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Stable-jet length controlling electrospun fiber radius: Model and experiment
Polymer 180 (2019) 121762
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Stable-jet length controlling electrospun fiber radius: Model and experiment a
Sailing Lei , Zhenzhen Quan Jianyong Yub a b
a,b,∗
a
, Hongnan Zhang , Xiaohong Qin
a,∗∗
T
a
, Rongwu Wang ,
Key Laboratory of Textile Science & Technology of Ministry of Education, College of Textiles, Donghua University, Shanghai, 201620, PR China Innovation Center for Textile Science & Technology, Donghua University, Shanghai, 201620, PR China
H I GH L IG H T S
exponential model between stable-jet length and fiber radius is established. • An scaling exponent is −2/3 for fully charged fibers in electrospinning. • The scaling exponent becomes smaller, when the fibers are partly charged. • The • The model can precisely predict and control the diameters of electrospun fibers.
A R T I C LE I N FO
A B S T R A C T
Keywords: Electrospinning Stable-jet length Terminal fiber radius
Generally, the precise prediction and control on the radius of electrospun polymer fibers is critical for their applications but still remains challenging. In the current work, a model has been established to predict the radius. It is shown that the correlation between the stable-jet length and the terminal fiber radius satisfies a scaling law with a power exponent −2/3 for fully charged fibers, while the exponent becomes smaller for the case in which the fibers are partly charged on surface during electrospinning. And a good agreement between the experimental and theoretical values for electrospinning poly(methyl methacrylate) (PMMA) fibers is obtained, thus further verifying the correctness of derived model between the stable-jet length and the terminal fiber radius.
1. Introduction
fundamental and crucial to control the submicron fibers radii in a narrow range in order to optimize their special performances [5], which demands comprehending how the electrospinning procedure transforms a millimeter-radius charged fluid into dry fibers with radius thinning of about four orders of magnitude [12]. The straight jet part, the connecting segment between the initial Taylor cone and the final whipping jet, plays a vital role in resulting fiber radius during the electrospinning process. However, there is no literature describing the relationship between the so-called stable zone and the terminal fiber radius. Previous researches on the stable zone mainly focus on two aspects: the stretch rate describing the variation of the stable jet radius in the axial direction [13,14] and the quantification of critical length affected by solution conductivity, mass flow rate and applied voltage [15–18]. All of them only focused on researches of the stable-jet length and radius, not on the terminal fiber radius. In this paper, we first successfully introduce the stable-jet critical radius to
Electrospinning is an attractive technique to generate polymeric fibers with radii in the range from 5 μm to 5 nm. The process begins with a so-called Taylor cone [1,2] hanged at the end of a metal capillary, then a straight jet is ejected from the tip of the Taylor cone [3], subsequently the jet loses stability after travelling a certain distance and transforms into whipping stage [4]. Here the stretching and thinning of jet will not disappear until the solvent completely evaporates and finally solid fiber lands on the grounded collector [5], as depicted in Fig. 1. Owing to the size effect resulted from small radius and extremely high surface area to mass ratio with about 40 m2/g [6], the electrospun fibers can have special physicochemical characteristics and can be applied into various fields including drug delivery [7], efficient sensors [8], tissue engineering [9], nanophotonics [10] and nanoelectronics [11]. For the diverse functional applications of electrospun fibers, it is
∗
Corresponding author. Key Laboratory of Textile Science & Technology of Ministry of Education, College of Textiles, Donghua University, Shanghai, 201620, PR China ∗∗ Corresponding author. E-mail addresses: [email protected] (Z. Quan), [email protected] (X. Qin). https://doi.org/10.1016/j.polymer.2019.121762 Received 29 July 2019; Received in revised form 27 August 2019; Accepted 28 August 2019 Available online 29 August 2019 0032-3861/ © 2019 Elsevier Ltd. All rights reserved.
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where Y and X are two variables describing an event, b is the power exponent. When b = 1, the relationship is isometric and when b ≠ 1, the relationship is allometric. In electrospinning, the allometric scaling law was previously derived by Kirichenko et al. [30] for stretch rate of fully charged jet in the form of r ~z −1/4 , which was also proven by other researchers theoretically [16,31,32] and experimentally [33]. Therefore, we will also apply an allometric approach to establish a power scaling relationship between stable-jet length and final fiber radius. In the straight jet region [34] and whipping jet region [35], the solvent evaporation is negligible and has little effect on the mass flow rate (Q). It is supposed that the mass flow rate (Q) and the current (I) remain unchanged during the electrospinning process, indicating the scaling relationships are Q~r 0 and I ~r 0 , respectively. From Eqs. (1) and (2), we have the scaling relationships Fig. 1. Schematic of the electrospinning jet.
build a bridge between stable-jet length and terminal fiber radius. We start to propose a model of controlling the stable-jet critical radius by stable-jet length and then identify the moving mode at the origin of unstable whipping jet to create the connection between the stable-jet critical radius and final fiber radius. Furthermore, considering the great effect of surface charge on the collected fiber radius [19–22], LiCl is introduced to study the power scaling law for partly charged fibers. This study also strongly suggests that the theoretical allometric scaling laws are highly consistent with the experiments. This work provides a novel method for modelling electrospinning to deepen the understanding of the electrospinning process. In addition, rapidly growing applications of electrospun fibers require precise controls over fiber radius and morphology [22,23], the proposed model can provide an efficient approach to solve the controllable problem of fiber radius and can be used to predict radius of polymeric fiber produced in a single-jet flow regime.
(7)
Substituting Eqs. (6) and (7) into Eq. (3), we obtain
rsj, end ~Lsj−1/2,
(8)
where rsj, end is the stable-jet critical radius at the end of straight jet part (point B in Fig. 1), and the model Eq. (8) will be verified in the experimental section. After the critical point B, the charge repulsive force and viscous force become dominant forces [18]. The large charge repulsive force promotes the short wavelength perturbations of whipping jet while the viscous force tends to suppress them. Assume that the two forces are balanced at the critical point B, thus the fastest growing mode will occur [36]. 1/3
9π 4σ 4 2⎤ ωmax = ⎡ ⎢ 8r 2 ρμε 2 (2 ln(χ ) − 3) ⎥ sj , end ‾ ⎦ ⎣
π 2σ ⎞ k = ⎜⎛ 2 ⎟ ⎝ rsj, end μ ⎠
(1)
where Q is the mass flow rate, r is the radius of the jet, υ is the jet velocity, ρ is the fluid density. Similarly, conservation of charges gives
2πrυσ + κπr 2E = I ,
where I is the current passing through the jet, σ is the surface charge density, k is the dimensionless conductivity of the polymer fluid, E is the applied electrostatic field intensity. Assume that the jet is stretched dominantly by the electrical force in the stable region and the surface current is equal to the volume current (2πrυσ = κπr 2E ) at the end of straight jet regime (point B in Fig. 1). Hence, stable-jet length gives [13].
⎡ ⎛ 2σQ ⎞ ⎜ ⎟ πρ2 I 2 ⎢ ⎝ πκρE ⎠ ⎣
⎤ − r0−2 ⎥, ⎦
(9)
1/6 2πρ ⎡ (2 ln(χ ) − 3) ⎤ . ⎣ ‾ε ⎦
(10)
As whipping jet moves away from the critical point B, the increasing specific surface area of the jet will make surface tension counteract the whipping instability [4]. Moreover, an alternative model proposed by Fridrikh et al. [37] magnifies the whipping part of the electrospinning jet and assumes that the final fiber radius is governed by an equilibrium between the charge repulsive force and surface tension. Hence, an analytical model is given for the electrospun fiber radius
(2)
−2/3
,
where ωmax is the maximum instability growth rate, μ is the fluid viscosity, ‾ε is the dielectric constant, χ is the aspect ratio of the jet [19]. Hereby, the corresponding wave number is expressed as 1/3
πr 2υρ = Q,
1/3
Q2 2 ⎤ rf = C1/2 ⎡γε‾ 2 ⎢ I π (2 ln χ − 3) ⎥ ⎣ ⎦
,
(11)
where rf is the terminal fiber radius, as shown in Fig. 1, C is the concentration of solution, γ is the coefficient of surface tension. On the basis of Eq. (11), we have a scaling relationship for the fiber radius
(3)
where Lsj is the stable-jet length (AB in Fig. 1) measured from the tip of Taylor cone to the head of unstable whipping jet. The study of scaling and dimensional analysis began with Newton [24], and was then developed separately in the turbulence [25], biological science [26–28] and astronomy [29]. Generally, the form of an allometric scaling relationship can be expressed as [17].
