Characterization of Poly(Ethylene Oxide) Nanoﬁbers—Mutual Relations between Mean Diameter of Electrospun Nanoﬁbers and Solution Characteristics

† This paper is an expanded version of “Electrospinning of poly(ethylene oxide) solutions—Quantitative relations between mean nanoﬁbre diameter, concentration, molecular weight, and viscosity ” published in Proceedings of Novel Trends in Rheology VIII, Zlin, Czech Republic, 30–31 July 2019. Abstract: The quality of electrospun poly(ethylene oxide) (PEO) nanoﬁbrous mats are subject to a variety of input parameters. In this study, three parameters were chosen: molecular weight of PEO (100, 300, 600, and 1000 kg / mol), PEO concentration (in distilled water), and shear viscosity of PEO solution. Two relations free of any adjustable parameters were derived. The ﬁrst, describing the initial stage of an electrospinning process expressing shear viscosity using PEO molecular weight and concentration. The second, expressing mean nanoﬁber diameter using concentration and PEO molecular weight. Based on these simple mathematical relations, it is possible to control the mean nanoﬁber diameter during an electrospinning process.


Introduction
At present, nanofibrous mats are efficiently used in many applications: filters, tissue engineering, drug delivery systems, antibacterial wound dressing, protective clothing, nanocomposite materials, to name a few. One of the ways one can produce nanofibrous mats is through the process of electrospinning. In this process, polymer solution or melt is exposed to a high-voltage electric field (in orders of tens kV) under which viscoelastic polymer jets emanate from so-called Taylor cones [1] formed at the polymer surface. After passing approximately 10-20 cm in length, the material of the jets (after evaporation of a solvent) is cumulated on an earthed collector [2][3][4] at the shape of individual nanofibers forming a non-woven textile.
The problem is that some promising materials, such as chitosan, keratin, and other protein-based materials, cannot be electrospun in their pure forms. This contrasts with the easy spinnability [5,6] of, e.g., poly(ethylene oxide) (PEO). Fortunately, even the negligible presence of PEO (up to 2%) in solutions of the above-listed materials completely changes their disposition to being electrospun (see below). Intensive study of PEO behavior during the electrospinning process has been undertaken due to this fact and because of the excellent biodegradability, biocompatibility, and non-toxicity. These attributes also reflect PEO nanofiber applications in biomedicine and the food industry [7][8][9][10] apart from the above already mentioned improvements in spinnability in combination with chitin or chitosan [11][12][13][14], keratin [15,16], silk [17,18] and other materials.

Rheological Characterization
Shear viscosity of the individual PEO solutions was determined at a constant temperature of 25 • C using a Physica MCR 501 device (Anton Paar, Graz, Austria) equipped with concentric cylinders (26.6/28.9 mm-inner/outer diameters). Each measurement was repeated at least three times with very good reproducibility.

The Electrospinning Process
Laboratory equipment consisting of a high voltage power supply (Spellman SL70PN150, Hauppauge, NY, USA), a carbon steel stick (10 mm in diameter) with a hollowed semi-spherical pit at the end for polymer filling, and equipped with a motionless flat metal collector (for details see [51]) was used for an electrospinning process. The drop of polymer solution filling the pit contains approximately 0.2 mL in volume, a tip-to-collector distance was fixed (20 cm) as well as nearly constant ambient conditions (temperature 23 ± 1 • C, relative humidity 41 ± 1%). Good quality of electrospun mats (elimination of appearance of web blobs) was ensured by a gradual voltage decrease from 25 kV fixed for M w = 100 kg/mol to 12 kV fixed for M w = 1000 kg/mol.

Nanofibrous Mat Characterization
A high-resolution scanning electron microscope (SEM) Vega 3 (Tescan, Brno, Czech Republic) was used for imaging of nanofibrous mats after their sputtering with a conductive layer to improve conductivity.

