Highly Efficient Fabrication of Polymer Nanofiber Assembly by

Apr 17, 2015 - ABSTRACT: Centrifugal jet spinning (CJS) is a highly efficient, low-cost, and versatile method for fabricating polymer nanofiber assemb...
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Highly Efficient Fabrication of Polymer Nanofiber Assembly by Centrifugal Jet Spinning: Process and Characterization Liyun Ren,† Rahmi Ozisik,† Shiva P. Kotha,‡ and Patrick T. Underhill*,§ †

Department of Materials Science and Engineering, ‡Department of Biomedical Engineering, and §Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180, United States

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S Supporting Information *

ABSTRACT: Centrifugal jet spinning (CJS) is a highly efficient, low-cost, and versatile method for fabricating polymer nanofiber assemblies, especially in comparison to electrospinning. The process uses centrifugal forces coupled with the viscoelastic properties and the mass transfer characteristics of spinning solutions to promote the controlled thinning of a polymer solution filament into nanofibers. In this study, three different spinning stages (jet initiation, jet extension, and fiber formation) were analyzed in terms of the roles of fluid viscoelasticity, centrifugal forces, and solvent mass transfer. Four different polymer solution systems were used, which enables a wide range of fluid viscoelasticity properties and solvent mass transfer properties, and polymer fibers were fabricated under different rotational speeds for these polymer solutions. The key dimensionless groups that determine the product morphology (beads, beads-on-fiber, and continuous fiber) and the radius of the fiber (when fibers are formed) were identified. The obtained morphology state diagram and fiber radius model were tested using a fifth polymer solution system. Results indicate that Weissenberg number and capillary number are important during the fiber extension stage to enable fiber formation while the elastic processability number is the determinative dimensionless number for fiber diameter prediction.

1. INTRODUCTION High surface area together with other physical, electrical, thermal, and mechanical properties make polymer microfibers and nanofibers suitable in various commercial sectors, including but not limited to electronics, energy, mechanical/chemical, consumer, and life sciences.1−13 Nanofiber-based advanced components are widely used in dye-sensitized solar cells, selfcleaning/stain-resistant textiles,2,4,7 stimuli-responsive biomimicking structures,6,9 multifunctional bioengineered structures,6,9,10 and high-density energy storage electronics.8,11−13 The applications of polymer nanofibers are expanding rapidly and playing invaluable roles in nanoscience, bioscience, and other engineering and technology fields.14−18 However, the low cost-versus-yield efficiency of the current nanofiber fabrication technologies hinders the further integration of nanofibers into a wider range of practical large scale applications and limits market applications driven by cost and performance. This substantial gap between supply and demand calls for the scale-up of nanofiber production methods with high costversus-yield efficiency and versatility.15,19,20 Many research efforts have focused on this scale-up including both upgraded electrospinning and alternative spinning methods such as melt spinning, solution spinning, and emulsion spinning.21−23 Specific examples of scaling-up nanofiber fabrication approaches include free-surface electrospinning,19,20 multineedle electrospinning,21−23 electroblowing,27 gas-assisted electrospinning,28,29 gas/air jet spinning,30,31 electrospinning,32 and shear wet spinning.33 Through these studies, substantial advances have been achieved in terms of the nanofiber production rate © 2015 American Chemical Society

and the fabrication method diversity. However, the further application of upscaling nanofiber fabrication methods requires additional improvement with respect to morphology control, nanofiber diameter uniformity control, the high cost of spinning equipment, and the low efficiency of production rate versus cost competitiveness. Centrifugal spinning has been a fabrication method of cotton candy, dating back to the 19th century.34 Centrifugal spinning is a high production rate and low-cost fiber fabrication method that utilizes the balance between the centrifugal force and fluid properties of the spinning solution.35−37 Previous works from our group and other research groups have expanded the use centrifugal spinning to fabricate polymer nanofiber and metallic fibers.14,35,37−42 Despite the flexibility and high efficiency of centrifugal spinning, the quality of the resulting fibers with regard to fiber production consistency, fiber diameter distribution, fiber alignment control, fiber morphology control, and fiber collection efficiency were not well controlled to push this technique forward into lab-scale or semi-industrial nanofiber fabrication due to the lack of a fundamental understanding of centrifugal spinning mechanism.35−37,43 Several research works are aimed to understand the mechanics involved in centrifugal spinning.38,39,45,46 Padron et al.45 utilized high-speed photography to capture the initial stages of fiber formation, the jet shape evolution over time, and jet propagation trajectory with Received: February 10, 2015 Revised: April 8, 2015 Published: April 17, 2015 2593

