1. Introduction

As an effective fabrication method, the electrospinning of polymer-based materials provides straightforward production of high-aspect-ratio fibers with controllable diameters that range from microns to several tens nanometers [1–4]. This technique produces ultra-fine fabrics via the ejection of a polymer solution under a strong electric field, by which highly charged polymer jets repel each other and cause the jet to split at the micro- or nanoscale. Prior to jet deposition on a ground collector, the solvent’s evaporation is accelerated and completed due to the dramatic surface increase of the downscaled polymer jets. In recent years, the focus of research on electrospun polymer fibers has gradually migrated from the development of electrospinning techniques to the exploration of advanced applications that utilize the unique properties of these one-dimensional nanomaterials. For instance, the high surface-to-volume ratio of electrospun nanofibers means that they are frequently used in applications such as high-performance filtration systems [5,6], surface functionalities as catalysts [7,8], drug release [9,10], and fluorescence-based sensing devices [11,12]. The enhanced mechanical strength of the fabric scaffolds has been employed in the applications of nanostructured materials [13,14] and tissue engineering [15,16]. Inorganic nanofibers, particularly for optoelectronic semiconductor materials, have also been fabricated via the electrospinning of polymer media that are preloaded with inorganic nanoclusters or presursors [17,18]. A post-calcination process at high temperatures was required for the removal of organic compounds and the formation of inorganic compositions.

A growing research interest in electrospun nanofibers has recently been identified for optical applications; it takes advantage of subwavelength diameters to achieve light confinement and propagation [19]. The electrospinning of optoelectronic polymers, such as MEH-PPV [20], poly(3-hexyl thiophene) [21], and polyacetylene derivatives [22], was conducted to explore the photo- and electro-luminescence characteristics of stretched conjugated polymer chains. Light-emitting nanofibers from non-conjugated polymers were also produced by the addition of fluorescent reagents to electrospinning solutions [19,23,24]. Individual electrospun polymer fibers have been incorporated with semiconductor quantum dots as an internal light source to demonstrate a micrometer optical waveguide [25]. Surface grating on a single electrospun polymer nanofiber was fabricated by room-temperature nanoimprint lithography for the similar purposes of waveguiding performance and emission tuneability [26]. Photolithography directly onto electrospun films produced micron-scale and multilayered architectures [27].

In these demonstrations, randomly deposited electrospun nanofibers with broad diameter distributions were excluded from being utilized in optical applications that require precise dimensional control and/or long-range periodic architectures. Without attempts to orient the fibers, the electrospinning technique leads to disordered nanofibers that lay horizontally on the substrate with an absence of perpendicular fibers. For a single nanofiber, the curved and randomly-orientated feature can only support momentary light confinement. Incident light that passes through a nanofiber scaffold easily induces multiple light scattering events and results in white deposition layers for most electrospun samples. In some cases, colorful fibers can be observed, particularly at the edges of thin fiber mats; this indicates that the subwavelength diameter effect is further directing the random nanofibers for anisotropic light scattering and confinement, with a dependence on the fiber diameter and other parameters.

In this research report, poly(methyl methacrylate) (PMMA) nanofibers with various fiber diameters were electrospun as light scattering and propagation materials. The preferred light scattering wavelengths of these samples were examined in terms of the fiber diameter and fiber deposition thickness. The scattering bands, as observed in the absorption spectra, were linearly proportional to the nanofiber diameters, which show strong agreement with a scattering model based on the Mie theory. In this model, the length of high-aspect-ratio nanofibers has a negligible effect on the scattering properties. Light propagation and prolonged light path lengths due to multiple scattering events inside of the nanofiber scaffolds were investigated by the addition of a fluorescent dye, Coumarin 6 (C6). Whether the incident light was confined to one nanofiber or scattered among them, the fluorescence emission of C6 quantified the total light absorption. The photoluminescence (PL) responses of electrospun PMMA-C6 nanofibers were measured and carefully normalized by the dye loading per unit area. This was further converted to the effective light path lengths. In comparison with spin-coated PMMA-C6 thin films, significant enhancement of the PL intensities in the PMMA-C6 nanofiber samples confirmed the light scattering and propagation. Diameter-dependent scattering bands also support the manipulation and the wavelength selectivity of light propagation to a certain degree, especially since the scattering bands matched the dye excitation wavelengths.

