Patent Application
20200027921
This invention relates to electronic microparticles.
Graphene and other 2D materials with atomic thickness exhibit exotic mechanical strength and flexibility and/or functional properties that have significantly advanced numerous fields of science and technology in the past decade. See, Novoselov, K. S. et al. Electric Field Effect in Atomically Thin Carbon Films. Science 306, 666-669, doi:10.1126/science.1102896 (2004), which is incorporated by reference in its entirety. Heterojunctions or composites (e.g. with other nanoparticles) derived from such materials can generate various micro- or nanosized functional hybrids as electronics, optoelectronics, catalysts, sensors, energy storage/generation devices amongst others. See, Liu, Y. et al. Van der Waals heterostructures and devices. Nature Reviews Materials 1, 16042, doi:10.1038/natrevmats.2016.42 (2016), Novoselov, K. S., Mishchenko, A., Carvalho, A. & Castro Neto, A. H. 2D materials and van der Waals heterostructures. Science 353, doi:10.1126/science.aac9439 (2016), Yin, P. T., Shah, S., Chhowalla, M. & Lee, K.-B. Design, Synthesis, and Characterization of Graphene—Nanoparticle Hybrid Materials for Bioapplications. Chemical Reviews 115, 2483-2531, doi:10.1021/cr500537t (2015), Fiori, G. et al. Electronics based on two-dimensional materials. Nat Nano 9, 768-779, doi:10.1038/nnano.2014.207 (2014), Wang, Q. H., Kalantar-Zadeh, K., Kis, A., Coleman, J. N. & Strano, M. S. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat Nano 7, 699-712 (2012), Deng, D. et al. Catalysis with two-dimensional materials and their heterostructures. Nat Nano 11, 218-230, doi:10.1038/nnano.2015.340 (2016), Shao, Y. et al. Graphene Based Electrochemical Sensors and Biosensors: A Review. Electroanalysis 22, 1027-1036, doi:10.1002/elan.200900571 (2010), El-Kady, M. F., Shao, Y. & Kaner, R. B. Graphene for batteries, supercapacitors and beyond. Nature Reviews Materials 1, 16033, doi:10.1038/natrevmats.2016.33 (2016), and Ferrari, A. C. et al. Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems. Nanoscale 7, 4598-4810, doi:10.1039/C4NR01600A (2015), each of which is incorporated by reference in its entirety.
In general, a particle can include a first sheet comprising a layer including a first material, wherein the first sheet includes a first outer surface and a first inner surface; and a second sheet comprising a layer including a second material, where the second sheet includes a second outer surface and a second inner surface, wherein the first sheet and the second sheet form a space, the space is encapsulated by the first sheet and the second sheet.
In certain embodiments, the first sheet further can include a second layer including the first material.
In certain embodiments, the second sheet can further include a second layer including the second material.
In certain embodiments, the first material can be graphene, molybdenum disulfide, hexagonal boron nitride (hBN), molybdenum diselenide, tungsten disulfide, tungsten diselenide, rhenium diselenide, rhenium disulfide, black phosphorus, platinum diselenide, tin sulfide, or tin selenide.
In certain embodiments, the second material can be graphene, molybdenum disulfide, hexagonal boron nitride (hBN), molybdenum diselenide, tungsten disulfide, tungsten diselenide, rhenium diselenide, rhenium disulfide, black phosphorus, platinum diselenide, tin sulfide, or tin selenide.
In certain embodiments, the first outer surface can be functionalized.
In certain embodiments, the first outer surface can be covalently functionalized.
In certain embodiments, the first outer surface can be noncovalently functionalized.
In certain embodiments, the first outer surface can be functionalized via π-π stacking.
In certain embodiments, the first inner surface can be functionalized.
In certain embodiments, the first outer surface can be covalently functionalized.
In certain embodiments, the first outer surface can be noncovalently functionalized.
In certain embodiments, the first outer surface can be functionalized via π-π stacking. In certain embodiments, the second outer surface can be functionalized.
In certain embodiments, the first outer surface can be covalently functionalized.
In certain embodiments, the first outer surface can be noncovalently functionalized.
In certain embodiments, the first outer surface can be functionalized via π-π stacking.
In certain embodiments, the second inner surface can be functionalized.
In certain embodiments, the first outer surface can be covalently functionalized.
In certain embodiments, the first outer surface can be noncovalently functionalized.
In certain embodiments, the first outer surface can be functionalized via π-π stacking.
In certain embodiments, the first sheet can include a plurality of nanopores.
In certain embodiments, the second sheet can include a plurality of nanopores.
In certain embodiments, the space can include a composition.
In certain embodiments, the composition can include electronics.
In certain embodiments, the composition can include liquid.
In certain embodiments, the composition can include gel.