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Macromolecules regard to key parameters, such as angular velocity and spinning solution viscosities, to provide an qualitative understanding of individual parameter influence on fiber trajectory and fiber diameter. Badrossamay et al.44 developed a fiber radius prediction equation for rotary jet spinning technique by balancing inertial force and viscous force and subsequently fitting with experimental data. It was concluded that the fiber radius can be predicted based on collector distance, angular speed, orifice radius, spinning solution surface tension, density, and viscosity. Taghavi and Larson46 proposed a theoretical model to describe quantitatively the fiber trajectory and diameter based on the ratio of Reynolds number and Rossby number with the consideration of centrifugal, inertial, and viscous forces. Although the important role of spinning solution elasticity and solvent mass transfer coefficient are recognized in many spinning techniques,32,47−49 the effects of spinning solution elasticity and solvent mass transfer coefficient have not been systematically studied in terms of their roles in fiber thinning dynamics among the existing studies of centrifugal spinning mechanism. On the basis of our previous demonstrations of centrifugal jet spinning (CJS) nanofiber fabrication technique with controlled fiber alignment and morphology, we examine the underlying fluid dynamics occurring in the CJS process using simple scaling arguments in this paper. By addressing the role of centrifugal thinning effect, inertial effect, spinning solution viscous effect, elastic effect, and solvent evaporation effect, the goal of this study is to examine the mechanisms governing fiber formation involved in the centrifugal spinning process for controlled fabrication of nanofibers. In order to achieve the goal, a variety of polymer−solvent solutions including polyvinylpyrrolidone (PVP) in ethanol (PVP−ETOH), PVP in water (PVP−H2O), PVP in dichloromethane (PVP−DCM), and poly(lactic acid) (PLLA) in dichloromethane (PLLA−DCM) have been tested in the CJS process along with characterization of their rheological response and measurement of other material properties. The experimental data and observations have been analyzed to relate successful fiber production and fiber morphology to the governing dimensionless groups. The obtained fiber morphology state diagram for successful fiber formation and the empirical fiber radius prediction model are then validated using a poly(ethylene oxide)−water (PEO−H2O) solution system. An understanding of the spinning mechanics will enable the application of CJS in various research and engineering fields, with the ease of tailoring nanofiber morphologies to explore new fibrous products.

Figure 1. Schematic drawing of centrifugal jet spinning (CJS) system (not to scale). distance between the center of the chamber and the product collecting posts was adjustable. The collection distance was set to 20 cm for this study. Spinning solutions were continuously fed into the chamber at a set flow rate of 1 mL/min. As the spinning chamber spins, the centrifugal force exceeded the capillary force of the spinning solution in the orifice, resulting in jets of spinning solution being ejected from the rotating chamber. The rotational speed of the chamber can be changed by adjusting the voltage applied on the motor. The ejected solution jet gets thinner and elongated due to drawing forces generated by a combination of centrifugal forces, resistance with air, and evaporation of solvent. The higher the angular speed of the spinning chamber, the larger the centrifugal force experienced by the jet. The viscoelastic properties of the solution maintain its continuous structure. The extent to which the jet thins determines the final diameter of the fiber, and one of the factors influencing this is the angular speed of the spinning chamber. As the spinning process proceeds, the evaporation of solvent makes the solution jet thinner until the liquid jet solidifies into fibers. The rotational speeds were characterized with a rotation meter as 3500, 5000, 7500, and 9000 rpm. A flexible air foil was attached on the spinning chamber to manipulate the air flow during spinning along with an aluminum sheet encircling the periphery of the system beyond the collecting rods. At the same time, any stray air flow disturbances in the laboratory were prevented by the aluminum sheet. All spinning experiments were performed at room temperature. 2.3. Scanning Electron Microscope (SEM). All samples were sputter-coated with platinum before observation with SEM (Supra 55 Carl Zeiss, Germany). SEM images were taken at three different locations for each sample with different magnifications. For each fiber sample, ten different SEM images were analyzed with the help of ImageJ software for calculation of averaged fiber diameter. 2.4. Surface Tension Measurement. The surface tension of polymer spinning solutions was measured using a pendant drop method with a Rame-Hart goniometer (Model 250 Rame-Hart, Succasunna, NJ). Each polymer solution was measured with 20 different drops from the needle tip of the goniometer. The surface tension of each polymer solution was obtained from the Rame-Hart drop analysis software. Figure 2 shows the change in surface tension with polymer concentration, from a pure solvent to 15 wt % polymer concentration. The surface tension slightly decreases with increasing polymer concentration. The error bars show the standard deviation between different measurements. 2.5. Steady Shear Viscometric Tests. Steady shear flow viscometric tests are used to determine the viscosity as a function of the shear rate, γ̇. An AR-G2 rheometer (TA Instruments, New Castle, DE) was used for viscosity measurements. A parallel plate geometry