Y ~X b ,
(6)
E ~r −2.
A charged jet that is pulled from the tip of the Taylor cone (point A in Fig. 1) and accelerated by an external electrostatic field can be regarded as a one-dimensional slender body flow. Conservation of mass gives
Lsj =
(5)
σ ~r , and
2. Theoretical analysis
4κQ3
υ~r −2,
rf ~(2 ln χ − 3)−1/3 .
(12)
As mentioned in Eq. (9) above, χ is the aspect ratio of the jet (wavelength λ to rsj, end ). The normal displacements caused by unstable fluctuations can be expressed by the dimensionless wavelength as
χ~
(4) 2
λ , rsj, end
(13)
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fully charged fibers. And the theoretical analysis will be completely verified in the experimental section.
where λ = 2π / k is estimated by the wavelength of the radial instability from the fastest growing mode [19]. So Eq. (13) can be reduced as
χ~
3. Experimental verification
1 . krsj, end
(14)
3.1. Materials
Substituting Eqs. (6) and (12) into Eq. (10), we have −1/2 k ~rsj−,1/3 . end r f
Poly(methyl methacrylate) (PMMA) with high flow injection grade was purchased from Shanghai Macklin Biochemical Co. Ltd. N,NDimethylformamide (DMF) was purchased from Shanghai Lingfeng Chemical Reagent Co. Ltd, and LiCl was purchased from Shanghai Aladdin Biochemical Technology Co. Ltd. These reagents were used without further purification. For the preparation of the polymer solutions without salt, PMMA was dissolved in DMF at mass concentrations between 25 wt% and 32 wt%. For salt system, 0.2 wt% LiCl was added to DMF and the solution was stirred for several hours till LiCl was dissolved completely. Then we added PMMA to the solution incrementally until the content of PMMA reaches 30 wt% in DMF solution. Polymer solutions with various concentrations of LiCl (0.4 wt%, 0.6 wt%, 0.8 wt%, 1.0 wt% and 1.2 wt%) were prepared to study the radius variation law of fibers formed by charged jet and same procedure was operated as previous step. Finally, the prepared solutions were stirred magnetically at room temperature for several hours until solutions were completely homogeneous. All electrospinning experiments were conducted at ambient room temperature and 55 ± 5% humidity.
(15)
Combining Eqs. (12), (14) and (15), we have 1/2 r f−3 ~ ln(rsj−,2/3 end r f ).
(16)
Then, substituting Eq. (8) into Eq. (16), we obtain −3
er f ~Lsj1/3. r 1/2 f
(17)
Considering the conversion of the exponential function into a polynomial, Taylor polynomial is applied
ex ≈ 1 + x +
x2 xn + ⋯+ . 2! n!
(18)
According to Eqs. (17) and (18), we establish a power scaling law for the terminal fiber radius controlled by the stable-jet length in the asymptotic limit
rf ~Lsj−2/3.
(19) 3.2. Experimental setups
The Eq. (19) derived from basic theories including conservation of mass, conservation of electric charges and differential momentum balance is valid for fully charged fibers, as follows from the later experimental results. It should be noted that the above theoretical prediction is applicable for a relatively low conducting system. In the process of electrospinning, the charges are carried partly on the walls of Taylor cone where the conductive current is dominant [38]. After a charged jet is ejected from the cone, the excess charges are driven by the radial Coulomb repulsive force towards the jet surface to meet the equilibrium condition that there is no electrical field inside a conductive polymer fluid [39]. In this stage, the conductive current fades away and the convective charges are dominant and moved down only by advection, together with the jet [40,41]. Moreover, the charges accumulated on the surface of the jet will interact with the tangential electric field, which results in the jet stretching and thinning [15]. Hence, in order to model the final fiber radius systematically, we also need to take into account the high conducting electrospinning system where jet is partly charged on surface. In the case of partly charged jet in electrospinning, Eq. (2) can be revised as
2πrυσ α + κπr 2E = I ,
The experimental apparatus used for electrospinning is depicted in Fig. 2. The homogeneous PMMA solution was held in a syringe with an 18-gauge stainless steel needle. The polymer solution was delivered to the tip by a syringe pump (LSP01-3A, Longer Pump, England) at a flow rate (Q = 0.4–0.5 ml/h). A positive high electrical voltage (V = 8.5–12 kV) was offered in the needle tip by a high-voltage regulated DC power supply produced by GAMMA (USA). The grounded collector with an aluminum foil was placed away the spinneret at some distance (H = 26–30 cm) to gather the electrospun submicron fibers. A high-speed camera (i-SPEED 716, Nikon, Japan) was used to photograph the stable jet part at rate 2000 frames/second with shutter speed as short as 499461 nsec. The camera was installed on a tripod, allowing the position with respect to the jet to be adjusted in the vertical direction. The electrospinning jet was illuminated by a 1000 W quartz lamp with a continuous light source. All the images used for the analysis were corrected by subtracting a background image. Through analyzing the images, the stable-jet length can be obtained (see Videos
(20)
Where α is the surface charge saturation parameter. When α = 0 , there is no charge on the jet surface. When α = 1, Eq. (20) becomes Eq. (2), indicating surface charge achieves ideally full state [15,17,31]. The partial surface charge is described by 0 < α < 1, the specific value of α depends on the concentration of salt added in the solution and can be regarded as fractal dimension of charge distribution on the surface of the jet [17]. From Eq. (20), Eq. (6) can be modified as the following scaling relationship (21)
σ ~r 1/ α.
Based on the above hypotheses and derivations, we establish a power scaling law for partly charged fibers
rf ~Lsj−(1 + α )/(1 + 2α ). When α = 1, we have
(22)
rf ~Lsj−2/3 ,
Fig. 2. Experimental apparatus of electrospinning.
which is consistent with Eq. (19) for 3
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Fig. 3. Correlation between stable-jet length and stable-jet critical radius. The stable-jet length is varied by changing the spinning voltage. Solid lines: the experimental fitting lines. Broken line: the theoretical line with slope −0.5.
Fig. 5. The final fiber radius as a function of the stable-jet length. Solid lines: the experimental fitting lines. Broken line: the theoretical line with slope −2/3.
4. Results and discussion S1 and S2). To measure the stable-jet critical radius (point B), a piece of slide glass adhered to a long glass rod was used to rapidly cut the jet at the end of the straight region, then the slide glass with the collected jet was placed under the optical microscope to measure the critical radius of the straight jet. The morphology of electrospun PMMA fibers collected on the aluminum foil was observed using a scanning electron microscope (SEM), and the average fiber radius was measured by SEM image analysis. The conductivities of the obtained solutions were measured by a conductivity meter (Seven2Go, METTLER TOLEDO, Switzerland) to reveal the effect of salt concentration on solution conductivity.