In certain embodiments, the composition can include a nanoparticle.
In another aspect, a method of making a particle can include preparing a first sheet including a first substrate and a first layer comprising a first material on a first substrate, wherein the first sheet includes a first outer surface and a first inner surface, depositing a composition, preparing a second sheet including a second substrate and a second sheet comprising a second material on the second substrate, wherein the second sheet includes a second outer surface and a first inner surface, annealing the first sheet and the second sheet, and autoperforating the first sheet and the second sheet.
In certain embodiments, the method can further include functionalizing the first outer surface.
In certain embodiments, the functionalizing can include covalent bonds.
In certain embodiments, the functionalizing can include non-covalent bonds.
In certain embodiments, the functionalizing can include π-π stacking.
In certain embodiments, the autoperforating can include selectively dissolving the first substrate and the second substrate.
In certain embodiments, the autoperforating can include applying mechanical force or heat treatment.
In certain embodiments, the first sheet can further include a second layer including the first material.
In certain embodiments, the second sheet can further include a second layer including the second material.
In certain embodiments, the composition can include electronics.
In certain embodiments, the composition can include liquid.
In certain embodiments, the composition can include gel.
In certain embodiments, the composition can include a nanoparticle.
In another aspect, a method of detecting an analyte can include applying the particle including a first sheet comprising a layer including a first material, wherein the first sheet includes a first outer surface and a first inner surface; and a second sheet comprising a layer including a second material, where the second sheet includes a second outer surface and a second inner surface, wherein the first sheet and the second sheet form a space, the space is encapsulated by the first sheet and the second sheet, wherein the space includes a sensor and detecting the analyte with the sensor.
In certain embodiments, the particle can be present in a solution.
In certain embodiments, the applying the particle can include aerosolizing the particle in a solution.
In another aspect, a device can include a sheet including a substrate material, a power source on the substrate, a switch on the substrate and a memory element on the substrate.
In certain embodiments, the power source can be a photodetector.
In certain embodiments, the photodetector can generate voltage when it is illuminated with light.
In certain embodiments, the photodetector can include a p-n heterojunction.
In certain embodiments, the photodetector can include a monolayer including MoS2 and a monolayer including WSe2.
In certain embodiments, the switch can be a chemiresistor.
In certain embodiments, the chemiresistor can change conductance upon interaction with an analyte.
In certain embodiments, the chemiresistor can include a monolayer including MoS2.
In certain embodiments, the memory element can be a memristor.
In certain embodiments, the memristor can be turned on when a voltage from the power source exceeds a threshold voltage and the chemiresistor detects an analyte.
In certain embodiments, the memristor can be positioned between a first electrode and a second electrode.
In certain embodiments, the first electrode can include gold.
In certain embodiments, the second electrode can include silver.
In certain embodiments, the memristor can include a material including MoS2.
In certain embodiments, the substrate material can include a polymer
In certain embodiments, the polymer can include an epoxy polymer.
In certain embodiments, a thickness of the sheet can be no more than 5 μm.
In another aspect, a method of making a device can include preparing a substrate, depositing a first monolayer of including MoS2 on the substrate, depositing a second monolayer including WSe2 at least partially in contact with the monolayer including MoS2, depositing a gold electrode on a portion of the first monolayer, depositing a gold electrode on a portion of the second monolayer, depositing a material including MoS2 in contact with the gold electrode on the first monolayer and in contact with the second monolayer, depositing a silver electrode in contact with the gold electrode, and depositing a silver electrode in contact with the material including MoS2.
In another aspect, a method of detecting an analyte can include applying the device including a sheet including a substrate material, a power source on the substrate, a switch on the substrate and a memory element on the substrate and detecting the analyte with the device.
In certain embodiments, the device can be present in a solution.
In certain embodiments, the applying the device can include aerosolizing the device in a solution.
Other aspects, embodiments, and features will be apparent from the following description, the drawings, and the claims.
