Luminescent solar concentrators based on melt-spun polymer optical fibers

Luminescent solar concentrators based on melt-spun polymer optical fibers

Materials and Design 189 (2020) 108518 Contents lists available at ScienceDirect Materials and Design journal homepage:

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Materials and Design 189 (2020) 108518

Contents lists available at ScienceDirect

Materials and Design journal homepage:

Luminescent solar concentrators based on melt-spun polymer optical fibers Konrad Jakubowski a,b, Chieh-Szu Huang c,d, Ali Gooneie a, Luciano F. Boesel c, Manfred Heuberger a,b, Rudolf Hufenus a,⁎ a

Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory of Advanced Fibers, Lerchenfeldstrasse 5, St Gallen 9014, Switzerland Department of Materials, ETH Zurich, 8092 Zurich, Switzerland Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory of Biomimetic Membranes and Textiles, Lerchenfeldstrasse 5, St Gallen 9014, Switzerland d Laboratory of Inorganic Chemistry, ETH Zurich, 8092 Zurich, Switzerland b c




• Bi-component melt spinning was explored as a novel way to manufacture fiber luminescent solar concentrators (LSCs). • Results revealed that solubility and dispersion of luminescent dye in polymers play an important role in LSCs' performance. • Presented LSCs are a cost-effective solution to enhance the illumination-angle dependence of solar cell power production. • Due to high industrialization potential and overall performance, such fibers may find their way into future applications.

a r t i c l e

i n f o

Article history: Received 16 December 2019 Received in revised form 20 January 2020 Accepted 21 January 2020 Available online 22 January 2020 Keywords: Luminescent solar concentrators Polymer optical fibers Energy harvesting Melt spinning

a b s t r a c t Luminescent solar concentrators (LSCs) collect incoming sunlight and direct it to a smaller-area photovoltaic cell. In the presented work, form factor and illumination angle-dependent performance of LSCs consisting of bicomponent melt-spun fibers is demonstrated. Three thermoplastic polymers act as dispersing host material for the luminescent dye Lumogen Red 305 (LR305). Molecular dynamics simulations provide numerical access to Hildebrand solubility parameters, which are an estimate for the mixing compatibility of dye with polymer matrix. Actual emission intensity measurements from material samples are compared to Monte Carlo ray tracing simulations. Some samples show an increased absorption, which led to the hypothesis that there exist optically passive dye aggregates if the dispersion is not optimal. The best-performing polymer/dye pair is identified and used to melt-spin fibers. Geometrically defined bundles of LSC fibers are studied in a scenario of white light illumination and variation of illumination-angle. This experiment simulates a theoretical daily course-of-sun illumination in absence of atmospheric effects. We report optical conversion efficiencies of the prepared LSCs between 2% and 15%, depending on illumination angle and bundle geometry. © 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://

⁎ Corresponding author. E-mail address: [email protected] (R. Hufenus). 0264-1275/© 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (


K. Jakubowski et al. / Materials and Design 189 (2020) 108518

1. Introduction Current photovoltaic (PV) cells exhibit efficiencies in the range 10% to 40% [1]. To increase PV system power, large-area panels are required. The costs scale essentially linearly with PV area [2], and the maximum power achieved is often limited by the available system integration area (e.g. roof top) [3,4]. The output power of planar solar cells depends on the cosine of the illumination angle, manifesting itself as a midday power peak, which has to be embraced by the power grid [5]. Luminescent solar concentrators (LSCs) were first proposed in 1976 to enhance the performance of PV solar cells. In practical use, a LSC must not only be efficient in collecting photons at fixed illumination angle, but ideally during the course of a whole day. Furthermore, the power gain by LSCs should be cost-effective compared to the PV panel's price per area. Polymer optical fibers (POFs) provide a suitable form factor to address those requirements [6]. The favorable impact of the fiber geometry becomes apparent in terms of the LSC gain factor F(α, λ), which is defined as the ratio of power generated by a solar cell with/without LSC [7,8]: F ðα; λÞ ¼

