Electrohydrodynamic Deposition of Polymeric Droplets under Low

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Electrohydrodynamic Deposition of Polymeric Droplets under Low-Frequency Pulsation Lei Xu,†,‡ Xiang Wang,† Tingping Lei,† Daoheng Sun,*,† and Liwei Lin*,†,§ †

Department of Mechanical and Electrical Engineering, Xiamen University, Xiamen 361005, China School of Mechanical and Electric Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333403, China § Department of Mechanical Engineering, University of California at Berkeley, Berkeley, California 94720-1740, United States ‡

bS Supporting Information ABSTRACT: Circularly shaped polymeric droplets with diameter of about 20 μm have been intermittently ejected and deposited in an orderly manner on a collector from a syringe needle by means of near-field, electrohydrodynamic reactions using pulsating voltages at around 2.25 kV. The needle has an inner diameter of 100 μm and was placed 1 mm above a silicon conductor substrate to have location control for droplet depositions. Under low-frequency operation of less than 100 Hz, the deposition frequency of droplets, fdep, has been observed to be equal to the frequency of the applied driving voltage divided by an integer, N, as small as 1. Furthermore, the diameter of the deposited droplets has been found to be linearly dependent on (Q/fdep)1/3, where Q is the polymer solution supply rate at around 30 nL/s. These experimentally observed droplet ejection rules under low-frequency pulsation provide useful design guidelines for controllable deposition of polymer droplets in various potential applications, including electrohydrodynamic printing.

1. INTRODUCTION Advancements in electrohydrodynamic deposition processes have demonstrated the feasibility of utilizing electric fields, instead of thermal or acoustic energy, to eject fibers or droplets onto conductive substrates.1 For example, electrohydrodynamic printing (EHDP), a process with controllable trajectory to eject liquid solutions in an orderly manner, has been shown to be a versatile tool to construct a wide variety of organized patterns, including planar shapes2,3 and 3D structures,4,5 by overprinting or overlapping ejected liquid solutions repeatedly. Some of the very early theoretical studies on electrohydrodynamics have paved the way for the recent applications of EHDP.6,7 For example, Poon analyzed the “cone-jet transition” region using the charge transfer mechanism to explain the stable, severalmillimeter-long jet region right below the nozzle for micrometersized colloidal jets where the fluid viscosity enhances the jet stability.8 Sun et al. reported the near-field electrospinning process to prevent the unstable whipping of liquid jets by utilizing this stage region in the deposition process.9 By reducing the capillary-to-collector distance, electrohydrodynamic deposition can achieve organized fine patterns with good position control in contrast to other conventional electrohydrodynamic deposition such as electrospinning with randomly distributed fiber depositions10 or electrospraying with uncontrolled depositions of droplets.11 Different materials and nozzles have been proposed and demonstrated for the electrohydrodynamic deposition processes with promising applications in biomedicines, r 2011 American Chemical Society

sensors, and electronics. For example, Jayasinghe et al. pioneered the printing of an alumina suspension by means of electrostatic atomization in the cone-jet mode,12 while Lee et al. structured a line conductor from a silver nanoparticle suspension by using EHDP.13 Multiple coaxial, tilted-outlet, and pole-type nozzles14
16 have also been demonstrated in various electrohydrodynamic process. However, polymer solutions and hole-type nozzles are still commonly used in the electrohydrodynamic jet experiments. Both DC and AC voltage inputs can generate micro/nano patterns using EHDP while most published papers have focused on DC voltage inputs to eject high-viscosity liquids and construct very fine patterns. Under near-field electrospinning with DC voltage inputs, a continuous fiber can be emitted for controllable and continuous nanofibers depositions,17,18 and high resolution features the patterns by means of rapid collector movement and fibrous stretch. It has also been demonstrated that suspensionfilled nanofibers can break into droplets as capillary forces guide the self-assembly of colloidal particles during the evaporation process to form arrays of single particles or particle clusters depending on the concentration of the suspensions.19 The deposited droplets were in the range of micrometers in diameter using nozzles of a few hundred micrometers in diameter.12,16,20 Recently, Park et al. demonstrated gold-coated microcapillary nozzles (i.d. = 0.3
30 μm) for high-resolution EHDP to Received: March 24, 2011 Published: April 20, 2011 6541

