Appendix B.1. Fiber Diamater Measurments and Uncertainty Budget
As is best practice for reporting measured values from micrographs [
34], we have constructed an uncertainty budget as outlined in the “Evaluation of measurement data—Guide to the expression of uncertainty in measurement” [
35]. We have modeled our uncertainty budget after Crouzier et al., which discuss the construction of an uncertainty budget for nanoparticle diameter determination and use a similar Zeiss scanning electron microscope [
34]. Adobe CS3 and CC graphic software (Illustrator, Fireworks, and Photoshop) were used to prepare and analyze fibers.
Initially, we attempted to use DiameterJ, an image software intended for nanofiber measurements [
36]. However, we observed undercounting of fiber diameter by the software relative to human counts, similar to the DiameterJ authors’ original finding (Figure 5C and D in [
36]). Our hand-produced measurements were in close agreement to a sample of more time-consuming measurements made following the work of Crouzier et al. [
34]. As reported, DiameterJ was substantially faster, and collected many more datapoints. Contrary to their findings, this was at expense of our interpreted accuracy. Using the test dataset provided in [
37], we were able to reproduce their results, which was especially useful for confirming that we used the software correctly. Although Crouzier et al. [
34] measured nanoparticles (not fibers), their use of measurement standards is well discussed in the literature, and their well-described uncertainty budget supports our decision to use their approach for quantification of our described measurements. We do not report any fiber values obtained from DiameterJ.
Fiber diameters were measured perpendicular to the longest dimension in settings where the edges of the fiber could be clearly distinguished, typically, in sections where the background was black or high contrast edges were unambiguously distinguishable. First, edges were identified along the fiber length. Second, we located edge pairs on the right and left sides of the fiber. Finally, a measurement was taken between the two identified edges. Each fiber was only measured once at the largest diameter along sections with clear edge pairs. The work of Öznergiz et al. describe a similar application of edge finding to nanofiber analysis [
38]. The edges of the fibers are diffuse in the micrographs, which adds uncertainty as to where the physical edge of the fiber begins. Crouzier et al. and Delvallée et al. both discuss this problem in relation to their nanoparticles, and determined that selecting the full width half max (FWHM) of their features (all smaller than 100 nm) resulted in measurements most accurate to AFM measurements [
34,
39]. However, we were concerned with the transferability of the high-quality SEM work demonstrated in both publications to our own capabilities, and instead decided upon base measurement (described in Crouzier et al. as D
Eq-base). According to previous work, a base measurement will result in an over estimation of the diameter [
34,
39]. No image threshold was selected due to complication of the fiber mat presenting both blank background, and fiber on fiber backgrounds. Previous work suggests that no threshold will also result in an overestimation of the diameter [
34]. Crouzier et al. recommends 3 kV [
34], but our micrographs were taken with 10 kV. We do not have any quantifications at our higher voltage, but using the data from 2 to 5 kV present in Crouzier et al. [
34], we estimate ± 2 nm uncertainty in our readings. Crouzier et al. [
34] presents an upper limit for pixel size. In
Table A1, we compare the ratio of Crouzier et al.’s [
34] recommendation to the feature sizes of this work to validate our pixel sizes and our use of the pixel size uncertainty contribution from Crouzier et al.
Table A1.
Comparison of the limit on pixel size to feature size ratio from Crouzier et al. and this work.
Table A1.
Comparison of the limit on pixel size to feature size ratio from Crouzier et al. and this work.
In comparing detailed fiber determinations as pictured in
Figure A11 to the previously described edge method, we determined an uncertainty in fiber edge due to image quality is ±0.87% relative to the fiber diameter. Our measurements of fiber diameters were human reproducible within ±0.24% relative to the fiber diameter. We determined that contrast and brightness adjustments on collected micrographs result in ±1.01% uncertainty relative to the fiber diameter. Our platinum coating is estimated to vary the observed thickness ±1 nm. For reasons discussed in Crouzier et al. [
34], we did not account for environmental conditions such as humidity. Leading edge distortion was not considered relevant since we had abundant images and could select for objects within the central 80% of the image. The limited depth of focus at high magnification, and the vertical distribution of fibers within our fiber mat were difficult to study, as evident in
Figure A12. In this sample, we performed diameter measurements on in- and out-of-focus fibers. Due to our conservative measurement technique, we expect that defocused fiber diameters were overestimated relative to the real diameter, but we did not pursue quantifying this uncertainty.
