Abstract
Microfluidic fluorescence-activated cell sorters (μFACS) have attracted considerable interest because of their ability to identify and separate cellsin inexpensive and biosafe ways. Here a high-performance μFACS is presented by integrating a standing surface acoustic wave (SSAW)-based, 3D cell-focusing unit, an in-plane fluorescent detection unit, and an SSAW-based cell-deflection unit on a single chip. Without using sheath flow or precise flow rate control, the SSAW-based cell-focusing technique can focus cells into a single file at a designated position. The tight focusing of cells enables an in-plane-integrated optical detection system to accurately distinguish individual cells of interest. In the acoustic-based cell-deflection unit, a focused interdigital transducer design is utilized to deflect cells from the focused stream within a minimized area, resulting in a high-throughput sorting ability. Each unit is experimentally characterized, respectively, and the integrated SSAW-based FACS is used to sort mammalian cells (HeLa) at different throughputs. A sorting purity of greater than 90% is achieved at a throughput of 2500 events s−1. The SSAW-based FACS is efficient, fast, biosafe, biocompatible and has a small footprint, making it a competitive alternative to more expensive, bulkier traditional FACS.
Keywords: acoustofluidics, fluorescence-activated cell sorters, sheathless focusing, standing surface acoustic waves
1. Introduction
A fluorescence-activated cell sorter (FACS) is a high-throughput, single-cell characterization, and sorting tool that has revolutionized how cells are studied and purified.[1–4] In the past few decades, FACS has become indispensable for a wide variety of applications in fundamental biological/biomedical research and clinical practice. Despite the significant impact, current benchtop FACS systems have the following drawbacks: high cost for use and maintenance, large size, complex configuration, low biocompatibility, biosafety concerns, and difficulty in handling small sample volumes. Microfluidic FACS (μFACS), the combination of micro-fluidics and cell sorting techniques, has been regarded as an excellent candidate to overcome the limitations of the traditional FACS. A μFACS sorts cells in an enclosed environment to avoid potential aerosol contamination and is inherently good at handling tiny amounts of samples, generating smaller volumes of waste, and utilizing less costly reagents. Additionally, the cost and size of a μFACS is expected to be much lower than traditional FACS.[5,6]
A typical FACS system includes three major units: 1) a cell-focusing unit to focus cells into a single file stream, 2) a cell-detection unit to detect fluorescent emissions and scattered light arising from individual cells, and 3) a cell-deflection unit to separate cells of interest from others. To date, many μFACS units have been developed, such as hydrodynamic,[6–8] inertial,[9,10] and acoustic[11–13]-based cell-focusing units as well as acoustophoretic,[14–19] dielectrophoretic,[20–22] optical,[23–25] mechanical,[26–30] and hydrodynamic[31–33]-based cell-deflection units. However, the integration of different on-chip units into an all-in-one, fully functional μFACS remains challenging due to their complex designs or incompatibility for integration. Among the various microfluidic techniques for FACS, acoustofluidics (i.e., the fusion of acoustics and microfluidics)[34–38] is well recognized because of its amenability to integration, miniaturization, and biocompatibility.[39] For example, Jakobsson et al. demonstrated an acoustofluidic FACS that uses bulk acoustic waves (BAW) for both cell focusing and cell deflection, and achieved a throughput of ≈150 events s−1.[40] Surface acoustic waves (SAWs) have also been extensively utilized to develop acoustofluidic cell sorters.[41–45] Unlike the BAW-based devices, SAW-based cell sorters use microfabricated interdigital transducers (IDT) as wave generators and demonstrate better resolution and controllability for cell manipulation,[46] therefore achieving a higher throughput. These SAW-based cell sorters use either standing SAW (SSAW) or traveling SAW for cell deflection; however, to our best knowledge, none of them use SAWs for both cell focusing and deflection. Most of these cell sorters still use hydrodynamic focusing, also known as sheath fluid-based focusing. Utilizing sheath fluids, however, is undesirable because multiple pumps and a significant amount of sheath fluid are required, it creates biohazards, and it often reduces the viability and integrity of sorted cells due to high flow speed. Furthermore, the SAW-based cell sorters are usually integrated with bulky, out-of-plane microscopic detection system to develop FACS and suffer from large footprint.
