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Langmuir 2009, 25, 2540-2549
Relaxation Times in Single Event Electrospraying Controlled by Nozzle Front Surface Modification Urszula Stachewicz,*,†,§ J. Frits Dijksman,† Dirk Burdinski,‡ Caner U. Yurteri,§ and Jan C. M. Marijnissen§ Department of Healthcare DeVices and Instrumentation, and Department of Biomolecular Engineering, Philips Research Europe, High Tech Campus, 5656 AE EindhoVen, The Netherlands, and Nano Structured Materials, DelftChemTech, Faculty of Applied Sciences, Delft UniVersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands ReceiVed July 7, 2008. ReVised Manuscript ReceiVed October 8, 2008 Single event electrospraying (SEE) is a method for on-demand deposition of femtoliter to picoliter volumes of fluids. To determine the influence of the size of the meniscus on the characteristics of the single event electrospraying process, glass capillaries were used with and without an antiwetting coating comprising a self-assembled 1H,1H,2H,2Hperfluorodecyltrichlorosilane-based monolayer to control the meniscus size. A large difference was found in driving single event electrospraying from a small meniscus compared to what is needed to generate a single event electrospraying from a large meniscus. Furthermore, after studying the different time constants related to the electrical and the hydrodynamic phenomena, we are able to explain the timing limitations of the deposition process from both a small and a large meniscus. The hydrodynamic relaxation time is significantly reduced in the case of the modified capillary, and the timing of SEE, which determines the deposition time, is limited by the resistor-capacitor RC time of the electrical circuit needed to drive the SEE. We have built a model that describes the almost one-dimensional motion of the liquid in the capillary during pulsing. The model has been used to estimate the hydrodynamic relaxation times related to the meniscus-to-cone and cone-to-meniscus transitions during SEE. By confining the meniscus to the inner diameter of the nozzle, we are able to deposit a volume smaller than 5 pL per SEE.
Introduction Electrospraying, also called electrohydrodynamic atomization (EHDA), is a technique for generating aerosols of fine droplets through electrostatic forces. Among its many applications, electrospraying is also used as a method for depositing a wide range of materials on various substrates.1 Compared to other technologies, such as ink jet printing, the main advantage of electrospraying is its ability to generate continuous jets and/or streams of droplets, with dimensions that are much smaller than the inner diameter of the nozzle used.2 The diameters of the jets and droplets can be tuned by adjusting the process parameters, such as the properties of the solution (conductivity, surface tension, and viscosity), the capillary configuration, the design of the electrical circuit, and the flow rate. In electrospraying, an electric potential difference is applied between the capillary filled with liquid and a grounded plate, which is placed at a certain distance from the tip of the capillary. Due to the high electric field strength in the region of the capillary tip, a surface charge builds up on the meniscus of the liquid, causing the meniscus to become conical. Upon increasing the voltage further, a jet emerges from the apex of the cone, which finally breaks up into droplets.3 The capillary dimensions and the wettability of the front of the nozzle (the tip of the capillary) have a large influence on the shape of the cone, the jet stability, and the electrospraying mode.4-6 Liquids * To whom correspondence should be addressed. E-mail: u.stachewicz@ tudelft.nl. Telephone: +31 15 27 81828. Fax: +31 15 278 4945. † Department of Healthcare Devices and Instrumentation, Philips Research Europe. § Delft University of Technology. ‡ Department of Biomolecular Engineering, Philips Research Europe. (1) Jaworek, A. J. Mater. Sci. 2006, 42, 266–297. (2) Basaran, O. A. AIChE J. 2002, 48, 1842–1848. (3) Hartman, R. P. A.; Borra, J. P.; Brunner, D. J.; Marijnissen, J. C. M.; Scarlett, B. J. Electrost. 1999, 47, 143–170. (4) Cloupeau, M.; Prunet-Foch, B. J. Aerosol Sci. 1994, 25, 1021–1036.
have a tendency to accumulate on the capillary tip and even to spread across the outer surface of the capillary. This leads to the formation of relatively large droplets at the capillary tip. It was reported by Lozano et al. that an antiwetting surface helps to localize the meniscus by anchoring it to the inner rim of the nozzle and thereby enhancing the electric field.5 Harmonic spraying, a pulsed electrospraying technique, has attracted particular attention due to its suitability for the production of a stream or spray of uniform droplets.7-11 In the context of droplet production, various driving schemes for electrospraying have been proposed. Yogi et al. presented an on-demand droplet spotter using the cone-jet mode. In their experimental method, two voltage pulses and a bias voltage were used. One pulse was applied to a wire inside the capillary, and the second one to an external electrode attached to the capillary. This external electrode was made by sputtering a thin gold layer onto the outer surface of the nozzle. In the driving scheme of the droplet spotter, pulses of 600 V, which were applied to the wire inside the capillary, were superposed on a bias voltage of 100 V for 5 ms. The counter electrode was placed at a distance of 25 µm from the capillary. The external electrode helped to focus the jet along the center line of the capillary, by increasing the Coulomb force between the center of the meniscus and the substrate.12,13 (5) Lozano, P.; Martinez-Sanchez, M.; Lopez-Urdiales, J. M. J. Colloid Interface Sci. 2004, 276, 392–399. (6) Lozano, P.; Martinez-Sanchez, M. J. Colloid Interface Sci. 2005, 282, 415–421. (7) Sato, M. J. Electrost. 1984, 15, 237–247. (8) Huneiti, Z.; Balachandran, W.; Machowski, W. J. Electrost. 1997, 40-41, 97–102. (9) Huneiti, Z.; Balachandran, W.; Hu, D.; Machowski, W. Proceedings of the 11th European Conference of ILASS-Europe on Atomization and Sprays, Nu¨rnberg, 1995; pp 211-222. (10) Balachandran, W.; Machowski, W.; Ahmad, C. N. IEEE Trans. Ind. Appl. 1994, 30, 850–855. (11) Sample, S. B.; Bollini, R. J. Colloid Interface Sci. 1972, 41, 185–193.