P LSC ¼ ηopt ðα; λÞ  Gðα Þ  ηcell ðλÞ P cell


where ηopt(α, λ) signifies the optical conversion efficiency [9,10]. We note that for a fixed illumination, ηopt(λ) contains the optical attenuation in the fiber. The factor ηcell(λ) is the wavelength-dependent efficiency of the solar cell and G(α) is the angle-dependent geometrical concentration factor, i.e. the ratio of the illumination angle dependent collection surface (projected LSC shadow area), divided by the LSC output area (out-coupling area facing photovoltaic cell). Gðα Þ ¼ Acollection ðα Þ=Aoutput


For illumination at a normal angle, the G-factor of a fiber is maximal and it is also proportional to the fiber aspect ratio, underlining the advantage of the length-scalable fiber form factor [11]. Synthetic fibers can be produced in large quantity, which speaks for the economic benefit and feasibility of the proposed approach. Meltspinning is a widely used technique for production of textile fibers [12], and we explore an adaptation for manufacturing fiber LSCs. Namely, bi-component melt-spinning enables a continuous, singlestep production of polymer optical fibers (POFs) [13]. The classical step-index POF consists of a light-conducting core, coaxially embedded inside a lower-refractive-index cladding. In-situ spinning with the cladding in place, elegantly removes the need for a solution coating process. Bi-component spinning is solvent-free and represents a cost-effective production method [14,15]. The most common polymer used in the design, production and research of LSCs is polymethyl metacrylate (PMMA). Several other transparent thermoplastics are available [16–18], which may offer a variation of mechanical or optical properties. Luminescent light converting dyes constitute a fast growing research and application field. Many different luminophores are being studied as sunlight-converting additives, such as organic dyes, nanocrystals or quantum dots [19–23]. Lumogen Red 305 (LR305) is a prominent example: this commercially available dye has a close-to-unity quantum yield and an excellent thermal stability up to 370 °C – a suitable additive for melt-spinning. A careful selection of the polymer host-luminescent dye pairing is crucial to help dispersion of luminescent molecules. The selfabsorption parameter [10,24] describes how the light emitted from a dye molecule is reabsorbed by adjacent dye molecules along the light path. Likewise, a low solubility of the dye in the host polymer melt may lead to dye aggregation, which leads to suppressed light emission via luminescence quenching [25,26]. While the dispersion of dye molecules in liquid solvents is well understood [27–29], solubility of dye in polymer melts has received less systematic attention.

In this study, some key material factors pertaining to the development of melt-spun fiber LSCs are considered. Three polymers, namely cycloolefin polymer (COP), polycarbonate (PC) and PMMA were evaluated as possible host materials for the here fixed choice of LR305 dye. To assess luminescent properties in these host polymers, we prepared dyedoped polymer plates. Monte-Carlo ray tracing and molecular dynamics simulations were used to link molecular properties to the plate geometry and results were validated experimentally. Prototype melt-spun bicomponent LSC fibers were manufactured using a doped COP core and low-refractive index sheath material, namely terpolymer of tetrafluoroethylene, hexafluoropropylene and vinylidene fluoride (THVP). The illumination-angle dependent performance in absence of atmospheric effects (such as scattering) was determined for defined bundles of such prototype LSC fibers. 2. Materials and methods 2.1. Materials Three polymers were tested as host materials for LR305 in the fiber core: COP granulate (Zeonor 1020R, refractive index 1.53) was purchased from Zeon Europe GmbH, Germany; PC granulate (Sabic Lexan 103R, refractive index 1.58) was purchased from Lenorplastics AG, Switzerland; PMMA granulate (Plexiglas 7 N, refractive index 1.49) was purchased from Evonik Industries AG, Switzerland. In addition, terpolymer of tetrafluoroethylene, hexafluoropropylene and vinylidene fluoride granulate (THVP 2030GZ refractive index 1.35) was purchased from 3 M Company, Germany, and used as a low-refractive-index, mechanically stable fiber sheath. The dye molecule LR305 was purchased from BASF SE, Germany. All materials were used without further purification. The chemical structures of the materials are shown in Fig. S1 in the supporting information. 2.2. Melt-processing of materials Polymer granulates were first dried overnight in a vacuum oven at elevated temperatures. LR305 powder was then added to the dried granulates of the fiber core polymer. To assure a uniform distribution of the dye, the granulate/powder mixtures were tumbled for 5 h. To prepare thin plates, the pre-mixed samples were melt-mixed at their respective processing temperatures for 2 min in a torque rheometer (HAAKE™ Rheomix OS Lab Mixer). The solidified extrudate collected after melt-mixing was grinded, and compression molded into 1 mmthick plates with a hot press (Lindenberg Technics). The fiber LSCs was melt-spun in a custom-made pilot plant described elsewhere [30]. The sheath (cladding) material and the core polymer melt were fed from two separate extruders. Metering pumps transferred the melts into the spin pack, and the bi-component fiber exited the spinneret into the quenching chamber, where it air-cooled and solidified. Finally, the POF was taken up, drawn by heated godets, and spooled onto a bobbin. Adapted godet speeds defined the optimal tension for each fiber type. The nominal throughput was 150 m of continuous fiber LSC per minute. More details on melt-processing, with exact processing temperatures and godet speeds, can be found in the Supporting Information. 2.3. Optical characterization of plates Absorption of the plates was measured using a UV–Vis spectrophotometer (Agilent Cary 4000 UV/Vis). Emission intensity was measured from the plates using a spectrofluorometer (Horiba FluoroMax) with a custom-made sample holder. Illumination and detection were set up at perpendicular sample faces. Each measurement was repeated three times.