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Langmuir fabricate fine patterns and showed that the dimensions of printed dots and lines scaled as the nozzle sizes.21 It has also been found that it is very difficult to control the onset of jetting for precise deposition due to high fluidic viscosity under DC voltage inputs. Chang et al. utilized a probe tip to mechanically initiate the formation of a local Taylor cone to activate the electrospinning process which is not suitable for large-scale, general printing processes.22 Under high-frequency AC pulsation (in the kHz range) inputs, the liquid jet has also been found to break up into discrete droplets.23 As a result, direct deposition of discrete droplets with controllable patterns can be accomplished under pulse voltages. Droplets are intermittently ejected on demand, as a feature of AC actuation, by adjusting the input pulsation power and frequency. In contrast to the DC actuation, there are only limited reports on AC-based electrohydrodynamic technology. Early studies were mainly concerned with the effect of AC field on surface waves of liquid jets.24,25 Huneiti et al. observed that the coupling of AC/DC field enabled highly conducting liquid to eject more uniform droplets.26,27 Li28 observed three pulsated spraying modes, including dripping, pulsating jet, and cone-jet; while Juraschek and Rollgen29 demonstrated that the periodic ejection of droplets is the result of an imbalance between emission and supply rates of the liquid solution. Chen et al.23 developed a scaling model to estimate the pulsating frequency and droplet size, and Choi et al.3 reported deposited droplets with diameters more than twice the inner diameter of the capillary tube using silver ink. Under various applied frequencies, Kim et al.30 have observed that the jetting frequency does not depend linearly with respect to the frequency of the applied voltage, and this nonlinear behavior results in the irregular size and uncertain position of deposited droplets. Here, near-field, electrohydrodynamic deposition of polymeric droplets under applied low-frequency (less than 100 Hz) pulsation is determined to have controllable droplet depositions. Specific jetting between the applied voltage frequency and droplet deposition frequency has been characterized to control the deposition position and size of polymer droplets. It is found that the droplet deposition frequency, fdep, can be related to the applied actuation frequency, fapp, as a general relationship of fapp/N, where N is an integer of 1, 2, 3, 3 3 3 , depending on the supply rate of the polymer solution and other parameters, such as solution concentration, magnitude, and duty cycle ratio of the applied voltages. Furthermore, the deposited droplet diameter, Ddep, could scale linearly with respect to (Q/fdep)1/3, where Q is the polymer solution supply rate. First-order analyses have been conducted in this work to provide possible explanation of these observed phenomena.

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Figure 1. (a) Experimental setup. Pulsewise voltage supplies were applied between the stainless steel capillary and collector for electrohydrodynamic printing of droplets. (b) The deposition frequency distribution of deposited droplets under a fixed 1% PEO solution with supply rate of 22 nL/s, applied voltage of 2250 V at 100 Hz, and 50% duty cycle ratio.

Table 1. Physical Properties of PEO Solutions concentration by density

conductivity

surface tension

mPa 3 s

mS 3 m
1

mN 3 m
1

kg 3 m
3

1%

0.995

5

7.30

69

2%

0.992

11

6.69

67

3%

0.990

20

5.58

65

4%

0.987

38

4.64

64

5%

0.984

74

4.13

62

mixed with deionized water as solvent was tested with various concentrations of 1
5% by weight as listed in Table 1. A high-speed camera (NAC MEMRECAM GX-1) with frame rate of 2500 fps (frames per second) was used to observe the polymer ejection process and distinguish possible multiple ejections of droplets. Mitutoyo microscope with a CCD video camera (Sony SSC-DC80) was used to measure droplet diameter and spacing between the deposited droplets with the assistance of image processing software (Ruler). Experimentally, the droplet deposition frequency fdep is defined as

2. EXPERIMENTAL DETAILS The experimental setup is schematically illustrated in Figure 1a, where a high-voltage power supply (Shenghuo HVP-402NP1) is used to control the electrostatic field. A 10-mm-long stainless steel capillary (i.d. = 100 μm, o.d. = 180 μm) was connected to the positive electrode and 350-μm-thck, 3-in.-diameter silicon wafers were used as the grounded collector. An XY stage (Googol GXY1515GT4) controlled the movement of the collector at a velocity of 4
50 mm/s. The capillary-tocollector distance was set as 1 mm to have better location control of the deposition. Polymer solution was supplied by a syringe pump (Harvard 11 Pico Plus) which has a resolution of 0.01 μL/h or 0.0028 nl/s. In the preliminary experiments, poly(ethylene oxide) (PEO, MW = 300 000 g/mol)

