiodide redox shuttle in acetonitrile. The first criterion is implemented for avoiding strong deviation in efficiency due to adsorption geometry and charge injection rates of dyes with different anchoring groups;19 the second and third are to ensure the data are originated from measurements under similar conditions. It has been noticed that the best current cells are based on cobalt(II/III) redox shuttle,20 but for the benefit of obtaining a larger statistical sample we consider iodide/triiodide redox shuttle. Next, we require a strategy to collect data that have been reported after the publication of Mishra et.al.’s review.1 The devised pseudo-random procedure guarantees the absence of bias, but is also fully reproducible by other researchers with the aim of collecting the chemical structure and the efficiency of ~60 dyes appeared in the literature over the past 6 years. All data are collected from the search results provided by Web of Science, using the keywords ‘dye-sensitized’ and ‘solar’ and ‘organic’ and ‘synthesi*’ by year, starting from year 2010 to year 2015. For each year the search results are sorted according to ‘relevance’ and are refined by ‘articles only’. Only dyes reported in journals with an impact factor of over 4 are considered, to limit the number of hits and ensure in a rough way that the data are of sufficient quality. We then include the first 10 dyes for each year in the search results. Many studies, however, reported more than one dye and it is generally difficult to achieve exactly 10 dyes for each year without omitting dyes from some studies. Hence, we have included all dyes reported within a study, except when a dye does not satisfy the criteria stated previously. The number of dyes for each year is therefore equal or greater than 10 dyes. The search results and the papers used have been recorded to insure reproducibility and given in the SI. From this preliminary data set (of 133 dyes) we have excluded the dyes which required more than 860 basis functions in the quantum chemical calculation (approximately those with more than 155 atoms) to make sure all calculation can be performed automatically and can converge without human intervention. The final data set contained 116 dyes. It should be noted that, D-π-A character is not a well-defined property of dyes. Many dyes have been classified as D-π-A dyes based primarily on chemical intuition. A number of qualitative and quantitative indices21–23 have been devised for D-π-A character, but they have yet been applied consistently to examine the efficacy of D-π-A character on improving power conversion efficiency. We have devised a descriptor for D-π-A character, namely the excitation dipole moment (EDM), which is similar to the descriptors introduced in ref. 21 and ref. 23. The EDM is computed as the difference between the centroid of the weight of HOMO ( CHOMO ) and the centroid of the weight of LUMO ( C LUMO ):

EDM = ± CHOMO − CLUMO 4


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CMO = ∑aiMOaiMOri + ∑∑aiMOajMO Sijri i

i

j >i

where aiMO is the atomic orbital coefficient of either HOMO or LUMO, Sij is the overlap matrix elements of basis functions i and j, and ri is the 3-dimensional Cartesian coordinates where the atomic orbital i is centred (see also Fig. 1). The sign of EDM is determined by the dot product of the vector between the centroids ( CHOMO − CLUMO ) and the vector of the Carbon-Carbon bond at the anchoring group, which indicates the direction of charge excitation. A more negative value of EDM corresponds to a stronger D-π-A character with acceptor closer to the semiconductor. We have considered also alternative descriptors of the D-π-A character strength including (i) the “orbital asymmetry” parameter, defined in ref. 17 as the ratio of the weight of LUMO and HOMO at the anchoring group of the dye, and (ii) the dipole difference between the ground-state and first excited-state dipole moments of the dye. These alternative measures (especially (ii)) show very good correlation with EDM and, for this reason, we report in the main manuscript only the correlation between EDM and efficiency, while including in the supporting information the correlation between these different measures and the efficiency. In essence, the conclusions of this paper are unaffected by the chosen measure of the D-π-A character. We note that the EDM measure is the least computational expensive and the distribution of EDM values in our data set is closer to a normal distribution.

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Figure 1 (top) Illustration of D-π-A character of a dye (from ref. 24) adsorbed onto a semiconductor such as TiO2. The acceptor part is close to the semiconductor to facilitate charge injection, whereas the donor part is far from the semiconductor to avoid charge recombination. The EDM of a dye is the separation between the LUMO’s centroid and the HOMO’s centroid. (bottom) Illustration of the HOMO and LUMO of the dye. The orbital coefficients, atom coordinates and overlap matrix required for computing EDM were acquired from single-point calculations of geometrically optimized dyes in acetonitrile. Geometry optimizations were performed with a relatively small basis set (3-21G*), and the energies of the optimized structures were 6


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subsequently re-evaluated with 6-31G* basis set. All calculations were performed with DFT/B3LYP hybrid functional, with the acetonitrile environment mimicked with polarized continuum model (PCM).25 All calculations were performed with Guassian03 package.26 Fig. 2 shows the correlation between power conversion efficiency (η) and EDM with 116 data points. A more negative EDM represents a stronger D-π-A character. It can be seen that there is no linear correlation between the two properties, which is supported by an extremely low Pearson’s correlation coefficient (r = −0.01) from simple linear regression analysis. By visual inspection it is unlikely that the fitting can be improved with higher order polynomials. The results do not directly imply that the D-π-A design does not work but that the combination of all other effects is so dominant that there is no measurable benefit in introducing a D-π-A character. Suppose, for example, that D-π-A character is only helpful (i.e. it correlates positively with the efficiency) if the dye molecule is correctly oriented on the surface and with the D-π-A director perpendicular to the surface – we have not included orientation effect in the analysis. Our results would therefore imply that the D-π-A character can be helpful or detrimental for the efficiency depending on the orientation and that helpful and detrimental orientations are equally likely. A completely opposite interpretation is that the D-π-A character has no influence. In the first case one should work toward better orientation of the dyes rather than strengthening the D-π-A character and in the latter one should consider a different design rule.