Table A2,
Table A3 and
Table A4 list our constructed uncertainty budgets for the samples featured in
Figure A12,
Figure A13 and
Figure A14, respectively.
Figure A11.
A detailed characterization of a fiber diameter (selected from
Figure A12). The sample of
Figure A12 depicts the micrograph of an example fiber, and the Pixel white value near red dotted line displays the white value of the pixel (a value from 0 to 100) for three transects across the fiber. In this example 1 pixel is equivalent to 1.52 nm. The baseline value would be selected near 9 and 47, resulting in a total pixel diameter of 38 pixels, or 57.8 nm.
Figure A11.
A detailed characterization of a fiber diameter (selected from
Figure A12). The sample of
Figure A12 depicts the micrograph of an example fiber, and the Pixel white value near red dotted line displays the white value of the pixel (a value from 0 to 100) for three transects across the fiber. In this example 1 pixel is equivalent to 1.52 nm. The baseline value would be selected near 9 and 47, resulting in a total pixel diameter of 38 pixels, or 57.8 nm.
Table A2.
Uncertainty budget for measured values presented in relation to
Figure A12.
Table A2.
Uncertainty budget for measured values presented in relation to
Figure A12.
Uncertainty Component Description | Estimated Uncertainty (nm) | Type | Probability Distribution | Standard Uncertainty | % Contribution |
---|
Pixel size 1 | 0.014 | B | 1σ | 0.014 | 0.0% |
Repeatability | 0.3 | A | 1σ | 0.3 | 1.1% |
Magnificaiton 2 | 0.26 | B | 1σ | 0.26 | 0.8% |
Beam Width 2 | 1.7 | B | 1σ | 1.7 | 35.9% |
Operator selection 2 | 0.2 | B | 1σ | 0.2 | 0.5% |
Operating voltage | 2 | B | Rect. | 1.1547 | 16.6% |
Contrast-Brightness | 1.21 | A | 1σ | 1.21 | 18.2% |
Fiber edge | 1.04 | A | 1σ | 1.04 | 13.4% |
Human-power | 0.29 | A | 1σ | 0.29 | 1.0% |
Platinum coating | 1 | B | 1σ | 1 | 12.4% |
Combined Uncertainty: | 2.8 | |
k (Coverage Factor): | 2.87 | |
Expanded Uncertainty: | 8.1 | |
Table A3.
Uncertainty budget for measured values presented in relation to
Figure A13.
Table A3.
Uncertainty budget for measured values presented in relation to
Figure A13.
Uncertainty Component Description | Estimated Uncertainty (nm) | Type | Probability Distribution | Standard Uncertainty | % Contribution |
---|
Pixel size 1 | 0.014 | B | 1σ | 0.014 | 0.0% |
Repeatability | 0.3 | A | 1σ | 0.3 | 0.1% |
Magnificaiton 2 | 0.26 | B | 1σ | 0.26 | 0.1% |
Beam Width 2 | 1.7 | B | 1σ | 1.7 | 2.2% |
Operator selection 2 | 0.2 | B | 1σ | 0.2 | 0.0% |
Operating voltage | 2 | B | Rect. | 1.1547 | 1.0% |
Contrast-Brightness | 8.4133 | A | 1σ | 8.4133 | 53.3% |
Fiber edge | 7.2471 | A | 1σ | 7.2471 | 39.6% |
Human-power | 1.9992 | A | 1σ | 1.9992 | 3.0% |
Platinum coating | 1 | B | 1σ | 1 | 0.8% |
Combined Uncertainty: | 11.5 | |
k (Coverage Factor): | 4.5 | |
Expanded Uncertainty: | 52.2 | |
Table A4.