10.1021/la8021408 CCC: $40.75 2009 American Chemical Society Published on Web 01/21/2009
Relaxation Times in Single EVent Electrospraying
Following a different approach, Chen et al. used a Teflon nozzle with an inner diameter (ID) of 50 µm to demonstrate the formation of a cone-jet from a meniscus attached to the inner rim of the tube, by applying pulses of 7.5 ms.14,15 A high voltage was applied through a steel fixture, to which the Teflon tube was attached. For pulses of 20 ms and longer, they reported the volume of the collected droplets to be proportional to the pulse duration. A time delay of approximately 3.6 ms for the Taylor cone formation was taken into account. Electrospraying behavior caused by a voltage pulse was also described in the work of Paine et al.16 During each applied pulse, a number of liquid ejections in the discontinuous spraying mode of electrospraying was reported. The duration of each ejection was 12-160 µs and increased steadily with the applied voltage. Voltage pulses of 400-500 V were used, and the counter electrode was placed at a distance of 0.3 mm from the nozzle. In the present paper, we go one step further and propose electrospraying as a novel and real on-demand deposition method. Our goal is to gain better control over the amount of fluid and the timing of the deposition. A particular aim of this study was to minimize the volume of fluid ejected per voltage pulse. To achieve this, the tip of a glass capillary (front nozzle) was modified with an antiwetting coating to restrict the meniscus to the inner rim of the glass pipet. Without such modification, the meniscus attaches to the outer diameter (OD) of the nozzle. In our system, the OD was 600 µm and the ID was 50 µm. We generated stable and short events of jetting for each applied pulse independent of the time delay between the pulses. Such a pulse-controlled fluid deposition is called single event electrospraying (SEE). To generate single electrospraying events, rectangular voltage pulses were superimposed on a constant bias voltage. The optimum setting of the bias DC voltage for starting a SEE was related to the effective surface tension before the onset of dripping. The effective surface tension equals the surface tension of the liquid, corrected for charge effects on the meniscus, and the attraction between the charge distributions on the meniscus and the counter electrode.17 We used a capillary with a larger outer diameter relative to that of previous work.12,14,16 In the experimental setup with a standard glass nozzle, at which the meniscus was attached to the outer rim, the total deposited volume ranged from several hundred picoliters to nanoliters per SEE. By modification of the wetting properties of the nozzle front, we were able to reduce the amount of liquid deposited per SEE to less than 5 pL. We did not use a controlled syringe pump to replenish the fluid that left the system during SEE, but the refilling took place autonomously by the pressure head of the fluid column above the nozzle and surface tension. The purpose of this study was to investigate the effect of the glass nozzle modification on the characteristic times of the electrospraying process and explain the difference between SEE from a large and a small meniscus.
Materials and Methods Experimental Setup. In our electrospraying setup, an electric potential difference was applied between a nozzle filled with liquid and a counter electrode, placed at 1-2 mm distance. The counter (12) Yogi, O.; Kawakami, T.; Mizuno, A. Anal. Chem. 2004, 76, 2991–2996. (13) Yogi, O.; Kawakami, T.; Mizuno, A. J. Electrost. 2006, 64, 634–638. (14) Chen, C. H.; Saville, D. A.; Aksay, I. A. Appl. Phys. Lett. 2006, 88, 154104. (15) Chen, C. H.; Saville, D. A.; Aksay, I. A. Appl. Phys. Lett. 2006, 89, 124103. (16) Paine, M. D.; Alexander, M. S.; Smith, K. L.; Wang, M.; Stark, J. P. W. J. Aerosol Sci. 2007, 38, 315–324. (17) Stachewicz, U.; Dijksman, J. F.; Yurteri, C. U.; Marijnissen, J. C. M. Appl. Phys. Lett. 2007, 91, 254109.
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Figure 1. Schematic drawing of the experimental setup. A glass capillary (Microdrop Technology) with a nozzle of ID 50 µm and OD 600 µm was used. The pressure at the nozzle front (meniscus pressure) was regulated with a pressure-control unit. The optical system for image capturing consisted of a microscope lens with a progressive scan CCD camera and a stroboscopic illumination system with an adjustable flash delay.
Figure 2. During the experiments, rectangular voltage pulses, Up, were either superposed on top of a bias voltage, Ub (method A), or applied without additional bias voltage (method B). In method A, the bias voltage was used to generate electrospraying events in experiments, in which the meniscus and the cone shape/size were defined by the OD of the nozzle.
electrode was grounded. The distance between the nozzle and the counter electrode was adjusted to obtain the desired spacing for stable jetting. The electrospray nozzle and the counter electrode were made adjustable in the X-Y-Z directions via computer controllable stages (Newport, GTS Series high-precision stages). The system comprised a glass pipet (Microdrop Technology). The end of the pipet is termed the nozzle, and the inside of the pipet with the nozzle we consider here as the capillary channel or capillary. The flat area around the nozzle is referred to as the nozzle front. The X-axis was used to focus the optics, the Y-axis to adjust the image in the field-of-view, and the Z-axis to adjust the gap between the pipet tip and the counter electrode. All motions were computer controlled by software written in LabVIEW 7.1.1. A high voltage power source (Trek model 5/80) was connected to the fluid in the glass capillary by a metal wire inside it. The pressure above the liquid in the capillary was controlled using an under-pressure control unit (Microdrop AD-E-130-NP) (Figure 1). All mechanical parts were mounted on a heavy plate, supported by soft rubber springs, in order to suppress mechanical vibrations from the environment. The whole mechanical setup was placed in a fume hood. A DC field with extra voltage pulses was applied to generate jets and droplets. We superposed rectangular voltage pulses at any given bias voltage (Ub g 0 V). Pulses were applied at a frequency of 0.6-10 Hz (Figure 2). Liquid was deposited on a grounded metal substrate (the counter electrode). The SEE experiments were recorded using an optical system, which consisted of an illumination system and an imaging system. In the imaging system, a microscope lens was combined with a progressive scan charge-coupled device (CCD) camera with an asynchronously triggered shutter (Jai CV-M10-SX), which was triggered by the leading edge of the voltage pulse. The 1/2 in. camera was able to provide images with a maximum resolution of 767 × 575 pixels (pixel size of 8.37 × 8.37 µm2). The
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Figure 3. Timing chart of the optical system electronics. The software generated a trigger pulse that was synchronized with the leading edge of the voltage pulse. This trigger pulse opened the camera shutter for 5 ms and started the flash delay. After the time delay, tds, the stroboscope flashed during 0.25-1.00 µs. After the camera shutter was closed, an extra pulse was sent to the computer to initiate the image transfer, which took approximately 30 ms.