viscosity

weight

fdep ¼ vcol =l

ð1Þ

where vcol is the velocity of the collector and l is the center-to-center distance between two consecutively deposited droplets. Data from at least 5 repeated tests have been collected to estimate the deposition frequency, fdep. In every experiment, droplets collected from the first half-hour were discarded to acquire steady deposition conditions under a stable solution supply. Furthermore, the deposition positions of more than 50 droplets in each experimental condition were analyzed to calculate the average fdep and standard deviation. Figure 1b shows the deposition frequency distribution of droplets using 1% PEO solution with supply rate at 22 nL/s under an applied voltage at 2250 V. The 6542

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Figure 2. Deposition frequency with respect to polymer solution supply rate under an applied voltage of 2250 V at 15 Hz and 50% duty cycle ratio: (a) 5% PEO solution is deposited under a collector velocity of 4 mm with varying polymer solution supply rates; (b) a discrete relationship was observed for the deposition frequency as fapp/N, where N is 1, 2, 3, and 4 depending on the supply rate and concentration of the polymer solution; (c) fdepDdep3 is approximately proportional to Q with a linear relationship. applied voltage frequency was 100 Hz under a 50% duty cycle ratio. The mean value of deposition frequency was 12.73 Hz with standard deviation of 0.342 Hz, and it followed the “fapp/N” observation where N was equal to 8 in this case.

3. EXPERIMENTAL RESULTS 3.1. Deposition Frequency and Solution Supply Rate. In the first set of experiments, the flow rates were changed in the range 5
27 nL/s and the deposition frequencies were measured under a fixed applied voltage of 2250 V and fixed applied voltage frequency, fapp, at 15 Hz and 50% duty cycle ratio. Figure 2a illustrates a typical set of experimental photos with 5% PEO solution collected under moving velocity of 4 mm/s. In this set of experiments, the first two photos had polymer droplet deposition frequencies of about 4.0 Hz which is close to 3.75 Hz or “fapp/N” where N = 4. The next three photos had deposition frequency of about 5.2 Hz, which is close to 5 Hz or “fapp/N” where N = 3. The rest of the five photos had deposition frequency of about 7.8 Hz, which is close to 7.5 Hz or “fapp/N” where N = 2. More results (error bars are not drawn in this figure for better clarity) were summarized in Figure 2b. In general, the deposition frequency, fdep, increased discretely from about 3.75, 5, 7.5, to 15 Hz using 1
5% PEO solutions as the polymer solution supply rate, Q, increased from 5 to 27 nL/s. Some slight deviations in the recorded frequency have been observed, and several sources could contribute to these variations: (1) inaccuracy in applied voltage frequency originating from the display error of voltage power supply; (2) uncertainty of measurements; (3) local variations in experimental parameters such as nonuniform polymer supply rate from the syringe pump which was driven by a stepping motor; and (4) environmental perturbations. Nevertheless, the relationship can be experimentally characterized to follow the relation of fdep = fapp/N, where N is a frequency dividing integer which can be 4, 3, 2, or 1 as shown in Figure 2b, depending on the polymer solution supply rate and concentration. The interesting phenomenon is that higher supply rate resulted in higher fdep (smaller N), while higher polymer concentration was in favor of lower fdep (larger N).

It is also observed that the diameter of deposited droplets, Ddep, increased as the polymer solution supply rate increased under a fixed fdep, while Ddep decreased when fdep increased under a fixed polymer solution supply rate. A simplified complex relationship can be summarized and represented in Figure 2c. The product of fdep (or fapp/N) and Ddep3 is linearly proportional to Q in the range 5
27 nL/s with a slope in the range 7.8
11.2. The polymer concentration variations seem to have minimum impact on this relationship.