The theoretical predictions, analyzed above, have been verified by comparing them with a series of experiments. We primarily focus on the predictions describing the dependency of the fiber radius on the stablejet length. It is tested that PMMA solution without salt has a relatively low conductivity (~10 μS/cm). Fig. 3 shows plots of the logarithm value of stable-jet critical radius (rsj, end ) against the logarithm value of stable-jet length (Lsj ). As can be seen in Fig. 3, there is a negative correlation between Lsj and rsj, end for a series of polymer solution concentrations. Stable-jet critical radius decreases with increasing value of stable-jet length. The phenomenon is due to the fact that the increasing electric field force caused by the rising voltage stabilizes the straight jet for a
Fig. 4. Images of 30 wt% PMMA solution jets with different voltages (H = 290 mm, Q = 0.5 ml/h): (a1) 8.5 kV, (b1) 9 kV, (c1) 10 kV, (d1) 11 kV. (a2)-(d2) are the corresponding SEM graphs of electrospun fibers, and (a3)-(d3) are the corresponding fiber diameter distributions. 4
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jet critical radius. Except 30 wt% PMMA solution, at the same stable-jet length, a higher solution concentration leads to a larger stable-jet critical radius, mainly attributing to the higher viscoelastic resistance making jet thinning much harder [44,45]. Therefore, it is reasonable and feasible to introduce the stable-jet critical radius and theoretical model Eq. (8) to establish the correlation between the stable-jet length and the terminal fiber radius. As indicated in Fig. 4 (a1)-(d1), the variation of straight jet part illustrates the dependency of the stable-jet length and jet shape on the applied voltage. Jet images have been further analyzed to measure the stable-jet length. Under the same spinning condition, the corresponding SEM images and diameter distributions of electrospun fibers are displayed in Fig. 4 (a2)-(d2) and Fig. 4 (a3)-(d3), respectively. In the process of electrospinning, it is apparent from Fig. 4 that jet becomes more unstable in the whipping region and the stable-jet length increases when the voltage is raised. Interestingly, the rule was also been obtained by other researchers theoretically [4,46] and experimentally [43]. On the fiber collector, the round and smooth electrospun fibers with no beads are produced and the corresponding fiber diameter decreases with increasing voltage. It is due to the existence of larger repulsive forces in the whipping jet, leading to a stronger drawing [42]. Furthermore, the variation trend is similar to the theoretical model Eq. (19). As the experimental data shown in Fig. 5, there is a significant correlation between the stable-jet length and the terminal fiber radius. Indeed, all the results seem to follow the similar slope, which means that there is an intrinsic physics and logical relationship between the
Fig. 6. Conductivities of 30 wt% PMMA solutions with different mass concentrations of LiCl. The top left icon represents the slope of conductivity growth.
longer distance [42,43], creating larger stretching responsible for thinner at the critical point B [15]. Further, the scaling of rsj, end with Lsj can all be described by a scaling law with a power exponent b ≈ −0.5, which agrees very well with the scaling law Eq. (8). In the other hand, the change of polymer solution concentration affects the value of stable-
Fig. 7. The final fiber radius as a function of the stable-jet length of PMMA solutions with different concentrations of LiCl ranging from 0.2 wt% to 1.2 wt%. 5
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Fig. 8. Images of jets with 0.4 wt% LiCl at different voltages (H = 260 mm, Q = 0.4 ml/h): (a1) 9 kV, (b1) 10 kV, (c1) 11 kV, (d1) 12 kV. (a2)-(d2) are the corresponding SEM graphs of electrospun fibers, and (a3)-(d3) are the corresponding fiber diameter distributions.
stable-jet length and fiber radius. Through further analysis and calculation, the linear scaling with stable-jet length obeys the −2/3 power law commendably, manifesting the experimental results agree extremely well with the model prediction Eq. (19). In what follows, we will compare the correlation between experimental data and theoretical predictions for partly charged fibers in high conducting system. Fig. 6 presents that the conductivity of PMMA solution increases dramatically with a slope of 1.48 when the content of adding LiCl is 0.2 wt%. In the process of increasing salt concentration gradually to 1.0 wt%, the conductivity grows slowly with a slope of 0.75. After the LiCl concentration exceeds 1.0 wt%, the change rate of conductivity decreases and even trends to be horizontal. Thus, the threshold value of concentration is about 1.0 wt%. Moreover, Fig. 7 shows that the scaling power exponent is nearly equal to −2/3 when the salt concentration is 1.0 wt% or 1.2 wt%. It reflects that the experimental fitting results correspond to the case of fully charged fibers [Eq. (19)]. Hereby, we have α = 1 when the salt concentration is equal to or larger than 1.0 wt%. Assumed that the value of α linearly depends on salt concentration when it is less than 1.0 wt%, thus we have
α=
c (wt %) , 1.0(wt %)
of salt can result in the remarkable reduction of stable-jet length. The phenomenon, which has also been encountered in the available literatures [18,42], can be explained that the increasing electrical conductivity resulting from adding LiCl is benefit to reduce the time required for the convective charges to move to the jet surface and then brings about bending earlier under mutual repulsion of surface charges [4]. In addition, as the charge on the fiber surface tends to stretch the jet in the axial direction [47], the pitch of the helix obviously widens in whipping region. In Figs. 4 and 8 for the collected fibers, the salt system leads to smaller fiber diameters, because much higher conductivity of the former can cause smaller reciprocal of volumetric charge density (df ~(Q/ I )2/3 ) [5,37]. The deeper reason is very probable due to the ion coordination effect [21]: the polymeric molecule chain is forced to move together with the coordinated ions accelerated by the high voltage, inevitably resulting in the stretched chain generating thinner fibers. Interestingly, as presented in Fig. 8 (a2)-(d2), flat ribbon-like structures are clearly observed by a higher voltage. It is likely to be the reason that the DMF molecules in the solvation will move quickly together with the evaporated ions causing the fast evaporation [21], which forms dry skin on the fiber surface. Subsequently, the skin of fiber collapses and flat fiber generates during drying time of fiber on the grounded collector [48].
(23)
where c is the salt mass concentration. When the concentrations of LiCl are 0.2 wt%, 0.4 wt%, 0.6 wt% and 0.8 wt% (α= 0.2, 0.4, 0.6 and 0.8), the theoretically specific exponents are respectively −0.857, −0.778, −0.727 and −0.692 according to the scaling law Eq. (22). As the experimental results shown in Fig. 7, we find that the scaling power exponent decreases after small amount of salt is added to the less conductive PMMA solution. Furthermore, the resulting scaling exponent is extremely well accord with the theoretical prediction Eq. (22). Fig. 8 shows pictures of the corresponding solid fiber forming process including stable and unstable segments. According to Fig. 4 (a1)-(d1) and Fig. 8 (a1)-(d1), it indicates the addition
5. Conclusion A model relating the stable-jet length to the terminal fiber radius has been proposed for partly as well as fully charged fibers in electrospinning. The power scaling law is rf ~Lsj−2/3 for fully charged fibers, while rf ~Lsj−(1 + α )/(1 + 2α ) for partly charged fibers. The theoretical predictions based on the model have been well verified by the experimental results. It is believed that the proposed theoretical model provides an efficient control means for polymer fibers with expected 6
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radius, which would facilitate the applications of the fibers significantly.