Similar to diffusion light propagation in porous silicon thin-film solar cells [28,29], the electrospun nanofiber scaffolds with light scattering performances can potentially be adapted as a light trapping and propagation matrix, optical filters [30], and photovoltaic devices [31]. In contrast to porous silicon materials with isolated holes, electrospun fiber mats provide two continuous and interpenetrated domains from fiber scaffolds and porosities (fiber spacing), which make them an excellent candidate for the collection of charge carriers. A large amount of fiber surface area also promotes the interfacial charge transfer. Experimental observations and modeling results in this work provide a basic understanding of the diameter-dependent light scattering and, more importantly, quantify the prolonged light path length inside of an electrospun nanofiber scaffold.

2. Experimental Section

As summarized in Table 1 , electrospinning solutions were formulated by dissolving poly(methyl methacrylate) (PMMA) (Mw = 120,000, Aldrich) in a co-solvent solution of methanol and MEK (methyl ethyl ketone) (volume ratio = 1:2). Both solvents were dried by anhydrous MgSO₄ prior to their use. PMMA concentrations in the range of 13 - 16 wt% were used to manipulate the diameters of the electrospun nanofibers. The addition of Coumarin 6 (98%, Aldrich) was controlled at a constant concentration of 0.25 wt% (solid ratio of C6/PMMA).

Table 1. Electrospinning formulas and the average diameters of the electrospun PMMA and PMMA-C6 fibers.

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Electrospinning of PMMA nanofibers was carried out as described elsewhere [32]. In brief, a PMMA solution was placed in a gas-tight syringe with a 21-gauge stainless-steel needle, which was equipped with a syringe pump to provide a desired and stable flow rate. A high-voltage supply of 15 kV was connected to the syringe needle. A quartz slide that served as the fiber deposition substrate was placed 10 cm away from the ejection needle. The nanofiber’s deposition was accurately manipulated by the steady ejection and electrospinning periods. In a separate experiment, several PMMA-C6 thin films were also spin-coated on quartz slides by using dilute solutions of the same PMMA-C6 recipe. A linear calibration curve between the C6 loading and its optical absorption at 455 nm was established with the C6 loading accuracy as low as 3.7 × 10⁻⁵ mg/cm², corresponding to the absorbance of 0.01. The film thicknesses of these PMMA-C6 spin-coated samples were also recorded with AFM (atomic force microscopy) step height measurements. Due to the constant C6 concentration for all of the electrospun samples, the precise nanofiber depositions were determined by re-dissolving PMMA-C6 nanofibers from a given fiber deposition area, which was followed by a UV-vis spectrum measurement. The resulting C6 absorption intensity at 455 nm calibrated its concentration, which was then converted to the precise weight of the original electrospun PMMA-C6 nanofibers. This method provided excellent accuracies even for those samples with low material loadings or short-period electrospinning depositions.

The average diameters and diameter distributions of these electrospun PMMA nanofibers were determined by Scanning Electron Microscopy (SEM, Philips XL-40). The absorption spectra of the electrospun nanofibers and the spin-coated films were examined with a photodiode array UV-visible spectrophotometer (SCINCO S-3150). The photoluminescence measurements of the C6-loaded samples were carried out in a fluorescence spectrophotometer (Hitachi F-700).

3. Results and discussion

In this work, the diameter of the electrospun PMMA nanofibers was successfully manipulated by the concentration of the electrospinning solutions. Table 1 summarizes the solution compositions and the resultant properties of the four fiber samples, which are labeled PMMA-13 to PMMA-16. For each sample, the diameter analysis was carried out by 150 diameter counts obtained from SEM images of three individual sample preparations. As shown in Fig. 1 , the SEM images of the four PMMA samples revealed their average fiber diameter ($\overline{D}$) to be in the range of 336 to 896 nm. The fiber diameter distributions of these samples were also measured and are illustrated in Fig. 1. Although the large-diameter samples had a broader diameter distribution and standard deviation ($Dst$), a coefficient of variation (CV, represented by $Dst/\overline{D}$) of no more than 28% was obtained for all of the electrospun PMMA nanofibers. The addition of polar C6 reagent at a low concentration led to a slight reduction in the electrospun nanofiber diameters, as summarized in Table 1. The diameter distributions and the coefficients of variation for the PMMA-C6 nanofibers remained similar.