Graphene and other two-dimensional (2D) materials possess desirable mechanical, electrical and chemical properties for incorporation into or onto new colloidal particles, potentially granting them unique electronic functions. However, this application has not yet been realized because conventional top-down lithography scales poorly for the production of colloidal solutions. Due to its inherent stochasticity, brittle fracture is seldom used as a fabrication method for materials at the nanometer scale. However, Griffith theory allows for the imposition of a specific strain field that can guide fracture along a pre-set design. Disclosed herein is autoperforation that provides a means of spontaneous assembly for surfaces comprised of 2D molecular surfaces. Chemical vapor deposited mono- and bi-layer graphene, molybdenum disulfide, or hexagonal boron nitride can autoperforate into circular envelopes when sandwiching a microprinted polymer or its composite spot of nanoparticle ink, allowing lift-off into solution and the simultaneous assembly. The resulting colloidal microparticles have two independently addressable, external Janus faces that can function as an intraparticle array of parallel, two-terminal electronic devices. As an example, a 0.9 wt % black phosphorous or 0.07 wt % MoS2 nanoflake-in-polystyrene ink is printed into mono-layer graphene sandwich particles, resulting in micro-particles possessing non-volatile, 15-bit memory storage via a spatially addressable memristor array throughout the particle interior. Such particles form the basis of particulate electronic devices capable of collecting and storing information in their environment. The 2D envelopes demonstrate remarkable chemical and mechanical stability for longer than four months of operation in aqueous buffer or even the highly acidic Human gastrointestinal environment at pH 1.5. Such particulate devices survive aerosolization and recollection for electronic interrogation. They can also possess specific surface chemical functionalities as capture sites to react with particular impurity metals and ions in water samples and soil matrices, respectively, and the ability to be recovered for electrical readout. Autoperforation of 2D materials into such envelope structures allows precise compositing of colloidal particulate devices with exotic functions, extending nanoelectronics into previously inaccessible environments.
Disclosed herein are a versatile colloidal micro-particle and its fabrication technique that integrates fully extended 2-dimensional materials into functional electronic circuits. These are used in the context of electronic state-machines, specifically water resistant multi-bit reversible non-volatile random access memory (RAM) devices, and aerosolizable electronics that functions as a stand-alone micrometer sized unit, and is capable of withstanding extreme conditions and harsh environments.
The particles can be used to measure and track things in a specific environment, for example, in the human body. The particles can act collectively. The particles can be constructed in a way to allow the particles or a collection of particles to respond to and collect near a signaling particle that finds an event, for example, a targeted event. An analogy is the human immune system where an infection causes a macrophage to signal to other macrophages who are recruited to the site to heal an infection. In this example, these 2D particles could form the basis of self healing systems where damage in a material is detected by one particle that then promotes the recruitment of others to the site of damage to start a healing process at the damage site. Other modes can include cellular materials, which are materials that can mimic the function of human tissue and its cellular nature. Materials that consist of semi-autonomous cells can transmit information by repeating the signal in each constituent cell, similar to the human nervous system. These particles can also store and use energy locally, avoiding the problems of fuel diffusion through the media leading to a loss of power density. In one example, human muscle tissue both stores and uses fuel in the form of glycogen using the property of a material made up of multifunctional cells. This type of energy storage can be utilized in the particles described herein.
An article can include a first sheet comprising a layer including a first material, wherein the first sheet includes a first outer surface and a first inner surface; and a second sheet comprising a layer including a second material, where the second sheet includes a second outer surface and a second inner surface, wherein the first sheet and the second sheet form a space, the space is encapsulated by the first sheet and the second sheet. Each surface is functionalized individually. Certain molecules can enter syncell through nanopores (
A method of making an particle can include preparing a first sheet including a first substrate and a first layer comprising a first material on a first substrate, wherein the first sheet includes a first outer surface and a first inner surface, depositing a composition, preparing a second sheet including a second substrate and a second sheet comprising a second material on the second substrate, wherein the second sheet includes a second outer surface and a first inner surface, annealing the first sheet and the second sheet, and autoperforating the first sheet and the second sheet.
A method of detecting an analyte can include applying the particle including a first sheet comprising a layer including a first material, wherein the first sheet includes a first outer surface and a first inner surface; and a second sheet comprising a layer including a second material, where the second sheet includes a second outer surface and a second inner surface, wherein the first sheet and the second sheet form a space, the space is encapsulated by the first sheet and the second sheet, wherein the space includes a sensor and detecting the analyte with the sensor. A method of making a device can include preparing a substrate, depositing a first monolayer of including MoS2 on the substrate, depositing a second monolayer including WSe2 at least partially in contact with the monolayer including MoS2, depositing a gold electrode on a portion of the first monolayer, depositing a gold electrode on a portion of the second monolayer, depositing a material including MoS2 in contact with the gold electrode on the first monolayer and in contact with the second monolayer, depositing a silver electrode in contact with the gold electrode, and depositing a silver electrode in contact with the material including MoS2.
A method of detecting an analyte can include applying the device including a sheet including a substrate material, a power source on the substrate, a switch on the substrate and a memory element on the substrate and detecting the analyte with the device.
Microrobots can penetrate inaccessible places and perform various tasks while remaining literally invisible. Furthermore, microrobots can possibly assemble into bigger robots, perform a task and then scatter away. To date, University of Michigan holds a record of miniaturization with millimeter-sized robots. Further reducing size of microrobots is associated with ineffective power supplies and electronics. To overcome this challenge, the synergy between nanotechnology and 2D electronics is used.