K. Jakubowski et al. / Materials and Design 189 (2020) 108518

2.4. Performance of melt-spun bi-component LSCs To study optical behavior of individual fiber LSCs, an established setup was used [31]. A glass optical fiber (Thorlabs M28L02) coupled to a green LED light source (Thorlabs M505F3), illuminating the fiber from the side, was translated along the fiber axis. At each position, the emitted light at the fiber's tip was collected by another glass optical fiber (Thorlabs M59L01), which was coupled to a mini-spectrometer (Hamamatsu C10083MD). 2.5. Performance of LSC bundles Melt-spun fibers were combined into defined bundles (Fig. 5b): each bundle consisted of 200 fibers. To define their arrangement, the fibers were inserted into transparent PMMA tubes (Rohm AG, Switzerland) of 5 mm inner and 7 mm outer diameter. The fibers covered 85% of the cross-sectional area of the tube's lumen. The tubed bundles had lengths of 20 mm, 40 mm and 80 mm. A calibrated photodetector head with input optics 11 mm diameter diffusor window and spectral responsivity between 400 and 1000 nm (RW-3705-2, Gigahertz-Optik GmbH, Germany), attached to an optometer (P 9710, Gigahertz-Optik GmbH, Germany) was placed on a rotational stage. The sensitive surface was masked with a black, non-transparent plate, leaving a circular opening of diameter corresponding to that of the inner diameter of the tubed fiber bunches. The rotational stage with the sensor resided inside a black box to prevent illumination by stray light. A Xenon short-arc lamp (OSRAM XBO 450 W OFR (6000 K)) was used as a white light source, placed 3 m from the detector to approximate a plane wave front, reducing square-distance intensity artefacts to b2%. Light intensity was measured with the masked photodetector and with perpendicular tubed fiber bundles on the circular opening. The detector in both configurations was rotated, and the intensity was recorded for a selection of illumination angles. Each measurement was repeated 3 times. In addition to these detector measurements, a PV solar cell with dimensions of 46 mm by 40 mm (Velleman SOL3N Polycrystalline Solar Module 1 V, Conrad Electronic AG, Switzerland) was used for similar measurements. The solar cell was also masked with a black, nontransparent foil, with a circular opening of diameter corresponding to that of the inner diameter of the tubed fiber bunches. The spectral sensitivity of the PV solar cell is more closely representing a real application, i.e. higher sensitivity in red and NIR. The mask was placed identically on the cell for all measurements to exclude variations of internal resistance from the shadowed area. The illumination-angle dependent power was measured, in the same setup as in the previous case, but now the maximum power point was followed on the I(V) curve. Each measurement was repeated 3 times. More details about these measurements can be found in the SI.