2. MATERIALS AND EXPERIMENTAL METHOD 2.1. Materials. Polyvinylpyrrolidone (PVP, Mw = 1 300 000 g/mol) and poly(ethylene oxide) (PEO, Mw = 900 000 g/mol) were purchased from Sigma-Aldrich. Poly(lactic acid) (PLLA, Mw = 500 000 g/mol) was obtained from Natureworks. Ethanol (ETOH, anhydrous), water (H2O, deionized), and dichloromethane (DCM, anhydrous) were all purchased from Sigma-Aldrich. All chemicals were used without further purification. 2.2. Fabrication of CJS System. The CJS technique exploits the centrifugal force of a spinning chamber and viscoelastic characteristics of spinning solutions to generate continuous fiber structures. As shown in Figure 1, the CJS system was made of a dc hobby motor (9−18 V, Radio Shack) powered hollow chamber with two orifices passing through the chamber wall and a set of product collecting posts. The spinning chamber was made from Teflon tubes and has an outer diameter of 15 mm and an inner diameter of 10 mm. The orifices in the wall of the spinning chamber were 500 μm in diameter. The 2594

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the dynamic response of polymer solutions in the linear viscoelastic regime. An oscillatory shearing motion is imposed on the sample by imposing an oscillatory angular displacement. SAOS test provides information on the in-phase and out-of-phase response to the oscillation under different frequencies. When an oscillatory deformation γ = γ0 sin(ωt) is applied to a solution, the corresponding shear stress σ(t) can be written in the linear region as σ(t) = γ0[G′(ω) sin(ωt) + G″(ω) cos(ωt)], where G′ and G″ are the storage modulus and loss modulus of the solution. Strain sweep tests were performed at ω = 5 rad/s for each spinning solution as shown for one mixture in Figure S2 of the Supporting Information. When the peak strain is low, the data are noisy due to the limitations of the instrument. The nonlinear viscoelastic regime is reached at high shear strains. To avoid the impact of noise and nonlinear effects, the peak strain used for SAOS test is thus determined from the linear viscoelastic regime at the middle of the plateau. We have used a peak strain of between 5 and 10%. The storage modulus and loss modulus of different spinning solutions as a function of frequency are reported in Figure 4. To determine the relaxation time of the spinning solutions, the SAOS test results are fitted to a generalized Maxwell model with four modes. The equations for the four-mode Maxwell model are shown in eqs 1 and 2. λk is determined with the help of TA Rheology Advantage Data Analysis software. The longest relaxation time λ1 calculated in this way for each polymer solution involved in this study is shown in Table 1.

Figure 2. Surface tension change with polymer concentration from 0 to 15 wt %. with plate diameter of 25 mm was applied in each test with a gap size of 1 mm. The viscosity of the solution mixtures was measured as a function of shear rate at 25 °C. All the raw data were analyzed with TA rheology analysis software to obtain the zero shear viscosity. The viscosity of four different polymer solutions with concentrations ranging from 1 to 15 wt % were tested with changing shear rate from 1 to 2000 s−1. This range is consistent with the rates of deformation experienced by the solutions during spinning. Most dilute polymer solutions have a plateau viscosity at low shear rate and are shear thinning at high shear rates. The plateau value is the zero shear rate viscosity η0.50 The typical shear viscosity change of different polymer solutions as a function of shear rate is shown in Figure S1 of the Supporting Information. The viscosity shows a weak dependence on shear rate. Figure 3 shows how the average shear viscosity depends

4

G′ =

∑ k=1

4

G″ =

∑ k=1

Gk (λk ω)2 1 + (λk ω)2

(1)

Gk (λk ω) 1 + (λk ω)2

(2)

2.7. Thermogravimetric Analysis (TGA). The evaporation of a solvent from a polymer solution is governed by internal diffusion and by the interfacial mass transport between the polymer solution and surrounding medium. The diffusion of solvent from the polymer solution to its surface is fast considering the small solvent molecule size and thin diameter of the polymer solution jet. Thus, it is assumed that the solvent evaporation process is governed by mass transfer. To study the solvent concentration change over time, TGA (TA Instruments, Q50) is used to monitor the mass change of the polymer solution due to evaporation as a function of time at room temperature, as shown in Figure 5. Nitrogen gas flow during TGA testing is set to 90 mL/min to measure solvent evaporation. The solvent concentration c(t) in the polymer solutions can be estimated by eq 3.51 h A ∂c c ∂V =− m c− ∂t V V ∂t

(3)

where c is the mass fraction of solvent, hm is the mass transfer coefficient of the solvent at sample surface, and A and V are the surface area and volume of the TGA sample, respectively. Considering the volume of the polymer solution decrease to be constant over time with a rate of k, eq 3 can be rewritten as

⎛ V0 ⎞ K c = c 0⎜ ⎟ , ⎝ kt + V0 ⎠

Figure 3. Average viscosity as a function of polymer concentration for the polymer solutions.

