Nanofibers are a matter of perspective: effects of methodology and subjectivity on diameter measurements

Nanofibers are currently among the most researched nanomaterials in materials science. Various high-resolution microscopy techniques are used for morphological investigations, with the diameter as primary characteristic. Since methodological factors influencing the diameter distribution are usually ignored, numerical values can hardly be compared across different or even within single studies. Here, we investigate influencing factors such as microscopy technique, degree of magnification, eventual coatings, and the analysts' bias in the image selection and evaluation. We imaged a single nanofiber sample using scanning electron microscopy (SEM), helium ion microscopy (HIM), atomic force microscopy (AFM), and transmission electron microscopy (TEM). These techniques yield significant methodological variations between the diameter distributions. We further observed a strong influence of analysts' subjectivity, with a consistent average deviation between 4 different analysts of up to 31%. The average deviation between micrographs within each category was 14%, revealing a considerable influence of micrograph selection and strong potential for cherry picking. The mean values were mostly comparable with the results using automated image analysis software, which was more reproducible, much faster, and more accurate for images with lower magnification. The results demonstrate that one of the most frequently measured characteristics of nanofibers is subject to strong systematic fluctuations that are rarely if ever addressed.


Introduction
For decades, nanobers have been studied in numerous elds of research, either as naturally occurring building blocks or as synthetic materials for a wide range of applications.Since the advent of electrospinning, polymeric nanobers, in particular, have become one of the most studied nanomaterials in materials science.Electrospinning enables the production of nano-bers from diverse polymers or polymer blends, optionally incorporating active ingredients, nanoparticles, and other additives.2][3] With their exceptional structural properties and unique surface characteristics, nanobers exhibit immense potential for diverse applications, including electronics, energy storage, ltration, tissue engineering, and environmental remediation, to name just a few. 4,5epending on the intended application, a variety of characteristics are typically investigated, such as the diameter, orientation, porosity, specic surface area, mat thickness, mechanical properties, electrical and magnetic properties, or permeability for gases or liquids. 6High-resolution microscopy is the primary method for nanober characterization, and most publications in this eld report diameter distributions based on micrographs.][9][10][11] The diameter can be well controlled by electrospinning via various process parameter; 12,13 however, even when determining such correlations, systematic methodological inuences on the diameter measurement are usually neglected.Although exact gures are not always of primary interest, many studies have reported correlations between material properties, environmental parameters, spinning solution, process parameters and the resulting ber diameters. 7,12,14wing to the sheer number of studies in which the diameter distribution is assessed, a better understanding of the systematic errors and inuencing factors is of utmost importance.
Scanning electron microscopy (SEM) is the workhorse of material science.It is widely accessible and thus by far the most oen applied technique for the morphological analysis of nanobers.Since it is fast, easy to use, and can image large amounts of nanobers with little sample preparation and high resolution, it is also most commonly used to determine diameter distributions.Transmission electron microscopy (TEM) is also widely used and excels in its ability to visualize the ber cross-section at up to atomic resolution.Helium ion microscopy (HIM) is in many regards similar to SEM, however, hitherto much less established and accessible.It has already been used in several studies to image nanobers 8,15,16 and it is of particular interest for diameter measurements due to its capacity to image insulating samples without prior coating. 179][20][21] The micrographs are commonly analyzed manually using image analysis soware to determine diameter distributions.Some automated image analysis tools have been developed that allow for rapid batch analysis, e.g.General Image Fiber Tool (GIFT), DiameterJ, or BoneJ, to name just a few.][24][25][26][27][28] Here, we discuss the results of diameter measurements performed on a single electrospun nanober nonwoven using different microscopic methods, i.e.SEM, HIM, TEM, and AFM.The results reveal signicant deviations in the diameter distribution depending on the imaging technique, imaged sample region, and subjectivity of the analysts.Deviations were also found between human analysts and automated image analysis using the GIFT and DiameterJ soware implemented in ImageJ.These factors are rarely if ever addressed, making published correlations between material properties and nanober diameters highly unreliable and difficult to reproduce, which may inadvertently contribute more broadly to the so-called reproducibility crisis in the eld of materials science. 29,30

Experimental
Nanobers were electrospun from a polymer solution of 16 wt% PAN (XPAN, Dralon, Germany) dissolved in dimethyl sulfoxide (DMSO, min 99.9%,S3 chemicals, Germany) using a wire-based spinning device Nanospider Lab (Elmarco Ltd., Liberec, Czech Republic).A sample of 5 mm × 5 mm was cut from the as produced nonwoven.One half of it was coated with gold with a nominal thickness of 10 nm using magnetron sputtering; the other half was covered during gold deposition and thus le unmodied.This sample was then investigated using SEM, HIM, and AFM: SEM images were taken with a Sigma 300 VP SEM (Carl Zeiss Microscopy GmbH, Oberkochen, Germany) with an acceleration voltage of 7 kV.10 micrographs with 4.8 mm × 6.4 mm eld of view (FOV) and 1 with 15.4 mm × 20.5 mm FOV were taken of the coated sample half each.