6409–6413. [19] M.M. Hohman, M. Shin, G. Rutledge, Electrospinning and electrically forced jets. I. Stability theory, Phys. Fluids 13 (2001) 2201–2220. [20] M.M. Hohman, M. Shin, G. Rutledge, Electrospinning and electrically forced jets. II. Applications, Phys. Fluids 13 (2001) 2221–2236. [21] B.B. Wang, X.D. Wang, T.H. Wang, Microscopic mechanism for the effect of adding salt on electrospinning by molecular dynamics simulations, Appl. Phys. Lett. 105 (2014) 121906. [22] L. Fan, Y.T. Xu, X. Zhou, Effect of salt concentration in spinning solution on fiber diameter and mechanical property of electrospun styrene-butadiene-styrene triblock copolymer membrane, Polymer 153 (2018) 61–69. [23] R. Casasola, N.L. Thomas, A. Trybala, Electrospun poly lactic acid (PLA) fibres: effect of different solvent systems on fibre morphology and diameter, Polymer 55 (2014) 4728–4737. [24] B.J. West, Comments on the renormalization group, scaling and measures of complexity, Chaos, Solit. Fractals 20 (2004) 33–44. [25] R. Benzi, Getting a grip on turbulence, Science 301 (2003) 605–606. [26] G.B. West, J.H. Brown, B.J. Enquist, A general model for the origin of allometric scaling laws in biology, Science 276 (1997) 122–126. [27] J.T. Kuikka, Scaling laws in physiology: relationships between size, function, metabolism and life expectancy, Int. J. Nonlinear Sci. Numer. Stimul. 4 (2003) 317–328. [28] J.H. He, H. Chen, Effects of size and PH on metabolic rate, Int. J. Nonlinear Sci. Numer. Stimul. 4 (2003) 429–432. [29] G. Iovane, Varying G, accelerating Universe, and other relevant consequences of a stochastic self-similar and fractal Universe, Chaos, Solit. Fractals 20 (2004) 657–667. [30] V.N. Kirichenko, S.I.V. PETRYANOV, N.N. Suprun, Asymptotic radius of a slightly conducting liquid jet in an electric field, Sov. Phys. Dokl. 31 (1986) 611–613. [31] A.M. Gañán-Calvo, Cone-jet analytical extension of Taylor's electrostatic solution and the asymptotic universal scaling laws in electrospraying, Phys. Rev. Lett. 79 (1997) 217–220. [32] J.J. Feng, Stretching of a straight electrically charged viscoelastic jet, J. NonNewtonian Fluid Mech. 116 (2003) 55–70. [33] Y.M. Shin, M.M. Hohman, M.P. Brenner, Experimental characterization of electrospinning: the electrically forced jet and instabilities, Polymer 42 (2001) 9955–9967. [34] Y. Cai, M. Gevelber, Analysis of bending region physics in determining electrospun fiber diameter: effect of relative humidity on evaporation and force balance, J. Mater. Sci. 52 (2017) 2605–2627. [35] I. Uematsu, K. Uchida, Y. Nakagawa, Direct observation and quantitative analysis of the fiber formation process during electrospinning by a high-speed camera, Ind. Eng. Chem. Res. 57 (2018) 12122–12126. [36] S.V. Fridrikh, J.H. Yu, M.P. Brenner, Nonlinear whipping behavior of electrified fluid jets, ACS Symp. Ser. 918 (2006) 36–55. [37] S.V. Fridrikh, J.H. Yu, M.P. Brenner, Controlling the fiber diameter during electrospinning, Phys. Rev. Lett. 90 (2003) 144502. [38] J. Fernández, The fluid dynamics of Taylor cones, Annu. Rev. Fluid Mech. 39 (2007) 217–243. [39] D.H. Reneker, A.L. Yarin, Electrospinning jets and polymer nanofibers, Polymer 49 (2008) 2387–2425. [40] J.J. Feng, The stretching of an electrified non-Newtonian jet: a model for electrospinning, Phys. Fluids 14 (2002) 3912–3926. [41] C.P. Carroll, Y.L. Joo, Electrospinning of viscoelastic Boger fluids: modeling and experiments, Phys. Fluids 18 (2006) 053102. [42] C. Wang, C.H. Hsu, J.H. Lin, Scaling laws in electrospinning of polystyrene solutions, Macromolecules 39 (2006) 7662–7672. [43] T. Han, A.L. Yarin, D.H. Reneker, Viscoelastic electrospun jets: initial stresses and elongational rheometry, Polymer 49 (2008) 1651–1658. [44] Z.M. Huang, Y.Z. Zhang, M. Kotaki, A review on polymer nanofibers by electrospinning and their applications in nanocomposites, Compos. Sci. Technol. 63 (2003) 2223–2253. [45] M. Montinaro, V. Fasano, M. Moffa, Sub-ms dynamics of the instability onset of electrospinning, Soft Matter 11 (2015) 3424–3431. [46] M. Šimko, D. Lukáš, Mathematical modeling of a whipping instability of an electrically charged liquid jet, Appl. Math. Model. 40 (2016) 9565–9583. [47] D.H. Reneker, I. Chun, Nanometre diameter fibres of polymer, produced by electrospinning, Nanotechnology 7 (1996) 216–223. [48] S. Koombhongse, W. Liu, D.H. Reneker, Flat polymer ribbons and other shapes by electrospinning, J. Polym. Sci. B Polym. Phys. 39 (2001) 2598–2606.
Acknowledgments This work was partly supported by the Chang Jiang Youth Scholars Program of China and grants (51773037) from the National Natural Science Foundation of China (51773037, 51803023, 61771123) to Prof. Xiaohong Qin as well as the “Innovation Program of Shanghai Municipal Education Commission, Shanghai, China”, “Fundamental Research Funds for the Central Universities, China” (2232018A3-11) and “DHU Distinguished Young Professor Program, Donghua University, China” to her. This work has also been supported by the Shanghai Sailing Program, Shanghai, China (18YF 1400400), the Project funded by China Postdoctoral Science Foundation, China (2018M640317). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.polymer.2019.121762. References [1] G.I. Taylor, Disintegration of water drops in an electric field, Math. Phys. Sci. 280 (1964) 383–397. [2] A.L. Yarin, S. Koombhongse, D.H. Reneker, Taylor cone and jetting from liquid droplets in electrospinning of nanofibers, J. Appl. Phys. 90 (2001) 4836–4846. [3] J. Doshi, D.H. Reneker, Electrospinning process and applications of electrospun fibers, J. Electrost. 35 (1995) 151–160. [4] D.H. Reneker, A.L. Yarin, H. Fong, Bending instability of electrically charged liquid jets of polymer solutions in electrospinning, J. Appl. Phys. 87 (2000) 4531–4547. [5] R. Stepanyan, A.V. Subbotin, L. Cuperus, Nanofiber diameter in electrospinning of polymer solutions: model and experiment, Polymer 97 (2016) 428–439. [6] A. Greiner, J.H. Wendorff, Electrospinning: a fascinating method for the preparation of ultrathin fibers, Angew. Chem., Int. Ed. Engl. 46 (2007) 5670–5703. [7] Z.Y. Hou, C.X. Li, P.A. Ma, Electrospinning preparation and drug-delivery properties of an up-conversion luminescent porous NaYF4:Yb3+, Er3+@Silica Fiber Nanocomposite, Adv. Funct. Mater. 21 (2011) 2356–2365. [8] M. Xi, X. Wang, Y. Zhao, Electrospun ZnO/SiO2 hybrid nanofibrous mat for flexible ultraviolet sensor, Appl. Phys. Lett. 104 (2014) 133102. [9] Y. Kang, P. Chen, X.T. Shi, Multilevel structural stereocomplex polylactic acid/ collagen membranes by pattern electrospinning for tissue engineering, Polymer 156 (2018) 250–260. [10] L. Persano, A. Camposeo, P.D. Carro, Distributed feedback imprinted electrospun fiber lasers, Adv. Mater. 26 (2014) 6542–6547. [11] S.H. Choi, B.H. Jang, J.S. Park, Low voltage operating field effect transistors with composite In2O3–ZnO–ZnGa2O4 nanofiber network as active channel layer, ACS Nano 8 (2014) 2318–2327. [12] Y.M. Shin, M.M. Hohman, M.P. Brenner, Electrospinning: a whipping fluid jet generates submicron polymer fibers, Appl. Phys. Lett. 78 (2001) 1149–1151. [13] J.H. He, Y. Wu, W.W. Zuo, Critical length of straight jet in electrospinning, Polymer 46 (2005) 12637–12640. [14] G.C. Rutledge, S.V. Fridrikh, Formation of fibers by electrospinning, Adv. Drug Deliv. Rev. 59 (2007) 1384–1391. [15] A.F. Spivak, Y.A. Dzenis, Asymptotic decay of radius of a weakly conductive viscous jet in an external electric field, Appl. Phys. Lett. 73 (1998) 3067–3069. [16] A.F. Spivak, Y.A. Dzenis, D.H. Reneker, A model of steady state jet in the electrospinning process, Mech. Res. Commun. 27 (2000) 37–42. [17] J.H. He, Y.Q. Wan, M.Y. Yu, Allometric scaling and instability in electrospinning, Int. J. Nonlinear Sci. Numer. Stimul. 5 (2004) 243–252. [18] X.H. Qin, Y.Q. Wan, J.H. He, Effect of LiCl on electrospinning of PAN polymer solution: theoretical analysis and experimental verification, Polymer 45 (2004)
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Polymer journal homepage: www.elsevier.com/locate/polymer
Stable-jet length controlling electrospun fiber radius: Model and experiment a
Sailing Lei , Zhenzhen Quan Jianyong Yub a b
a,b,∗
a
, Hongnan Zhang , Xiaohong Qin
a,∗∗
T
a
, Rongwu Wang ,
Key Laboratory of Textile Science & Technology of Ministry of Education, College of Textiles, Donghua University, Shanghai, 201620, PR China Innovation Center for Textile Science & Technology, Donghua University, Shanghai, 201620, PR China
H I GH L IG H T S
exponential model between stable-jet length and fiber radius is established. • An scaling exponent is −2/3 for fully charged fibers in electrospinning. • The scaling exponent becomes smaller, when the fibers are partly charged. • The • The model can precisely predict and control the diameters of electrospun fibers.