Figure 2 Correlation between η (%) and EDM of 116 dyes. Mean of EDM (μ(EDM)) = -6.61. Standard Deviation (S.D.) of EDM = 2.43. μ(η) = 5.31 %. S.D. of η = 1.80 %. Pearson’s correlation coefficient (r) =−0.01. To illustrate that some correlations can be found and can provide new physical 7



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insight we consider the correlation between η and the dye reorganization energy (λ), one of the most studied parameters for the interfacial charge transfer processes27 first explored statistically for a large sample of dyes in ref. 17. The reorganization energy is computed for the process Dye → Dye + + e − in acetonitrile following the procedure described in ref. 17 (the component of the reorganization energy associated with the iodide/triiodide redox shuttle in a number of possible chain of reactions28 is neglected as it is expected to be common to all dyes). As shown in Fig. 3(a), the correlation is only moderate and negative (r=−0.26) but agrees with predictions originated from physical principles, where in the evaluation of charge recombination rate decreasing λ would retard charge recombination,29 and hence should increase η. The correlation shown in Fig. 3(a) illustrates how statistical analysis could be useful to validate any given physical model of DSSC. Due to the correlation observed between η and λ, it should be meaningful to examine also the correlation between EDM and λ, in order to study whether D-π-A character could influence η through associated λ. Fig. 3(b) shows the correlation between EDM and λ, where large absolute value of EDM (strong D-π-A character) would generally associate with low λ. Such observation clearly disagrees with the suggestions in ref. 3 that a stronger D-π-A character is associated with higher λ (another example of how a statistical analysis can support or disprove physical hypotheses). A study of this type can be also used to look at extreme values of the parameters of interest. We have labeled in Fig. 3(b) the data point corresponding to the extreme high and low vales of EDM and λ. Low λ is seen with very delocalized donors (specifically in molecules G and H with identical and large donor groups). Expectedly, short molecules with localized excitation tend to have high λ (C and D) and low D-π-A character (E and F). Looking at the full sample, we have found modest correlations between λ and the size of the dyes, and between the D-π-A character and the size (see Fig.S2 in the SI). In view of the observed correlations between λ and η, and λ and EDM, one could argue that an increased D-π-A character should lower λ and therefore increases η. If there are no other benefits from the D-π-A character apart from reducing λ, we would expect the correlation coefficient between EDM and η to be still a significant

−0.22, which is estimated based on the correlation coefficients between λ and η (r = −0.26), and between λ and EDM (r = 0.4) (see SI5 for details). Having observed a correlation coefficient of just r = −0.01 between EDM and η one can even speculate that the D-π-A character is detrimental to efficiency (the standard error on the correlation coefficient with this sample size is approximately 0.09 as discussed in the SI).

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(a)

(b)

A

B

O

D

O

C S

COOH S

nhexO

S

NC

COOH N

N C4H9

CN C6H13O

F

E

COOH

H S

G

S

CN

S

Ph2N S

Ph2N

Figure 3 (a) Correlation between η (%) and λ (eV) of 116 dyes; μ(λ) = 0.70 eV. S.D. of λ = 0.06 eV. (b) Correlation between λ (eV) and EDM of 116 dyes. Labeled dyes are the two dyes with the largest (A, B) and smallest (E, F) EDM, and largest (C, D) and smallest (G, H) λ. 9



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In conclusion, we have considered a large set of dyes and found no correlation between their D-π-A character and the experimental power conversion efficiency. Equivalently, this means that other effects are much more important and wash out any potentially beneficial effects of the D-π-A character. We have shown that such type of statistical analysis can be used to validate structure-property hypotheses derived from basic physical principles. For examples we have seen that, as predicted, there is an improved efficiency for dyes with reduced reorganization, while it is not true that the increased D-π-A character increases the reorganization energy. We can speculate that the erroneous emphasis on the D-π-A character has been due to a number of factors. Probably there has been an element of confirmation bias (i.e. good D-π-A dyes are used to support the theory but counter examples are ignored). The lack of quantification of D-π-A character and the predominance in literature of papers comparing the performances of just few dyes have certainly contributed to this misconception. More importantly, we think, the popularity of this design rule has caused a large majority of new dyes to be synthesized with the D-π-A character built in. High performing dyes have therefore been discovered with higher probability within this class of compounds, i.e. confirming the erroneous hypothesis by a bias in the sampling. A retrospective look at a uniform set of data is probably the best way to test the validity of any given design rule. Acknowledgments. CMI’s work is supported by an EPRSC studentship. We are grateful to Myeong Lee and Rocco Fornari for useful discussions. Supporting Information. List of dyes and raw data for the analysis. Correlations with other metrics for the D-π-A character and dye’s size. Note on the correlation coefficient of mutually dependent variables. References (1)

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(30) The search result (1016) on WoS for an idea on the volume on work devoted to D-π-A scheme was obtained using the keywords ‘dye-sensitized’ and ‘solar’ and ‘donor and acceptor’ or ‘push-pull’ or ‘donor-pi*’ or ‘donor-π*’ or ‘D-pi*’ or ‘D-π*’. The search date is 25/01/2016.

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Does the Donor-Ï-Acceptor Character of Dyes Improve the Efficiency

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