HIM images were taken with a HIM Orion Plus (Carl Zeiss, Jena, Germany) using an acceleration voltage of 33.5 kV, a beam current of 0.2 pA and spot control of 7. The pristine bers were imaged using an electron ood gun for charge compensation.10 micrographs with 3 mm × 3 mm FOV and 1 with 20 mm × 20 mm FOV were taken of the pristine and coated sample half each.
AFM micrographs were taken in a FlexAFM Axiom (Nanosurf, Liestal, Switzerland) in tapping mode with a TAP190Al-G cantilever (tip radius 10 nm, half cone angle 10°at the apex), which was regularly renewed.The FOV was 5 mm × 5 mm.The standard settings were: 512 points per line, scan rate 1.4 s per line, set point 60%, P-gain 550, I-gain 1000, D-gain 0, free vibration amplitude 4-6 V, depending on the surface roughness.It should be mentioned that these free vibration amplitude values are necessarily much higher than in case of very at surfaces, leading to less sharp images and stronger tracking effects, as depicted in Fig. 1c.
For TEM imaging, an additional sample of 1 mm × 1 mm was cut from the initial nonwoven, inserted in a 1 : 1 mixture of acetone and epoxy resin (TAAB Laboratories Equipment Ltd, UK), then incubated at room temperature for 20 min, followed by inltration in a desiccator for 1 h.Aer curing of the resin at 70 °C for 12 h, ultra-thin lamellae of about 70 nm was prepared using an ultramicrotome (Ultracut, Reichert-Jung, Austria).The lamella was then contrasted for 5 min by lead citrate (Plano GmbH, Germany) and uranyl acetate (Science Services GmbH, Germany).TEM images were taking using a eld emission electron microscope JEOL JEM-2200FS (JEOL Ltd., Japan) operating at 200 kV.A total of 20 micrographs with 3 mm × 3 mm FOV and 1 micrograph of 26.7 mm × 26.7 mm FOV were examined.