A R T I C LE I N FO
A B S T R A C T
Keywords: Electrospinning Stable-jet length Terminal fiber radius
Generally, the precise prediction and control on the radius of electrospun polymer fibers is critical for their applications but still remains challenging. In the current work, a model has been established to predict the radius. It is shown that the correlation between the stable-jet length and the terminal fiber radius satisfies a scaling law with a power exponent −2/3 for fully charged fibers, while the exponent becomes smaller for the case in which the fibers are partly charged on surface during electrospinning. And a good agreement between the experimental and theoretical values for electrospinning poly(methyl methacrylate) (PMMA) fibers is obtained, thus further verifying the correctness of derived model between the stable-jet length and the terminal fiber radius.
1. Introduction
fundamental and crucial to control the submicron fibers radii in a narrow range in order to optimize their special performances [5], which demands comprehending how the electrospinning procedure transforms a millimeter-radius charged fluid into dry fibers with radius thinning of about four orders of magnitude [12]. The straight jet part, the connecting segment between the initial Taylor cone and the final whipping jet, plays a vital role in resulting fiber radius during the electrospinning process. However, there is no literature describing the relationship between the so-called stable zone and the terminal fiber radius. Previous researches on the stable zone mainly focus on two aspects: the stretch rate describing the variation of the stable jet radius in the axial direction [13,14] and the quantification of critical length affected by solution conductivity, mass flow rate and applied voltage [15–18]. All of them only focused on researches of the stable-jet length and radius, not on the terminal fiber radius. In this paper, we first successfully introduce the stable-jet critical radius to
Electrospinning is an attractive technique to generate polymeric fibers with radii in the range from 5 μm to 5 nm. The process begins with a so-called Taylor cone [1,2] hanged at the end of a metal capillary, then a straight jet is ejected from the tip of the Taylor cone [3], subsequently the jet loses stability after travelling a certain distance and transforms into whipping stage [4]. Here the stretching and thinning of jet will not disappear until the solvent completely evaporates and finally solid fiber lands on the grounded collector [5], as depicted in Fig. 1. Owing to the size effect resulted from small radius and extremely high surface area to mass ratio with about 40 m2/g [6], the electrospun fibers can have special physicochemical characteristics and can be applied into various fields including drug delivery [7], efficient sensors [8], tissue engineering [9], nanophotonics [10] and nanoelectronics [11]. For the diverse functional applications of electrospun fibers, it is
∗
Corresponding author. Key Laboratory of Textile Science & Technology of Ministry of Education, College of Textiles, Donghua University, Shanghai, 201620, PR China ∗∗ Corresponding author. E-mail addresses: [email protected] (Z. Quan), [email protected] (X. Qin). https://doi.org/10.1016/j.polymer.2019.121762 Received 29 July 2019; Received in revised form 27 August 2019; Accepted 28 August 2019 Available online 29 August 2019 0032-3861/ © 2019 Elsevier Ltd. All rights reserved.
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where Y and X are two variables describing an event, b is the power exponent. When b = 1, the relationship is isometric and when b ≠ 1, the relationship is allometric. In electrospinning, the allometric scaling law was previously derived by Kirichenko et al. [30] for stretch rate of fully charged jet in the form of r ~z −1/4 , which was also proven by other researchers theoretically [16,31,32] and experimentally [33]. Therefore, we will also apply an allometric approach to establish a power scaling relationship between stable-jet length and final fiber radius. In the straight jet region [34] and whipping jet region [35], the solvent evaporation is negligible and has little effect on the mass flow rate (Q). It is supposed that the mass flow rate (Q) and the current (I) remain unchanged during the electrospinning process, indicating the scaling relationships are Q~r 0 and I ~r 0 , respectively. From Eqs. (1) and (2), we have the scaling relationships Fig. 1. Schematic of the electrospinning jet.
build a bridge between stable-jet length and terminal fiber radius. We start to propose a model of controlling the stable-jet critical radius by stable-jet length and then identify the moving mode at the origin of unstable whipping jet to create the connection between the stable-jet critical radius and final fiber radius. Furthermore, considering the great effect of surface charge on the collected fiber radius [19–22], LiCl is introduced to study the power scaling law for partly charged fibers. This study also strongly suggests that the theoretical allometric scaling laws are highly consistent with the experiments. This work provides a novel method for modelling electrospinning to deepen the understanding of the electrospinning process. In addition, rapidly growing applications of electrospun fibers require precise controls over fiber radius and morphology [22,23], the proposed model can provide an efficient approach to solve the controllable problem of fiber radius and can be used to predict radius of polymeric fiber produced in a single-jet flow regime.
(7)
Substituting Eqs. (6) and (7) into Eq. (3), we obtain
rsj, end ~Lsj−1/2,
(8)
where rsj, end is the stable-jet critical radius at the end of straight jet part (point B in Fig. 1), and the model Eq. (8) will be verified in the experimental section. After the critical point B, the charge repulsive force and viscous force become dominant forces [18]. The large charge repulsive force promotes the short wavelength perturbations of whipping jet while the viscous force tends to suppress them. Assume that the two forces are balanced at the critical point B, thus the fastest growing mode will occur [36]. 1/3
9π 4σ 4 2⎤ ωmax = ⎡ ⎢ 8r 2 ρμε 2 (2 ln(χ ) − 3) ⎥ sj , end ‾ ⎦ ⎣
π 2σ ⎞ k = ⎜⎛ 2 ⎟ ⎝ rsj, end μ ⎠
(1)
where Q is the mass flow rate, r is the radius of the jet, υ is the jet velocity, ρ is the fluid density. Similarly, conservation of charges gives
2πrυσ + κπr 2E = I ,
where I is the current passing through the jet, σ is the surface charge density, k is the dimensionless conductivity of the polymer fluid, E is the applied electrostatic field intensity. Assume that the jet is stretched dominantly by the electrical force in the stable region and the surface current is equal to the volume current (2πrυσ = κπr 2E ) at the end of straight jet regime (point B in Fig. 1). Hence, stable-jet length gives [13].
⎡ ⎛ 2σQ ⎞ ⎜ ⎟ πρ2 I 2 ⎢ ⎝ πκρE ⎠ ⎣
⎤ − r0−2 ⎥, ⎦
(9)
1/6 2πρ ⎡ (2 ln(χ ) − 3) ⎤ . ⎣ ‾ε ⎦
(10)
As whipping jet moves away from the critical point B, the increasing specific surface area of the jet will make surface tension counteract the whipping instability [4]. Moreover, an alternative model proposed by Fridrikh et al. [37] magnifies the whipping part of the electrospinning jet and assumes that the final fiber radius is governed by an equilibrium between the charge repulsive force and surface tension. Hence, an analytical model is given for the electrospun fiber radius
(2)
−2/3
,
where ωmax is the maximum instability growth rate, μ is the fluid viscosity, ‾ε is the dielectric constant, χ is the aspect ratio of the jet [19]. Hereby, the corresponding wave number is expressed as 1/3
πr 2υρ = Q,
1/3
Q2 2 ⎤ rf = C1/2 ⎡γε‾ 2 ⎢ I π (2 ln χ − 3) ⎥ ⎣ ⎦
,
(11)
where rf is the terminal fiber radius, as shown in Fig. 1, C is the concentration of solution, γ is the coefficient of surface tension. On the basis of Eq. (11), we have a scaling relationship for the fiber radius
(3)
where Lsj is the stable-jet length (AB in Fig. 1) measured from the tip of Taylor cone to the head of unstable whipping jet. The study of scaling and dimensional analysis began with Newton [24], and was then developed separately in the turbulence [25], biological science [26–28] and astronomy [29]. Generally, the form of an allometric scaling relationship can be expressed as [17].
