Morphology and pore size distribution of electrospun and centrifugal forcespun nylon 6 nanofiber membranes

Abstract

The porosity and high surface-area-to-volume ratio of nanofiber membranes offer potential for diverse applications, including high-efficiency filters and barrier fabrics for use in protective textiles. The objective of this research is to examine the morphology and pore size distribution of nanofiber membranes prepared using two spinning methods, that is, electrospinning and forcespinning. The results indicate that fiber diameter is impacted by spinning solution viscosity in an analogous way for both spinning methods. Higher concentrations resulted in larger fiber diameters in both electrospun and forcespun membranes. Fiber diameter and membrane areal density were found to significantly impact membrane pore size distribution. A theoretical model was used to describe pore size variation and was found to agree with the empirical patterns in the case of electrospun membranes.

Keywords

nanofibers electrospinning forcespinning porosity pore size distribution fiber diameter probability density function modeling

Nanofiber membranes have been acclaimed for high surface-area-to-volume ratio and superior porosity that allow potential applications in many fields, such as tissue engineering,¹ drug delivery,² filtration,³ and protective textiles.⁴ In all these applications, porosity and the structural characteristics associated with it are of critical importance for the performance of the nanofibrous membranes. For instance in tissue engineering, the pore size distribution affects the fiber fraction and voids that are available for cell adhesion and ingrowth.^5,6 In filtration, the pore size distribution determines the selectivity and separation efficiency of the membrane as well as the pressure drop across the filter.⁷ Likewise in protective clothing applications, porosity is a determinant factor in both transport and barrier properties of the fibrous structures.⁸

Electrospinning is the most popular method to spin nanofibers. It has focalized attention in recent years due to its capability of producing polymer fibers with diameters ranging from a few nanometers to a few micrometers.⁹ In electrospinning, a polymer solution or melt is charged using a high-voltage power supply and forced through the tip of a needle using a syringe pump. When a sufficiently high voltage is applied to the needle, the electric field between the needle and a grounded collector induces charge accumulation on the surface of the polymer droplet, which subsequently elongates into a conical shape referred to as a Taylor cone.¹⁰ When the applied electric field reaches a critical value, the charged liquid jet originating from the tip of the Taylor cone undergoes a stretching and whipping action caused by the electrostatic forces. This results in a rapid evaporation of the solvent followed by the formation of a nanofiber mat on the collector.^11–14 It is notable here that the solidifying electrospun fibers hit the collector at their peak velocity; indeed, studies have shown that the velocity of the jet increases as a function of the distance from the Taylor cone along the jet.^15,16 As a result, nanofiber mats or membranes can be deposited as a conformal coating on a substrate or peeled as standalone membranes from the surface of the collector. The morphology of electrospun nanofibers can be affected by a number of factors.^17–19 Those include solution characteristics (solution concentration, viscosity, conductivity, etc.), process parameters (voltage, distance between needle and collector, etc.) and ambient conditions, such as temperature and humidity.^17–19

In recent years, a new nanofiber spinning technology called forcespinning was developed²⁰ and was made commercially available by FibeRio Technology Corp. (McAllen, TX). In forcespinning, polymer solutions or melts are ejected through orifices or needles lining the periphery of a spinneret that rotates at high speed (Figures 1(a) and (b)). The centrifugal force draws fibers from the liquid jet and attenuates their diameter into the nano-scale.^20–23 The principle of forcespinning makes it feasible to spin conductive and nonconductive polymer melts and solutions into nanofibers.²⁴ Thus, one of the potential advantages of forcespinning is its versatility, as it offers both melt- and solution-spinning capability with a broad range of spinnable materials.²⁴ Forcespinning equipment, including both industrial and laboratory-scale machines, can produce nanofiber coatings or standalone membranes (Figure 1(c)), as well as bulk fibers from the nano- to the micro-scale (Figure 1(b)).

Figure 1.

Cyclone L-1000M/D laboratory forcespinning machine: (a) solution spinning spinneret; (b) melt spinning spinneret and vertical bar collector with bulk fibers; (c) vacuum box collector with the substrate for coating/membrane processing.

