Star-shaped fluorene-BODIPY oligomers: versatile donor-acceptor systems for luminescent solar concentrators

Luminescent solar concentrators (LSCs) are waveguides doped with luminescent centers that can spectrally and spatially concentrate sunlight. They can reduce the cost of photovoltaic energy production and are attractive prospects for photobioreactors and building-integrated applications. Reabsorption, caused by non-zero overlap between the absorption and emission spectra of the light-emitting centers, often limits LSC efficiency. Donor-acceptor energy-transfer complexes are one method to mitigate reabsorption by shifting the emission away from the main absorption peak. Here we introduce versatile star-shaped donor-acceptor molecules based on a central BODIPY energy acceptor with oligofluorene donor side units. Varying the oligofluorene chain length alters the relative oscillator strengths of the donor and acceptor, changing the severity of reabsorption for a given donor density, but also changing the luminescence yield and emission spectrum. We performed comprehensive device measurements and Monte Carlo ray tracing simulations of LSCs containing three oligofluorene-BODIPY donor-acceptor systems with different oligofluorene chain lengths, and then extended the simulation to study hypothetical analogs with higher donor-acceptor ratios and different terminal acceptors. We found that the measured structures permit waveguide propagation lengths on a par with state-of-the-art nanocrystalline emitters, while the proposed structures are viable candidates for photobioreactor and energy production roles and should be synthesized. and F4B have EQEs of 1.69% and 1.82%, respectively. However, IQE values, which are not sensitive to incomplete absorption, are relatively high. F3B has an IQE of 38.4%, while F2B and F4B have IQEs of 36.4% and 34.7% respectively. There is good agreement between measurement and simulation results, which suggests raytracing can clarify the overlapping effects of changing PLQEs and emission spectrum blue-shifts among the three FnB materials. The calculated F700 values show a similar spread, peaking at 0.76 for F3B. We note that a sub-unity flux gain is unsurprising for the small size of the devices produced ( G =8.3), and we show later that positive flux gain is predicted at a slightly larger G . These results demonstrate that to understand the effect of oligofluorene length on LSC performance it is necessary to consider not just the influence of increasing donor relative to acceptor oscillator strength as the arms are lengthened, but also the effects of spectral shifts and changes in PLQE.


Introduction
Luminescent solar concentrators (LSCs) consist of a transparent waveguide doped with highly luminescent chromophores. Sunlight incident on the LSC is absorbed by the chromophores and emitted into waveguide modes, confining the light for transport to a useful output 1 . As the input aperture of an LSC is larger than the output aperture, LSCs can concentrate light spatially as well as spectrally (Figure 1 (a)). Photovoltaic (PV) cells can be attached to the output aperture, increasing the photon flux available to the cell compared to direct illumination by sunlight [2][3][4] .
The narrow emission spectrum of the LSC can also be tuned to improve conversion efficiency 4 .
The primary motivation for this LSC-PV combination has traditionally been the high cost of PV cells, with the LSCs intended as a cheap replacement for large areas of expensive cell.
However, as the cost of PV modules has decreased, other applications are under consideration.
The aesthetic and structural properties of LSCs are being viewed as increasingly important 1 .
PV modules in general are heavy, non-structural, and available in limited colors, while LSCs are light, can be formed into a range of shapes and as part of structures, and are colorful. This makes them a strong prospect for integration into energy-generating structures 1,3 . In addition, LSCs are being explored as a means to enhance photobioreactors 5 , as daylighting sources 6 and as antennae for visible-light communications 7 .
The power conversion efficiency (PCE) of an LSC is given by , where is the absorbed fraction of the solar spectrum, is the fraction of energy lost in down conversion, is the probability of remission into waveguide modes, and accounts for all the propagation-related losses. G, the geometric ratio, is the ratio of input to output aperture areas [8][9][10] . The need to guide light over long distances within a heavily-doped matrix means reabsorption typically dominates the losses embedded in 4, 11,12 , except in unusual cases of emitters with very large Stokes shifts where parasitic matrix losses take over 13 .
Reabsorption can be diminished by increasing the Stokes shift of the emitting chromophore 14 , or through separating the absorbing and emitting chromophores and minimizing the concentration of the latter [15][16][17] . Increasing Stokes shift directly is typically pursued for inorganic emitters such as quantum dots, where varying composition and size, and the use of core-shell structures, allow the absorption and emission properties to be controlled 18,19 . For organic molecules where the Stokes shift may be considered intrinsic, the donor-acceptor strategy is prevalent, and many LSCs using donor-acceptor systems based on Förster resonance energy transfer (FRET) have been reported [20][21][22][23][24] . FRET permits efficient radiationless energy transfer between donors and acceptors, but only if the coupled molecules are within 5 nm of each other 16,[25][26][27] . This degree of proximity in molecules containing large -systems often leads to aggregation and decreased photoluminescence quantum efficiencies (PLQEs) [28][29][30][31][32] , which hinder LSC performance. Combining the donor and acceptor species into one supramolecule can avoid this problem, albeit at the price of increased synthetic complexity 16,33 . One of the best examples of a donor-acceptor supramolecular system is the bacterial phycobilisome ( Figure 1(c)). Phycobilisomes are highly organized complexes of different protein chromophores and linker peptides arranged to produce rapid and directional energy migration to a central core emitter 34 . Indeed phycobilisomes have been used directly in novel LSCs 16 .
Boron-dipyrromethene (BODIPY) conjugated systems are a popular class of organic dyes that show high fluorescence yields and absorptivity, good photostability, and solubility in common solvents [35][36][37][38] . BODIPY dyes have been used as biological labels [39][40][41] , laser dyes [42][43][44] , monomer units in low-bandgap polymers [45][46][47] , and in LSCs 15,48 . Due to aggregation, achieving efficient emission from a BODIPY dye in the solid state is difficult, but this can be remedied by incorporating the BODIPY core into a larger molecular scaffold [49][50][51][52] . In this work, we investigate LSCs containing a donor-acceptor system based on a central BODIPY emitter with three covalently-bound oligofluorene donor side units arranged in a star configuration (OFBMs, Figure 1 (b)) 33 . The oligofluorene side units absorb light and transfer energy via FRET to the BODIPY core, where it is emitted. We study the effect of a systematic increase in the number of fluorene units per molecule.
The emission peak of the BODIPY core used in this work, at 610 nm ( Figure 2 (a)), would not produce an effective LSC based on silicon PV cells. However, many proposed photobioreactors for the cultivation of microalgae are too expensive for practical applications due to the high cost of providing artificial illumination 53 . Further, it has been shown that spectral tuning can be used to improve growth efficiency for certain strains of microalgae and plants 54,55 . Thus LSCs based on OFBMs represent potentially useful candidates for lighting systems used in bioreactors 56 . Optimizing LSC efficiency is still important in this application.
Through a concerted device and raytracing study, we find that interplay between the different effects of extending the oligofluorene donor arms mean simple heuristics for optimizing LSC efficiency are inadequate. Extending the OFBM structure through simulated spectra, we find that this family of donor-acceptor molecules holds promise for low-reabsorption LSC applications.