Y ~X b ,
(6)
E ~r −2.
A charged jet that is pulled from the tip of the Taylor cone (point A in Fig. 1) and accelerated by an external electrostatic field can be regarded as a one-dimensional slender body flow. Conservation of mass gives
Lsj =
(5)
σ ~r , and
2. Theoretical analysis
4κQ3
υ~r −2,
rf ~(2 ln χ − 3)−1/3 .
(12)
As mentioned in Eq. (9) above, χ is the aspect ratio of the jet (wavelength λ to rsj, end ). The normal displacements caused by unstable fluctuations can be expressed by the dimensionless wavelength as
χ~
(4) 2
λ , rsj, end
(13)
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fully charged fibers. And the theoretical analysis will be completely verified in the experimental section.
where λ = 2π / k is estimated by the wavelength of the radial instability from the fastest growing mode [19]. So Eq. (13) can be reduced as
χ~
3. Experimental verification
1 . krsj, end
(14)
3.1. Materials
Substituting Eqs. (6) and (12) into Eq. (10), we have −1/2 k ~rsj−,1/3 . end r f
Poly(methyl methacrylate) (PMMA) with high flow injection grade was purchased from Shanghai Macklin Biochemical Co. Ltd. N,NDimethylformamide (DMF) was purchased from Shanghai Lingfeng Chemical Reagent Co. Ltd, and LiCl was purchased from Shanghai Aladdin Biochemical Technology Co. Ltd. These reagents were used without further purification. For the preparation of the polymer solutions without salt, PMMA was dissolved in DMF at mass concentrations between 25 wt% and 32 wt%. For salt system, 0.2 wt% LiCl was added to DMF and the solution was stirred for several hours till LiCl was dissolved completely. Then we added PMMA to the solution incrementally until the content of PMMA reaches 30 wt% in DMF solution. Polymer solutions with various concentrations of LiCl (0.4 wt%, 0.6 wt%, 0.8 wt%, 1.0 wt% and 1.2 wt%) were prepared to study the radius variation law of fibers formed by charged jet and same procedure was operated as previous step. Finally, the prepared solutions were stirred magnetically at room temperature for several hours until solutions were completely homogeneous. All electrospinning experiments were conducted at ambient room temperature and 55 ± 5% humidity.
(15)
Combining Eqs. (12), (14) and (15), we have 1/2 r f−3 ~ ln(rsj−,2/3 end r f ).
(16)
Then, substituting Eq. (8) into Eq. (16), we obtain −3
er f ~Lsj1/3. r 1/2 f
(17)
Considering the conversion of the exponential function into a polynomial, Taylor polynomial is applied
ex ≈ 1 + x +
x2 xn + ⋯+ . 2! n!
(18)
According to Eqs. (17) and (18), we establish a power scaling law for the terminal fiber radius controlled by the stable-jet length in the asymptotic limit
rf ~Lsj−2/3.
(19) 3.2. Experimental setups
The Eq. (19) derived from basic theories including conservation of mass, conservation of electric charges and differential momentum balance is valid for fully charged fibers, as follows from the later experimental results. It should be noted that the above theoretical prediction is applicable for a relatively low conducting system. In the process of electrospinning, the charges are carried partly on the walls of Taylor cone where the conductive current is dominant [38]. After a charged jet is ejected from the cone, the excess charges are driven by the radial Coulomb repulsive force towards the jet surface to meet the equilibrium condition that there is no electrical field inside a conductive polymer fluid [39]. In this stage, the conductive current fades away and the convective charges are dominant and moved down only by advection, together with the jet [40,41]. Moreover, the charges accumulated on the surface of the jet will interact with the tangential electric field, which results in the jet stretching and thinning [15]. Hence, in order to model the final fiber radius systematically, we also need to take into account the high conducting electrospinning system where jet is partly charged on surface. In the case of partly charged jet in electrospinning, Eq. (2) can be revised as
2πrυσ α + κπr 2E = I ,
The experimental apparatus used for electrospinning is depicted in Fig. 2. The homogeneous PMMA solution was held in a syringe with an 18-gauge stainless steel needle. The polymer solution was delivered to the tip by a syringe pump (LSP01-3A, Longer Pump, England) at a flow rate (Q = 0.4–0.5 ml/h). A positive high electrical voltage (V = 8.5–12 kV) was offered in the needle tip by a high-voltage regulated DC power supply produced by GAMMA (USA). The grounded collector with an aluminum foil was placed away the spinneret at some distance (H = 26–30 cm) to gather the electrospun submicron fibers. A high-speed camera (i-SPEED 716, Nikon, Japan) was used to photograph the stable jet part at rate 2000 frames/second with shutter speed as short as 499461 nsec. The camera was installed on a tripod, allowing the position with respect to the jet to be adjusted in the vertical direction. The electrospinning jet was illuminated by a 1000 W quartz lamp with a continuous light source. All the images used for the analysis were corrected by subtracting a background image. Through analyzing the images, the stable-jet length can be obtained (see Videos
(20)
Where α is the surface charge saturation parameter. When α = 0 , there is no charge on the jet surface. When α = 1, Eq. (20) becomes Eq. (2), indicating surface charge achieves ideally full state [15,17,31]. The partial surface charge is described by 0 < α < 1, the specific value of α depends on the concentration of salt added in the solution and can be regarded as fractal dimension of charge distribution on the surface of the jet [17]. From Eq. (20), Eq. (6) can be modified as the following scaling relationship (21)
σ ~r 1/ α.
Based on the above hypotheses and derivations, we establish a power scaling law for partly charged fibers
rf ~Lsj−(1 + α )/(1 + 2α ). When α = 1, we have
(22)
rf ~Lsj−2/3 ,
Fig. 2. Experimental apparatus of electrospinning.
which is consistent with Eq. (19) for 3
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Fig. 3. Correlation between stable-jet length and stable-jet critical radius. The stable-jet length is varied by changing the spinning voltage. Solid lines: the experimental fitting lines. Broken line: the theoretical line with slope −0.5.
Fig. 5. The final fiber radius as a function of the stable-jet length. Solid lines: the experimental fitting lines. Broken line: the theoretical line with slope −2/3.
4. Results and discussion S1 and S2). To measure the stable-jet critical radius (point B), a piece of slide glass adhered to a long glass rod was used to rapidly cut the jet at the end of the straight region, then the slide glass with the collected jet was placed under the optical microscope to measure the critical radius of the straight jet. The morphology of electrospun PMMA fibers collected on the aluminum foil was observed using a scanning electron microscope (SEM), and the average fiber radius was measured by SEM image analysis. The conductivities of the obtained solutions were measured by a conductivity meter (Seven2Go, METTLER TOLEDO, Switzerland) to reveal the effect of salt concentration on solution conductivity.