The morphology of forcespun fibers is a function of spinning fluid characteristics, such as solution concentration (in the case of solution spinning) and melt viscosity (for melt spinning), as well as operating parameters that include rotational speed and orifice size of the spinneret, heating temperature, and collection system.^21,23–26 Sarkar et al.²¹ reported that spinneret rotational speed is negatively correlated to fiber diameter in limited spinning tests conducted on poly(ethylene oxide) (PEO). Shanmuganathan et al.²³ used a laboratory forcespinning machine to melt-spin poly(butylene terephthalate) nanofibers. The researchers found that melt temperature and thus fluid jet viscosity had the most determinant effect on fiber diameter (higher temperature yielded finer fibers), whereas spinneret rotation speed had a limited impact on fiber diameter.²³ Recent work on solution forcespinning of nylon 6 (PA6) by Hammami et al.²⁵ showed a positive relationship between spinning solution viscosity and fiber diameter. Other spinning parameters, that is, spinneret speed and spinning nozzle size, played a minor role relative to the polymer solution viscosity in determining both processability and fiber diameter distribution.²⁵

Nanofiber membranes processed through electrospinning have been investigated by numerous researchers for their potential application in protective clothing as barriers to various substances, including water or other liquids,^27,28 as well as potentially harmful particles and hazardous agents.^29,30 On the other hand, studies centered on the other nanofiber spinning technology, that is, centrifugal force spinning, have mostly focused on engineering applications such as ultra-filtration membranes or energy storage.^31–33 In the aforementioned applications, pore size distribution of the membranes is critical to both the barrier performance and the breathability of the protective clothing system through vapor transfer. Thus, the objective of this research is to examine the morphology and pore size distribution of nanofiber membranes prepared using both methods from the same polymer solutions. Factors impacting fiber diameter and membrane pore size distribution are examined and a formal analysis of pore size distribution is discussed using models based on stochastic fiber network theory.

Materials and methods

Medium viscosity PA6 pellets (Aegis® H95ZI, 1.13 g.cm^–3 density) were purchased from the Honeywell Corporation. Formic acid (concentration >88%) was purchased from Sigma-Aldrich Chemical Corporation. The PA6 was dissolved in formic acid and the solution was mixed in a sealed beaker for more than 24 hours at room temperature. Once the mixing was complete and the polymer was fully dissolved, the prepared solution was set to stand for 1 h at room temperature to ensure stability.

Nanofiber membranes were prepared using both electrospinning and forcespinning. For electrospinning, a high-voltage power supply (Gamma High Voltage Research, ES100P-10 W/DAM) was used with the voltage fixed at 25 kV. A syringe pump (Harvard Apparatus) was used to feed the polymer solution at a rate of 4 ul/min and through an 18-gauge needle (Harvard Apparatus). A grounded adjustable height platform covered with aluminum foil was used as the collector and the tip-to-collector distance was set to 12 cm.

A laboratory-scale forcespinner (Cyclone L-1000M/D, Fiberio Technology Corp., McAllen, TX) was used for forcespinning. The solution spinneret (Figure 1(a)) was fitted with two 30-gage or 0.159-mm inner diameter needles (Exel International, Corp.) A nonwoven substrate was placed on the vacuum box collector (Figure 1(c)), and the fan was activated at 60% of capacity to draw fibers towards the substrate while maintaining spinning stability.

Based on preliminary spinnability tests, two levels of polymer solution concentration offering stable spinning and consistent membranes, that is, 15 and 20 wt%, were selected for electrospinning. Attempts to forcespin the 15 wt% solution were unsuccessful and yielded excessively thin membranes with weak structure. On the other hand, solution concentration levels of 20 and 25 wt% appeared adequate for forcespinning samples and thus were selected to offer both a comparative basis with electrospun samples and an insight into the impact of solution concentration on fiber membrane morphology.

Membrane areal density (fiber mass by unit area) was controlled at three levels, 5, 10 and 15 g.m^–2 (GSM), by varying spinning duration in both electrospinning and forcespinning. It can be noted here that the difference in throughput between the two lab spinners is sizeable and that achieving the targeted web areal density took significantly less spinning time on the laboratory forcespinner. Upon completion of the spinning cycles, all nanofiber membranes were carefully peeled from the substrate and collected for testing. Three independent replications were conducted for each spinning condition to ensure adequate variance estimation.