In this work, we present an integrated FACS that uses SSAW for both cell focusing and deflection. With the assist of inertial forces, the SSAW-based sheathless focusing technique[11] achieved precise 3D focusing of cells in a single-layer device. It greatly simplifies the fabrication and fluid operation of μFACS and reduces the amount of biohazard waste. The impact of shear stress on cells, an issue that arises with sheath fluid-based focusing methods because of their extremely high flow rates, can also be avoided. In the cell-deflection unit, a design of focused IDTs produced the SSAWs, which in turn generated a narrow, powerful acoustic beam for deflecting cells and achieving a high sorting throughput.[42] Furthermore, an in-plane-integrated optical fiber detection system was used to replace the bulky, out-of-plane microscopic detection system, which significantly decreases the size and cost of the FACS.[47] By integrating the three units together, an all-in-one SSAW-based FACS chip was demonstrated. The high performance of the SSAW-based FACS was proven by sorting mammalian cells with a purity greater than 90% at a throughput of 2500 events s−1.
2. Results and Discussion
2.1. Design of the SSAW-Based FACS
Figure 1 schematically shows the integrated SSAW-based FACS. In the cell-focusing unit, the x and z-direction components of the primary acoustic radiation force, respectively, translates cells from their initial trajectory to the closest pressure node. By properly manipulating the relative positions of the pressure node and cells, we can focus all cells into a single pressure node to achieve 3D focusing. Here, a serpentine channel is introduced between the inlet and the SSAW focusing region to pre-concentrate the cells around a designated pressure node; it can also prevent cells from aggregating together and creates uniform spacing between neighboring cells.[48] The focused cells are then interrogated by an in-plane-integrated optical detection system, which has a single-mode optical fiber (SMF) connected to a laser and a multimode optical fiber (MMF) connected to a photomultiplier tube (PMT). When a fluorescent-labeled cell is detected and enters the deflecting region, the SSAW-based cell-deflection unit is turned on. Compared to the pressure node of the focusing SSAW field (PNOF, red dash line in Figure 1c), the pressure node of the deflecting SSAW field (PNOD, black dash line in Figure 1c) is shifted and aligned to the collection outlet. The cell is thus pushed to a new balanced position in the deflection region and finally exits via the collection outlet.
Figure 1.
a) Schematic of the SSAW-based FACS chip. b) Microscopic image of the SSAW-based focusing and deflection units. Scale bar: 200 μm. c) Schematic indicates the position of pressure nodes of the deflecting IDT (PNOD, black dashed line) and pressure nodes of the focusing IDT (PNOF, red dotted line).
In an SSAW field, the acoustic radiation force that acts on cells can be expressed as[49,50]
| (1) |
| (2) |
where P0, λ, Vc, ρc, ρw, βc, and βw are the acoustic pressure, acoustic wavelength, volume of the cell, density of the cell, density of the fluid, compressibility of the cell, and compressibility of the fluid, respectively. φ(β, ρ) is the acoustic contrast factor. In addition to the acoustic wavelength, the distribution of acoustic pressure, P0, can also be affected by the geometry and material of the fluidic channel. To achieve the desired acoustic pressure pattern for 3D focusing and deflection, a numerical simulation was first carried out (2D numerical model, Figure S1, Supporting Information)[51] to optimize the device design. The computed acoustic potential in the x–z plane of the SSAW focusing region and deflection region is shown, respectively, in Figure 2a,d, where the designated balanced positions (pressure nodes) of cells are indicated by green dots. The acoustic wavelength is 150 μm for the cell-focusing unit and 120 μm for the cell-deflection unit. The polydimethylsiloxane (PDMS) channel is 120 μm wide and 70 μm high.
Figure 2.
Numerical simulation of acoustic radiation potential in x–z plane in a) SSAW focusing region and d) SSAW deflection region. The x-direction acoustic radiation force Fx (along the white line) and z-direction acoustic radiation force Fz (along the red line) are plotted in (b), (c) and (e), (f), respectively. Green dots are used to indicate the force balanced position, and only the balanced position in the region where particles have been pre-focused is plotted.