The theoretical predictions, analyzed above, have been verified by comparing them with a series of experiments. We primarily focus on the predictions describing the dependency of the fiber radius on the stablejet length. It is tested that PMMA solution without salt has a relatively low conductivity (~10 μS/cm). Fig. 3 shows plots of the logarithm value of stable-jet critical radius (rsj, end ) against the logarithm value of stable-jet length (Lsj ). As can be seen in Fig. 3, there is a negative correlation between Lsj and rsj, end for a series of polymer solution concentrations. Stable-jet critical radius decreases with increasing value of stable-jet length. The phenomenon is due to the fact that the increasing electric field force caused by the rising voltage stabilizes the straight jet for a
Fig. 4. Images of 30 wt% PMMA solution jets with different voltages (H = 290 mm, Q = 0.5 ml/h): (a1) 8.5 kV, (b1) 9 kV, (c1) 10 kV, (d1) 11 kV. (a2)-(d2) are the corresponding SEM graphs of electrospun fibers, and (a3)-(d3) are the corresponding fiber diameter distributions. 4
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jet critical radius. Except 30 wt% PMMA solution, at the same stable-jet length, a higher solution concentration leads to a larger stable-jet critical radius, mainly attributing to the higher viscoelastic resistance making jet thinning much harder [44,45]. Therefore, it is reasonable and feasible to introduce the stable-jet critical radius and theoretical model Eq. (8) to establish the correlation between the stable-jet length and the terminal fiber radius. As indicated in Fig. 4 (a1)-(d1), the variation of straight jet part illustrates the dependency of the stable-jet length and jet shape on the applied voltage. Jet images have been further analyzed to measure the stable-jet length. Under the same spinning condition, the corresponding SEM images and diameter distributions of electrospun fibers are displayed in Fig. 4 (a2)-(d2) and Fig. 4 (a3)-(d3), respectively. In the process of electrospinning, it is apparent from Fig. 4 that jet becomes more unstable in the whipping region and the stable-jet length increases when the voltage is raised. Interestingly, the rule was also been obtained by other researchers theoretically [4,46] and experimentally [43]. On the fiber collector, the round and smooth electrospun fibers with no beads are produced and the corresponding fiber diameter decreases with increasing voltage. It is due to the existence of larger repulsive forces in the whipping jet, leading to a stronger drawing [42]. Furthermore, the variation trend is similar to the theoretical model Eq. (19). As the experimental data shown in Fig. 5, there is a significant correlation between the stable-jet length and the terminal fiber radius. Indeed, all the results seem to follow the similar slope, which means that there is an intrinsic physics and logical relationship between the
Fig. 6. Conductivities of 30 wt% PMMA solutions with different mass concentrations of LiCl. The top left icon represents the slope of conductivity growth.
longer distance [42,43], creating larger stretching responsible for thinner at the critical point B [15]. Further, the scaling of rsj, end with Lsj can all be described by a scaling law with a power exponent b ≈ −0.5, which agrees very well with the scaling law Eq. (8). In the other hand, the change of polymer solution concentration affects the value of stable-
Fig. 7. The final fiber radius as a function of the stable-jet length of PMMA solutions with different concentrations of LiCl ranging from 0.2 wt% to 1.2 wt%. 5
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Fig. 8. Images of jets with 0.4 wt% LiCl at different voltages (H = 260 mm, Q = 0.4 ml/h): (a1) 9 kV, (b1) 10 kV, (c1) 11 kV, (d1) 12 kV. (a2)-(d2) are the corresponding SEM graphs of electrospun fibers, and (a3)-(d3) are the corresponding fiber diameter distributions.
stable-jet length and fiber radius. Through further analysis and calculation, the linear scaling with stable-jet length obeys the −2/3 power law commendably, manifesting the experimental results agree extremely well with the model prediction Eq. (19). In what follows, we will compare the correlation between experimental data and theoretical predictions for partly charged fibers in high conducting system. Fig. 6 presents that the conductivity of PMMA solution increases dramatically with a slope of 1.48 when the content of adding LiCl is 0.2 wt%. In the process of increasing salt concentration gradually to 1.0 wt%, the conductivity grows slowly with a slope of 0.75. After the LiCl concentration exceeds 1.0 wt%, the change rate of conductivity decreases and even trends to be horizontal. Thus, the threshold value of concentration is about 1.0 wt%. Moreover, Fig. 7 shows that the scaling power exponent is nearly equal to −2/3 when the salt concentration is 1.0 wt% or 1.2 wt%. It reflects that the experimental fitting results correspond to the case of fully charged fibers [Eq. (19)]. Hereby, we have α = 1 when the salt concentration is equal to or larger than 1.0 wt%. Assumed that the value of α linearly depends on salt concentration when it is less than 1.0 wt%, thus we have
α=
c (wt %) , 1.0(wt %)
of salt can result in the remarkable reduction of stable-jet length. The phenomenon, which has also been encountered in the available literatures [18,42], can be explained that the increasing electrical conductivity resulting from adding LiCl is benefit to reduce the time required for the convective charges to move to the jet surface and then brings about bending earlier under mutual repulsion of surface charges [4]. In addition, as the charge on the fiber surface tends to stretch the jet in the axial direction [47], the pitch of the helix obviously widens in whipping region. In Figs. 4 and 8 for the collected fibers, the salt system leads to smaller fiber diameters, because much higher conductivity of the former can cause smaller reciprocal of volumetric charge density (df ~(Q/ I )2/3 ) [5,37]. The deeper reason is very probable due to the ion coordination effect [21]: the polymeric molecule chain is forced to move together with the coordinated ions accelerated by the high voltage, inevitably resulting in the stretched chain generating thinner fibers. Interestingly, as presented in Fig. 8 (a2)-(d2), flat ribbon-like structures are clearly observed by a higher voltage. It is likely to be the reason that the DMF molecules in the solvation will move quickly together with the evaporated ions causing the fast evaporation [21], which forms dry skin on the fiber surface. Subsequently, the skin of fiber collapses and flat fiber generates during drying time of fiber on the grounded collector [48].
(23)
where c is the salt mass concentration. When the concentrations of LiCl are 0.2 wt%, 0.4 wt%, 0.6 wt% and 0.8 wt% (α= 0.2, 0.4, 0.6 and 0.8), the theoretically specific exponents are respectively −0.857, −0.778, −0.727 and −0.692 according to the scaling law Eq. (22). As the experimental results shown in Fig. 7, we find that the scaling power exponent decreases after small amount of salt is added to the less conductive PMMA solution. Furthermore, the resulting scaling exponent is extremely well accord with the theoretical prediction Eq. (22). Fig. 8 shows pictures of the corresponding solid fiber forming process including stable and unstable segments. According to Fig. 4 (a1)-(d1) and Fig. 8 (a1)-(d1), it indicates the addition
5. Conclusion A model relating the stable-jet length to the terminal fiber radius has been proposed for partly as well as fully charged fibers in electrospinning. The power scaling law is rf ~Lsj−2/3 for fully charged fibers, while rf ~Lsj−(1 + α )/(1 + 2α ) for partly charged fibers. The theoretical predictions based on the model have been well verified by the experimental results. It is believed that the proposed theoretical model provides an efficient control means for polymer fibers with expected 6
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radius, which would facilitate the applications of the fibers significantly.