All sample regions to be imaged were chosen arbitrarily by the operators without instructions or suggestions regarding an expected outcome.However, areas with major morphological deviations such as large agglomerates or membranous areas were intentionally excluded during the imaging.The following numbers of nanobers have been measured in parallel by 4 different analysts using the ImageJ soware: HIM and AFM of coated nanobers -10 bers in 10 images each; HIM and AFM of pristine nanobers -10 bers in 10 images each; SEM -10 bers in 10 images each for higher magnication and 30 bers in 1 image with lower magnication; TEM -5 bers in 20 images each for higher magnication and 30 bers in 1 image with lower magnication.The analysts evaluated the ber diameters by marking two opposite edges of a ber either by visual judgment directly in the image or in the grey scale plot, with the connection line perpendicular to the ber axis, as depicted in Fig. 1.Although there are methods for manual image analysis that assure more precise measurements, those are rarely used or at least virtually never disclosed in publications.Thus, no strict instructions were prescribed.Due to the rapid greyscale change between a ber and its environment (cf.Fig. 1), there was no advantage of applying line scans and measuring at the full-width half-maximum (FWHM) or using similar image processing techniques.It should be mentioned that the minimum uncertainty is of the order of one pixel, which corresponds to 3.8 nm (high mag.SEM), 10 nm (low mag.SEM),
In addition, the images have been analyzed using GIFT and DiameterJ, which are implemented in ImageJ, here, using version 1.54f and 1.51w, respectively.The underlying algorithms have been described in detail elsewhere. 24,31,32GIFT automatically ts a Gaussian peak function to the primary peak in the generated diameter histogram.For the batch analysis of the highly magnied SEM and HIM images (10 and 5, respectively), the raw data of each individual image has been combined and tted by a Gaussian function in the OriginPro 2023 soware.It should be mentioned that the amount of generated data points can vary signicantly between different micrographs, which is why some images might be overrepresented in the combined data set.An alternative approach would be to calculate the mean and STD of the individual image results.DiameterJ combines the data sets from batch analysis automatically and calculates the cumulative average value as a result.The Gaussian ts were again calculated using Origin-Pro 2023.DiameterJ uses 3 different segmentation algorithms, each generating 8 segmented images.Based on visual judgement of the operator, the most accurate segmentation is chosen for further processing.The results can vary depending on this subjective choice.

Results & discussion
To investigate the inuence of the methodology on the diameter distribution, we used four different microscopy techniques to take multiple images of the same nanober sample, which were independently analyzed by four different analysts (all micrographs can be found in the ESI †).The methodology of the analysis was discussed in advance to ensure that any differences were due to the subjective selection of nanobers included in the analysis.
Fig. 1 provides an overview of the techniques used: (a) SEM is by far the most frequently used method.To avoid charging of the sample during imaging, it is typically sputter-coated with a nanometer-thin conductive material such as gold, which has a potential inuence on the diameter measurement.(b) HIM is much less common, but has some advantages over SEM.Its working principle is very similar to that of SEM; however, it uses He + ions instead of electrons as the primary particle beam.In contrast to the SEM, this causes positive surface charging on insulation materials such as pristine, uncoated nanobers, which can be compensated by an electron ood gun without compromising the bers by a sputter coating. 33,34Here, we acquired HIM images from both pristine and coated nanobers.Although the theoretical resolution of HIM is higher than that of SEM, imaging of freestanding, insulating, and highly ionpenetrable materials is much more challenging and time consuming, which is why the resolution is lower compared to SEM in this case.(c) AFM is oen used because it provides more information than mere imaging, such as topographical, mechanical, electrical, or magnetic properties. 20,35Again, both pristine and coated bers were imaged by AFM.As we will see, it is, however, the least reliable method for diameter measurements.(d) TEM is probably the second most frequently used technique for nanober characterization.Its greatest strength compared to the other methods is the imaging of ber crosssections with very high resolution, revealing structural heterogeneity within the nanobers up to atomic resolution. 36For sample preparation, nanobers are usually embedded in resin, followed by thin sectioning by ultramicrotomy.An alternative

Nanoscale Advances
Paper method, which is, due to its simplicity, frequently used for sample preparation, is to disperse the nanobers in a liquid and then deposit them directly onto a grid.This method visualized the bers from the side, similar to SEM images.It has not been examined in this study.The comparison reveals several systematic variables in the analysis of nanober diameters from micrographs, as depicted in Fig. 2: SEM and HIM of gold sputter-coated nanobers are in good agreement.As illustrated in Fig. 1a, nonconformal conductive coatings for electron microscopy are typically produced by sputter deposition.They are affected by clustering (particularly on organic substrates 37 ) and shadow casting, which may distort the appearance of the ber.The HIM images showed a difference in mean diameter between pristine and gold-coated nanobers of 16 and 24 nm with the same standard deviations (STD) at high and low magnication, respectively, which could be attributed to the coating (nominal thickness 10 nm).The nanobers imaged by TEM were not coated.Their mean diameter was also lower than in SEM, but slightly higher than in HIM.Possibly the ber cross-sections appear slightly thicker as a result of the absorption of resin components during embedding or shearing during ultramicrotomy.It is unclear whether this effect is of methodological origin or due to mere chance.It can be assumed that the results of chargecompensated HIM imaging are closest to the true diameters, as there is apparently no systematic distortion.The apparent thickness should not be affected by the charge compensation and ghosting effect, which results from the transmission of He + ions and emission of secondary electrons from the underlying bers, 38 as illustrated in Fig. 1b.