microscope objective delivered a 7:1 zoom ratio with a field-ofview from 4.2 × 5.6 mm2 to 0.61 × 0.81 mm2 (Optem 70XL 2920-39) and was mounted onto a second zoom objective with an extra 2:1 zoom (Optem 29-90-80). The software used to control the optical system was implemented in LabVIEW 7.1.1. The illumination system comprised a stroboscope (LumiLED, LUXEON - Lambertian Star) with a computer-controlled adjustable flash delay. The stroboscope was rigidly fastened to the mounting plate. The camera and lens could be moved along the X- and Y-axes, together with the counter electrode support structure. The optical components outlined in the previous paragraph were capable of capturing a still image of a droplet in flight. The principle was to generate droplets with a fire pulse from the voltage amplifier, the leading edge of which was used to trigger the opening of the camera shutter and to start the stroboscope delay timer. After the delay time, the stroboscope flashed during 0.25-1.00 µs, illuminating the droplet and generating a shadow image of the droplet on the CCD image sensor. Finally, the shutter of the camera was closed, and the image was transferred to the computer. The timing chart is graphically outlined in Figure 3. The adjustable flash delay enabled us to take pictures at different moments in time during and after the applied pulse. Electrospray Liquid. All experiments were carried out using a mixture of ethylene glycol (Merck, purity GC g 99.5%) and deionized water in proportions of 70%/30% (v/v), respectively. The properties of the solution were as follows: conductivity κ ) 8.7 × 10-6 S/m (25 °C), measured with a Meterlab ION 450 conductivity meter, and surface tension σ ) 55.4 mN/m, measured with a Dataphysics OCA30 contact angle system. In this system, we used the pendant drop method and the surface tension was determined by fitting the observed shape of the meniscus to a second order curve. A viscosity value of η ) 6.11 mPa · s (25 °C) was measured with a Physica MCR 300 rheometer with a cone-plate arrangement. The upper cone had a diameter of 50 mm, and the cone angle was 1°. The density of the solution, Fs ) 1078.64 kg/m3, was calculated according to the equation Fs ) Fegceg + Fwcw, where Feg and ceg are the density and mass concentration of ethylene glycol, respectively, and Fw and cw are the density and mass concentration of water, respectively. The relative permittivity of the electrospraying liquid (solution of ethylene glycol and water) was εl ) 50.02 (25 °C), the permittivity of a free space was ε0 ) 8.85 × 10-12 C2/Nm2, and the relative permittivity of the air was εr ) 1. Glass Nozzle Modification. In order to confine the meniscus to the inside rim of the nozzle, we modified the outer surface of the glass capillary, close to its orifice, with an antiwetting coating based on a self-assembled monolayer (SAM). It is important to prevent an extension of the antiwetting coating toward the inner capillary surface, since this could block the liquid feeding to the tip, due to
Figure 4. Schematic drawing based on a microscope image of the capillary. An antiwetting coating based on a SAM was formed on the front side of the nozzle. This coating defines the attachment of the meniscus to the inside rim of the nozzle orifice (ID ) 50 µm, OD ) 600 µm).
Figure 5. Micrographs representing the effect of the antiwetting coating on the meniscus size, which depends on the OD at an unmodified capillary (left) but is restricted to the ID of the capillary if the nozzle front is modified with SAM layers (right).
repulsion of the hydrophilic liquid by the hydrophobic capillary wall. To effect such a selective modification, we utilized microcontact printing.18-20 A similar approach recently has been used independently in the development of a graphic printing technique, based on EHDA. In that process, a hydrophobic SAM was formed on a glass capillary coated with gold.21 In our modifications, there was no pretreatment necessary for the glass nozzle. A poly(dimethysiloxane) (PDMS) stamp was prepared from Sylgard-184 PDMS (Dow Corning), which was mixed in a 1:10 curing agent/prepolymer ratio and cured overnight at 65 °C. The stamp was impregnated with a 10 mM solution of 1H,1H,2H,2H-perfluorodecyltrichlorosilane (PTS, ABCR Germany) in hexane for 0.5 h. After removal of the stamp from the solution, the nozzle was quickly brought into contact with the surface of the stamp for about 30 s to transfer the amphiphilic PTS molecules from the stamp onto the glass surface selectively in the area of contact, where they formed a densely packed SAM (Figures 4 and 5). After stamp contact, the nozzle was placed on a hot plate (110 °C) for 10 min to drive the formation of covalent bonds between the alkylsilane molecules and hydroxyl groups of the glass surface, thus curing the coating. Although the resulting SAM is not thicker (18) Xia, Y.; Rogers, J. A.; Paul, K. E.; Whitesides, G. M. Chem. ReV. 1999, 99, 1823–1848. (19) Rogers, J. A.; Nuzzo, R. G. Mater. Today 2005, 8, 50–56. (20) Gates, B. D. Mater. Today 2005, 8, 44–49. (21) Park, J. U.; Hardy, M.; Kang, S. J.; Barton, K.; Adair, K.; Mukhopadhyay, D.; Lee, C. Y.; Strano, M. S.; Alleyne, A. G.; Georgiadis, J. G.; Ferreira, P. M.; Rogers, J. A. Nat. Mater. 2007, 6, 782–789.
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Figure 6. Droplet and jet formation during SEE of an ethylene glycol/water (70/30) mixture in the experiment with an unmodified capillary in which the shape and size of the meniscus and cone depended on the OD of the capillary (600 µm). The glass capillary was placed at a distance of ∼1.7 mm from the counter electrode. The indicated times are relative to the start of the pulse.