 

Fig. 1 SEM images and diameter distributions of the electrospun PMMA nanofibers.

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The PMMA and PMMA-C6 nanofibers were electrospun and deposited on quartz slides for the following optical investigations. The fiber deposition was carefully controlled by the electrospinning period, which was pre-calibrated according to the steady ejection rate. With the presence of C6 molecules, the weights of the PMMA-C6 nanofibers per unit deposition area were further determined by the optical adsorption of C6, as described previously.

Since PMMA is an optical polymer, the absorption spectra of PMMA materials remained transparent in the long-wavelength UV and visible regions (see bottom spectrum in Fig. 2 ). However, due to light scattering within the nanostructured materials, the UV-vis spectra of the four PMMA nanofibers in the transmission mode revealed that the intensive scattering bands were centered from 295 to 760 nm (Fig. 2). Similar to the broad fiber diameter distributions, as previously discussed, the scattering spectra in Fig. 2 also had substantial bandwidths, particularly for the thick fiber samples. The FWHM (the full-width half-maximum) of these scattering bands reached several hundred nanometers, which easily covered the entire visible wavelength region. More importantly, these scattering bands were linearly proportional to the average fiber diameter (see line a in the insert of Fig. 3 ), which suggests that the light scattering was highly sensitive to the diameter of these high-aspect-ratio nanomaterials. The lengths of the nanofibers were considered to have no effect on their optical performance.

 

Fig. 2 Scattering spectra for the four electrospun PMMA nanofibers and the absorption spectrum of the spin-coated PMMA film (bottom).

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Fig. 3 Scattering spectrum for sample PMMA-14 and the corresponding simulation spectra (c and d group). The inserted image illustrates the linear relationships between the scattering bands and the average fiber diameter for both the experiment (a) and the simulation (b).

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The light scattering in the electrospun nanofibers was modeled with the Mie theory, which is an analytical solution of Maxwell’s equation for the scattering of optical waves by uniformly distributed spherical particles [28,29]. In this simulation, the refractive indexes of the PMMA and the surrounding air were set at 1.49 and 1.0, respectively. The diameter of the spherical particles that was originally used in the Mie theory was replaced by the fiber diameter. It was noticed that the simulation parameters of the refractive index and the fiber diameter exclusively determined the scattering wavelength. Two other parameters, the thickness of the deposition layers and the volume porosity, only influenced the scattering band intensity.

A series of scattering spectra from mono-dispersed fiber diameters were first created. These individual scattering spectra were then integrated in accordance with the diameter distributions that were obtained in previous measurements (shown in Fig. 1). Figure 3 illustrates one simulation example from sample PMMA-14. Eleven scattering spectra with fiber diameters from 180 to 780 nm were simulated and plotted proportionally to their diameter distribution (spectra of d group). The integrated scattering spectrum (c in Fig. 3) had its band centered at 350 nm, which is very near to the scattering band of sample PMMA-14 at 379 nm. Similar simulations were carried out for the other three PMMA nanofiber samples. The simulated scattering bands are also outlined in the insert of Fig. 3 versus the corresponding fiber diameters (line b). The simulated and experimental scattering bands as a function of the fiber diameter exhibited two parallel linear relationships, which indicated good agreement between the Mie scattering theory and the spectrometer observations in the electrospun nanofibers.

As mentioned previously, the depositions of PMMA-C6 nanofibers were controlled by the ejection solutions or the electrospinning periods, while the sample weights were further calibrated by the optical absorption of C6 molecules. Figure 4 illustrates an example of the scattering spectra from the PMMA-C6-14 nanofibers, which were individually electrospun from 25, 50, 75, 100, 150, and 200 μl ejection solutions. Intensive scattering bands completely covered the trace of the C6 absorption at 456 nm. The band intensities of these samples showed a proportional growth to the electrospinning deposition. By recalibrating the ejection solutions to the sample weights, the insert of Fig. 4 reveals that the scattering intensities of the four PMMA-C6 electrospun samples linearly increased with the C6 or PMMA deposition per unit area (mg/cm²). The linear profiles of the scattering band intensities also suggest that the scale of light scattering in the nanofiber scaffolds primarily follows a first-order relationship with the material loading, which is similar to the optical absorption equation of the Beer-Lambert Law. Lacking any nanostructures, the spin-coated PMMA-C6 thin films with comparable sample weights per unit area only had minor irradiation loss that was mainly due to the optical absorption of C6. The bottom line in the insert of Fig. 4 illustrates the optical absorption of the PMMA-C6 thin films at 456 nm as a function of the C6 loading per unit area. The slope of this line also gives the C6 absorption coefficient ($\epsilon abs$ = 255.2 cm²/mg) for this particular PMMA-C6 composition.