In all categories, the analysts reported signicantly higher mean values and STD for low mag.images than for high mag.images: the increase in mean value from low to high mag.was 17% for SEM, 38% for HIM coated, 36% for HIM pristine, and 45% for TEM.A less accurate evaluation with a higher STD was to be expected because of the lower resolution/pixel width (see Experimental section).However, with a sufficient number of measurements, this should not affect the mean value.Identical bers do not appear thicker at lower magnication, which was conrmed by imaging the same sample region at different levels of magnication (these results are shown in Fig. S6 in the ESI †).Therefore, the fact that larger mean values were measured in all categories can be attributed only to subjective preferences in the selection of nanobers.It is plausible that larger bers were measured preferentially because of their better visibility; smaller bers might have even been barely noticeable.
Analysis of the AFM images shows by far the largest average values and STD, approximately twice as large as the values obtained from HIM images of uncoated bers.There are two major reasons for this apparent increase in diameter: (1) the radius of the AFM tip broadens the apparent diameter 39 (here, we expect about twice the tip radius of 10 nm) and ( 2) the individual or collective elastic displacement of bers in scan direction depending on morphological characteristics, such as nonwoven density and orientation.These effects lead to a smudged appearance of the bers, which makes an accurate evaluation difficult, causing a large STD and a strong inuence of subjectivity in the evaluation of micrographs.When comparing the forward and backward scan directions, a clear hysteresis effect can be seen in the bers that are not parallel to the scan direction, which, as shown in Fig. 1c, can affect the Fig. 2 Comparison of nanofiber diameters obtained from various microscopy techniques and analyzed by 4 different analysts each, referred to as A1 (teal), A2 (blue), A3 (orange), and A4 (green).Data points shown in purple have been generated by the GIFT macro in the ImageJ software (the number of generated data points has been drastically reduced in the figure for better visibility).These data are shown again as a histogram in comparison with data generated by DiameterJ in Fig. S7 in the ESI.† In the software-generated data sets, the Gaussian distribution plot has been fitted to the primary peak of the histogram, whereas for the analyst's data sets, the plots are calculated for all data points.All numerical values were rounded to whole numbers.The total mean and STD values shown on top of the diagram do not contain the software-generated data.

Paper
Nanoscale Advances measured diameter.An exemplary difference image between forward and backward scan direction is shown in Fig. S5 in the ESI.† This tracking effect is inuenced by set point, free vibration amplitude, scan rate, and gains.The difference between the gold-coated and pristine bers can be attributed to the lower rigidity of the pristine bers, which increased the average displacement in scan direction.As the mobility varies across different positions within the nonwoven, this is accompanied by an elevated STD with very large outliers.This also manifested in a comparably large number of failed imaging attempts for the pristine bers.Based on these results, more accurate measurements are expected when a metallic coating is applied prior to AFM imaging.It is striking that the relative results of the different analysts A1-A4 for each microscopy method are very similar.For instance, A1 reported the highest mean value in most categories.A3 and A4 measured the lowest mean values in almost all categories.A2 measured larger diameters than A3 in every category (average difference 17%), implying a strong subjective factor in the methodology or choice of nanobers to include in the analysis.The average deviation for all categories between lowest and largest reported mean value is a remarkable 31%.The average STD of mean values reported by the analysts within each category is 19%, which can be interpreted as the variation to be expected solely based on the choice of analyst.