As used herein, the term “syncell” is a sub-millimeter programmable state machine, where each syncell is comprised of two sheets with encapsulated 2D electronics, liquid, gel and nanoparticles. The two sheets can be graphene or another 2D layered material. The syncell operates like a synthetic cell, with the ability to hold materials or a payload in an internal cavity between the two sheet layers. The bulged shape is nearly 2D, with an aspect ration of a long dimension to a narrow dimension of at least about 2, at least about 5, at least about 10, or at least about 100. The dimensions of the syncell can be nanoscale, with the average particle size being about 10 nm, 12 nm, 15 nm, 20 nm, 25 nm, 30 nm, 35 nm, 40 nm, 45 nm, 50 nm, 55 nm, 60 nm, 65 nm, 70 nm, 75 nm, 80 nm, 85 nm, 90 nm, or 95 nm. For other applications, syncells can have an average particle size of greater than 100 nm, for example, less than 250 nm, less than 200 nm, or between 100 nm and 200 nm. While 2D electronics dramatically reduces size of the syncell, the configuration has further advantages. Firstly, 2D materials can serve as molecular barriers, which define fluid and gel regions separated from the surrounding solution, in very close analogy to a living cell. Secondly, nanopores present in graphene can be used to control mass transport between the interior and exterior of the syncell. Mediated by 2D electronics, syncell nanopores can serve as switches, energy sources or even as detectors of external species. Thirdly, nanoparticle encapsulation extends any advantages of nanoparticles to the syncell. Fourthly, each of four surfaces of two graphene sheets can be functionalized individually. Such broken symmetry particles remain challenging to fabricate with current nanoparticle synthesis. Finally, syncell's broken symmetry is further favorable for creating functional aggregates.
The syncells can be prepare from graphene, transition metal sulfides, or other sheet-like materials that can be fabricated into thin and flat plates.
Graphene itself, with high electron-density in its sp2-bonded aromatic rings, is impermeable to all molecules except for protons, making it the thinnest membrane for liquid/biological sample encapsulation (even in vacuum conditions) and the ideal protective barrier against harsh environments. See, Bunch, J. S. et al. Impermeable Atomic Membranes from Graphene Sheets. Nano Letters 8, 2458-2462 (2008), Hu, S. et al. Proton transport through one-atom-thick crystals. Nature 516, 227-230, doi:10.1038/nature14015 (2014), Mohanty, N., Fahrenholtz, M., Nagaraja, A., Boyle, D. & Berry, V. Impermeable Graphenic Encasement of Bacteria. Nano Letters 11, 1270-1275, doi:10.1021/n1104292k (2011), Yuk, J. M. et al. High-Resolution EM of Colloidal Nanocrystal Growth Using Graphene Liquid Cells. Science 336, 61-64, doi:10.1126/science.1217654 (2012), and Prasai, D., Tuberquia, J. C., Harl, R. R., Jennings, G. K. & Bolotin, K. I. Graphene: Corrosion-Inhibiting Coating. ACS Nano 6, 1102-1108, doi:10.1021/nn203507y (2012), each of which is incorporated by reference in its entirety. Meanwhile, introducing nanopores onto graphene membranes allows transport of biomolecules, salts and water with high selectivity. See, Schneider, G. F. et al. DNA Translocation through Graphene Nanopores. Nano Letters 10, 3163-3167 (2010), Garaj, S., Liu, S., Golovchenko, J. A. & Branton, D. Molecule-hugging graphene nanopores. Proceedings of the National Academy of Sciences 110, 12192-12196 (2013), Surwade, S. P. et al. Water desalination using nanoporous single-layer graphene. Nat Nano 10, 459-464, doi:10.1038/nnano.2015.37 (2015), Celebi, K. et al. Ultimate Permeation Across Atomically Thin Porous Graphene. Science 344, 289-292, doi:10.1126/science.1249097 (2014), and Cohen-Tanugi, D. & Grossman, J. C. Water Desalination across Nanoporous Graphene. Nano Letters 12, 3602-3608, doi:10.1021/n13012853 (2012), each of which is incorporated by reference in its entirety. Analogously, the smallest unit of life—cell, consisting of cytoplasm enclosed within a thin plasma membrane, can perform various functions like transport of molecules, chemical reactions (i.e. metabolism), locomotion, and reproduction. Graphene can be used as a membrane material to encapsulate small-sized functional devices, just like those organelles in a biological cell, and by taking advantage of recent advances in 2D materials, to generate prototype “synthetic cells” (SynCell) that can flow freely in solution and perform simple functions. Note that nano or microsized SynCells or state-machines that can perform very simple tasks such as computing, data storing, sensing, and actuation can be interconnected into complex nanonetworks for novel applications in environmental, biomedical, and military technologies. See, Akyildiz, I. F., Jornet, J. M. & Pierobon, M. Nanonetworks: a new frontier in communications. Commun. ACM 54, 84-89, doi:10.1145/2018396.2018417 (2011), and Akyildiz, I. F., Brunetti, F. & Blázquez, C. Nanonetworks: A new communication paradigm. Computer Networks 52, 2260-2279 (2008), each of which is incorporated by reference in its entirety. Herein, the controlled fracturing (termed “autoperforation”) of 2D materials as a scalable fabrication technique for free-flowing microparticles that function as two-terminal electronic devices with multiple embedded memristor elements (