Uncertainty budget for measured values presented in relation to
Figure A14.
Table A4.
Uncertainty budget for measured values presented in relation to
Figure A14.
Uncertainty Component Description | Estimated Uncertainty (nm) | Type | Probability Distribution | Standard Uncertainty | % Contribution |
---|
Pixel size 1 | 0.014 | B | 1σ | 0.014 | 0.0% |
Repeatability | 0.3 | A | 1σ | 0.3 | 0.7% |
Magnificaiton 2 | 0.26 | B | 1σ | 0.26 | 0.5% |
Beam Width 2 | 1.7 | B | 1σ | 1.7 | 21.1% |
Operator selection 2 | 0.2 | B | 1σ | 0.2 | 0.3% |
Operating voltage | 2 | B | Rect. | 1.1547 | 9.8% |
Contrast-Brightness | 2.1412 | A | 1σ | 2.1412 | 33.5% |
Fiber edge | 1.8444 | A | 1σ | 1.8444 | 24.9% |
Human-power | 0.5088 | A | 1σ | 0.5088 | 1.9% |
Platinum coating | 1 | B | 1σ | 1 | 7.3% |
Combined Uncertainty: | 3.7 | |
k (Coverage Factor): | 2.87 | |
Expanded Uncertainty: | 10.6 | |
Appendix B.2. Demonstration on Select Compositions
The yield and diameter of fibers were sensitive to changes in system parameters, especially solution viscosities and relative humidity. We characterized fiber yields of 0.5 to 2 g per hour using a solution of 3.8 wt% polyvinylpyrrolidone, 4.3 wt% CsH2PO4, 63.4 wt% water, and 28.5 wt% ethanol, a cylindrical electrode 3 inches long with a 1.25 inch diameter rotating at 5 rpm, a 2-inch diameter collector drum rotating at 33 Hz (~5 m/s), 40%–48% relative humidity, air temperature of 20 °C, spinning electrode biased to +40 kV, and collector drum biased to −30 kV. We spent no effort in optimizing device, solution or environment parameters for a specific fiber morphology or size.
Figure A12.
Polyvinyl alcohol- polyvinylpyrrolidone fiber containing conductive CsH2PO4. The fibers have varying diameters along their length, which we interpret to indicate a ribbon like morphology. The median diameter of this sample was 120 nm. The vertical distribution of fibers in the 3D fiber mat made image collection somewhat difficult at this magnification.
Figure A12.
Polyvinyl alcohol- polyvinylpyrrolidone fiber containing conductive CsH2PO4. The fibers have varying diameters along their length, which we interpret to indicate a ribbon like morphology. The median diameter of this sample was 120 nm. The vertical distribution of fibers in the 3D fiber mat made image collection somewhat difficult at this magnification.
We produced the smallest fibers (
Figure A12) from a solution with low viscosity and similar to compositions which have been studied previously [
40]. This sample was produced from a solution of 1.2 wt% polyvinyl alcohol, 1.2 wt% polyvinylpyrrolidone, 5.3 wt% CsH
2PO
4, 46.4 wt% water, and 45.9 wt% ethanol, spun on a cylinder electrode (−30 kV) in 40% relative humidity, 13.5 cm below the collector (+45 kV) with a total voltage drop of 75 kV. The surface speed of the collector was 14.9 m/s and a yield of 1.4 g/hr was collected. Microscopy of collected samples indicated minimum diameter of 39 nm, maximum diameter of 403 nm. In 116 analyzed fibers, median diameter was 120 nm, mean diameter was 132 nm, first quartile 90 nm and third quartile at 160 nm. The uncertainty of individual measurement was estimated to ±8.1 nm, as presented in
Table A1 and discussed in
Appendix B.1. Dynamic viscosity at bath conditions was 3 poise.
Figure A13.
Polyvinylpyrrolidone fibers produced from our device. Median diameter of fibers from this sample was 833 nm.
Figure A13.
Polyvinylpyrrolidone fibers produced from our device. Median diameter of fibers from this sample was 833 nm.