Figure 7. Example of meniscus deformation when a high voltage pulse was applied in the absence of a bias voltage. Pulses of 3.8 kV for 2 ms were applied, and the distance between the counter electrode and the nozzle was approximately 2 mm ((0.1 mm).
than the length of individual PTS molecules (∼2 nm), it is characterized by a generally high chemical and mechanical stability.22
Results and Discussion SEE with an Unmodified Capillary. In the experiments carried out with an unmodified capillary, the size of the liquid meniscus depended on the outer diameter of the nozzle. After achieving static equilibrium at zero volts, we increased the bias voltage to increase the fluid volume enclosed in the meniscus before the onset of the dripping mode. This onset point was related to a critical value of the effective surface tension. In order to generate a single electrospraying event, rectangular pulses were applied on top of the bias voltage.17 At a certain total voltage (bias plus pulse voltage), the electrostatic forces acting on the surface were sufficiently high to modify the meniscus to the conical shape. This led to jetting or spraying of liquid from the tip of the cone. To generate SEE, 2 ms rectangular pulses of 0.5 kV were applied every 1 s on top of the bias voltage of 2.5 kV (Figure 2, method A). Since the event was highly reproducible, we were able to image details of the whole process in a stepwise fashion by adjusting the flash delay and taking one picture per event. We found the following sequence of events to occur during each pulse (Figure 6): 1. After the start time, the equilibrium meniscus of the liquid changes into a cone. 2. Liquid starts to discharge from the top of the cone as a thin jet. 3. The jet breaks up into fine droplets. 4. After a while, the spraying stops and the meniscus returns to its equilibrium shape. Droplet and jet sizes generated in SEE were in the diameter range of 5-17 µm, which typically translates to a volume in the nanoliter range per event. One of the important parameters for the stability of SEE was the pulse width. With pulses of 2 ms applied with a frequency range of 0.63-1.47 Hz, SEE was easy to reproduce. As can be seen in Figure 6, there was a delay of approximately 1.3 ms after application of the voltage pulse before the first (22) Onclin, S.; Ravoo, B. J.; Reinhoudt, D. N. Angew. Chem., Int. Ed. 2005, 44, 6282–6304.
visible jet or droplet was observed. The end of SEE was also delayed beyond the end of the pulse, as some droplets can be still ejected from the shrinking meniscus (not shown in Figure 6). At the end of SEE in Figure 6, it was observed that when the cone/meniscus returned to the equilibrium situation, the meniscus height was usually smaller than the meniscus height before SEE was generated. This is a result of the recording method, in which hundreds of events were generated one after another to follow the whole process in detail. As a consequence, the height of the liquid column in the capillary and thus the meniscus size were reduced. However, the liquid ejected during any individual SEE was so small that it did not influence the liquid column height and subsequently generated SEE. Therefore, SEE was a reproducible process. In other experiments, we noticed an influence of the pulse time on SEE stability. It was not possible to achieve reproducible SEE with a pulse time of less than 2 ms. In an alternative approach to achieve a stable spray, the application of rectangular pulses in the absence of a bias voltage was tested. Liquid ejection could, however, only be observed after application of a voltage pulse of 3700-3800 V, which already caused an unstable spraying from the meniscus (Figure 7) and therefore did not allow for stable SEE. SEE with a Modified Capillary. By using the capillary that was selectively modified at the nozzle front with a self-assembled PTS monolayer, we were able to carry out experiments with a much smaller meniscus size, which in this case was defined by the inner rim of the nozzle measuring 50 µm in diameter. In contrast to the experiments with an unmodified capillary, no under-pressure control was required, since in the modified capillary the surface tension force on the meniscus was higher and kept the liquid column in place. Our first approach was to repeat the experimental scheme that was used for the standard capillary. This required optimization of the bias voltage. By increasing the bias voltage in a stepwise fashion, we reached 3.5 kV, at which value the intermittent spraying mode started (Figure 8). We tried to determine an optimum bias voltage. This voltage was always below the voltage at which dripping started. However, this voltage could not be found. Following the next steps of SEE
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Stachewicz et al. Table 1. Dimensions of the Capillary and Meniscus, and Characteristic Values of Electrospraying Processes in Which the Meniscus Depends on the ID or OD of the Capillary
parameter Figure 8. Series of pictures of an experiment in which a glass capillary with a PTS coating was used. The intermittent mode was observed at 3.5 kV. The pictures were taken every 10 µs. The distance between the capillary and the counter electrode was approximately 2 mm ((0.1 mm).
Figure 9. Continuous jetting from the capillary with PTS coating. The bias voltage was set at 3.5 kV, and block pulses (pulse duration tp ) 1-5 ms) of 0.2 kV were applied every 400 ms. The distance between the capillary and the counter electrode was approximately 2 mm ((0.1 mm).
Figure 10. Droplet and jet formation during SEE of an ethylene glycol/ water (70/30) mixture in an experiment in which the shape and size of the meniscus and the cone depend on the ID of the capillary (50 µm). The 300 µs rectangular pulses of 2.7 kV were applied every 100 ms. The glass capillary was placed at a distance of ∼0.9 mm from the counter electrode.
generation, rectangular pulses of 0.2 kV were superposed on the same 3.5 kV bias voltage. This caused only a continuous jetting instead of SEE (Figure 9). The jet diameter was in the range of 2-5 µm. None of the tested combinations of bias and pulse voltages allowed for stable SEE with a modified capillary. Due to the antiwetting coating on the nozzle front, a high bias voltage was needed to pull the solution out of the capillary. This voltage was already too high to observe the dripping mode, which usually appears at lower electric field strengths. Moreover, the ID-limited meniscus surface area was much smaller than the meniscus defined by the OD of the capillary. However, if the pulses were applied without a bias voltage, just starting from 0 V, it was possible to obtain a reproducible SEE for the range of pulse times starting from 200 µs. (Figure 10). Droplets and jet sizes obtained in this way had dimensions of 2-5 µm. With a frequency range of 1-10 Hz, SEE was stable and easy to reproduce. For the modified capillary, we could reduce the distance between the nozzle and the counter electrode, because of the small dimensions of the cone. In case of the unmodified
meniscus size depended on OD
diameter of meniscus base [m] 60 × 10-5 liquid height in the capillary H [m] 0.03 2500 bias voltage Ub [V] 500 pulse voltage Up [V] gap height d + h [m] 1.7 × 10-3 mean value of field strength at Ub [V/m] 1.45 × 106 mean value of field strength at Umax [V/m]a 1.73 × 106 meniscus height h [m] 297 × 10-6 meniscus curvature radius rc [m] 30 × 10-5 capacity CS [F] 36.6 × 10-15 capacity Cl [F] 2.3 × 10-15 RC time τRC(2) [s] 800 × 10-6 reshaping time τm-c [s] 1.72 × 10-3 refill time τrf [s] 454 frequency in capillary fc [Hz] 0.18 256 damping in capillary Γc [1/s] a Umax is considered here as the sum of Ub and Up.