K=

hm, TGA A + k k

(4)

which shows that the mass fraction of solvent decreases with time. Equation 4 is used to fit the TGA data to extract the mass transfer coefficients, hm,TGA, for different solvents involved in this study. The mass transfer coefficient of solvent for each polymer solution examined in this study is then calculated based on the fitted curves as exemplified in Figure 5. To account for the impact of air flow on the solvent evaporation rate during the CJS process, it is important to correlate the solvent evaporation rate data obtained from TGA experiments to the actual solvent evaporation under different rotational speeds in CJS. Considering that the air flow velocity varies with different rotational speeds, computer fluid dynamics simulation of the CJS process is

on polymer concentration in the solution. Each polymer−solvent solution has been tested five times. The error bars are the standard deviation between different measurements. 2.6. Small-Amplitude Oscillatory Shear and Determination of Longest Relaxation Time. In order to determine the relaxation time of different spinning solutions, small-amplitude oscillatory shear (SAOS) tests at constant shear strain were performed at 25 °C on all the solutions. An AR-G2 rheometer (TA Instruments, New Castle, DE) was used to perform the SAOS tests in a parallel plate geometry (25 mm EHP steel plate) with gap size of 1 mm. SAOS is used to test 2595

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Figure 4. Small-amplitude oscillatory shear sweeps as a function of frequency for different polymer solutions with polymer concentration from 1 to 15 wt %: (a, b) storage and loss modulus of PVP−ETOH solutions; (c, d) storage and loss modulus of PVP−H2O solutions; (e, f) storage and loss modulus of PVP−DCM solutions; (g, h) storage and loss modulus of PLLA−DCM solutions. employed to simulate the air flow at different rotational speeds. The details of building CFD model can be found in the Supporting Information. The air flow velocities at the orifices of the CJS system under varying rotational speeds are shown in Table 2. Lennert and

Nielson52 studied the existing models accounting for solvent evaporation rate and concentration evolution under various air flow velocities. According to their study, a simple evaporation model, denoted as NIOH-2,52 predicts changes in the rate of solvent evaporation 2596

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Macromolecules Table 1. Longest Relaxation Time of Studied Polymer Solutions λ1 (s) 1 wt % PVP−ETOH PVP−H2O PVP−DCM PLLA−DCM

3.84 4.36 1.64 2.26

× × × ×

3 wt % −4

10 10−5 10−5 10−4

6.21 1.85 3.50 1.08

× × × ×

5 wt % −4

6.99 3.83 6.34 6.02

10 10−4 10−4 10−3

× × × ×

Table 2. Air Velocity Change at the Jet Outlet under Various Rotational Speeds air velocity at jet outlet (m/s)