Recent studies suggests that the classic Griffith criterion of brittle fracture remains valid for graphene. See, Zhang, P. et al. Fracture toughness of graphene. Nature Communications 5, 3782 (2014), and Yin, H. et al. Griffith Criterion for Brittle Fracture in Graphene. Nano Letters 15, 1918-1924, doi:10.1021/n15047686 (2015), each of which is incorporated by reference in its entirety. A crack propagates while new crack surfaces generate to release the elastic energy. See, Griffith, A. A. The Phenomena of Rupture and Flow in Solids. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 221, 163-198 (1921), which is incorporated by reference in its entirety. A characteristic length scale, known as the Griffith length (L), defined as the ratio of the surface energy (γ) to the elastic energy (Eε2, where E is the elastic modulus and ε the strain). A crack will not grow when its size is less than L. Large-area graphene or other 2D materials prepared by the chemical vapor deposition (CVD) method (see, Reina, A. et al. Large Area, Few-Layer Graphene Films on Arbitrary Substrates by Chemical Vapor Deposition. Nano Letters 9, 30-35 (2009), Kim, K. S. et al. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 457, 706-710 (2009), and Li, X. et al. Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils. Science 324, 1312-1314 (2009), each of which is incorporated by reference in its entirety, albeit mechanically robust (see, Lee, G.-H. et al. High-Strength Chemical-Vapor-Deposited Graphene and Grain Boundaries. Science 340, 1073-1076 (2013), which is incorporated by reference in its entirety), usually carries intrinsic nanometer-sized defects originated from the CVD and subsequent transfer processes, and these seed crack formation is stochastic in nature. In the Griffith formulation, L depends on ε, thereby allowing us to regulate the strain field on the graphene or other 2D surfaces, and manipulate the fracture trajectory for device fabrication. Placing isolated stiff islands (e.g. semiconductor devices) on top of an otherwise compliant substrate, such as a polymer film, can create a strain field that reduces the tension built-in the substrates covered by the those islands. See, Hsu, P. I. et al. Spherical deformation of compliant substrates with semiconductor device islands. Journal of Applied Physics 95, 705-712 (2004), and Sun, J.-Y. et al. Debonding and fracture of ceramic islands on polymer substrates. Journal of Applied Physics 111, 013517 (2012), each of which is incorporated by reference in its entirety. A more recent study shows that conforming a flat elastic sheet to a rigid substrate with Gaussian curvature can control the sheet crack growth upon stretching. See, Mitchell, N. P., Koning, V., Vitelli, V. & Irvine, W. T. M. Fracture in sheets draped on curved surfaces. Nat Mater 16, 89-93 (2017), which is incorporated by reference in its entirety.
An active area of exploration for constrained environment sensing is external imaging, including ultrasound for geological exploration and human body applications, thermal imaging for chemical reactors and gas leak detection, magnetic resonance to probe the human body and porous material beds. Such imaging methods are necessarily indirect and limited in their penetration depth. Inaccessibility often results from systems where the scaling of sensor networks is highly unfavorable, such as pipelines or geological targets. For other systems, direct methods are available, such as endoscopes and borescopes, while the problem of oil well monitoring has benefited from fiber optic cabling for temperature and other measurements, but such approaches are typically limited to major pathways and arteries of accessibility. See Mooney, W. D. & Brocher, T. M. Coincident seismic reflection/refraction studies of the continental lithosphere: A global review. Reviews of Geophysics 25, 723-742 (1987), Frøkjær, J. B., Drewes, A. M. & Gregersen, H. Imaging of the gastrointestinal tract-novel technologies. World Journal of Gastroenterology: WJG 15, 160-168 (2009), Jarenwattananon, N. N. et al. Thermal maps of gases in heterogeneous reactions. Nature 502, 537 (2013), Murvay, P.-S. & Silea, I. A survey on gas leak detection and localization techniques. Journal of Loss Prevention in the Process Industries 25, 966-973 (2012), Amitay-Rosen, T., Cortis, A. & Berkowitz, B. Magnetic Resonance Imaging and Quantitative Analysis of Particle Deposition in Porous Media. Environmental Science & Technology 39, 7208-7216 (2005), Hara, A. K., Leighton, J. A., Sharma, V. K., Heigh, R. I. & Fleischer, D. E. Imaging of Small Bowel Disease: Comparison of Capsule Endoscopy, Standard Endoscopy, Barium Examination, and CT. RadioGraphics 25, 697-711 (2005), Inaudi, D. & Glisic, B. Long-Range Pipeline Monitoring by Distributed Fiber Optic Sensing. 763-772 (2006), Kurniawan, N. & Keuchel, M. Flexible Gastro-intestinal Endoscopy—Clinical Challenges and Technical Achievements. Computational and Structural Biotechnology Journal 15, 168-179 (2017), and Galappaththi, U. I. K., De Silva, A. K. M., Macdonald, M. & Adewale, 0. R. Review of inspection and quality control techniques for composite wind turbine blades. Insight—Non-Destructive Testing and Condition Monitoring 54, 82-85 (2012), each of which is incorporated by reference in its entirety.