Steady-state optical properties of OFBMs
The OFBM molecules are named by the convention FnB, where n is the number of 9,9dihexylfluorene units per arm. Molecules with n = 2, 3 and 4 were used (Figure 1    Moving from F2B through to F4B increases the intensity of the 350 nm absorption peak, due to the increased number of fluorene units, while the BODIPY peak intensity is unchanged. The position of the absorbance peak associated with the fluorene units undergoes a bathochromic shift of 13 nm per fluorene unit added to an arm (Supplementary Figure 1). This is due to extension of conjugation through the oligofluorene arms 33 .
Two-dimensional excitation-emission fluorescence spectra of the OFBMs (Figure 2  and F4B respectively, measured using a standard quinine disulfate reference 57 .

Figure 2: (a) Extinction and emission spectra of OFBMs in solution. (b)-(d) Two-dimensional emission/excitation spectra clearly showing that, under any excitation, emission occurs from
the BODIPY core at 610 nm.

LSC fabrication
Three LSCs were fabricated using a polymer matrix of lauryl methacrylate ( Emission spectra showed a blue-shift relative to solution for all OFBMs (F2B 15 nm, F3B 10 nm, F4B 20 nm) (Figure 3 (b)-(d)). We attribute this to a change in the microenvironment of the BODIPY center, which is known to shift the emission spectrum 61 .
The concentration of OFBM in the LSCs was 0.0130 mM, 0.0176 mM and 0.0126 mM for F2B, F3B and F4B respectively, as determined by absorption measurements.

LSC external quantum efficiency and flux gain
While the application of LSCs using the OFBM molecules studied is not anticipated to be in PV power generation, PV cells were used as convenient photodetectors in most of our device characterisations. Here, each LSC was coupled to four 10 x 0.3 cm silicon PV cells. No index matching between the LSC and PV cells was carried out. The current-voltage (I-V) characteristic of each LSC-PV system under AM 1.5G illumination was measured and used to calculate the external quantum efficiency (EQE), the ratio between the number of photons leaving the output aperture and the number of incident photons entering the input aperture.
Using the measured absorption spectrum, we also calculated the internal quantum efficiency (IQE), the ratio of edge-emitted photons to photons absorbed by the LSC. EQEs and IQEs were simulated using the LSC raytrace program (see Methods section) with the experimental parameters of concentration, absorbance and emission spectra, PLQY and device geometry as inputs. Measured and simulated EQEs and IQEs are shown in Table 1.
Using the simulation results, we calculated the flux gain, a detection-agnostic metric given by the ratio of photons leaving the output aperture to photons arriving over an equivalent area of the input aperture, for photons with energy exceeding a threshold value. For the three OFMBs measured, we chose a threshold of 700 nm, amenable to photobioreactors or some thin-film PV cells 53,62 . The flux gain at 700 nm (denoted F700) is shown in Table 1. note that a sub-unity flux gain is unsurprising for the small size of the devices produced (G=8.3), and we show later that positive flux gain is predicted at a slightly larger G.
These results demonstrate that to understand the effect of oligofluorene length on LSC performance it is necessary to consider not just the influence of increasing donor relative to acceptor oscillator strength as the arms are lengthened, but also the effects of spectral shifts and changes in PLQE.