3.1

5.4

7500 rpm

9000 rpm

7.9

9.5

10 10−4 10−3 10−3

3.09 1.55 1.84 2.41

× × × ×

10 wt % −2

10 10−3 10−2 10−2

5.03 1.39 3.01 4.88

× × × ×

−2

10 10−2 10−2 10−2

15 wt % 8.42 5.50 1.35 1.50

× × × ×

10−2 10−2 10−1 10−1

Reynolds number (Re), and the capillary number (Ca). Each of these groups is proportional to a velocity scale that “drives” the motion. For problems that are not thinning due to external action (called “self-thinning”), all three groups are zero, and the response is determined by dimensionless groups that only contain material properties. The most common such groups are the Ohnesorge number (Oh), the “intrinsic Deborah number” (De), elastocapillary number (Ec), and elasticity number (El). The values of Oh, De, and Ec can be written as the ratio of two time scales. During self-thinning capillary breakup of a Newtonian filament, the breakup is caused by surface tension and slowed down by inertia and viscous stresses. If inertia were neglected, the filament would breakup in a characteristic viscous time scale (tviscous = ηR0/γ), where η is the viscosity, γ is the surface tension, and R0 is the initial filament radius. If viscous stresses were neglected, the filament would break up on the Rayleigh time scale, tR = (ρR03/γ)1/2, where ρ is the density. The ratio of these time scales is Oh = tviscous/tR. Note that it is the larger time scale that is the dominant factor; e.g., for small Oh, viscosity is not important, while for large Oh, inertia is not important. One of the simplest models of viscoelasticity is the upper-convected Maxwell model, which introduces another parameter λ, the relaxation time. If the breakup time is faster than the relaxation process, then elastic effects will be important. If the breakup time is slower than the relaxation process, then the fluid will act like a Newtonian fluid. If Oh is small, then the Rayleigh time is the relevant one and De = λ/tR quantifies elastic effects. If Oh is large, the viscous time is the relevant factor and Ec = λ/tviscous quantifies elastic effects. In the CJS process, the thinning is also “driven” by centrifugal forces. We can quantify this driving with a characteristic velocity scale or time scale (using the initial filament radius to relate them). These two scales are denoted Ucent and tcent = R0/Ucent, respectively. One approach to determine these would be to calculate the thinning dynamics under the action of centrifugal forces and calculate the scales from this thinning. We take an alternative approach which simply examines the dynamical equations and identifies the scales that would quantify the centrifugal forces. In particular, the fluid leaving the orifice is rotating at an angular velocity of ω and is a distance a0 from the spinning axis. Therefore, it is subjected to a centrifugal acceleration of ωa02. Matching this with an acceleration constructed from our scales R0/tcent2 gives tcent = (R0/a0)1/2/ω and Ucent = ω(R0a0)1/2. Note that this velocity is not equal to the mean velocity of the fluid as it exits the orifice, which is related to the volumetric flow rate through the system by u0 = Q/πR02 and which is constant throughout the experiments here. It is common to use this velocity, u0, within definitions of two other numbers: the Reynolds number (Re) and the Rossby number (Rb). These groups are defined as Re = ρu0a0/η and Rb = u0/ωa0. For the materials and conditions used here, Re ranges between values of order 1 and a few hundred while Rb ranges from 0.03 at the lowest spinning speeds to 0.01 at the highest spinning speeds.

Figure 5. Selected polymer−solution solvent evaporation as a function of time measured by TGA and fitted mass transfer coefficient functions.

3500 rpm 5000 rpm

8 wt % −3

with air velocity under both turbulent and laminar air flow. In the NIOH-2 model, it has been proved that evaporation rate Rii depends on the air flow velocity Uair as Rii ∝ Uair0.62 under the assumption of constant solvent vapor pressure and surface area. The solvent evaporation rate Rii in the NIOH-2 model is equivalent to the mass transfer coefficient hm of solvent evaporation. Therefore, the NIOH-2 model is used to estimate the influence of air flow velocity on the mass transfer coefficient of hm under different rotational speeds in CJS, based on the experimental data of solvent mass transfer coefficient obtained from TGA testing. The evaporation rate of solvent is highly dependent on the air flow velocity at the orifice. hm for polymer solutions at different spinning speeds are included in the processability numbers in the rest of this study. The specific calculation procedure of hm is presented in the Supporting Information.

3. RESULTS AND DISCUSSION 3.1. Dimensionless Numbers in CJS Process. The essential fluid physics of a system is dictated by a competition between various phenomena, which is captured by a series of dimensionless numbers expressing their relative importance. These dimensionless numbers form a parameter space for exploring fluid physics. A wide variety of physical phenomena occur in the CJS process, the importance of which must be judged against competing phenomena. Dimensionless numbers expressing the ratio of these phenomena provide a sense of where a system sits in fluidic parameter space. As described by McKinley,53 the thinning of filaments can be described by three dimensionless groups: the Weissenberg number (Wi), the 2597

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Figure 6. Micro/nanofiber morphology spun from different polymer solutions at 9000 rpm.

To quantify the thinning of the filament due to centrifugal force, we can compare the time scales used in self-thinning to the centrifugal time, tcent. The comparison with the Rayleigh time can be identified as (We)1/2 = tR/tcent, in which Ucent is used as the velocity in the definition of the Weber number. Similarly, the comparison with the viscous time can be identified as Ca = tviscous/tcent. Finally, we can compare the centrifugal time with the relaxation time to identify Wi = λ/tcent. All three of these numbers are proportional to the rotational rate of the chamber. Therefore, for a given fluid, they are proportional to each other. Finally, the thinning of the filament occurs simultaneously with evaporation of the solvent. Previously, Tripathi et al.51 proposed a processability number, P = hmη/γ, which compares evaporation time scale, tevap = R0/hm, and a viscocapillary time scale, tviscous = ηR0/γ, where hm is the mass transfer coefficient of the solvent at sample surface (characterized in section 2.7). The governing principle was that the Newtonian fluid was selfthinning due to a viscocapillary balance, and P quantifies how fast the solvent can evaporate compared to this time. For most cases examined here that form fibers, the values of Oh and Ec are large. Therefore, the self-thinning that occurs after the action of the centrifugal forces will likely take place due to elastocapillary balance which leads to a thinning with the elastic time scale, λ. This is the relevant time scale to compare with the evaporation. Therefore, we define a new group that we call an elastic processability number by Pe = λ/tevap. This dimensionless group will be important when we quantify the final thickness of the fibers. 3.2. Analysis of CJS Processes. To form polymer fibers using CJS from a polymer solution, three different stages must occur, starting with jet initiation, to jet extension and finally fiber formation. At the first stage, the spinning solution in the rotating chamber is initiated from the orifice by centrifugal