Due to the fabrication process, the syncell top and bottom graphene layers can be electronically insulated, which provides an ideal vertical structure of a duo-electrode system where graphene sheets are used as the two electrical terminals. It should be noted that the coverage of graphene over the syncell surface is perfect, as characterized using Raman spectroscopy of the lifted-off syncells (
The in-plane conductivity of these colloidal particles was explored and an in-plane sheet resistance was 2×10−4 times that of the polystyrene control without the graphene top and bottom layer. This sheet resistance increased 1.5 times after storing the syncells 4 months in solution (water/ethanol mixture) (
By placing liquid exfoliated black phosphorus (BP) nano-flakes within the interior of the graphene cell (
Due to the limited range of the spreading current on the syncell surface, multiple bit can be addressed separately over the entire syncell surface (
Mechanical Stability as Syncells Travel Through Air Like Aerosols
Syncells are capable of surviving highly turbulent area travel after been nebulized from a water solution and sprayed across a 30 cm distance in air with an air brush (
The statistics of the syncells survived air travel was plotted as a function of distance to center where the nebulizer points (
i. Chemical Stability as Syncells Travel Through Mammalian Digestive Track (In Vitro Results Using Stomach Acid Model Solution)
The mammalian digestive track corrosive environment was mimicked to test syncell stability, an in vitro protocol that was widely used was borrowed as the test environment: SBET (Simple Bioaccessibility Extraction Test): 100±0.5 mL extraction fluid (0.4 M glycine adjusted to pH 1.5 with concentrated HCl) is added to 1.0±0.5 g of dry weight of things to be digested. This mixture is rotated end-over-end at 37 C at 30±2 rpm for 1 h. It should be noted that syncells subjected to this test suffers no loss in integrity (
Microrobots are not so small, mainly because of power limitations. However, even with basic capabilities, new capabilities of simple chemiresistors can sense analytes over big volumes. Moreover, using 2D materials dramatically reduces size and weight of such devices, making them actually freely flow in air.
Here, aerosolizable electronic microparticles are capable of detecting analytes in air with subsequent to access to the detection event through electronic readout. This will be the first micrometer particle incorporating electrical contact on its surface. In certain embodiment, a microparticle can consist of polymer base, golden contacts and monolayer MoS2 acting as a sensor.
Design
Fog droplets are in the range of 10-100 um, while rain droplets are bigger. Similar design rules apply to the particles: simple calculations on drag show that particles need to be smaller than 100 um to successfully float in air.
While many nanoparticles and microparticles exist that can sense analytes in air, the condition of post-electrical readout puts new constrains. Normally electrical circuits are designed on planar interfaces and only recently starting on bended flexible ones. The difficulty of fabricating a particle with electrical contacts is associated with the careful choice materials and their respective developers that often have to be orthogonal, meaning that independent photolithography steps can be performed. All fabrication steps should not dissolve substrate, but eventually syncell should be lifted off.
MoS2 Sensing
MoS2 monolayers are changing their properties when analytes adsorb on their surface. This happens because of electron or holes MoS2 doping, depending on the analyte type. Change in carrier concentration affects MoS2 conductivity σ:σ=e×n×μ, where e is electron charge, n carrier concentration and μ electron mobility. Number of carrier also modifies non-radiative decay time, affecting MoS2 photoluminescence. Indeed, MoS2 photoluminescence is caused by radiative decay of photoexcited excitons. Modification of non-radiative lifetime leads to photoluminescence modification and peak spectral shift.