Theoretically, an acoustic potential pattern with a single pressure node is required for 3D focusing of cells. However, using PDMS as the channel material introduces additional pressure nodes at the PDMS-fluid interface (Figure S2, Supporting Information).[51] Figure 2b,c elucidates, respectively, the x-direction component of acoustic radiation force, Fx, and z-direction component, Fz, along the white and red lines in Figure 2a. Additional balanced positions, which can attract cells around them and compromise the 3D focusing performance, appear at both sides (x = 0 and 120 μm) and top (z = 70 μm) of channels. To counteract this problem, we used a serpentine channel[48] to preconcentrate all cells within the working range (20 μm < x < 80 μm) of the central pressure node. In the z-direction, the influence of undesired balanced positions is negligible due to gravity and the size of cells (the top pressure node traps cells when the center of the cells is less than 5 μm away from the top). Therefore, all cells are 3D focused in the central pressure node (x = 51 μm, z = 26 μm, Figure 2a) in the focusing region with the assistance of the serpentine channel. Using a longer acoustic wavelength can reduce the complexity of acoustic pressure distribution in the channel; however, it will also decrease the acoustic force for precise focusing. It is worthwhile to mention that the use of the serpentine channel can be avoided by using a hard material for the channel such as glass instead of PDMS.
In the cell-deflection region, a new acoustic potential pattern is formed (Figure 2d) and the cells are pushed to the closest pressure node (x = 69 μm, z = 36 μm, Figure 2e,f) from their focusing position. The shift in the x-direction from the focusing position to the deflecting position is around 20 μm and is sufficient for successful sorting of most human cells (5–20 μm).
2.2. Characterization of SSAW-Based Focusing and Deflection Units
Experimentally, fluorescent (green) polystyrene particles (7.0 μm in diameter) were used to characterize the cell-focusing unit. A fast camera was used to record the movement of each particle from a top view and stacked images from 100 frames were used to illustrate the trajectories of particles. As shown in Figure 3a, particles are preconcentrated at the center of channel by the serpentine channel due to inertial force. They are distributed within a region that is ≈30 μm wide. When the SSAW is turned on, the particles are focused along the pressure node line. The stacked trajectory has a width that is close to the diameter of the particles, indicating a high focusing performance in the x–y plane.
Figure 3.
a) Characterization of the performance of SSAW-based focusing when SSAW is off and on. Scale bar: 50 μm. b) Schematic of the in-plane optical detection system from side view. c) Histogram of fluorescent signal collected by the in-plane detection system and analyzed by Kytos software.
The focusing performance in the z-direction was quantitatively characterized with the in-plane-integrated optical detection unit. As shown in Figure 3b, an SMF was employed on one side of the channel and connected to a 485 nm laser to serve as the excitation source, while an MMF was employed on the other side of the channel and connected to a PMT for signal detection. Kytos software and Azurite hardware (DarklingX, USA) were used to record the fluorescent signals from the particles and analyze the coefficient of variances (CV). As shown in Figure 3c, the main population of polystyrene particles (90.8% of the total 5000 events) had a CV of 7.6%. The same sample was analyzed using a commercial flow cytometer (FC 500, Beckman Coulter, USA), and the CV (87.0% of total 5000 events) was 6.8%. Thus the CV from our device is comparable to that from commercial flow cytometers and is better than those from many reported microfluidic cytometers (14–26%).[52–54] Here, the laser beam from the SMF is uncollimated, thus the fluorescent intensity of individual particles is sensitive to their z-positions. A small CV value indicates that the SSAW-based focusing method can achieve excellent focusing not only in the x–y plane, but in the z-direction. To further prove the z-direction focusing, we characterized the velocity distribution of 100 particles and translated the velocity distribution into a z-position distribution based on the velocity profile of laminar flow. The results (Figure S3, Supporting Information) show that the position fluctuation of particles in the z-direction is less than 10 μm. The same experiments were conducted with HeLa cells and a fine focusing result is shown in Figure S4 in the Supporting Information. Since the focusing unit is a single-layer, planar (2D) microfluidic structure, the device can be conveniently fabricated via standard soft-lithography, which makes it ideal for integrating with other existing modules in FACS. Furthermore, the sheathless manner reduces the number of necessary hydraulic pumps to one and requires no control over flow rate, which dramatically diminishes the size and cost of the system.