forces after overcoming the capillary force of the spinning solution. Once the spinning solution comes out of the orifice, the liquid jet enters the second stage where it is extended into a thin filament. At this stage, the liquid jet thins under the action of capillary and centrifugal forces which is resisted by inertia and elastic and viscous stresses. The successful formation of a continuous liquid jet is the key for fiber formation in the third stage. At the third stage, the liquid jet is thin enough to reach the glassy state of the polymer solution, which, coupled with evaporation of solvent, leads to solidification of fibers. These polymer fibers are subsequently collected using the collecting posts. The morphology of spinning products (continuous fiber, beads-on-fiber, and beads) varies with polymer solutions and rotational speeds. Figure 6 shows the morphology of spinning products in terms of spinning solution types and polymer concentration at 9000 rpm. The morphologies of the spinning products have not shown any direct correlation with polymer concentrations. The influence of other parameters, including polymer molecular weight, spinning chamber orifices sizes, and collection distance, has been studied in detail, in our previous studies.40−42 Here, we focus on examining the viscoelastic properties of the spinning solution and physics involved in the spinning process. 3.2.1. Polymer Solution Jet Initiation Stage. The first stage of fiber formation is polymer solution jet initiation from the spinning chamber orifice. Centrifugal forces overcome the surface tension forces that would hold the fluid inside the chamber. We can estimate the critical rotational speed for jet initiation by considering a fluid cap at the chamber orifice that is half of a sphere of radius R0. The centrifugal force exerted on the fluid cap at the edge of the spinning chamber can be expressed as Fcentrifugal = (2/3)πρR03ω2a0. The surface tension of the spinning solution induces capillary force (Fcapillary = γ2πR0) at the orifice on the spinning chamber. Equating these two 2598

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Macromolecules forces leads to a critical rotational speed of jet initiation given as ωc = (3γ/(ρR02a0))1/2. For the solutions used here, this theoretical critical rotation speed ranges between 1750 and 3500 rpm and is determined primarily by the solvent. The rotation speeds used in the experiments were equal to 3500 rpm or higher, and all conditions show jet initiation. This is consistent with our theoretical estimate. Experiments at the lower rotational speeds needed to test this theoretical prediction for the critical speed cannot be performed reliably with the hobby motor used here. 3.2.2. Initiated Polymer Solution Jet Extension Stage. After the polymer solution is initiated from the rotational chamber orifice, the jet extension stage kicks in to stimulate the thinning of the solution liquid jet where polymer solution elasticity effects, viscous effects, inertia effects, and centrifugal spinning effects are all engaged in the extension of solution jets. Hence, ejected material is subject to breakup induced by both centrifugal force and Rayleigh−plateau instability, which inhibits the formation of continuous solution jets. The suppression of jet breakup strongly depends on the viscoelastic properties of spinning solution. Thus, viscoelasticity of polymer solution is critical to determine the formation of beads, beads-on-fibers, or continuous fiber morphologies, as shown in Figure 6. We use the dimensionless groups described previously to determine how these properties determine the morphology. We begin by examining the groups that are determined solely by material properties (they do not depend on the spinning speed) and thus determine how a filament would self-thin because of capillary forces. Of the four dimensionless groups (Oh, De, Ec, and El), only two are independent. For the four polymer−solvent pairs and six polymer concentrations (24 total solutions), the dimensionless groups are shown in Figure 7. For small Oh, the filament would initially want to thin with the Rayleigh time, and De quantifies whether this thinning stretches the polymers to give significant elastic effects. For large Oh, the filament would initially want to thin with the viscous time, and Ec quantifies whether this thinning stretches the polymers to give significant elastic effects. The solutions used span a wide range of Oh, and for most of them, elastic effects are expected to play a role even if the filaments thinned without centrifugal forces. The only exception is the lowest concentration systems which have both small Oh and small De. With these in mind, we can correlate the morphology of the spun fibers to the dimensionless groups. The 24 polymer solutions were used at four spinning speeds, and the morphology of all 96 cases were quantified. Recall that there are three dimensionless groups that are proportional to the spinning speed. Figure 8 shows the fiber morphology on a state diagram that uses Oh to denote the fluid, and Wi or Ca is used to quantify the spinning speed. Note that Oh alone does not fully determine the fluid but is a useful way to present the data. The other parameter needed to determine the fluid can be found from Figure 7. Finally, note that for a single fluid, Wi and Ca are proportional (Wi = Ec*Ca). But since the fluids do not all have the same value of Ec, the state diagrams using Wi or Ca are different. Figure 8 shows that there are clear boundaries between the regions that produce beads, beads-on-fibers, or continuous fibers. All cases with Ca < 1 form beads, and all cases with Ca >2 form continuous fibers. All systems with 1 < Ca < 2 form beads-on-fibers. The boundaries using Wi are almost as clear, but with Wi of 5 and 28. The only exception is the system with PLLA in DCM at a concentration of 3 wt % with a spinning