3.2. Deposition Frequency and Applied Voltage Frequency. The second experiments investigate the influence of varying applied voltage frequency, fapp, (in the range 5
100 Hz) on the deposition frequency, fdep, under a fixed applied voltage of 2250 V and 50% duty cycle ratio. Figure 3a presents experimental photos of deposited droplets by using 5% PEO solution under a supply rate of 33 nL/s and moving velocity of the collector of 10 mm/s. The calculated deposition frequencies of different testing conditions are summarized in Figure 3b. Each data point in the figure is the measured mean value of more than 50 deposited droplets (histogram of individual data point and standard deviations are provided in the Supporting Information). In general, the standard deviation is typically less than 0.5 Hz and less than 5% of the mean deposition frequency. In this set of data, the deposition frequency seems to be a few percentage points higher than the predicted values of fdep = fapp/N, consistently. These could be the results from aforementioned variations in experiments. In other case, such as deposition frequency data for the 22 nL/s tests in Figure 3b, the deposition frequencies were recorded in the range a bit higher or a bit lower than the predicted values of fdep = fapp/N. Furthermore, under low applied frequency, the deposition frequency could follow the applied frequency and the N value is as low as 1. As the applied frequency increased, the N value also increased consistently and the deposition frequency seems to be confined in the range 5
16 Hz in this case. It is noted that, under high N values, less data is available and the measurement uncertainty of (0.5 Hz itself could cause false identification for the true N number as shown in Figure 3a. However, the general trend of fdep = fapp/N is observed for lower N values. Figure 3c shows the average deposition frequencies from various samples, and the general trends suggest that, under low-frequency 6543

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Figure 3. Deposition frequency results with respect to various applied voltage frequencies with 50% duty cycle ratio under an applied voltage of 2250 V: (a) 5% PEO solution deposits under a fixed polymer supply rate of 33 nL/s and collector velocity of 10 mm/s with varying frequencies of applied voltage; (b) the deposition frequencies and the 1/N relationships of the droplets shown in the above photos; (c) more experimental data with 1% and 5% PEO solutions show that the droplet deposition frequencies are on the lines with slope of 1/N where N is a frequency dividing integer; (d) the deposition frequency has a saw-shaped transition following the 1/N slope lines with respect to the applied voltage frequency under a fixed 1% PEO solution at supply rate of 33 nL/s. pulsation, fdep can follow up with fapp with a slope of 1. Under high applied frequencies, the deposition frequencies followed different slopes of 1/N where N is the frequency-dividing integer as defined previously. From the 90 testing runs of various conditions, the 1/N trend was observed when N had lower values of 1, 2, or 3. When the N value was higher than 3, larger deviations were observed from the 1/N lines. Figure 3d shows the extracted testing data from Figure 3c with 1% PEO solutions under polymer supply rate of 33 nL/s. It is observed that fdep followed the lines with slopes of 1/N where N increased from 1, 2, 3 3 3 , up to 6. The saw-shaped transition of the deposition frequency, fdep, was experimentally observed from as low as 5 Hz to as high as 18 Hz as fapp increased.

3.3. Deposition Frequency and Applied Voltage Amplitude and Duty Cycle. The influences of applied voltage amplitude (in the range 2050
2350 V) and the duty cycle ratio (in the range 10
90%) were also characterized using 1% and 5% PEO solutions. When the applied voltage frequency was fixed at 15 Hz with 50% duty cycle ratio, the deposition results are shown in Figure 4a using 5% PEO solution with supply rate of 11 nL/s and under moving velocity of the collector of 4 mm/s. Results show that the deposition frequency approached 3.8, 5, or 7.5 Hz as expected. This is consistent with the previous results, while higher applied voltage was shown to be in favor of

higher deposition frequency. On the other hand, Figure 4b shows results when the duty cycle ratio increased from 10% to 90% under a fixed applied voltage at 2250 V and a fixed applied voltage frequency at 20 Hz. The polymer was 5% PEO solution with supply rate of 33 nL/s and the collector velocity was 10 mm/s. It is observed that the deposition frequency was around 10 Hz for 10
60% duty cycle ratios and 20 Hz for 70
90% duty cycle ratios. More measured data for these two experiments are recorded in Figure 4c and d, respectively. It is observed in Figure 4c that higher applied voltage and higher supply flow rate promoted higher deposition frequency. Figure 4d shows that low polymer concentration (1% PEO) and high supply rate (33 nL/s) resulted in 20 Hz deposition frequency or N = 1, independent of the duty cycle ratio. Low polymer concentration (1% PEO) and low supply rate (11 nL/s) resulted in deposition frequency at 6.7 Hz or N = 3, which was also independent of the duty cycle ratio. However, for relatively higher polymer concentration (5% PEO), duty cycle ratio can impact the droplet deposition frequency as demonstrated. Therefore, the viscosity of the polymer solution as well as the duty cycle ratio can both affect the droplet deposition frequency. In summary, all aforementioned experiments show that the deposition frequency fdep is related to the applied frequency fapp with a frequency dividing integer, N. The minimum value of N is 1 when the 6544