Deflection of cells in the SSAW-based FACS was achieved by a pair of focused IDTs, as shown in Figure 1a. Compared to a BAW device or straight IDT design, the focused IDTs we employed here have better space resolution and energy efficiency, contributing to a higher throughput. As mentioned previously, the cell-focusing unit, cell-deflection unit, and fluidic channel were precisely aligned for successful sorting. When the cell-deflection unit is OFF, all cells are focused in the main fluidic channel and exit via the waste outlet. Once the cell-deflection unit is ON, the target cells are pushed away from their original position and exit via the collection outlet (Figure S5, Supporting Information). The height of the two tubing outlets were slightly tuned to ensure that the flow resistances of the outlets were even.
To demonstrate the ability of high-throughput sorting, we sorted fluorescent-labeled (Calcein-AM) HeLa cells from unlabeled cells at a flow rate of 180 μL min−1. The Azurite system was used to activate the deflection unit based on the fluorescent signal from the cells. As shown in Figure 4, the fluorescent-labeled cell was excited by the laser in the detection area (blue area) at 0 ms. At 0.4 ms, the cell (indicated by the green circle) entered the deflection region (yellow area) and the feedback system turned the focused IDTs on for 100 μs. Consequently, the fluorescent-labeled cell was deflected away from the main cell stream and exited through the collection outlet. In our experiment, seven fluorescent-labeled cells were accurately sorted from a total of 70 cells during 20 ms without errors (Video S1, Supporting Information). The average space between neighboring cells was around 120 μm, which is close to the acoustic wavelength. A deflection time of 100 μs corresponds to a theoretical maximum sorting rate of 10 000 events s−1, found by taking the inverse of the deflection time for one event. Both the small deflection area and short working time significantly contribute to achieving a high throughput.
Figure 4.
A time-lapsed image of high-throughput acoustic sorting. The fluorescent-labeled Hela cell was sorted into the top outlet (collection), while the nonlabeled cells exited through the bottom outlet (waste). The fluorescent-labeled cell was excited by the laser at 0 μs and thereafter was presented as a green dot. The blue area indicates the detection area while the yellow area indicates the deflecting area. Scale bar: 50 μm.
2.3. An Integrated SSAW-Based FACS
The performance of our integrated SSAW-based FACS was characterized by sorting fluorescent-labeled cells from unlabeled cells at various throughputs. We first analyzed the sorting purity and yield based on videos recorded by the fast camera. The sorting purity and yield are defined by the following equations
| (3) |
| (4) |
A consistent flow rate was used, meaning the change of throughput was achieved by altering the concentrations of cells. As shown in Figure 5a, sorting purities higher than 90% were achieved when the throughput was below 2500 events s−1. The purity decreased dramatically as the throughput increased beyond 3000 events s−1. Although the yield also decreased when the throughput was increased, a yield higher than 85% could still be achieved at 3500 events s−1 (Figure 5b). The decrease of purity is mainly attributed to the decrease in the distance between neighboring cells. Since the minimum width of the deflecting area is constrained by the diffraction limit of the acoustic wave, an average cell interval that is close to the acoustic wavelength is required in order to guarantee a high purity. In other words, the throughput in our experiments is limited by the flow rate (throughput = cells’ velocity/width of deflecting area) rather than the sorting speed limit of the SSAW unit. In addition, sorting errors caused by the Azurite hardware are also responsible for the decrease in sorting performance (Video S2, Supporting Information). Because of a lack of data buffering and data selection functions, the Azurite hardware can neither process the next sorting signal before the previous one has been executed nor recognize a target cell that is too close to a nontarget cell and abort the sorting order. Other than the video-based analysis, we also used a commercial flow cytometer (FC500) to analyze samples which were sorted by our chip at a throughput around 2000–2500 events s−1. As shown in Figure 6, the sorted sample has an average purity of 91.6% ± 1.6%, compared to 10% of the original sample. This value is consistent with the video-based analysis.
Figure 5.
Characterization of a) the sorting purity and b) the yield of SSAW-based FACS at different throughputs.
Figure 6.
Sorting HeLa cells at a throughput of ≈2500 events s−1 using the SSAW-based FACS device. The samples collected from the collection outlet was analyzed by the commercial flow cytometer. The average purity over three measurements is 91.6% ± 1.6%.