Figure 7. (a) Quantification of fluid material properties in a space of De and Oh. (b) Quantification of fluid material properties in a space of Ec and Oh.

speed of 3500 rpm For this system, Wi ∼ 10 but the system forms beads rather than beads-on-fibers. These state diagrams are important in part because they eliminate the need for trialand-error studies to determine the final fiber morphology. They also give insight into the mechanism for the final fiber morphology. The values of Ca and Wi compare the centrifugal time scale to the viscocapillary time and fluid relaxation time, respectively. In order to form continuous fibers, the centrifugal time scale must be small enough (meaning fast enough stretching due to centrifugal forces) that it suppresses breakup and bead formation. This process can be somewhat counterintuitive. One might think that fast stretching due to centrifugal forces would lead to thin filaments that would breakup easier. This is not the case, and we think this is for two possible reasons. First, the fast stretching could lead to large polymer stresses that resist breakup. This could be the case for the systems at relatively small Oh, which also have relatively small De. However, it then seems surprising that the morphology is determined so nicely by fluid properties like the viscosity determined in shear. It should also be noted that the fluids at large Oh used here also have large Ec. This means that capillary self-thinning is strong enough to stretch the polymers leading to elastic stresses that resist thinning. Additional centrifugal forces are not needed to induce these resistive elastic stresses. 2599

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to occur due to elastocapillary balance, causing a thinning with time scale, λ. Thus, the processability number in this study can be defined as the ratio of elastic time scale to evaporation time scale. Pe =

λh λ = m = EcP tevap R0

(5) 51

The analysis by Tripathi et al. found that under some conditions the final fiber size scaled as exp(−0.035/P). Very fast evaporation leads to large P and a fiber which cannot thin significantly before it solidifies. Figure 9 shows our results for

Figure 9. Final fiber diameter as a function of the elastic processability parameter. Figure 8. (a) State diagram of fiber morphology in a space of Ca and Oh. (b) State diagram of fiber morphology in a space of Wi and Oh.

the final fiber radius scaled by the initial radius as a function of 1/Pe. Although the data do not collapse exactly onto a single curve, this relationship seems to work better than any other relation that was investigated. Additionally, the dependence is not an exponential, but a power law with exponent ∼-0.5. Equation 6 is the fitting function between R/R0 and 1/Pe based on the experimental data from the studied spinning solutions with fiber morphology.

The second role that centrifugal forces play is to produce a relatively rapid initial thinning of the filament. After this initial thinning, the filament thins primarily due to a self-thinning mechanism from a new “starting” configuration. As shown by Bhat et al.,54 passive breakup naturally produces a beads-onfibers morphology only within a regime of Oh and De. The stretching of filament by centrifugal forces could act to make the filament thin enough and with high enough polymer stresses to put the system outside of this regime. 3.2.3. Fiber Formation Stage. When a steady spinning solution jet is formed successfully without breakup, the liquid jet is further thinned under centrifugal force extension as well as experiencing solvent evaporation. The evaporation of the volatile solvent is necessary to asymptotically increase viscosity and stabilize the liquid jet with increasing elasticity until the solvent content in the solution reaches to the glass transition of the polymer solution. Previously, the magnitude of the rate of thinning was compared to the rate of solvent evaporation in a dimensionless group called the processability number, P, according to Tripathi et al.51 This processability number was interpreted as the ratio of viscous time scale and evaporation time scale for Newtonian fluid.51 For all cases that formed fibers, De > 1, Ec > 1, and Wi > 1. Therefore, elastic stresses will be important. Because of the use of an airfoil in the CJS design, solvent evaporation is minimal during the initial jet extension phase in which centrifugal forces are important. During the fiber formation stage, this stretched filament continues to thin during evaporation. We expect this thinning