used in the experiment. For the presented analysis, the histograms were fitted using Origin 2018. 2.7. Molecular dynamics simulations Fully atomistic molecular dynamics (MD) simulations were performed in order to calculate the Hildebrand solubility parameters of different molecules of interest from the cohesive energy density (CED) [33–35]. Boxes containing 100 molecules were generated using the Amorphous Cell module of the BIOVIA Materials Studio simulation software [36]. The molecules were allowed to interact with each other using the COMPASS force field of the Forcite module of Materials Studio. Prior to CED calculations, the simulation box was equilibrated in the NPT ensemble for 2–7 ns to reach equilibrium at 298 K and 1 atm. 3. Results and discussion 3.1. Luminescent properties of the dye-polymer systems In order to examine how different polymer hosts influence the luminescence of LR305, the optical emission was measured from dye-doped polymer plates. PMMA, PC and COP plates were prepared with different LR305 concentrations, as summarized in Table 1. Absorbance spectra of three host materials (COP, PMMA and PC) with 0.05 wt% LR305 concentration were measured to determine the absorption coefficients for each wavelength required for ray-tracing simulations described later in the paper, as well as potential selfabsorption region of the LR305. Fig. 1 displays those results. To quantify the emission strength of each of the host materials with different quantities of LR305, the emission spectra of all prepared plates were measured and comparatively shown in Fig. 2. To avoid spectral overlap between emission spectra and excitation beam, the plates were excited by the fixed wavelength 450 nm. This wavelength lies far from the expected emission and exhibits similar absorbance for LR305 in the three host materials (Fig. 1). The illumination was perpendicular to the plate's surface, and measured in transmission at the same angle. As can be seen in Fig. 1, different plates exhibit a similar absorbance at that wavelength. For each of the host materials, two prominent emission peaks are visible (Fig. 2): namely at ≈590 nm and at ≈640 nm. A third, significantly smaller peak is present at ≈675 nm, which can be deconvoluted by means of more detailed peak analysis. For PMMA and PC samples, both emission and absorption spectra seem red-shifted with respect to COP samples – this effect occurs due to the polarity of the host material [37]. It can also be observed, that the position of the first peak shifts towards longer wavelengths. To gain additional insight, Fig. 3 displays the integral spectral area for all the measured thin-plate samples, calculated from the data in Fig. 2. We observe that the LR305 yields a higher emission intensity in the COP matrix than in PMMA or PC. In addition, the position of the first

2.6. Monte-Carlo ray tracing simulations An open-source, Python-based ray-tracing software PVTRACE (version 2.0.4) [32] was used to track random photons inside each of the prepared polymer plates. The measured absorption and emission spectra of LR305/polymer host systems were used as input data for these calculations. For the simulation, a point light source was placed inside the plate geometry next to the illuminated plate/air interface. The molecular emission spectrum in the simulation corresponded to the previously measured emission spectrum of LR305. For each simulation, 250,000 random photons were generated. Each generated photon's initial wavelength was randomly selected based on the defined emission spectrum. The simulation accounts for photons that undergo different optical processes inside the geometry of the LSC plate (like selfabsorption, re-emission, absorption by the polymer matrix, etc.). The resulting distribution of emitted photon wavelengths was statistically analyzed in a histogram (Fig. 4), which imitates the spectral analysis

Table 1 LR305 concentration in the prepared melt-processed thin plates. Sample

LR305 concentration [wt%]

LR305 concentration [μmol/cm3]


0.002 0.01 0.05 0.07 0.1 0.25 0.002 0.05 0.1 0.25 0.002 0.05 0.1 0.25

0.02 0.09 0.47 0.66 0.94 2.34 0.02 0.55 1.10 2.76 0.02 0.56 1.11 2.78


K. Jakubowski et al. / Materials and Design 189 (2020) 108518






Normalized intensity

Absorbance [a.u]