The biocompatibility of SSAW-based FACS was also confirmed experimentally. Unlabeled HeLa cells were divided into experimental and control groups. The control group was kept at room temperature, while the experimental group was passed through the device and sorted by a periodic signal (200 Hz). The applied voltage (11.0 Vp-p for focusing and 28.0 Vp-p for deflection) and deflection time (100 μs) are the same as those used in the experiments for characterization of individual units. HeLa cells collected from the collection outlet and from the control group were stained with a viability dye, Calcein AM, and then analyzed by FC500. As shown in Figure 7, most sorted cells were viable (Calcein AM-positive) and a normalized viability of 94.9% ± 2.0% (the viability of the experimental group compared to that of the control group) was achieved. The SSAW-based FACS could realize high-throughput cell sorting while preserving cells’ viability.
Figure 7.
HeLa cells demonstrated a normalized viability of 94.9% ± 2.0% after SSAW-based sorting (averaged from three measurements). a) Untreated cells as control group. b) Cells sorted by a periodic signal using the SSAW-based FACS device.
3. Conclusion
In conclusion, we have demonstrated a fully functional SSAW-based FACS and its performance has been characterized. By integrating the cell focusing, detection, and deflection units into a single chip, the device has a size of several square centimeters. At a throughput of 2500 events s−1, the SSAW-based FACS sorted fluorescent-labeled HeLa cells with a purity ≈90% and viability of 94.9% ± 2.0%. Compared to other microfluidic FACS, the SSAW-based approach significantly increases the degree of integration by using a simple channel design and eliminating the need for sheath fluid. It also demonstrates excellent sorting performance in terms of throughput and post-sorting cell viability. Although its sorting speed is around one order of magnitude slower than commercial FACS, the SSAW-based FACS has a much smaller size and is more biosafe and biocompatible. Further improvements, such as developing sophisticated feedback and logic systems to eliminate sorting errors, using hard materials for the channel in order to remove the serpentine channel and support higher flow rates and utilizing novel acoustofluidic designs to generate larger deflecting distances,[55] will make our SSAW-based approach an excellent alternative to current commercial FACS.
4. Experimental Section
Microfabrication:
The device was comprised of a lithium niobate (LiNbO3) substrate with two pairs of interdigital transducers (standard IDT and focused IDT) and a microfluidic channel with detection windows for optical fiber insertion. The IDTs were fabricated by patterning the structures on a LiNbO3 wafer (128° Y-cut, 500 μm thick and polished on both sides) via standard photolithography and sequential deposition of two metal layers (Cr/Au, 5 nm/50 nm). Each set of IDTs has 20 pairs of fingers and their resonant frequency is 26.2 MHz (wavelength 150 μm) for focusing and 32.8 MHz (120 μm) for deflection. The arc angle and radius of the focused IDT are 20° and 500 μm, respectively. The microfluidic channel was made of PDMS by soft lithography. There are two channels, termed optical detection windows, on each side of the fluidic channel for insertion of optical fibers. One window is perpendicular to the fluidic channel and the other is 45° to the fluidic channel. Both windows are aimed at the same position in the fluidic channel. Because the detection windows require at least 125 μm of height to accommodate the fiber diameter and the fluidic channel is 70 μm in height, a double-layer patterning process was needed. A 70 μm thick SU-8 layer was first spin coated on a silicon wafer for patterning the fluidic channel structures. On top of the first layer, another SU-8 layer of 60 μm thick was coated, followed by patterning the detection window on both of the layers. After development, A SU-8 master mold was obtained with a channel of 70 μm high and a detection window of 130 μm high. A PDMS channel was then fabricated from the master mold, and the replicate was bonded onto the LiNbO3 substrate. The minimum and maximum widths of the serpentine channel are 60 and 400 μm, respectively, while the widths of the straight channel and detection window are 120 and 130 μm, respectively.
Optical Detection and Feedback Control System:
The in-plane optical detection unit was composed of a single-mode optical fiber, three multimode optical fibers, an off-chip diode laser (488 nm; 20 mW; Blue Sky Research, USA), and a set of PMTs (Hamamatsu C6780–20, Japan). The flat end of the single-mode fiber (Thorlabs, USA; core diameter = 3 μm, cladding diameter = 125 μm, numerical aperture (NA) = 0.12) was inserted into the detection window normal to the channel, and the other end was connected to the laser by a fiber coupler. The laser-excited fluorescent light was collected by the multimode optical fiber (Thorlabs, USA, core diameter = 105 μm, NA = 0.22), which was inserted into the other optical detection window and was detected by the PMT with a band-pass filter (530/40 nm). A SMF was used to generate a Gaussian distribution light field for detection and to minimize the detection errors caused by the position fluctuation of particles. Meanwhile, a MMF, which has a higher capacity for collecting light signals, was used to increase the detection sensitivity.