In the literature, the diameter distribution is usually determined by one analyst from a single micrograph, so that the mere choice of the imaged sample region can substantially inuence both qualitative and quantitative results, which is even more problematic, when considering the scientist's expectations and conrmation bias.The mean values per micrograph vary with an average STD of ±22 nm averaged over all categories, which is an average of 14% of the mean value within each category.Such strong variations between micrographs even on a small sample area and within common categories pose the risk of misinterpretation of apparent correlations along with great potential for cherry-picking. 30 variety of automated image analysis tools are available.The algorithms underlying the measurement process may differ, however, a common approach is to t a Gaussian function in the primary peak of the diameter histogram to dispose of apparently faulty measurements.Here, we use GIFT as well as DiameterJ, both implemented in ImageJ, for a comparison with the manual measurements.As these tools were developed for SEM images (like most comparable soware), reasonable data could only be obtained from the SEM images and some of the high magnication HIM images of coated bers.In most HIM images and all AFM images the ber edges were too blurred for both algorithms to provide reliable data.In such cases, GIFT produced random diameter distributions with no clear peak in the histogram, whereas DiameterJ's results became highly dependent on the subjective choice of segmented images, oen resulting in distorted distributions insufficient for an accurate analysis.GIFT's results are shown in purple in Fig. 2 and DiameterJ's results are shown for comparison in Fig. S7 in the ESI.† Some studies compared the results of automated versus human diameter measurements (usually to validate the former) and mostly found good agreement, oen emphasizing signicant advantages in labor intensity and reproducibility. 22,24,32,40Such studies usually focus on over-ideal cases of high resolution, high contrast SEM images of monodisperse, narrowly distributed ber diameters on a discernible clear background.Non-Gaussian diameter distributions and suboptimal micrograph resolution are, however, likely to introduce systematic errors, as real diameter measurements deviating from the normal distribution are indistinguishable from noise.Most of the analysts' results as well as the sowaregenerated results show slightly asymmetric distributions with data spread out more towards larger diameters.It is unsurprising then, that the mean values obtained from GIFT and DiameterJ are slightly smaller than the analysts', as larger values are discarded as noise.Using a log-normal distribution instead of the conventional Gaussian distribution might actually be a more accurate approach in general.Interestingly, in contrast to the analysts, both soware tools gave the same mean value for SEM images with high and low magnication, again conrming that the higher mean value for low magnication measured by the analysts is due to unconscious selection bias, which may be circumvented by automated analysis soware.

Conclusion
Depending on the microscopy technique, a variety of factors can lead to an apparent increase in nanober diameter, with chargecompensated HIM of uncoated bers likely to yield the most accurate values, and AFM of uncoated bers is likely to yield the least accurate values.It was found that different analysts consistently reported different results across all tested categories and tended to measure thicker bers at lower magnications, which led to signicant overestimation of the diameter.Signicant variations within the categories have been observed both between different micrographs (14% STD of the mean value) and between different analysts (19% STD of the mean value).Automated image analysis soware, although relatively scarcely used, is reproducible and much faster than manual measurements.The mean values were slightly lower, likely discarding larger diameters as noise, but the results were mostly comparable with the analysts' at high magnication.In contrast to the analysts, the soware gave the same mean values at high and low magnication.However, meaningful results were only obtained for SEM images and few HIM images owing to the soware's demands on image type and quality.
When using numerical values, it is important to consider the strong inuence of methodology and subjectivity, and possibly bias, in determining the ber diameter distributions.If systematic inuencing factors are not taken into account, it can be assumed that many published correlations between ber diameter and material properties are signicantly less reliable and more difficult to reproduce than they appear based merely on their standard deviation.

Fig. 1
Fig. 1 Overview of some common microscopy techniques for nanofiber characterization: (a) SEM, (b) HIM, (c) AFM, and (d) TEM.On the top are exemplary micrographs with inserted grey-scale plots (arrows indicate where the diameter was measured) and on the bottom are schematic illustrations of the respective technique's working principles.