Results and Discussion
Due to a non-negligible number of entry parameters, the process of electrospinning cannot be simultaneously analyzed from all material, geometrical, and process aspects. It is always necessary to fix a substantial majority of entry parameters and concentrate on a moderate number of selected parameters. The impacts of the individual parameters are usually interlaced, and in the following analysis, we will pay attention to a mutual interplay between PEO molecular weight, PEO concentration, viscosity of a PEO solution in distilled water, and a mean diameter of the resulting nanofibers.
Specifically, the emphasis will focus on the derivation of two dependencies: (1) A determination of functional relation between shear viscosity (η), PEO concentration (c), and PEO molecular weight (M w ); (2) A determination of functional relation between the diameter of nanofibers (dia), PEO concentration (c), and PEO molecular weight (M w ).
From the viewpoint of easy and clear applicability of the proposed relations, they should exhibit the following attributes: (a) Usage of elementary algebraic functions only; (b) Absence of adjustable parameters; (c) Their validity should cover sufficiently broad regions of two entry material characteristics-PEO molecular weight and PEO concentrations in distilled water (a range of concentrations shifts with respect to successful electrospinability of PEO solutions dependent on M w ); (d) The correctness of the approximate relations-deviations of their predictions from the experimental data should potentially exceed the experimental errors only moderately.
The least accurate determination of a precise value out of the four studied parameters (M w , c, η, dia) is represented by the mean nanofiber diameter dia.
A mean nanofiber diameter derived from 300 measurements taken from three different images was determined by applying the Adobe Creative Suite software (San Jose, CA, USA). Figure 1 displays SEM images of PEO nanofibers created from various molecular weights at different concentrations. The histograms attached to the individual molecular weights depict a variance of nanofiber diameters. This is also documented in Table 2. A mean nanofiber diameter derived from 300 measurements taken from three different images was determined by applying the Adobe Creative Suite software (San Jose, CA, USA). Figure 1 displays SEM images of PEO nanofibers created from various molecular weights at different concentrations. The histograms attached to the individual molecular weights depict a variance of nanofiber diameters. This is also documented in Table 2.  After analyzing and processing the experimental data obtained by consecutive electrospinning of PEO solutions differing in PEO molecular weight (100, 300, 600, and 1000 kg/mol) and concentration (see Table 2), we can calculate the correlation coefficients for the experimental data sets  After analyzing and processing the experimental data obtained by consecutive electrospinning of PEO solutions differing in PEO molecular weight (100, 300, 600, and 1000 kg/mol) and concentration (see Table 2), we can calculate the correlation coefficients for the experimental data sets (c, dia). Their proximity to one (pure linearity behavior, see Table 3) indicates the possibility to approximate a mutual dependence of the mean nanofiber diameter on the concentration by a simple linear relation. To unify this approach, it is also necessary to express a general coefficient of linearity through the values of PEO molecular weights, which results in a slight deviation from the optimized values for the individual molecular weights. with a linear proportionality between the mean nanofiber diameter and concentration, and with a linear dependence between the mean nanofiber diameter and molecular weight. The numerical values of the constants are a 1 = 0.00008 and a 2 = 1.6. The correspondence between the experimental and predicted data is depicted in Figure 2, with the mean deviation attaining 6.7%. Relation (1) complies with the tendencies introduced in literature [52,53], i.e., an increase in the nanofiber diameter both with increasing molecular weight and increasing concentration. Dependence between shear viscosity, molecular weight, and concentration is a little more complicated. If we apply an analogous approach to that above, we obtain the correlation coefficients for the data sets (log(c), log(η)), again in close proximity to one (see Table 3). It justifies the proposal of a linear relation between log(c) and log(η). Unifying both a slope and an intercept with respect to the range of PEO molecular weights, a proposed relation is still algebraically simple.
where b 1 = 4.71, b 2 = −0.82, b 3 = 12.7, b 4 = −48.8. As can be seen, Relation (2) is composed of two separate members, the first one expressing a contribution of concentration only and the second one (in brackets) representing the participation of molecular weight exclusively. Figure 3 documents the courses of the proposed predicted curves attaining a mean deviation of 6.3% in the semi-log coordinates (concentration-linear, shear viscosity-logarithmic), in fully linear coordinates, a mean  Table 3. Correlation coefficients between (c, dia) and (log(c), log(η)).

M w (kg/mol) Correlation Coefficient [-]
(c, dia) Finally, we propose the following relation with a linear proportionality between the mean nanofiber diameter and concentration, and with a linear dependence between the mean nanofiber diameter and molecular weight. The numerical values of the constants are a 1 = 0.00008 and a 2 = 1.6. The correspondence between the experimental and predicted data is depicted in Figure 2, with the mean deviation attaining 6.7%. Relation (1) complies with the tendencies introduced in literature [52,53], i.e., an increase in the nanofiber diameter both with increasing molecular weight and increasing concentration. Dependence between shear viscosity, molecular weight, and concentration is a little more complicated. If we apply an analogous approach to that above, we obtain the correlation coefficients for the data sets (log(c), log(η)), again in close proximity to one (see Table 3). It justifies the proposal of Processes 2019, 7, 948 6 of 9 a linear relation between log(c) and log(η). Unifying both a slope and an intercept with respect to the range of PEO molecular weights, a proposed relation is still algebraically simple.
where b 1 = 4.71, b 2 = −0.82, b 3 = 12.7, b 4 = −48.8. As can be seen, Relation (2) is composed of two separate members, the first one expressing a contribution of concentration only and the second one (in brackets) representing the participation of molecular weight exclusively. Figure 3 documents the courses of the proposed predicted curves attaining a mean deviation of 6.3% in the semi-log coordinates (concentration-linear, shear viscosity-logarithmic), in fully linear coordinates, a mean deviation attained 11.8%. In the log-log coordinates (Figure 4), there is a linear dependence of shear viscosity on PEO concentration with the fixed slope attaining a value of 4.71.
Processes 2019, 7, x FOR PEER REVIEW 7 of 10 deviation attained 11.8%. In the log-log coordinates (Figure 4), there is a linear dependence of shear viscosity on PEO concentration with the fixed slope attaining a value of 4.71.

Conclusions
The introduced relationships propose a hint as to which way the geometrical arrangement of the Processes 2019, 7, x FOR PEER REVIEW 7 of 10 deviation attained 11.8%. In the log-log coordinates (Figure 4), there is a linear dependence of shear viscosity on PEO concentration with the fixed slope attaining a value of 4.71.

Conclusions
The introduced relationships propose a hint as to which way the geometrical arrangement of the resulting electrospun nanofibrous mats can be modified. Based on the relatively simple functional Relation (1), it is possible to alter a mean nanofiber diameter by a suitable choice of PEO material