The feedback system, Azurite (DarklingX, USA), driven by Kytos software (DarklingX, USA), was connected to the PMTs to process the signal. After receiving the fluorescent signal, Azurite sent a 400 μs delayed pulse signal to turn on a function generator (E4422B Agilent, USA) for 100 μs. The radio frequency (RF) signal from the function generator was amplified by a power amplifier (100A250A, Amplifier Research, USA) and was then applied to the focused IDTs.
Sample Preparation:
Fluorescent polystyrene particles of 7.0 μm in diameter (Dragon Green, Bangs Laboratories, USA) were used to characterize the focusing performance. The particles were diluted in 0.1% sodium dodecyl sulfate in water, and the concentration was 1 × 106 particles mL−1. HeLa cells (ATCC, CCL-2, USA) were cultured using Dulbecco’s Modification of Eagle’s Medium/Ham’s F-12 50/50 Mix supplemented with 10% fetal bovine serum and 1% penicillin-streptomycin solution in a 37 °C cell culture incubator. Before the experiment, cells were stained with Calcein-AM (Biolegend, USA) for 30 min and rinsed. The Calcein-AM labeled cells were mixed with unlabeled cells at a ratio of 1:9, serving as the samples for sorting.
Video-Based Characterization:
The SSAW device was mounted on the stage of an inverted microscope (TE2000U Nikon, Japan) which was equipped with a fast camera (SA4, Photron, Japan). A syringe pump (neMESYS, Cetoni GmbH, Germany) was employed to deliver the samples of different concentrations into the microfluidic channel. The flow rate, unless otherwise specified, was fixed at 180 μL min−1 throughout the experiments. To characterize the focusing performance, the movement of particles was recorded from a top-down view using the fast camera and stacked 100 frames of the recorded video to visualize the trajectory of particles. For characterization of sorting purity and yield, 1-second-long videos were periodically recorded at the frame rate of 10 000 frame s−1 for each sample. In each video, a total of 1000 cells were counted including the number of sorted fluorescent labeled cells, sorted unlabeled cells, and unsorted fluorescent labeled cells. The purity and yield were calculated based on Equations (3) and (4), while the throughput was calculated as 1000 events divided by the time lapsed. The data represents the average and standard deviation of three independent measurements (n = 3).
Supplementary Material
Acknowledgements
The authors acknowledge support from the National Institutes of Health (R01 GM112048 and R33 EB019785), the National Science Foundation (IIP-1534645), and the National Natural Science Foundation of China (No. 51536003).
Footnotes
Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.
Conflict of Interest
The authors declare no conflict of interest.
Contributor Information
Liqiang Ren, Department of Engineering Science and Mechanics The Pennsylvania State UniversityUniversity Park, PA 16802, USA.
Shujie Yang, Department of Mechanical Engineering and Materials Science Duke University, Durham, NC 27708, USA.
Peiran Zhang, Department of Mechanical Engineering and Materials Science Duke University, Durham, NC 27708, USA.
Zhiguo Qu, Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China.
Zhangming Mao, Ascent Bio-Nano Technologies, Inc., Research Triangle Park, NC 27709, USA.
Po-Hsun Huang, Department of Mechanical Engineering and Materials Science Duke University, Durham, NC 27708, USA.
Yuchao Chen, Department of Engineering Science and Mechanics The Pennsylvania State UniversityUniversity Park, PA 16802, USA.
Mengxi Wu, Department of Mechanical Engineering and Materials Science Duke University, Durham, NC 27708, USA.
Lin Wang, Ascent Bio-Nano Technologies, Inc., Research Triangle Park, NC 27709, USA.
Peng Li, C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, WV 26506, USA.
Tony Jun Huang, Department of Mechanical Engineering and Materials Science Duke University, Durham, NC 27708, USA.
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