The morphology of the nanofibers was examined by scanning electron microscopy (SEM, Hitachi S-5500). All samples were sputter coated with gold prior to SEM analysis. Fiber diameter was measured using Image J (NIH, http://rsbweb.nih.gov/ij/) on SEM micrographs. A minimum number of 100 fibers were measured for each sample. To measure pore size distributions, a PMI (Ithaca, NY) Advanced Capillary Flow Porometer was used in this research. Capillary flow porometery appears adequate for this application because the test pressure is low, such that the membrane will not be distorted.^34,35

Results and discussion

Fiber morphology

SEM images of selected electrospun and forcespun nanofiber mats are presented in Figures 2 and 3, respectively. All the images captured exhibited a majority of fibers in the sub-micron range. However, electrospun samples appeared to show more regular and uniform fiber morphology. The difference in fiber formation mechanisms, that is, electrical field versus centrifugal force, is likely to yield differences in morphology along the fiber. For instance, McEachin and Lozano²⁴ empirically observed variations in fiber diameter at different spinning times on a laboratory-scale forcespinning machine, which suggest a tapered morphology along the fiber axis. Using a parametric model, Padron et al.³⁶ also demonstrate a reduction in fiber radius at different positions along the forming fiber arc length. A quantitative analysis of fiber diameter will be presented in the next section and will provide additional insight into fiber diameter variability.

Figure 2.

Scanning electron microscopy images of fibers electrospun from the 15 wt% solution (a) and from the 20 wt% solution (b). The scale bar is 1 µm.

Figure 3.

Scanning electron microscopy images of fibers forcespun from the 20 wt% solution (a) and from the 25 wt% solution (b). The scale bar is 2 µm.

An interesting morphological feature observed exclusively on electrospun samples was the occurrence within the nanofiber mats of nano-nets with interlinked ultra-fine fibrils exhibiting diameters in the nanometer to the low tens of nanometers range (Figure 4). The formation of nano-nets was reported by multiple researchers and with a variety of polymers, including PA6 and poly (acrylic acid), as well as PA6 and polyurethane nanocomposites with multiwalled carbon nanotubes and TiO₂ nanoparticles.^37–39 Kimmer et al.³⁸ attributed the formation of those nano-nets to the “increased ionization of the polymer solution in the presence of TiO₂” and did not observe such structures in pristine PA6. It is apparent from our results that nano-nets may also occur when spinning neat polymer solutions with no nano-fillers. Ding et al.³⁷ cite high applied voltage and low relative humidity as potential conditions that could favor the appearance of nano-nets, regardless of the presence or not of nano-fillers. Because those nano-net structures divide the voids between the coarser nanofibers, they may have a significant effect on pore size distribution and barrier properties. Therefore, the mechanism and prevalence of their formation, as well as the impact they have on membrane properties, shall be further scrutinized in future research.

Figure 4.

Scanning electron micrographs of electrospun nylon 6 nanofibers exhibiting ultra-fine nano-nets. The scale bar is 10 µm in (a) and 1 µm in (b).

Fiber diameter distribution

Figure 5 depicts fiber diameter distributions obtained on both electrospun and forcespun samples from the different spinning solution concentrations. Note that the ultra-thin fibrils constituting the nano-nets described above (Figure 4) were not included in the electrospun fiber diameter analysis.

Figure 5.

Electrospun and forcespun fiber diameter distributions: (a) fibers electrospun from 15 wt% nylon 6 solution; (b) fibers electrospun from 20 wt% solution; (c) fibers forcespun from 20 wt% solution; (d) fibers forcespun from 25 wt% solution.

All observed distributions appeared to conform to log-normal probability density functions (Figure 5). The x-axes were scaled to the diameter range covered by each sample, but were maintained consistent for the plots depicting fibers that were electrospun and forcespun from the same solution (Figures 5(b) and (c)). All fibers electrospun from the low viscosity solution (15 wt%) exhibit diameters ranging from 60 to 260 nm, with the 95th percentile being in the vicinity of 200 nm (Figure 5(a)). Fibers electrospun from the higher concentration (20 wt%) had diameters ranging from 100 to 600 nm (Figure 5(b)), while fibers forcespun from the same solution exhibited a broader diameter distribution with a shift to cover a range between 200 and 1000 nm (Figure 5(c)). Finally, the increase of the spinning solution concentration to 25 wt% further shifts the forcespun fiber diameter distribution towards coarser fibers with approximately 7% of the observations being over 1 µm in diameter.