To demonstrate MoS2 sensing capabilities, triethylamine droplets were dispersed on the way of aerosolized syncells (
Similarly, gas detection was demonstrated on example of ammonia detection (
The particles described herein can be made using alternative synthetic routes. For example, synthetic cells can be produced from 2D material fracture and self assembly or by top-down lithography. There are other methods that can be used as well. For example, the synthesis of self assembling Janus particles that have different functions incorporated in a radially asymmetric way can form larger clusters with pre-designed functions within. Also, a heirarchy of cellular particles can be used to build up more complex particles from them. This can include placing smaller cells within a larger cell to isolate certain functions. Biological cells do this in the formation of organelles that have specific functions. Smaller 2D material cells that serve the function of memory, energy, sensing, light detection, communications, reproduction and repair (and not limited to this list) could be combined and incorporated into larger particles to serve specific tasks.
Autoperforation of Graphene for Free-Flowing 2D Electronic Microparticles with Memory
Due to its inherent stochasticity, brittle fracture is seldom used in fabrication. Herein, fracture in 2D materials can be templated and guided by encapsulating particles that create a local strain field. For polymer-supported chemical vapor deposited graphene, molybdenum disulfide, hexagonal boron nitride (hBN), molybdenum diselenide, tungsten disulfide, tungsten diselenide, rhenium diselenide, rhenium disulfide, black phosphorus, platinum diselenide, tin sulfide, or tin selenide, when sandwiching an printed microspot array and lifted-off into solution, fracture-driven perforation, or “autoperforation”, of 2D sheets occurs along the edges of each spot. This generates colloidal microparticles with well-defined 2D surface layers and controllable surface functionalities on either side. Graphene-based particles function as free-flowing electronic devices with complex functionality. For example, printing a mixed ink of polystyrene (PS) nanoparticles and black phosphorous (BP) nanoflakes yields a percolated BP (0.9 wt %)/PS composite spot and turns each particle into a two-terminal memristor array with time-dependent electrical memory. These particles exhibit extraordinary chemical-resistivity and mechanical stability during months of preservation in an aqueous environment, overnight gastrointestinal test, and aerosolization. Autoperforation of the 2D materials, in this way, opens the door to precise compositing of 2D materials with various micro- and nano-objects for function manipulation/generation.
Disclosed herein is an “autoperforation” method that exploits the strain field induced by the encapsulated materials to guide crack propagation within CVD-grown 2D films, and prepare microparticles consisting of functional nanoparticles sandwiched in between two graphene membranes (
For example, an addition to the particles that could grant them locomotion is putting Pt on one side in such a way that they will move in a H2O2 bath by decomposition of this molecule to O2 and H2O. The use of glucose oxidase near the Pt could result in the same locomotion with glucose in the medium instead of H2O2, since glucose reacts at this enzyme to the lactone, yielding H2O2 which then can decompose. This ability to use a chemical bath to power the particle and give it the ability to move solves the problem of finite energy storage inside of the particle itself. One can also design a ‘governor’ in the form of a hydrogel that is porous, which can swell and contract in response to some input stimulus. Temperature, pH and specific chemical binding can all be used to dynamically control this swelling. If the Pt catalyst is placed on the other side of this hydrogel, separated from the solution, then the reaction and the resulting impulse for motion can be slowed or accelerated by the contracting or expanding of the hydrogel, respectively. This can allow functions within the particle such as detection and memory to control motion, via stimuli to the hydrogel such as temperature, pH, chemical binding etc. A particle that releases acid, for example, can influence this governor and control motion. This release can also stimulate other nearby moving particles, causing them to move or stop collectively, hence mimicking aspects of the human immune system where signaling, recruitment and locomotion are controlled for a collection of actors.
In another example, 2D materials can be implemented as atomically-thin molecular barriers. These barriers can encapsulate analytes inside microparticle with an ability of releasing analytes through pores in 2D materials. Additionally, these pores can allow flux of analytes inside microparticles. Such liquid and gas exchange can also take place inside the microparticle, where 2D materials form isolated volumes, similarly to cells' organelles.
In certain embodiments, outer surface can have patterned electronic layouts. The interaction of several microparticles with such layouts can shortcut electrical connection, altering electronic layout and changing particle functions and capabilities. Microparticle function is therefore determined by the presence of other microparticles. Different microparticles can induce different circuits on top of the microparticle upon their contact.
The microparticle has well-preserved graphene on both surfaces and the graphene sheet significantly improves the colloidal stability during the liftoff and storage (
The lateral profiles of microparticles were measured (
A coarse grained finite element model was first constructed to visualize the folding dynamics of a PMMA/graphene film onto the printed microspots (regular microcylinders with an aspect ratio h/D=1/100 were used in the model,
where ε1 and ε2 refer to the graphene lattice strain under tensile force F, interior and exterior to the microspot, respectively. The microspot height h (μm) is a function of its radius r (
The graphene fracture process was numerically simulated with randomized initial seed cracks, and observed that this strain heterogeneity can both attract crack growth, and guide the crack trajectory along the maximum hoop strain (
with observations that lifting-off microparticle array printed with 0.2 wt % PS ink generated a cluster of unperforated microparticles (
The graphene microparticle has high surface conductivity and can function as a two-terminal electronic device when compositing PS with BP (
Interestingly, this conductive mode can be manipulated to an electrically bistable resistive switch by compositing a very small amount (0.9 wt %) of liquid-exfoliated BP nanoflakes (1-3 layers,
The G-PS/BP-GS microparticle is essentially a non-volatile reversible random access memory (RRAM) device.