meniscus size depended on ID 5 × 10-5 0.03 0 2700 0.9 × 10-3 0 3 × 106 10 × 10-6 3.63 × 10-5 4.11 × 10-15 2.3 × 10-15 90 × 10-6 4.92 × 10-5 547 0.0845
Figure 11. Correlation between pulse time and duration of SEE when a SAM-modified capillary was used. The measurements were taken using 0.2-2 ms rectangular pulses of 2.7 kV, applied every 100 ms. For the linear fit to data points, R2 ) 0.9963.
capillary, however, it was necessary to increase the distance between the nozzle and the grounded counter electrode plate. Otherwise, the accumulated liquid on the counter electrode started to interfere with the cone, due to slow evaporation of the ethylene glycol/water mixture. To provide a more practical measure for comparing the different experimental settings, in Table 1, next to the voltage, we also report the resulting field strength. To better understand this process, we investigated the dependence of the duration of the SEE on the applied pulse time. The SEE time has been defined as the time difference between the appearance of the first visible jet from the cone and the last droplet. The experimental data summarized in Figure 11 indicate a linear correlation between the length of the SEE time and that of the applied pulse. From a linear regression analysis of these data, the delay time for SEE from a SAM-modified capillary could be determined to be 0.1 ms as deduced from the intersection of the regression line with the X-axis. Based on the volume of liquid collected on the counter electrode during the series of SEE with the same pulse time, we estimated the volume of fluid ejected during single electrospraying events. If pulses of 200 µs were applied, we were able to deposit
Relaxation Times in Single EVent Electrospraying
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Cl ) εlε0
1 Lx
(1)
∑ πr 2 x
where L is the distance between the tip of the metal wire inside the capillary and the end of the capillary. This distance, L, can be divided into many small parts of length, Lx, with an internal radius, rx, for which the capacitance and the resistance of the liquid inside the capillary, RC, are calculated. For our cases, in order to calculate the values of C1 and Rc, we have divided the length between the tip of the electrode placed in the capillary and the end of the nozzle in 19 segments (see the Supporting Information, page S2). The total resistance of the whole capillary is the sum of all parts
RC ) Figure 12. Schematic drawing of the nozzle dimensions based on macroscopic pictures (cross section). The symbols describing the dimensions of the large meniscus are identical to those used for the small meniscus.
approximately 5 pL of fluid by SEE. Chen et al. deposited volumes of 50-100 pL, which were also reported to be proportional to the pulse time.14 With our system, we were able to deposit significantly less fluid volume and to monitor the whole process in detail (including cone formation, droplet size, and deposition). We achieved stable SEE using modified and unmodified capillaries. A large difference in the meniscus size, thus the volume of liquid enclosed in the meniscus, was observed between the two configurations. In both cases, a time delay was identified for the transition of the meniscus to a cone as well as for the relaxation of the cone to the equilibrium shape of the meniscus (Figures 6 and 10). In this context, it is instructive to note that, for a given capillary configuration, the volume of liquid enclosed in the cone was found to be larger than that enclosed in the meniscus in the equilibrium situation just before application of the pulse. This implies that some time is required for the delivery of the extra liquid into the cone as well as for the meniscus to reach the equilibrium state again. In order to explain the indicated timing issues, the relaxation times involved in the electrospraying events were analyzed. Relaxation Times in Electrospraying. The relaxation time characterizes the time that a system requires to adjust to a new situation, such as a change in the applied voltage. In case of electrospraying, the involved relaxation times are related to electrical and hydrodynamic phenomena. To analyze how fast charges move through the liquid in the nozzle when the voltage is applied, the system can be described as an RC circuit (Figure 12). A description of the RC circuit, in turn, requires the capacitance of the system and its resistance to be calculated. The capillary system can be seen as a combination of two electrical circuits, an inside circuit consisting of the capacitance C1 and resistance Rc placed in parallel inside the fluid in the capillary between the tip of the electrode and the end of the nozzle, and another circuit consisting of the resistance Rc and the capacitance between the meniscus and the counter electrode plate. When the counter electrode is moved away, the charging of the capacitor C1 takes place via the resistor Rc. Note that for this case C1 and Rc are placed in series. We model the circuit between the tip of the electrode and the meniscus as a flat plate capacitor of which the dielectric is also the resistor. The capacitance Cl is calculated as (23) Smythe, W. R. Static and Dynamic Electricity; McGraw-Hill Book Co.: New York, 1950; pp 118–121. (24) COMSOL, version 3.3.0.405; 2006.