A comparison of summary statistics and dispersion patterns of these results can be seen in Figure 6. As indicated above, fiber diameter increased with higher polymer concentration for both spinning methods. In addition, the boxplots in Figure 6 show that the fiber diameter distribution tended to be broader for the higher concentration solution and for the forcespun samples when the concentration was constant. We should note here that during these experiments, spinning parameters other than solution viscosity were set to levels that allow stable and consistent spinning operations in both processes. Variations in spinning conditions, for example voltage in electrospinning or spinneret rotation speed in forcespinning, may affect the observed relative differences and thus the results are valid within the current experimental design limitations. However, it was noted from previous research that spinning fluid viscosity is the major determining factor and that spinneret speed has very limited impact on fiber diameter.^23,25 We now examine the impact of these fiber morphological characteristics on membrane pore size distribution.

Figure 6.

Boxplots exhibiting the increasing dispersion of diameter distribution with solution concentration and spinning method.

Membrane pore size distribution

The results discussed above with respect to fiber morphology and diameter distribution are likely to lead to differences in membrane pore size distribution across processing methods and spinning conditions. Fiber diameter and membrane areal density have been found by Li et al.³⁵ to be strongly associated with pore size and pore size distribution of electrospun fibrous membranes. Eichhorn and Sampson⁵ applied models based on stochastic fibrous network theory to describe the porosity of electrospun membranes. The authors emphasize the dominant role of fiber diameter in determining pore size at a given membrane areal density. Based on this research, it would be expected that pore size distribution of our samples will differ depending on the spinning method and solution concentration, given the impact of those factors on fiber diameter, as discussed in the previous section. In what follows, we first examine the empirical results obtained through capillary flow porometry, and then discuss their variability in the context of the theoretical predictions cited above.

Pore size distributions of electrospun and forcespun samples obtained from the different solutions and with varying areal densities are shown in Figure 7. Each plot on the figure combines empirical histograms of the low and high areal density samples (5 and 15 g.m^–2) obtained from the same solution. The two plots on the top row (Figures 7(a) and (b)) depict electrospun samples (noted E in the series legend), whereas the plots on the bottom row (Figures 7(c) and (d)) depict forcespun samples (noted F in the series legend). Because the ranges covered by the pore size distributions obtained in different conditions are very different, the x-axes were scaled differently across plots.

Figure 7.

Pore size distribution of nanofiber membranes processed in varied conditions with different areal densities: (a) electrospun from 15 wt% nylon 6 (PA6) solution; (b) electrospun from 20 wt% PA6 solution; (c) forcespun from 20 wt% PA6 solution; (d) forcespun from 25 wt% PA6 solution.

It appears from these figures that the pore sizes of the electrospun membranes are all in the sub-micron range and most are within the 200–400 nm range, with sizeable variations depending on membrane areal density and solution concentration. On the other hand, pore sizes of the forcespun membranes are at least one order of magnitude larger and mostly ranged between 1 and 5 µm. Similarly, significant shifts are observed in the pore size distributions depending on areal density and solution concentration. In all cases, the pore size distribution shifts towards lower diameter values when the fiber mass per unit area increases. Within the same areal density levels, the pore size distribution shifts towards lower values when spinning solution concentration, and consequently fiber diameter, decrease. One notable feature shown by the electrospun membrane pore size distributions of Figure 7(b) is that the shape of the distribution suggests a bimodal pattern. The potential link between pore size distribution shapes and the occurrence of nano-nets observed above is worth exploring in future research.

The resulting pore size mean plots are depicted in Figure 8 for all prepared nanofiber samples. As expected, mean pore size was found to decrease with the increase of web density regardless of the spinning method and solution concentration. This is due to the superposition of more fiber layers leading to smaller inter-fiber space. On the other hand, polymer solution concentration also appears to affect pore size distributions of the nanofiber webs because of the impact it has on fiber diameter. As can be seen in Figure 8, the electrospun (E) nanofiber networks obtained from the 20 wt% solution concentration tend to have larger pore sizes than those obtained from the 15 wt% concentration. Likewise, pore sizes of the forcespun samples processed from the 25 wt% concentration are larger than those obtained from the 20 wt% concentration. Due to the fact that increasing polymer concentration results in higher fiber diameter, this change in pore sizes can be explained by the widening inter-fiber space caused by higher fiber diameter.