6409–6413. [19] M.M. Hohman, M. Shin, G. Rutledge, Electrospinning and electrically forced jets. I. Stability theory, Phys. Fluids 13 (2001) 2201–2220. [20] M.M. Hohman, M. Shin, G. Rutledge, Electrospinning and electrically forced jets. II. Applications, Phys. Fluids 13 (2001) 2221–2236. [21] B.B. Wang, X.D. Wang, T.H. Wang, Microscopic mechanism for the effect of adding salt on electrospinning by molecular dynamics simulations, Appl. Phys. Lett. 105 (2014) 121906. [22] L. Fan, Y.T. Xu, X. Zhou, Effect of salt concentration in spinning solution on fiber diameter and mechanical property of electrospun styrene-butadiene-styrene triblock copolymer membrane, Polymer 153 (2018) 61–69. [23] R. Casasola, N.L. Thomas, A. Trybala, Electrospun poly lactic acid (PLA) fibres: effect of different solvent systems on fibre morphology and diameter, Polymer 55 (2014) 4728–4737. [24] B.J. West, Comments on the renormalization group, scaling and measures of complexity, Chaos, Solit. Fractals 20 (2004) 33–44. [25] R. Benzi, Getting a grip on turbulence, Science 301 (2003) 605–606. [26] G.B. West, J.H. Brown, B.J. Enquist, A general model for the origin of allometric scaling laws in biology, Science 276 (1997) 122–126. [27] J.T. Kuikka, Scaling laws in physiology: relationships between size, function, metabolism and life expectancy, Int. J. Nonlinear Sci. Numer. Stimul. 4 (2003) 317–328. [28] J.H. He, H. Chen, Effects of size and PH on metabolic rate, Int. J. Nonlinear Sci. Numer. Stimul. 4 (2003) 429–432. [29] G. Iovane, Varying G, accelerating Universe, and other relevant consequences of a stochastic self-similar and fractal Universe, Chaos, Solit. Fractals 20 (2004) 657–667. [30] V.N. Kirichenko, S.I.V. PETRYANOV, N.N. Suprun, Asymptotic radius of a slightly conducting liquid jet in an electric field, Sov. Phys. Dokl. 31 (1986) 611–613. [31] A.M. Gañán-Calvo, Cone-jet analytical extension of Taylor's electrostatic solution and the asymptotic universal scaling laws in electrospraying, Phys. Rev. Lett. 79 (1997) 217–220. [32] J.J. Feng, Stretching of a straight electrically charged viscoelastic jet, J. NonNewtonian Fluid Mech. 116 (2003) 55–70. [33] Y.M. Shin, M.M. Hohman, M.P. Brenner, Experimental characterization of electrospinning: the electrically forced jet and instabilities, Polymer 42 (2001) 9955–9967. [34] Y. Cai, M. Gevelber, Analysis of bending region physics in determining electrospun fiber diameter: effect of relative humidity on evaporation and force balance, J. Mater. Sci. 52 (2017) 2605–2627. [35] I. Uematsu, K. Uchida, Y. Nakagawa, Direct observation and quantitative analysis of the fiber formation process during electrospinning by a high-speed camera, Ind. Eng. Chem. Res. 57 (2018) 12122–12126. [36] S.V. Fridrikh, J.H. Yu, M.P. Brenner, Nonlinear whipping behavior of electrified fluid jets, ACS Symp. Ser. 918 (2006) 36–55. [37] S.V. Fridrikh, J.H. Yu, M.P. Brenner, Controlling the fiber diameter during electrospinning, Phys. Rev. Lett. 90 (2003) 144502. [38] J. Fernández, The fluid dynamics of Taylor cones, Annu. Rev. Fluid Mech. 39 (2007) 217–243. [39] D.H. Reneker, A.L. Yarin, Electrospinning jets and polymer nanofibers, Polymer 49 (2008) 2387–2425. [40] J.J. Feng, The stretching of an electrified non-Newtonian jet: a model for electrospinning, Phys. Fluids 14 (2002) 3912–3926. [41] C.P. Carroll, Y.L. Joo, Electrospinning of viscoelastic Boger fluids: modeling and experiments, Phys. Fluids 18 (2006) 053102. [42] C. Wang, C.H. Hsu, J.H. Lin, Scaling laws in electrospinning of polystyrene solutions, Macromolecules 39 (2006) 7662–7672. [43] T. Han, A.L. Yarin, D.H. Reneker, Viscoelastic electrospun jets: initial stresses and elongational rheometry, Polymer 49 (2008) 1651–1658. [44] Z.M. Huang, Y.Z. Zhang, M. Kotaki, A review on polymer nanofibers by electrospinning and their applications in nanocomposites, Compos. Sci. Technol. 63 (2003) 2223–2253. [45] M. Montinaro, V. Fasano, M. Moffa, Sub-ms dynamics of the instability onset of electrospinning, Soft Matter 11 (2015) 3424–3431. [46] M. Šimko, D. Lukáš, Mathematical modeling of a whipping instability of an electrically charged liquid jet, Appl. Math. Model. 40 (2016) 9565–9583. [47] D.H. Reneker, I. Chun, Nanometre diameter fibres of polymer, produced by electrospinning, Nanotechnology 7 (1996) 216–223. [48] S. Koombhongse, W. Liu, D.H. Reneker, Flat polymer ribbons and other shapes by electrospinning, J. Polym. Sci. B Polym. Phys. 39 (2001) 2598–2606.
Acknowledgments This work was partly supported by the Chang Jiang Youth Scholars Program of China and grants (51773037) from the National Natural Science Foundation of China (51773037, 51803023, 61771123) to Prof. Xiaohong Qin as well as the “Innovation Program of Shanghai Municipal Education Commission, Shanghai, China”, “Fundamental Research Funds for the Central Universities, China” (2232018A3-11) and “DHU Distinguished Young Professor Program, Donghua University, China” to her. This work has also been supported by the Shanghai Sailing Program, Shanghai, China (18YF 1400400), the Project funded by China Postdoctoral Science Foundation, China (2018M640317). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.polymer.2019.121762. References [1] G.I. Taylor, Disintegration of water drops in an electric field, Math. Phys. Sci. 280 (1964) 383–397. [2] A.L. Yarin, S. Koombhongse, D.H. Reneker, Taylor cone and jetting from liquid droplets in electrospinning of nanofibers, J. Appl. Phys. 90 (2001) 4836–4846. [3] J. Doshi, D.H. Reneker, Electrospinning process and applications of electrospun fibers, J. Electrost. 35 (1995) 151–160. [4] D.H. Reneker, A.L. Yarin, H. Fong, Bending instability of electrically charged liquid jets of polymer solutions in electrospinning, J. Appl. Phys. 87 (2000) 4531–4547. [5] R. Stepanyan, A.V. Subbotin, L. Cuperus, Nanofiber diameter in electrospinning of polymer solutions: model and experiment, Polymer 97 (2016) 428–439. [6] A. Greiner, J.H. Wendorff, Electrospinning: a fascinating method for the preparation of ultrathin fibers, Angew. Chem., Int. Ed. Engl. 46 (2007) 5670–5703. [7] Z.Y. Hou, C.X. Li, P.A. Ma, Electrospinning preparation and drug-delivery properties of an up-conversion luminescent porous NaYF4:Yb3+, Er3+@Silica Fiber Nanocomposite, Adv. Funct. Mater. 21 (2011) 2356–2365. [8] M. Xi, X. Wang, Y. Zhao, Electrospun ZnO/SiO2 hybrid nanofibrous mat for flexible ultraviolet sensor, Appl. Phys. Lett. 104 (2014) 133102. [9] Y. Kang, P. Chen, X.T. Shi, Multilevel structural stereocomplex polylactic acid/ collagen membranes by pattern electrospinning for tissue engineering, Polymer 156 (2018) 250–260. [10] L. Persano, A. Camposeo, P.D. Carro, Distributed feedback imprinted electrospun fiber lasers, Adv. Mater. 26 (2014) 6542–6547. [11] S.H. Choi, B.H. Jang, J.S. Park, Low voltage operating field effect transistors with composite In2O3–ZnO–ZnGa2O4 nanofiber network as active channel layer, ACS Nano 8 (2014) 2318–2327. [12] Y.M. Shin, M.M. Hohman, M.P. Brenner, Electrospinning: a whipping fluid jet generates submicron polymer fibers, Appl. Phys. Lett. 78 (2001) 1149–1151. [13] J.H. He, Y. Wu, W.W. Zuo, Critical length of straight jet in electrospinning, Polymer 46 (2005) 12637–12640. [14] G.C. Rutledge, S.V. Fridrikh, Formation of fibers by electrospinning, Adv. Drug Deliv. Rev. 59 (2007) 1384–1391. [15] A.F. Spivak, Y.A. Dzenis, Asymptotic decay of radius of a weakly conductive viscous jet in an external electric field, Appl. Phys. Lett. 73 (1998) 3067–3069. [16] A.F. Spivak, Y.A. Dzenis, D.H. Reneker, A model of steady state jet in the electrospinning process, Mech. Res. Commun. 27 (2000) 37–42. [17] J.H. He, Y.Q. Wan, M.Y. Yu, Allometric scaling and instability in electrospinning, Int. J. Nonlinear Sci. Numer. Stimul. 5 (2004) 243–252. [18] X.H. Qin, Y.Q. Wan, J.H. He, Effect of LiCl on electrospinning of PAN polymer solution: theoretical analysis and experimental verification, Polymer 45 (2004)
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