1 κ
L
∑ πrx 2
(2)
x
where κ is conductivity of the liquid. In the second circuit, the capacitor between the meniscus and the counter electrode, Cs, has to be charged also through the resistor, Rc, and the resistance of the meniscus, Rm. The resistors, Rc and Rm, and the capacitor, Cs, are in series (Figure 12). As will be pointed out later, the resistance between the tip of the electrode and the meniscus is by far the largest compared to, for example, the resistances in wiring between the electrospraying setup and the electronic equipment used to drive the system. Assuming for the second RC circuit the meniscus to be a part of a spherical conductor and the counter electrode to be a large flat conductor (Figure 13), the capacitance between the meniscus and the counter electrode is23
CS )
(
4πε0εr 1 1 rc 2(d + rc)
)
(3)
where d is the distance between the liquid meniscus and the counter electrode and rc is the meniscus radius of curvature, which is calculated based on the meniscus height h (Figure 12) using eq 4, in which 2a is the capillary OD:
rc )
a2 + h2 2h
(4)
Figure 13 shows the schematic drawing of the electric field lines of a spherical conductor. This model of a capacitor is considered to be the best available approximation for the system studied here. To test whether eq 3 can be used for our capillary system, two simulations in COMSOL 3.324 were run, one for a whole sphere and another for a part of the sphere (the meniscus surface), both with a flat counter electrode (Figure 14). In the area of
Figure 13. Capacity model for the spherical conductor and the flat counter conductor showing the approximate shape of the electric field lines, which are drawn schematically.
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and an increase of the Coulomb force across the gap between the meniscus and the grounded counter electrode. The spherical surface of the meniscus all of a sudden changes into a cone, and fluid has to be transported through the nozzle in order to replenish the extra volume of liquid needed to accommodate the change in meniscus shape (from dome to cone). Besides the electrical time constants, there is a hydrodynamic relaxation time involved in the electrospraying processes. To discuss the hydrodynamic movements inside the capillary during electrospraying, we start with defining the equilibrium situation. The static pressure of the liquid column is Pfc ) FsgH, where g is the acceleration due to gravity and H is the total liquid height in the capillary. Sometimes, it is necessary to apply an underpressure in relation to atmospheric pressure, Pgauge, in order to keep the system in balance. There is also a capillary pressure of the meniscus inside the capillary, Pmc)2cos Θ σ/b, where Θ is the contact angle between the liquid and the inside of the glass capillary. The contact angle was measured using pictures of the capillary, taken with a microscope. The capillary pressure caused by the liquid meniscus protruding beyond the end of the capillary is Pm ) 2σx/rc, where σx is the surface tension on the meniscus. In the case of a large meniscus, charge on the meniscus is counteracting the surface tension during the application of the bias voltage. Under these conditions, the total effective surface tension is defined as follows:
σeff-total ) σ -
Figure 14. Simulation in COMSOL 3.324 of the electric field lines for a spherical conductor with a flat counter electrode (a) and for a meniscus hanging outside the glass capillary (b). The electric field lines for the meniscus are shown only for an axial symmetric case of which the field line distribution is in the r-z plane.
interest, the shape and density of the electric field lines are rather similar. This justifies the use of eq 3, even if it might overestimate the capacitance of our setup. For the modified capillary the meniscus shape is still unclear; however, it is not critical for the analysis presented in this paper. The decay time of charge from the capacitor C1 through the resistance Rc, called the characteristic time of a RC circuit, is τRC(1) ) RCC1 and gives the value of 50.3 µs. This decay time defines also the characteristic time of charge transport in the liquid. For such an arrangement, the charge time constant (charge relaxation time) follows from eqs 1 and 2 and equals τRC(1) ) RCC1 ) ε0εl/κ.25 For a mixture of ethylene glycol and water (70/30), the charge relaxation time is approximately 50 µs. Using eq 2 for our capillary, the resistance RC was calculated to be 21.86 GΩ. For an estimation of the resistance of the meniscus, Rm, the same equation can be applied, using L ) h and rx ) a, which gives 0.093 GΩ. The resistance of the meniscus is therefore negligible. All other resistances in the circuit such as the wiring between the SEE experimental setup and the electronics needed to drive the spraying event are extremely small compared to the values mentioned here. Consequently, the RC time of the second circuit is τRC(2) ) RCCs (Table 1). In SEE, a high voltage pulse is applied to the liquid, which causes a redistribution of charge carriers over the meniscus surface (25) Crowley, J. M.; Chang, J. S.; Kelly, A. J.; Crowley, J. M. Dimensionless Ratios in Electrohydrodynamics. In Handbook of Electrosatic Processes; Marcel Dekker, Inc: New York, 1995; pp 99-119.
(
Cs2 2
2
+
16π ε0εrrch
Csrc 4πda2
)
U2
(5)
where U is the applied voltage. In the calculations of the effective surface tension, only the capacitance between the meniscus and the counter electrode, Cs, is considered, as the surface tension is related to the charge on the meniscus.17 In the case in which the meniscus size is limited by the OD capillary, we use for the further calculations the effective surface tension, σx ) σeff-total for the bias voltage. For the small meniscus, there is no change in surface tension because there is no bias voltage applied. In this case, σx ) σ will be used. For the static equilibrium situation, pressure balance at the nozzle front is
Pfc + Pm - Pmc - Pgauge ) 0
(6)
Now, let us consider a small deviation from the equilibrium by a small fluid displacement x(t) in the nozzle (x is defined positive outward). In case the volume of the fluid in the meniscus is increased, the radius of curvature becomes smaller and the capillary pressure becomes larger, opposing the volume displacement like a mechanical spring. As the fluid displacement is time dependent, the fluid in the capillary must be accelerated and feels a viscous drag. The viscous drag damps the motion of the fluid column. Consequently, we can model the fluid motion in the capillary.26 The model is one-dimensional, because the main liquid displacement occurs in one direction along the main axis of the capillary. The general form of the equation describing the one-dimensional motion of the fluid in the nozzle is given by
mx¨ + cx˙ + kx ) 0
(7)
This equation is similar to the equation describing the free oscillations of a mass–spring–damper system, and m relates to the mass contained in the capillary, c is the damping coefficient, and k describes the springlike action due to the change of the (26) Wu, C. S.; Chen, M. A.; Li, S. K. Comput. Mater. Sci. 2004, 31, 147–154.