0.2 0.0








Wavelength [nm]







Concentration [Pmol/cm ]

peak apparently shifts towards longer wavelength with increasing dye concentration (Fig. 2), which is the result of a marked self-absorbance in this wavelength range (Fig. 1). As expected, the position of the second and the third peak remain unchanged, in agreement with negligible self-absorbance above 650 nm. We used Monte Carlo ray-tracing simulations to connect the previously measured emission data to the light path in this plate geometry. Normalized emission spectra of COP0, PMMA0 and PC0 (0.002 wt% LR305 each) were used as reference emission spectra in the simulation, since they were measured at minimal self-absorption (i.e. at low LR305 concentration). The absorption behavior of the plates with 0.05 wt% LR305 (COP2, PMMA1 and PC1) was then simulated, assuming the previously measured absorption behavior (Fig. 1). Fig. 4 shows a comparison between simulated and measured emission spectra of these samples. The simulated emission spectra reproduce the peak positions and peak shapes rather well. A comparison reveals, however, that the simulation predicts a relatively stronger first emission peak. For quantification of this effect, peak area ratios are calculated using the following relation: Afirst peak Asecond peak þ Athird peak



Fig. 1. Absorption spectra (with standard deviation) of COP2, PMMA1 and PC1 (all with 0.05 wt% LR305). The results indicate good absorption of blue, green and a small portion of red light by LR305. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Rpeak area ¼



This parameter estimates the intensity of the first emission peak (i.e. the one most affected by die self-absorption) relative to the other two peaks (unaffected by self-absorption). The comparison of fitted

Fig. 3. Normalized integrated emission intensities of the measured thin-plate samples.

simulated and experimental results is thus summarized in Table 2. One can readily recognize a trend; namely, that theory predicts higher peak ratios—an effect most prominent for the PC, and least prominent for the COP sample. Table 2 and Fig. 4 indicate the presence of additional attenuation effects not accounted for in the simulation; these effects depend on the host material. Collected results thus suggest there is an excess of self-absorption, which is more pronounced in PMMA and PC samples. It is reasonable to hypothesize that aggregation-induced quenching of the luminescent dye molecules is the likely cause; it can explain the observed dependence on the host polymer matrix. To investigate this hypothesis, we performed molecular dynamics (MD) simulations on pure COP and LR305 individually to compute their respective Hildebrand solubility parameters, δ. This parameter represents the cohesive energy density for each pure phase. The square of the difference between them, Δ = (δA − δB)2, is a simple estimate of the dispersion quality. A lower parameter Δ would indicate a better dispersion of the dye in the polymer matrix [38]. For the MD computation, the structures of COP and LR305 were taken from previous publications [39,40]. Hildebrand solubility parameters of pure PMMA and PC were taken from literature [41]. The MD simulation is described in more detail in the Experimental Section. Table 3 summarizes the solubility parameters and Δ values. The predicted best matrix for the dispersion of LR305 is indeed COP. Therefore, we would expect less dye aggregates in COP than in PMMA or PC [25,26].

Fig. 2. Luminescence spectra of a) COP plates, b) PMMA plates and c) PC plates with different LR305 concentrations (see: Table 1), measured perpendicular to the plates.

K. Jakubowski et al. / Materials and Design 189 (2020) 108518


Fig. 4. Simulated (gray histogram) and measured (red curve) emission spectra of a) COP2 b) PMMA1 c) PC1 (all with 0.05 wt% LR305) in the plate geometry. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

We think the systematically higher absorption of the first peak observed in the previously simulated spectra (Fig. 4, Table 3) can be explained by aggregate formation, particularly since this 600 nm-peak would be selectively affected by absorption from non-emitting dye aggregates. The intensity ratio (“sim/exp” in Table 2) can thus be regarded as a simple measure for dye-aggregate formation in the polymer matrix.