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Figure 4. Effects of voltage amplitude and duty cycle ratio on the deposition frequency: (a) deposition results of 5% PEO solution at supply rate of 11 nL/s deposits under various applied voltages at 15 Hz and 50% duty cycle ratio and a collector velocity of 4 mm/s with varying applied voltage magnitudes; (b) deposition results of 5% PEO solution at supply rate of 33 nL/s deposits under an applied voltage of 2250 V at 20 Hz and various duty cycle ratios and a collector velocity of 10 mm/s; (c) 1% and 5% PEO solutions spray under various applied voltages at 15 Hz and 50% duty cycle ratio, (d) 1% and 5% PEO solutions spray under an applied voltage of 2250 V at 20 Hz and various duty cycle ratios from 10% to 90%. maximum ejection frequency is equal to the applied voltage frequency. The relationship among the deposited droplet size, deposition frequency, polymer supply rate, and applied frequency is very complex, while it is observed that the product of fdep and Ddep3 was approximately proportional to Q.

4. DISCUSSIONS In an attempt to analyze the observed phenomena, first-order models were formulated to examine the possible relationships of key parameters from the experiments. In the low-frequency pulsation operation of EHDP, a pendant is extruded outside the capillary nozzle with a spherical shape due to the surface tension force. Electrical field can help the formation of a Taylor cone to cause electrospinning if the applied voltage is higher than a critical voltage. Under low-frequency pulsation, discrete droplets can be deposited periodically if the applied voltage is high enough to eject the polymer droplets. Figure 5 illustrates the time sequences of the droplet deposition process. Several time variables have been defined as shown in Figure 5. Specifically, ton and toff are periods when the applied voltage is on and off, respectively; tacc and tfor are periods representing the accumulation of droplet volume and Taylor-cone formation; and tjet is the combination period including of formation of polymer jet plus the ejection of the droplet.

Figure 5. Timing sequence of the ejection of droplets. Vcr is the critical volume for ejection to occur; toff and ton are the off and on times for the duty cycle; tacc, tfor, and tjet are periods representing the accumulation of droplet volume, Taylor-cone formation, and the combination of formation of polymer jet plus the ejection of the droplet. The ejection of droplets: (a) single voltage pulse, and (b) two voltage pulses. 6545

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Figure 6. Polymer ejection process photographed at a frame rate of 2500 fps under a fixed 1% PEO solution with supply rate of 11 nL/s, and applied voltage of 2400 V at 20 Hz and 50% duty cycle ratio. Three periods are shown in one ejection cycle: (a) the first 25.6 ms for accumulation of droplet volume, (b) the following 9.2 ms for Taylorcone formation, and (c) the final 16.4 ms for continuous polymer ejection.

There are several control parameters in the EHDP process, including the polymer solution concentration and supply rate; applied voltage and frequency; and duty cycle ratio. In general, surface tension force dominates in this scale such that inertial effect due to gravity will not be able to provide the necessary force to eject the polymer solution. The accumulation period occurs when the polymer solution is pushed out of the syringe continuously and the flow rate of the syringe controls the size of the droplet. When a pulse voltage is applied as illustrated in Figure 5a, the spherically shaped polymer solution outside the capillary is prolonged to a hyperboloid profile.31 The time required for the prolonged section of the polymer solution outside the capillary to reach a critical volume, Vcr, is defined as tfor, which is influenced by the magnitude and time of the applied voltage, viscosity of the fluid, as well as the fluid supply rate. If the radius of curvature, Rapex, at the apex of the Taylor cone reaches a critical value, Rcr, then the electric force exceeds the surface tension force and the liquid meniscus is broken up to eject the polymer solution on to the collector substrate. This is the period defined as tjet. The deposited polymer on the substrate can form a hemispherical shape due to surface tension force in favor of minimum energy state.