 

Fig. 4 Scattering spectra for the six PMMA-C6-14 nanofibers that were electrospun from 25, 50, 75, 100, 150, and 200-μl solutions (spectra a to f). The insert shows the intensities of the scattering bands from four electrospun PMMA-C6 samples as a function of the PMMA or C6 deposition (mg/cm2). With no scattering bands, the profile of the PMMA-C6 films illustrated the C6 absorption at 455 nm.

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Even though intensive scattering bands were observed in the single-beam UV-vis spectrometer, most electrospun nanofibers visually appeared “white” due to multiple scatterings upon exposure to the isotropic ambient light. The scattering spectra that are shown in Fig. 3 and Fig. 4 reveal only the preferred scattering wavelengths and not the actual light absorption that occurred within the fiber scaffolds. The investigation of light scattering and light propagation was therefore conducted obliquely by monitoring the fluorescence emission from the C6 additives. With negligible optical absorption from PMMA itself and the low dye concentration to avoid possible fluorescent self-quenching, the PL emissions of the PMMA-C6 nanofibers at a certain wavelength indicated the total absorption of the single-beam excitation light passing through the sample. As a result, the emission spectra of seven PMMA-C6-14 nanofibers (see Fig. 5 ) also showed proportional increases in their PL intensities, which is similar to their scattering bands, see Fig. 4.

 

Fig. 5 Photoluminescence spectra for the PMMA-C6-14 nanofibers that were electrospun from 25, 50, 75, 100, 150, and 200-μl solutions (spectra a to f).

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Figure 6 illustrates the PL intensities of all of the electrospun and spin-coated samples versus the material deposition per unit area (mg/cm²). For the spin-coated PMMA-C6 samples, the effective light path length was equal or proportional to the film thickness, which depended on the light’s incident angle. The thickening of the PMMA-C6 coating linearly intensified the optical absorption and PL emission as indicated by the bottom line in Fig. 6 (marked with solid squares). To describe the linear PL profile, the Beer-Lambert Law ($A=\epsilon cl$) was modified as $PL=\epsilon PL\overline{M}C6$, where $PL$ and $\epsilon PL$ are the PL intensity and the C6 emission coefficient, respectively. $\overline{M}C6$ represents the C6 loading per unit area, which was in fact equal to the value of $cl$, as shown in the x-axis of Fig. 6. According to the linear PL growth in the spin-coated PMMA-C6 samples, the profile slope of 1.51 × 10⁷ cm²/mg was the emission coefficient ($\epsilon PL$) of C6 at this particular PMMA-C6 composition.

 

Fig. 6 Photoluminescence intensities of the electrospun and spin-coated PMMA-C6 samples as a function of the PMMA or C6 deposition (mg/cm2). The right axis represents the effective light path length that was obtained from the $PL$calculations.

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As the same amount of PMMA-C6 material was electrospun into a fiber scaffold, the nanofiber samples demonstrated remarkably enhanced PL emissions. In Fig. 6, the PL intensities of the electrospun samples approximately followed the linear Beer-Lambert profile at the region of low fiber deposition, in which the sparse PMMA-C6 nanofibers had not yet built up the operative scaffolds to interact with the incident light. With more electrospinning deposition, the accumulated nanofibers and scaffold structures gradually introduced effective light scattering. The upward curvatures of the PL profiles (four dashed curves in Fig. 6) that shift away from the Beer-Lambert baseline serve as direct evidence of PL enhancement and light scattering. The deposition of C6 per unit area ($\overline{M}C6$) was originally determined by fiber dissolving and calibration of the C6 loadings. Therefore, the actual light path lengths in the fiber scaffolds could be estimated by $PL=\epsilon PL\overline{M}C6$ and $\overline{M}C6=c\overline{l}$, where $\overline{l}$represents the effective light path length. Because the C6 concentration (c = 2.5 mg/cm³) and its emission coefficient ($\epsilon PL$ = 1.51 × 10⁷ cm²/mg) in these samples were both constant, the calculated $\overline{l}$ was linearly proportional to the PL intensity (see the right axis of Fig. 6).