R /R 0 = 0.00162Pe 0.5

(6)

The importance of this relationship should be noted. The value of Pe is taken only from independent measurements of fluid properties and an estimate of the mass transfer rate taken from experiments and simulations of the air flow in the CJS apparatus. From the relation found in Figure 9, this single parameter can be used to predict the final fiber radius to within about a factor of 2. Future work can examine the additional scatter about this power law to better understand what determines the final radius. An initial analysis has found that, for a given fluid, higher spinning speeds give higher Wi and radii on the lower side of the curve, while lower Wi are on the higher side of the curve. This can be explained by the fact that higher Wi leads to more of an initial thinning by centrifugal forces and a thinner filament. Note that higher spinning speeds also lead to higher air velocities and faster evaporation of the solvent. These competing effects combine to give the response found in Figure 9. 3.3. Validation of Empirical Model. In section 3.2, the key dimensionless numbers were used to better understand the mechanics of fiber formation. In this section, PEO−H2O 2600

DOI: 10.1021/acs.macromol.5b00292 Macromolecules 2015, 48, 2593−2602

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Macromolecules solutions 5 wt %) between solution

Table 3. Fiber Diameter and Pe from PEO−H2O Solutions

with different polymer concentrations (1, 3, and are used to test the general relationship developed product morphology, fiber diameter, and polymer viscoelastic properties. Figure 10 illustrates the

solution PEO-H2O-5 wt % @ 7500 rpm PEO-H2O-5 wt % @ 9000 rpm

fiber diam (μm)

R/R0

Pe

1/Pe

predicted R/R0

0.2688

0.0005376

0.01803

55.4631

0.000218

0.0951

0.0001902

0.02389

41.8585

0.00025

that the empirical model can provide useful quantitative information for evaluating fiber diameters based on the Pe value of polymer solutions. In future work, a more accurate quantitative relationship to predict the fiber diameter can be developed based on current understanding of the fiber formation process and mechanism.

4. CONCLUSIONS We have investigated experimentally and theoretically the role of fluid viscoelasticity in CJS at three different stages of spinning. The use of four different polymer solutions allowed us to evaluate the role of fluid elasticity and viscosity at different stages of CJS process with the help of dimensionless numbers, including Deborah number, Weissenberg number, capillary number, and Ohnesorge number. Experimental solutions covered a broad range of relaxation times, viscosity, and solvent evaporation rates. It was also found that when the capillary number is below 1, only beads are formed. For capillary numbers above 2, uniform fibers are observed. Thus, spinnability of the polymer solutions is determined by the capillary number. For all but one system, the morphologies could have also been quantified in terms of critical Weissenberg numbers. The final fiber diameter is strongly dependent on the elasticity of spinning solution and solvent evaporation rate. The final radius was found to be approximately a power law function of an elastic processability parameter that relates the thinning of the filament to the solvent evaporation. Both the morphology diagram and fiber size relationship were validated using an additional polymer solution made with PEO in H2O.

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Figure 10. Morphologies found for PEO−H2O solutions (1, 3, and 5 wt %) placed on a state diagram using Wi vs Oh (a) or Ca vs Oh (b). Open symbols represent beads, half-filled symbols represent beads-onfiber, and filled symbols represent fibers.

ASSOCIATED CONTENT

S Supporting Information *

Figures S1−S3. This material is available free of charge via the Internet at http://pubs.acs.org.

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morphologies resulting from PEO−H2O solutions in terms of Wi or Ca vs Oh. PEO−H2O solutions with Ca < 1 form beads while continuous fibers were formed for those with Ca > 2 form. Beads-on-fiber morphology appeared with in the range of 1 < Ca < 2. Meanwhile, the boundaries of Wi for different spinning product morphologies were also in agreement in section 3.2. When 5 < Wi < 28, the PEO−H2O spinning solutions yielded beads-on-fiber morphology. When Wi > 28, continuous fiber structures were formed from the spinning solution. PEO−H2O solutions with Wi < 5 spun into beads morphology. These results were consistent with the critical dimensionless numbers found in section 3.2 and are further evidence that Ca and Wi in the jet extension stage determine final product morphology. For PEO−H2O solutions that formed continuous fibers, Table 3 lists the fiber diameters and elastic processability numbers for the PEO−H2O solution at different evaporation rates. The predicted fiber diameters from the power law prediction of eq 6 are also listed in Table 3. Errors of the predicted R/R0 relative to experimental measurements are 59.5% and 31.6%, respectively. This suggests

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (P.T.U.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge NSF CBET award 1138018 and NSF CMMI award 1200270 and helpful discussions on rheological tests with Edmund Tang.

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