3.2. Properties of melt-spun, bi-component fiber LSCs Based on previous results, a continuous bi-component fiber LSC was produced on a pilot melt-spinning plant with COP as a core and THVP as a cladding material. The production rate was 150 m per minute. The obtained fibers exhibit a numerical aperture of 0.72. The LR305 dye concentration was 0.05 wt% in the core – this value was found to have the highest emission intensity (Fig. 4). More details on the continuous fiber production can be found in the Experimental section as well as in the Supporting Information. Fig. 5a shows a cross-section of the studied melt-spun bi-component fiber LSC – its core radius was 139 ± 1μm, with an outer radius of 163 ± 2μm, amounting to a core portion of 73 ± 1vol%. This geometry allowed easy handling and characterization. Melt-spinning provides excellent uniformity of produced fiber LSCs. The hence obtained fiber LSC was studied with respect to the spectral characteristics of the emitted light. Therefore, a point light source was translated along the fiber axis, illuminating it from the side and the light emitted at the tip was recorded using a fiber-coupled spectrometer. The distance dependence of the emitted spectrum in Fig. 6a served as basis to calculate a wavelength-dependent attenuation as displayed in Fig. 6b, described in more detail the SI. As seen in Fig. 6a, the spectrum maxima apparently shift towards longer wavelength as the distance to the illumination point increases; this is, again, the result of dye self-absorption. Light is lost along the way in an exponential manner, which can be described by an attenuation ratio [dB]. As seen in Fig. 6b, the attenuation spectrum resembles the L305 absorption spectrum in COP (Fig. 1). Light in a wavelength range below 615 nm is attenuated below measurement noise within a traveling distance of 1 mm. On the other hand, the light in the range above 615 nm can travel longer distances. For example, this can be quantified in Fig. 6a (pink curve) where around 16% of the total light can travel 160 mm to the fiber tip. Additional details about the setup of the optical measurements are available in the SI.

Fiber bundles were prepared to test their light concentrating performance with respect to the illumination angle. Bundles of three different lengths were used, namely 20 mm, 40 mm and 80 mm (Fig. 5b). The maximum length was chosen in accordance to the previously presented attenuation measurements for a single fiber. To preserve a well-defined orientation of the 200 fibers as part of a 5 mm diameter bundle, they were held together by transparent PMMA tubes. Due to geometric constraints, a portion of ~62% of the tube area was covered with emitting fiber cores. The photodetector used for intensity measurements was masked with a fixed circular aperture matching the inner diameter of the PMMA tubes. A Xe-arc lamp was used as an excitation light source; it exhibits a quasi-white light illumination that approximates the solar spectrum. A calibrated photodetector was rotated on a stage to vary the relative direction of the incoming light and thus simulate different sun positions on the sky with respect to the receiver, disregarding atmospheric effects such as Rayleigh scattering. We adapt the following convention: angle α = 0° for the illumination parallel to the surface of the detector and α = 90° for the illumination perpendicular to the surface of the detector. Fig. 7a compares the recorded intensities at different bundle lengths as well as the masked bare sensor. The highest power was measured for the bare photodetector (PD) at perpendicular illumination (α = 90 °). We note that the measured intensity exhibits a distinctively different angular dependence in presence of the fiber bundles. Namely, at shallower illumination angles, the intensity recorded for bundles is higher, as the incoming light is received by a larger projected area of the LSC bundle, which is expressed by the following equation: Acollection ðα Þ ¼ L∙2r∙ cosα þ π∙r 2 ∙ sinα


where L is the length of the cylinder and r is its radius. To study the length-dependence of the bundle LSC efficiency from such angledependent measurement, we split the incoming illumination into two orthogonal components: Iðα Þ ¼ A  cosα þ B  sinα


where I(α) is the angle dependent intensity, and A and B are the orthogonally convoluted contributions containing geometrical and optical

Table 3 Hildebrand solubility parameters of luminescent dye and polymer hosts.

Table 2 Peak area ratios (Rpeak area) for simulated and experimental results.