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If the flow rate is too slow and/or the applied voltage frequency is too high such that the liquid solution does not have enough time to reach the critical volume Vcr under the applied voltage in a single pulse cycle, there will be no droplet deposition, as surface tension force prevents the breakage of the polymer solution. The prolonged droplet will retract back when the applied voltage is in the “off” cycle. As a result, the droplet deposition frequency does not keep up with the applied voltage frequency. Several pulse cycles could be needed for the liquid to reach Vcr as illustrated in Figure 5b and they result in a large volume of polymer solution in the droplet from the continuous supply of the liquid. This is the fundamental reason that the droplet deposition frequency is discretely related to the applied voltage frequency as fapp/N as experimentally verified in this work. Figure 6 is the set of droplet ejection photos using a highspeed camera with 1% PEO solution under polymer supply rate of 11 nL/s, applied voltage of 2400 V at 20 Hz, and 50% duty cycle ratio. In the accumulation period, droplet size increased in the first 64 frames (25.6 ms) from the end of a previous polymer ejection as the vague image of a polymer jet can be barely observed in frame #1. For the 20 Hz, 50% duty cycle voltage source, each cycle will last 50 ms. Therefore, the voltage application will start initiating at 25 ms. From frame #65 to #87, one can observe the formation of Taylor cone and it lasts 23 frames (9.2 ms) when the pendant expands due to applied voltage to the formation of Taylor cone. At frame #88, one can observe the formation of a polymer jet in a vibratory fashion and the total polymer ejection period last for 41 frames (16.4 ms). The polymer jet stabilized in the later stage of the ejection period probably due to the direct connection and support of the polymer jet from the collector substrate. Several interesting phenomena were also observed here. First, after the ejection of the polymer jet, liquid polymer solution seemed to contract back to the capillary as suggested in frame #128. Second, within one frame period (from frame#88 to #89), the majority of the pendant seemed to disappear as shown, and this suggests that extra polymer solution was drawn from inside the syringe during the rest of the polymer jet ejection process. This is very different from the typical electrospinning process where Taylor cone is maintained during the whole process.22 Third, the polymer jet was always present from frame #88 to #128 (most of these repeated photos were not shown in this paper) and this suggested that only a single polymer ejection occurred during this cycle under the frame rate of 2500 fps. The possibility of multiple ejections of droplets during this single cycle is not likely because frame #88 to #89 suggests that the pendant was consumed already. Without the pendant, it will take time to accumulate the polymer solution as shown in the accumulation stage. These photos suggest that the pendant was converted to polymer jet from frame #88 to #128 and the sudden drop of the voltage supply cut off and the polymer jet formation released to go back to the original form in frame #1. In the extreme cases when the pulse duration is very short or the viscosity of the solution is very high, the required Taylor cone formation time tfor could exceed the active pulse duration. In these cases, no discrete ejection can be observed and only random, large depositions are recorded. Similarly, when the pulse duty cycle is very high (close to the situation of DC power supply), continuous jet stream can occur and the result is the typical near-field electrospinning process.22 These cases are disregarded in this study. On the other hand, reports have shown 6546

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that multiple ejections of droplets under DC power supply can occur under the right polymer type; concentration and supply rate; and applied voltage and syringe size.22 These have not been observed in this work as illustrated in Figure 6. The Taylor cone formation effect, which occurred repeatedly from the spherical shape to the Taylor-cone shape during every pulse cycle in the current experiment, dominates the observed periodic droplet ejection. The relationship, as demonstrated in the experiments, between deposition frequency fdep and applied voltage frequency fapp, can be expressed as fdep =fapp ¼ 1=N

ðN ¼ 1, 2, 3, 3 3 3 Þ

ð2Þ

when the period of applied voltage is longer than the formation of Taylor cone, or ton > tfor