Figure 8.

Mean pore diameter of electrospun (a) and forcespun (b) nanofiber webs as a function of solution concentration and membrane areal density (g.m^–2).

The impact of fiber diameter and membrane areal density will be examined further through the theoretical analysis of the next section. In addition to the impact of membrane density and fiber diameter, the substantial difference in pore sizes between spinning methods is confirmed on all spinning conditions (Figure 8). Forcespun webs can have mean pore sizes more than 10 times larger than those of electrospun counterparts obtained from comparable solutions and with the same web density. Although the difference in fiber diameter between electrospun and forcespun nanofibers partially explains this disparity in pore size distributions, other factors, including the occurrence of the ultra-fine nano-nets described above in electrospun membranes, as well as the different fiber formation and collection mechanisms, appear as potentially critical factors in determining membrane pore sizes. Indeed, the different fiber drawing and collection systems may lead to different fiber orientation and area coverage, as well as to different inter-fiber structure. As previously mentioned, the velocity of the spinning fluid jet in electrospinning increases as a function of the distance from the Taylor cone along the jet,^15,16 and thus electrospun fibers hit the collector at their peak velocity. Consequently, continuous spinning over a period of time is likely to result in tightly condensed and intermingled fiber network layers. On the other hand, although tangential velocity of forcespun jets was shown to increase along the arc length,⁴⁰ the fibers follow an orbital trajectory that gradually expands outward to reach the collector.^36,40 Thus, forcespun samples appear relatively loftier compared to electrospun membranes of similar areal density, which tend to be more densely compacted. The resulting larger voids within the thickness of the forcespun membranes along with the fiber orientation may explain the significant order of magnitude difference observed in pore size results. However, further analyses of the structure of those membranes, including quantitative evaluation of nano-net formation and analysis of the structure and inter-fiber cohesion within the web thickness, would offer more insight.

Pore size theory

To better understand the results discussed above, we attempt in this section to contrast observed trends with theoretical predictions based on stochastic fiber network theory. We base this analysis on work by Sampson⁴¹ on the general case of near-planar fiber networks, and later by Eichhorn and Sampson,⁵ specifically focusing on porous nanofibrous assemblies. According to this work inspired from the paper industry, fibrous membranes can be modeled as multi-planar structures or stacks of two-dimensional (2D) networks. Sampson⁴¹ writes the probability density function of pore radii distribution in the 2D network as a gamma distribution of the form

f (r) = \frac{b^{k}}{Γ (k)} r^{k - 1} e^{- br}

(1)

where

k and b

are the distribution’s parameters defined by the mean

\bar{r} = \frac{k}{b}

, and variance

σ^{2} = \frac{k}{b^{2}}

. The probability density function of pore radii in a stack of n 2D layers is given by

g (r) = \frac{n}{ɛ} (\frac{Γ (k, br)}{Γ (k)})^{\frac{n}{ɛ} - 1} \frac{b^{k}}{Γ (k)} r^{k - 1} e^{- br}

(2)

where n is the number of 2D layers and ɛ is the fractional open area or porosity of the 2D network.^5,41 Thus, ɛ corresponds to the probability that the area coverage (expected number of fibers covering a point in the plane) is zero, where coverage is modeled as a random process with Poisson probability.^5,41 The number of layers n in a three-dimensional (3D) stack of 2D networks can be expressed as a function of membrane areal density β, fiber linear density δ, fiber width (or diameter assuming circular cross-section) ω and ɛ:

n = \frac{β ω}{δ log \frac{1}{ɛ}}

(3)

Details on the derivation of the equations above can be found in Sampson⁴¹ and Eichhorn and Sampson.⁵ For our purposes, we use Equation (2) to derive the predicted mean pore sizes for a range of fiber diameters and membrane areal densities by numerically evaluating the integral

\bar{r} = \int_{0}^{\infty} r g (r) dr

(4)

Given the ultra-fine diameter of fibers constituting the nanofibrous networks, ɛ will tend to 1 as the network approaches the elemental single-layer structure. As a practical matter, the calculations discussed below were computed using a range of 0.7–0.99 for ɛ. Predictions obtained with the higher values more closely matched observed pore sizes and are shown below.