For the six spin-coated samples, the effective light path length from the $PL$ calculations was approximately equal to the film thickness (determined from the AFM step height measurement). The actual $\overline{l}$ in the electrospun PMMA-C6 samples, on the other hand, easily increased by a factor of 2 - 3 relative to the spin-coated counter samples. Figure 7 illustrates the $\overline{l}$ increase ratios between the electrospun and spin-coated PMMA-C6 samples that contain the same material depositions. Interestingly, four linear profiles suggest increases in the original $\overline{l}$ profiles in Fig. 6 that contained nonlinear curve fits by second-order polynomial equations. Because $\overline{l}$ was linearly proportional to the $PL$ output, the light path length in the spin-coated films was described as $\overline{l}=\beta \overline{M}C6$, and the nonlinear light path length in the electrospun nanofibers was proposed as $\overline{l}=\alpha {(\overline{M}C6)}^2+\beta \overline{M}C6$. In Fig. 4, the scattering band intensities of the electrospun nanofibers have a linear relationship with the nanofiber deposition. The second-order polynomial fit for $PL$ and $\overline{l}$ implied agreement with both light scattering and dye absorption. The constant β of 0.3367 cm³/mg was determined by the slope of the PMMA-C6 profile in Fig. 6. The curve fits gave the second-order coefficient α of four PMMA-C6 samples as 9874, 5582, 7374, and 4029 (cm⁵/mg²). In these fitted equations, the first-order coefficient β corresponded to the emission coefficient of the fluorescent reagent. The second-order coefficient α represented the additional contribution from the scattering effect. The higher second-order coefficient α indicated a more significant prolonged light path length ($\overline{l}$).

 

Fig. 7 Light path length ratios of the electrospun PMMA-C6 nanofibers compared to their spin-coated counter-samples with the same C6 loadings per unit area.

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Figure 8 illustrates the excitation spectrum of C6 by monitoring the 490-nm emission and the second-order coefficients of the PMMA-C6 nanofibers versus their scattering bands (275, 355, 465, and 670 nm). Surprisingly, the two scattering bands of the high-α samples (PMMA-C6-13 and PMMA-C6-15) approximately matched the two excitation bands of C6 that were centered at 275 and 456 nm. This result suggests that a nanofiber scaffold is likely to trap or to scatter more incident light with a wavelength near its preferred scattering band. Greater scattering led to more absorption and excitation of fluorescence reagent as its emission output. Samples of PMMA-C6-14 and PMMA-C6-16 without direct overlap between their scattering bands and dye excitation wavelengths also had considerable PL and $\overline{l}$enhancement. It is believed that the broad diameter distributions and the high scattering band widths from the electrospun samples were responsible for the preliminary scattering effect.

 

Fig. 8 Second-order coefficient (α) versus the scattering bands of the electrospun PMMA-C6 nanofibers. The excitation spectrum that is shown above was recorded by monitoring the C6 emission at 494 nm.

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4. Conclusion

In conclusion, electrospun PMMA nanofibers with desired fiber diameters were fabricated to investigate light scattering and propagation effects in randomly deposited nanofiber scaffolds. From the UV-vis spectra, the absorption bands revealed that the preferred scattering wavelength was linearly proportional to the fiber diameter, which shows good agreement with a scattering model based on the Mie theory. In addition, the presence of Coumarin 6 in the electrospun nanofibers successfully converted the scattered light to enhanced fluorescence emission, which was further normalized to quantify the light absorption and the effective light path length. Significantly enhanced fluorescence from electrospun nanofibers revealed a second-order dependence on the dye loading per unit area, which is in contrast to the thin-film samples without nanostructures. Despite the broad scattering bands, the scattering effect in electrospun nanofibers showed considerable wavelength selectivity. Fluorescence enhancement was amplified more in those cases where the scattering bands matched the dye excitation wavelengths. These results demonstrate the strong potential for electrospun nanofibers as a light and energy propagation matrix in the light-emitting and photovoltaic devices as well as for other optical applications, such as optical filters and waveguides.