Relaxation Times in Single EVent Electrospraying
Langmuir, Vol. 25, No. 4, 2009 2547
capillary pressure and the change in column height.27 The inertial force is considered first. The liquid inside the capillary is divided into two parts with regard to the different inner diameters of the capillary. The displacement of the liquid inside the capillary in the part with the largest inner diameter, b, is smaller than that in the part with the smallest inner diameter, rn, which is considered in the equation describing the inertial force:
[
mx¨ ) Fs(H - l)
πrn2 2
πb
]
πb2 + Fslπrn2 x¨ ) πrn2FsHx¨
(8)
The height of the meniscus is neglected, because it is small with respect to H. Next, the viscous effects in the capillary have been calculated, which is represented by the second term in eq 7, where Poiseuille′s law is used.28 The pressure difference, ∆Pv, between the end of the capillary and the position, at which the capillary becomes wider, is
8 l ∆Pv ) η 4 Q π r
(9)
n
where Q represents the flow rate and l is the total length of the thinnest part of the nozzle, 240 µm (see the Supporting Information, page S3). With known capillary dimensions, the pressure difference can be calculated and then converted into a force describing the damping term in eq 7:
cx˙ ) 8πηlx˙
∆Pfc ) Fsg∆H ) Fsg
rn2 b2
x
(14)
The next component of the change in the equilibrium situation is
∆Pm )
8σxrn2
(a2 + h2)2
(
1-
)
2h2 x a2 + h2
(15)
(see the Supporting Information, page S5). Adding up these two dynamic contributions to the equation of motion, we find
kx ) (∆Pfc + ∆Pm)πrn2
(16)
As all coefficients are now known, the final equation of describing the one-dimensional motion of the fluid in the nozzle is
mx¨ + cx˙ + kx ) πFsHrn2x¨ + 8πηlx˙ +
[
8πσxrn4
(
)
]
rn4 2h2 1- 2 + Fsgπ 2 x ) 0 (17) (a2 + h2)2 (a + h2) b
Using the equation of motion (eq 17), the natural frequency fc and damping Γ inside the capillary are calculated:27
fc )
1 2π
Γ)
(10)
mk
(18)
c 2√km
(19)
Lastly, to calculate the term including the spring constant, we consider all changes in pressures involved in the system going from the static equilibrium situation to the disturbed state. In the dynamic situation, in which the liquid displacement, x, in the nozzle takes place, the column height in the pipet is changed with ∆H (Figure 12). Consequently, the component of eq 6, Pfc, has the following form:
In SEE, before the first jet or droplet is formed, after applying the pulse, it takes some time for the cone to be formed. In case of a large meniscus, the application of the bias voltage reduces the influence of the surface tension force.17 Thus, the time constant related to the reshaping of the meniscus including the delivery of the extra liquid to the cone, τm-c, can be calculated based on eq 17, omitting the part related to the fluid displacement x:
Pfc ) Fsg(H - ∆H)
mx¨ + cx˙ ) 0
(11)
The meniscus radius of curvature, ∆rc, is changed as well:
Pm )
2σx rc + ∆rc
∆H )
rn2 b2
x
The equation has the solution in the form of x˙ ) x˙0 e the time constant τm-c given as27
(12)
The remaining pressures from eq 6, Pmc and Pgauge, stay the same. By comparing the static and dynamic situation in the nozzle, the term in the equation of motion of the fluid in the nozzle (eq 7) related to the fluid motion, x, can be calculated. The difference, ∆Pfc, between the static and dynamic equilibrium situations is due to the pressure difference that occurs when the liquid column height changes. The pressure difference, ∆Pm, is caused by the change of shape in the liquid meniscus protruding beyond the capillary. Consequently, the term representing the spring constant depends on both of them. To calculate ∆Pfc, ∆H must be known, but this is related to the displacement, x, of the liquid in the capillary:
(13)
This gives (27) Thompson, W. T. Theory of Vibration with Applications, 2nd ed.; PrenticeHall: Englewood Cliffs, NJ, 1981; pp 1-126. (28) Nguyen, N.-T.; Wereley Steven, T. Fundamentals and Applications of Microfluids, 1st ed.; Artech House: Boston, 2002; pp 11-65.
(20) -(t/τm-c)
τm-c )
rn2FsH 8ηl
with
(21)
τm-c is not considered in the case of SEE with the small meniscus. There is only a small amount of extra liquid delivered to the cone. Mainly, it is a process of meniscus reshaping. Therefore, the pulse time is much shorter to create SEE with the modified capillary. In the phase of SEE, in which the cone is formed and the jet is generated, the electric force at the tip of the cone is dominant. Upon further analyzing the SEE phases, the last step of the SEE process is related to the reshaping of the liquid to the meniscus equilibrium state and the refilling of the liquid inside the capillary, which was consumed during SEE. Consequently, this liquid displacement inside the capillary requires a certain time. When calculating the refill time during SEE, the mass effect is disregarded (eq 17), because the viscous effect completely dominates over it. Moreover, in the case of the large meniscus, the system is overdamped, Γc > 1 (Table 1). For the small meniscus the system is underdamped, Γc < 1, but the mass term influencing the final result is in the range of 0.2%. We therefore decided to use the same model for both cases. By omitting the mass term in eq 17, the equation becomes
2548 Langmuir, Vol. 25, No. 4, 2009
Stachewicz et al.