Figure 9 depicts the expected variation of mean pore diameter with areal density for a range of fiber diameters, along with the observed data points for the electrospun samples. Increasing areal density results in rapidly decreasing mean pore diameter in a pattern that corresponds to a power function. On the other hand, increasing fiber diameter (ω) results in higher mean pore diameter. The theoretical trends are in concordance with those described in the literature.^5,41 In addition to the model-predicted curves, the empirical data points appear to conform to the general expected pattern, with a non-linearly decreasing pore size with membrane areal density and a shift in pore size levels with fiber diameter variation. However, the observed mean pore diameters appear to decrease with areal density less rapidly and less dramatically than what the model suggests. In fact, the experimental results show a pattern that overlaps expected curves across a range of fiber diameters. Multiple factors may explain these observations, including potential errors in capillary flow measurements and in modeling assumptions. For instance, the stochastic fiber network model considers the fiber population as having a uniform diameter and does not take into account the observed variability seen in Figure 5. Likewise, potential variation in areal density, that is, the distribution of fiber mass over the sample area, is not taken into account. In addition, the parametrization of the 3D fibrous network as a multi-planar stack of 2D layers appears as a good approximation but may not reflect the inter-fiber interactions within the third dimension of the structure.

Figure 9.

Influence of areal density and fiber diameter $(ω)$ on mean pore diameter. (Line plots show predicted curves for different fiber diameters, while data points represent observations obtained on the electrospun samples).

The hypothesis above can be examined by observing the relationship between observed and predicted mean pore diameters for the samples tested (Figure 10). It appears from these results that within the parameter ranges and experimental conditions of this research, the model tends to underestimate mean pore diameter towards the lower end of the observed range, that is, when the number of stacked near-planar layers increases for a given fiber diameter. Nevertheless, the relationship between the observed and predicted results is highly significant (p < .001), which indicates that the model adequately accounts for the general patterns of pore diameter variability in electrospun nanofiber membranes.

Figure 10.

Model-predicted versus observed mean pore diameters for the electrospun nanofibrous membranes (equality line added for reference).

Finally, it is worth noting here that pore size results obtained on the forcespun membranes were out of the ranges covered by the current model parameters, which further reinforces the conclusion made above to the effect that inter-fiber interaction in the web thickness could be a critical factor.

Conclusions

Nanofiber membranes were processed from PA6 solutions using two different methods, that is, electrospinning and forcespinning. The former is the most commonly used and well-known method, while the latter represents a relatively recent development in nanofiber spinning technology. Fiber diameter and pore size distributions were measured in order to gain insight into the applicability and potential of these membranes as barrier structures in protective textiles.

Differences in fiber morphology between spinning methods and polymer solution properties within spinning methods were observed. One notable morphological feature observed exclusively with electrospun membranes was the presence of nano-nets formed of ultra-fine fibrils with diameters in the nanometer to the low tens of nanometers range. It was also found based on SEM micrograph analysis that fiber diameter is impacted by spinning solution concentration in an analogous way for both spinning methods. Higher concentrations resulted in larger fiber diameter in both electrospun and forcespun membranes. In addition, membranes produced by forcespinning tended to have higher fiber diameter and broader diameter distributions than the counterparts electrospun from the same solution.

Pore size distribution of all membranes was measured using a capillary flow porometer and was found to vary significantly with membrane areal density and fiber diameter. The impact of fiber diameter and areal density on pore size was described using a theoretical model inspired from the paper industry and assuming a stochastic fiber network. Observed and model-predicted mean pore diameters exhibited closely concordant patterns and were shown to increase with increasing fiber diameter and to decrease with increasing membrane areal density. Furthermore, the spinning method appeared to have a substantial impact on membrane porosity as forcespun membranes had mean pore sizes more than one order of magnitude larger than the electrospun counterparts. The difference in fiber diameter between the two processes only partially explains this variability in porosity. It appears likely that other factors, such as the presence of the nano-nets in electrospun membranes, as well as differences in fiber orientation, in inter-fiber cohesion within the structure thickness and the apparent loftiness of forcespun membranes, may also affect pore size distribution. These factors are currently the subject of further research, in addition to the investigation of their impact on both transport and barrier performance features relevant to protective textile applications.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

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