Figure A13 was produced from a solution of 12 wt% polyvinylpyrrolidone and 88 wt% methanol, spun on a cylinder electrode (−20 kV) in 33% relative humidity, 12 cm below the collector (+40 kV) with a total voltage drop of 60 kV. The surface speed of the collector was 24.4 m/s. Microscopy of collected samples indicated minimum diameter of 202 nm, maximum diameter of 2.67 μm, with occasional features 3 to 10.8 μm large most likely the result of undried polymer flung onto the collector. In 100 analyzed fibers, median diameter was 833 nm, mean diameter was 881 nm, first quartile 584 nm and third quartile at 1.07 μm. The uncertainty of individual measurement was estimated to ±52.2 nm, as presented in
Table A1 and discussed in
Appendix B.1.
Figure A14.
Cesium metaphosphate electrospun fibers produced from our device. Median diameter of fibers from this sample was 212 nm.
Figure A14.
Cesium metaphosphate electrospun fibers produced from our device. Median diameter of fibers from this sample was 212 nm.
Figure A14 was produced from a solution of 69 wt% CsPO3, 31 wt% water which then allowed to evaporate. The viscosity was observed to increase as the concentration of the solvent (water) decreased relative to the solute (CsPO3). Addition of alcohol would induce immediate precipitation of the solute. Addition of polyvinylpyrrolidone or polyvinyl alcohol to high-concentration metaphosphate solutions would induce immediate coagulation of a white rubber-like solid. Electrospinning of a similar solution from a capillary needle has been previously described [
41], but this is the first larger volume need-free demonstration of this solution. Reports of electrospinning other metaphosphates employed a carrier polymer, which is not used in our test [
42,
43]. It was spun on a saguaro electrode (−20 kV) in 36% relative humidity, 12 cm below the collector (+50 kV) with a total voltage drop of 70 kV. The surface speed of the collector was 4.9 m/s. Microscopy of collected samples indicated minimum diameter of 86 nm, maximum diameter of 1.01 μm. In 94 analyzed fibers, median diameter was 212 nm, mean diameter was 245 nm, first quartile 174 nm and third quartile at 282 nm. The uncertainty of individual measurement was estimated to ±10.6 nm, as presented in
Table A1 and discussed in
Appendix B.1. Dynamic viscosity at bath conditions was 110 poise, the solution exhibits shear thinning, but this was not further investigated.
Appendix B.3. System Paramaters
Parameters relevant to electrospinning include device parameter (electric field, electrode-collector distance, rotating collector speed, etc.), solution parameters (surface tension, conductivity, viscosity, solution temperature, etc.), and environment parameters (air temperature, relative humidity, air pressure, etc.). Our device was intended to present a large range of device parameters such that operators were unlikely to be limited by device conditions when preforming experimental tests.
Table A5 reports the range of parameters that are influenced by the design, materials and construction of this particular device.
Table A6 reports environmental parameters that we achieved by incorporating accessory equipment inside the fume hood.
Table A5.
Range of possible system parameters capable of being studied with this device.
Table A5.
Range of possible system parameters capable of being studied with this device.
Parameter | Minimum | Maximum | Units |
---|
Total bias | 0 | 93,000 1 | volts |
Collector electrode distance at peak voltage | 11 | 33 | cm |
Electrode rotational frequency | 0.03 | 0.2 | Hz |
Electrode rotational frequency | 2 | 12 | rpm |
Collector rotational frequency | 0 | 105 | Hz |
Collector rotational frequency | 0 | 6300 | rpm |
Collector surface speed | 0 | 50 | m/s |
Table A6.
Environment parameters controlled by accessory equipment.
Table A6.
Environment parameters controlled by accessory equipment.
Parameter | Minimum | Maximum | Units | Source |
---|
Air temperature | 19 | 55 | C | External air heaters |
Air flow | 0 1 | 0.6 | m/s | Fans and fume hood |
Relative humidity | 15 2 | 85 | % | Dehumidifier or humidifiers |