cx˙ + kx ) 0
(22) -(t/τrf)
The equation has the solution in the form of x ) x0 e the refill time, τrf, equals
τrf )
[
8σxrn4
(
8ηl
)
rn4 2h2 1- 2 + Fsg 2 (a2 + h2)2 (a + h2) b
]
, and
(23)
Comparison of SEE with Unmodified and Modified Capillaries. Comparing the volume of the fluid in the meniscus equilibrium state in the absence and presence of the antiwetting coating, the volume Vm is more than 3000 times smaller for the modified capillary. For the capillary without the antiwetting coating, the capacity CS is 36.6 × 10-15 F, and for the capillary with the antiwetting coating it is 4.12 × 10-15 F. The capacity difference of a factor of approximately 10 causes an equivalent reduction of the RC time. All calculated results are summarized in Table 1. In general, the SEE time can be divided into three parts. First, time is needed for the formation of the cone from the meniscus. Second, the jetting process removes fluid from the system. Finally, the meniscus returns to its equilibrium shape, and refilling inside the capillary takes place. For the SEE presented in Figure 6, it takes approximately 1.3 ms for the cone formation. In addition, the calculated time of the reshaping of the meniscus into the cone is in the same order of magnitude, and τm-c is 1.7 ms. This hydrodynamic relaxation time can explain why the most stable SEE for the OD-defined meniscus is with the pulse time of 2 ms. For the ID-defined meniscus, τRC(2) is approximately 90 µs. However, it is difficult to experimentally obtain stable SEE with a pulse shorter than 200 µs. It was observed that the pulse time had to be approximately twice the calculated value of τRC(2) to get enough charge for the stable electrospraying event with the modified capillary. The refill time inside the unmodified capillary has been calculated to be greater than 7 min, which confirms the experimental observations that it is only possible to get stable SEE at very low frequencies. After stopping the series of SEE (voltage is switched off), the meniscus size becomes smaller than it was before SEE was started. Our calculation is consistent with the observation that there was insufficient time to refill the liquid inside the capillary between electrospraying events. In the case of the modified capillary, the reshaping of the meniscus into the cone is mainly controlled by the electric force. The surface tension is higher on the small meniscus than on the large one; thus, there is hardly any flow inside the capillary. As the difference between the volume of fluid enclosed in the meniscus and the cone is very small, the refilling time is expected to be short. Consistent with this, the refill time, τrf, for the modified capillary was calculated to be only about 50 µs. To verify if liquid is delivered outside of the capillary, the difference in the volume of liquid enclosed in the meniscus and in the formed cone was analyzed. For the large meniscus, a nanoliter volume has to be delivered to the equlibrium meniscus at the bias voltage (or cone at voltage pulse), whereas for a small meniscus the liquid volume is in the picoliter range from the equilibrium meniscus to the cone. The volume of deposited liquid during SEE is similar to the excess volume needed to reshape the spherical meniscus into a cone in both cases. The equation of motion for the capillary system studied here also provides information about the damping and frequency of the liquid oscillations inside the capillary (Table 1). We note that the system is overdamped (Γc > 1) for the unmodified capillary but underdamped (Γc < 1) for the modified capillary. For the
modified capillary, the frequency is high, approximately 0.5 kHz. The frequency of liquid oscillations inside the unmodified capillary is very low (in the range of 0.1 Hz), and the damping of the liquid inside it is very high. As a consequence, the frequency of the liquid oscillation is not important.
Conclusions Single event electrospraying (SEE) is a method for the ondemand deposition of femtoliter to picoliter volumes of fluid. To determine the influence of the size of the meniscus on the characteristics of the SEE process, we used a glass capillary with and one without an antiwetting coating to control the meniscus size. By studying the different time constants related to the electrical and the hydrodynamic phenomena, we have explained the time limitations in the deposition process. Two methods of SEE using two different capillary configurations have been discussed. In one case, the meniscus shape depended on the OD of the capillary, and in the second on the ID of the capillary. By using an antiwetting coating on the outer surface of the nozzle, we could very effectively manipulate the meniscus geometry, which has a significant influence on the capillary liquid-air interface. It provided us with a tool to control the boundary conditions for SEE. Moreover, the capillary configuration and especially the meniscus size influence the jet and droplet size and the amount of deposited liquid during SEE. For the large meniscus, a bias voltage was required before applying the pulses for SEE. For the modified capillaries, the preconditioning was not necessary and the pulses could be applied directly, without the need to apply the bias voltage. To better understand the observed delays and the pulse time limitation for SEE, different time constants related to the electrical and the hydrodynamic phenomena were studied. It was shown that the reduction of the meniscus size reduces the refilling time and the deposited amount of liquid. From the hydrodynamic point of view, the time constant related to reshaping the blob of fluid from the meniscus to the cone is important. This time constant provides insight into the time needed to deliver the required additional liquid to form the new shape. The total volume delivered during the meniscus-to-cone transition is the part of the volume finally deposited during SEE. Moreover, when the meniscus returns to the equilibrium state, a refilling process takes place inside the capillary. As expected, this refilling was shown to take more time for the unmodified capillary than for the modified one. The SEE time is strictly related to the amount of deposited liquid and also depends on the pulse time. The pulse time for the unmodified capillary is limited due to the hydrodynamic relaxation time related to the time of the reshaping of the meniscus into the cone. In the case of the modified capillary, the pulse time is limited by the RC time. The capacity of the system was significantly reduced when the meniscus was smaller, which means that there was less time needed to charge the capacitor and consequently the voltage pulses can be shorter. Here, the charge relaxation time was negligible, since it was significantly shorter than the RC time. There are different relaxation times involved in the electrospraying process, and they can significantly influence the controllability and timing of the deposition process. We proved that the relaxation times are particularly important during SEE. A detailed analysis of all times involved in SEE allowed us to get a clear picture of the technology limitations with respect to the time of the liquid deposition, and we can now predict the amount of deposited liquid per SEE. Using shorter relaxation times, we gained better control over SEE. With SEE pulses of 0.3 ms, a deposition volume of
Relaxation Times in Single EVent Electrospraying
approximately 5 pL could be achieved. This result indicates the wide applicability of SEE in the deposition of small amounts of fluids, which is a key enabler for potential high resolution surface patterning applications of this technique. For the large meniscus, we studied SEE generated in the frequency range of 0.63-1.47 Hz, and for the small meniscus in the range of 1-10 Hz. Further studies will address SEE stability in a higher frequency regime of applied pulses. Acknowledgment. This study was supported by the European research program, Marie Curie Actions, Early Stage Fellowship, Project Number MEST-CT-2004-505006 and Philips Research
Langmuir, Vol. 25, No. 4, 2009 2549
Europe. We thank Peter Barendse, Albert Geven, Martin Vernhout, and Leo van den Besselaar for assistance with the building of the experimental setup. Supporting Information Available: Details on the calculation of the distance between the tip of the metal wire inside the capillary and the end of the capillary, L, and the length of the thinnest part of the nozzle, l, are provided. Additionally, the calculation of ∆Pm, the pressure difference caused by the change of shape in the liquid meniscus protruding beyond the capillary, is described. This material is available free of charge via the Internet at http://pubs.acs.org. LA8021408