3.3. Characterization of multi-fiber bundle LSCs




Ratio (sim/exp)

2.37 1.55 1.81

1.85 1.14 1.28

1.28 1.36 1.42


Hildebrand solubility parameter [(J/cm3)0.5]

Δ [J/cm3]

17.05 15.47 19.00 19.90

– 2.50 3.80 8.12


K. Jakubowski et al. / Materials and Design 189 (2020) 108518

Fig. 5. a) Microscopic image of a cross-section of the prepared melt-spun bi-component fiber LSC. b) 20 mm, 40 mm and 80 mm PMMA tubes filled with fiber LSCs.

factors influencing the performance of bundle LSC. By fitting the curves in Fig. 7a to Eq. (5), parameters A and B can be extracted. The hence obtained values are plotted in Fig. 7b for different lengths of fiber bundles. As expected, the portion A grows with increasing bundle length, due to enhanced collection of lateral light by the LSC. We note that the growth of A is sub-linear with bundle length. Fitting the observed asymptotic behavior of this component reveals the useful LSC length of around 80 mm, as imposed by fiber attenuation, presented in Fig. 6b. This maximum effective length will depend on dye and agglomerate concentration. The portion B encompasses a light collection maximum for bare detector, and sharply decreases with implementation of bundles. This relates to the attenuated direct transmission of illuminating light along the bundle axis, i.e. mainly in-coupling at the open fiber tip end. To study angle-dependent optical conversion within the fiber, we expand the analysis used in literature by, for example, R. Reisfeld et al. [9], E.-H. Banaei et al. [10], S. Correia et al. [42] and I. Parola et al. [43], and calculate the optical efficiency ηopt as a ratio between optical power produced by bundle LSC, to power received from the illumination, taking into account the effect of varying illumination angle: ηopt ðα Þ ¼

Iout ðα Þ∙Aoutput P out ðα Þ ∙100% ¼ ∙100% P in ðα Þ Iin ∙Acollection ðα Þ


where Pout(α) and Pin(α) are produced and received powers, respectively, Iout(α) and Iin are output and incoming intensities, respectively, and Aoutput and Acollection(α) are emitting and collecting areas, respectively. In the case of cylindrical geometry, such as the bundle LSC presented, the collecting area is changing with the angle following

Eq. (4). Fig. 8 shows the calculated efficiencies for varying angles α, in comparison with previously published references. We note that the values obtained for bundle LSCs are comparable to those reported in other studies [14,15,42–46], underlining the competitiveness of the presented bi-component polymer optical fibers. The 80mm-long bundle, despite yielding the highest absolute intensities (Fig. 7a), achieves the lowest optical efficiencies among studied configurations (Fig. 8), while the 20-mm-long bundle performs in the opposite way. The increase of optical efficiency above 80° is presumably caused by the non-ideal structure of a bundle – as luminescent fibers do not cover the whole cross section, direct light outside the fiber cores can reach the detector at α = 90°. We now assess a more realistic scenario comprising the spectral response of a polycrystalline silica (pSi) PV solar cell, i.e. additionally benefitting from the conversion of blue into red light. As before, we disregard atmospheric effect. Fig. 9 shows the maximal power generated by the pSi cell, again without and with fiber bundles of different lengths, using the same illumination setup as before. The power is determined at the maximum power point of the I (V) curve. The polycrystalline silica solar cells have increased sensitivity around 760–800 nm. [47] Compared to the white-calibrated photodetector, the light conversion by LR305 thus explains the excess of power recorded (viz. Figs. 9 and 7a). This conversion gain is known in the LSC literature [48]. For α = 0°, the F-factor (Eq. (1)) reaches values of 2.8, 4.3 and 5.3 for bundle lengths of 20 mm, 40 mm, and 80 mm, respectively. To estimate the theoretical performance of a LSC-enhanced PV solar cell at varying angles (i.e. simulating different arrangements between the sun and

Fig. 6. a) Spectrum of light reaching the fiber LSC's tip for different distances between illumination point and emitting tip. b) Calculated attenuation of light as a function of wavelength. For wavelengths b 615 nm it was calculated between 0 mm and 2 mm and for wavelengths N 615 nm attenuation was calculated between 0 mm and 160 mm.