Spatially-dependent external quantum efficiency
Spatially-dependent EQE was measured by scanning a 2 × 2 mm square of AM 1.5G radiation across the surface of each LSC-PV device while measuring short-circuit photocurrent. 121 points were measured per device and then averaged over the four quadrants. EQE(x,y) was then calculated by dividing the total detected photocurrent, in units of e, by the incident photon flux. Simulations were conducted by spatially constraining the excitation source in the raytracer to mimic the grid of measurement points, and calculating EQE for each grid point.  The degree of reabsorption associated with increased propagation length is determined by the spectral overlap between the luminophore emission and its absorbance spectrum. The spectrum of the emission from the output aperture was recorded as the propagation length increased.
Excitation was by a 532 nm laser beam. All three LSCs showed a red shift in emission and a decrease in intensity with increasing distance (Figure 4 (d)) and Supplementary Figure 4   The EQE in the ultraviolet increases as oligofluorene length increases, although the increase is not linear with fluorene count since the absorbed fraction scales logarithmically with optical density. The red-shifting of the oligofluorene feature accords with the measured absorption spectra. As expected, the EQE of the BODIPY feature is essentially constant across the three devices, with small differences ascribed to the PLQE and emission blue-shift differences of the three.

Figure 5: Spectrally-resolved external quantum efficiency of the fabricated LSC-PV system (squares) and simulated data (lines). Error bars represent the deviation in multiple EQE
measurements.

Study of optimized devices using raytracing
As the simulation results accord with our experiments, we turn to simulations to predict the performance of optimized LSCs based on the three OFBMs studied. First, we repeated the EQE simulations presented in Table 1, maintaining the device geometry and PV cell characteristics, but stepping through dye concentration to find the optimum performance. The results are shown in Figure 6 (a Calculated F700 results are shown in Figure 6

Simulations of extended dye structures
The potential applications of the LSCs studied above are inherently limited by solar flux in the UV region, low absorption coefficients in the visible region of the spectrum and an emission which is too high in energy. It is known that chromophores made from BODIPY cores and extended chromophore -systems are highly versatile [64][65][66] and can be conveniently tailored to span the entire visible spectrum [67][68][69] . We present hypothetical structures that overcome these shortcomings by generating plausible absorption and emission spectra and testing their behavior in simulated LSCs. The BODIPY-fluorene systems presented in this study are synthesized without linker sections between the separate chromophores, allowing efficient energy transfer into the BODIPY core. We thus expect that this donor-acceptor scheme can be   Simulated peak EQEs increased through the F8B, F8GB and 2(F8GB)D LSCs, and broadly followed the same trend with dye concentration (Figure 7 (g)). If these hypothetical molecules were used in our experimental set up they would produce peak EQEs of 7.2%, 8.0% and 13.4% respectively, which is a considerable gain over the molecules studied. This is due to the This warrants the synthesis and characterization of these larger donor-acceptor structures. With the addition of redder-emitting chromophores, OFBMs may even function effectively with silicon PV cells, assuming a moderately high PLQE can be maintained.

Conclusions
Oligofluorene-BODIPY donor-acceptor molecules represent attractive candidates for luminescent solar concentrators due to their synthetic versatility, high absorption coefficients, high PLQEs and efficient energy transfer to the BODIPY core. LSCs containing three different OFBMs were fabricated and characterized using a variety of optical measurements. A Monte-Carlo raytracing simulation was used to successfully replicate these results. We subsequently used this simulation to study optimized LSCs based on the three starting compounds, along with three hypothetical OFBM structures which extended the donor-acceptor functionality in a plausible fashion. We found that in optimized conditions, the proposed OFBM molecules perform on-par with leading nanocrystalline emitters, warranting further investigation into the synthesis of these extended antennae complexes and their incorporation into LSCs.

Synthesis of oligofluorenes molecules:
The oligofluorene molecules used in this study were synthesized with a modified Suzuki coupling using K3PO4 33 . Synthetic yields were between 29-58%. All molecules showed good thermal stability with decomposition temperatures above 400 o C.
Steady-state spectral measurements: Absorption spectra were measured using a HP 8453 spectrophotometer. Dye samples were dispersed in toluene at a concentration of ca. 1 mg ml -1 and a 1 mm path length was used. Film absorption spectra were measured using off-cuts from the produced LSCs. LSCs containing no active molecules were used as the blank.  For the LSC measurements the silicon photodiode (quantum efficiency 89.5% at the emission wavelength) was placed on the edge of the LSCs. The excitation position was in the center of the LSC, 5 mm from the edge.
Simulations: The LSC raytrace model was constructed in Matlab and has been previously reported. 70

Table of Contents Figure and Text
Energy transfer in star-shaped donor-acceptor molecules reduces self-absorption in luminescent solar concentrators.