ð3Þ

fdep ¼ 1=tdep ¼ 1=ðtacc þ tfor þ tjet Þ

ð4Þ

fapp ¼ 1=tapp ¼ 1=ðton þ toff Þ

ð5Þ

where

Equation 2 describes the relationship between the applied voltage frequency and the droplet deposition frequency with the 1/N relationship as experimentally observed. Equation 3 describes the constraint on the droplet formation that the period of active voltage must be longer than the period of Taylor cone formation. Otherwise, the pendant will retract without forming the polymer jet or droplet. Equation 4 implies that accumulation, Taylor cone formation, and ejection are required for the ejection of droplet, and this could take multiple periods from the pulsated applied voltage. Therefore, the highest possible deposition frequency is equal to the applied voltage pulsation frequency and other lower possible deposition frequencies are fapp/N. Furthermore, the polymer supply rate also plays an important role as shown in Figure 2b, as fast supply rate reduces the accumulation period, tacc, for the critical volume Vcr. This implies that higher supply rate promotes higher deposition frequency as observed. High applied voltage amplitude can also reduce the Taylor cone formation time, tfor, such that it also promotes higher deposition frequency as observed in Figure 4c. Larger duty cycle ratio can prolong the applied pulse duration for the formation of Taylor cone (longer Taylor cone formation time), and this is helpful for high-frequency droplet ejection as shown in Figure 4d. Low fluidic viscosity and higher polymer solution supply rate also encourage higher droplet deposition rate as shown in Figure 4d. When the polymer solution jet hits the collector, deposition occurs as the combination of splashing, evaporation, and condensation. The impacting velocity of a jet is expressed as 2 vjet ¼ Q =πrjet

ð6Þ

where rjet is the radius of the ejected jet stream. In the experimental setup, Q is in the range 5
27 nL/s and rjet = 1
10 μm, so vjet is less than 10 m/s. This impact velocity does not produce a high Sommerfeld number32 such that the dominant phenomenon is deposition in the experiments. Furthermore, the volume, Vdep, of the droplet with a hemispherical shape on the collector can be approximated as Vdep ¼ Q =fdep

ð7Þ

By the geometrical correlation, the droplet volume is proportional to the droplet diameter to the cubic power, Ddep3, a scaling relation is derived as Q ∼ fdep Ddep 3

or

Q =fapp ∼ Ddep 3 =N

ð8Þ

Therefore, fdepDdep3 is linearly proportional to Q as experimentally demonstrated in Figure 2c. In all of the experiments, data have been collected by using a stepping motor to control the polymer supply rate, and this could cause slight discontinuation in the supply of polymer solution. A small set of experiments have been conducted by utilizing gravity as the pressure source to produce continuous flow rate (using the height differences to control the pressure instead of stepping motor). Results have shown good consistency with the current experimental results to confirm the fapp/N relationship while the deposited droplets have more uniform size on the collector. Another set of experiments were conducted by adding ethanol into deionized water to modify the surface tension of liquid. Furthermore, sodium chloride was also added as mixing solute to change the electrical conductivity of liquid. In all these experiments, it is observed that the deposition frequencies indeed follow the aforementioned based relationship of fapp/N. However, it is noted that excessively low surface tension of liquid results in the tendency of multijet depositions with smallerfrequency dividing integers, while high electrical conductivity of liquid results in high-frequency dividing integers. Furthermore, although results presented from this work only represent a range of several control parameters, experimental results coupled with analytical characterizations could build solid foundation for further investigations. It is believed that these results could provide important design guidelines for various printing applications, including EHDP.

5. CONCLUSIONS The jetting rule of polymer solution is experimentally characterized under low-frequency pulsation. Experiments reveal that the droplet deposition frequency, fdep, is related to the applied voltage frequency as fapp/N where N is a frequency dividing integer. It is noted that high applied pulse voltage supply, large duty cycle ratio, fast solution supply rate, and low fluidic viscosity results in small frequency dividing integer and high droplet deposition frequency. This phenomenon is qualitatively explained and experimentally validated with a high-speed camera that periodic ejection of polymer jets for droplets can result from multiple periods of active voltage to accumulate large enough droplets to break the surface tension force. Furthermore, it is observed that the deposited droplets on the collector have their diameter scales as (Q/fdep)1/3. Further investigations on mathematical, numerical, and experimental studies will be necessary to build a more comprehensive understanding for the electrohydrodynamic deposition of droplets under low pulse pulsation for possible practical applications. ’ ASSOCIATED CONTENT

bS

Supporting Information. Additional figures as described in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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’ AUTHOR INFORMATION Corresponding Author

*E-mail addresses: [email protected] (D. Sun), lwlin@ me.berkeley.edu (L. Lin).

’ ACKNOWLEDGMENT This work is funded by Key Project of Chinese Ministry of Education (No. 708055), National Hi-Tech Research and Development Program of China (2007AA04Z308), and State Key Lab of Digital Manufacturing Equipment & Technology of Huazhong University of Science and Technology (DMETKF2009003).

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