K. Jakubowski et al. / Materials and Design 189 (2020) 108518


Fig. 7. a) Intensity of light detected by a bare photodetector, as well as a photodetector in contact with LSC bundles of three different lengths. b) Calculated values of A and B deconvolution parameters for bundles of different length.

cell's surface without considering atmospheric effects), one can integrate the measured intensity of Fig. 9 over the full range of angles; Table 4 summarizes the results. We estimate that the pSi cell, enhanced with 40 mm and 80 mm bundles, can be improved 13% and 26% respectively, compared to the bare PV panel. A beneficial side effect is that power generation is now distributed more evenly over the angles, as compared to the reference pSi cell without LSC. This angular redistribution property is interesting to mitigate the mid-day power peak generated by conventional photovoltaics with fixed orientation.

polymer melts. The here described methods are suitable to study other polymer-dye systems. A prototype of an endless melt-spun bi-component fiber LSC demonstrates the feasibility and up-scaling capability of the proposed solution. Fiber-based LSCs could enhance and complement the illumination-angle dependency of commercial PV solar panels. More generally, the high values of the F-factors for shallow angles suggest that fiber-based LSCs, in form of textiles or bundles, could also find photovoltaic applications in more indirect illumination scenarios. Our results suggest that there is a significant potential in utilizing industrial melt-spinning as cost-effective means for fiber-based LSC production.

4. Conclusions


20mm bundle 40mm bundle 80mm bundle


ηopt [%]

Ref. 46

Ref. 15 Ref. 14


Ref. 44

Konrad Jakubowski: Conceptualization, Investigation, Validation, Visualization, Formal analysis, Writing - original draft. Chieh-Szu Huang: Investigation, Validation. Ali Gooneie: Methodology, Validation. Luciano F. Boesel: Conceptualization, Validation. Manfred Heuberger: Conceptualization, Validation, Writing - review & editing, Supervision. Rudolf Hufenus: Conceptualization, Validation, Writing - review & editing, Supervision.

Unassisted cell 20mm bundle power & 40mm bundle power & 80mm bundle power &




F-factor F-factor F-factor

5 0.8 4 0.6 3 0.4



1 0

0.0 0







Angle D [ ] o

Fig. 8. Angle-dependent optical efficiencies of the studied bundle LSCs. Reference values, reported previously in the literature, are marked on the graph at α = 0°, as reported.



Ref. 43, Ref. 45 0.1


Calculated F-factor

Ref. 42

CRediT authorship contribution statement

Normalized maximal power

Three transparent thermoplastic polymers, COP, PMMA and PC, were evaluated as host matrices for LR305. COP was best suited as host material for LR305, in terms of luminescent properties. Comparison of measured spectra and ray tracing simulations revealed an excess absorption in plate model samples that we attribute to the formation of dye aggregates in the polymer matrix. Molecular dynamics simulation were invoked to estimate the interactions between luminescent dye and polymer host in melt-processing, providing a tool to predict dispersion of (luminescent) additives in





Angle D [o] Fig. 9. Maximal power registered as a function of the illumination angle α (solid lines) and values of the F-parameter (dashed lines), for a bare PV solar cell and an enhanced cell with LSC bundles of different lengths, in absence of atmospheric scattering effects.


K. Jakubowski et al. / Materials and Design 189 (2020) 108518

Table 4 Integral of the theoretical maximal power between illumination angles of 0° and 90° of the LSC-assisted solar cell, in proportion to the unassisted cell. Measurement configuration


Ratio between area under curves (Fig. 9) of LSC-assisted and unassisted cell

Unassisted solar cell Cell with 20 mm fiber LSC bundle Cell with 40 mm fiber LSC bundle Cell with 80 mm fiber LSC bundle

– 0.92 1.13 1.26



Declaration of competing interest


The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Acknowledgements The authors thank Martin Amberg and Urs Schütz for assistance with the solar cell measurement setup, Mathias Lienhard and Benno Wüst for assistance with polymer melt-processing, Dr. René Rossi for valuable discussions, as well as Dr. Sergii Yakunin for assistance with photoluminescent quantum yield measurements. Data availability The raw and processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.matdes.2020.108518.




[22] [23]





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