The unique chemistry of BP nanoflakes and the percolated structure of BP/PS composite made this memory. BP nanoflakes degrade and react with oxygen and/or solvent molecules during liquid exfoliation and generate complex functional groups with oxygen atoms (e.g., phosphates and phosphonates) on the flake surface or edge (see, Brent, J. R. et al. Production of few-layer phosphorene by liquid exfoliation of black phosphorus. Chemical Communications 50, 13338-13341, (2014), and Hanlon, D. et al. Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics. Nature Communications 6, 8563, doi:10.1038/ncomms9563 (2015), each of which is incorporated by reference in its entirety, and XPS results of
Scanning electron microscope (SEM) image of the PS/BP composite in
Interestingly, the long-term memristor behavior of these microparticles, i.e., ON/OFF ratio N, depends on the time they spend in solution (
N=2.26×104e−0.10t (2)
This yields a half-life of 7 days for the N decay. Therefore, even though these microparticles seem to remain their robustness (or sustained N values) upon subjected to water with a relatively short time, e.g., 8×10 min (see
The scaling suggests that dissolved oxygen and/or water may gradually permeate into the BP/PS interior through intrinsic defects and nanopores within the CVD graphene membranes.26 Water and oxygen can react with and etch out superficial BP irreversibly, 27, 28 as evidenced by XPS comparisons between 0 and 90-day microparticles (
Digital information can be electrically written to the microparticles by lifting them off as freely dispersing colloids into a solvent like ethanol and then recapturing them with a subsequent read out the written information (
The particulate nature of these two-terminal devices renders them the property of fluid dispersion, and therefore convective mobility, which allows one to bring electronics to otherwise inaccessible locations. Applications include “aerosolizable electronics” as probes for remote sensing and recording of environmental information from unconventional spaces. To test the ability of aerosolization of G-PS-G particles, an airbrush at 1.7 atm (
The unique capability of the autoperforation technology to engineer the surface chemical functionalities and the interior filler composition of the microparticles can further bring the two-terminal electronic devices desirable functions. For example, possessing capture sites to react specific impurity metals and ions in water samples and soil matrices, respectively, and the good recoverability (
The graphene microparticles are acid proof and mechanically stable and flexible. For example, G-PS-G can retain their circular shapes after treated with a pH=1.5 solution (0.4 M glycine adjusted by concentrated HCl) mimicking human gastrointestinal tract overnight (
Autoperforation is highlighted as a platform technology that can also generate 2D Janus particles with different surface chemistry and/or 2D surfaces (
Microparticles were also prepared with various 2D surfaces, like G/PS/MoS2, MoS2/PS/MoS2 (
In summary, an autoperforation method is developed to guide the fracture of 2D materials, by controlling its strain filed with a sandwiched microspot array. Using this method, a free-flowing two-terminal electronic device was prepared—a microparticle consisting of two graphene sheets as surface electrodes and the percolated BP/PS composites as interior memory storage materials. It functions as an aerosolizable and multi-bit memristor device and the memory behavior (i.e. ON/OFF ratio) depends on its storage time in the aqueous environment. The autoperforation is also a platform technology to prepare 2D Janus particles with broken chemical symmetry using various 2D surfaces and interior fillers. The autoperforation technology for the scalable development of 2D microparticles can pave the way for next generation free-floating electronics or state-machines that can integrate into a nanonetwork for complex tasks.
This is the first example of scaling electronics down to a micro-particular level that can survive in harsh conditions. Any other technology based “smart dust”, “smart colloidal particles” on the market or in academia is either orders of magnitude larger than the ones disclosed herein (2 mm3 as demonstrate by Berkeley recently) or not qualified as electronics (pH sensing colloids using polymer chemistry). This is also the first time that one can fabricate 2d material electric/colloidal devices on such a large scale with a lithography-free industrially scalable method. There aren't many competing visions in this space. Immense commercial applications are within reach followed by the mature development of this technology. Portable micro-meter scaled random access memory (RAM) devices as well as “aerosolizable chemical sensor” are demonstrated, which should both find immediate applications in the biomedical and chemical industry space. These devices should find applications in scavenging environments that are otherwise unattainable: such as in an oil well or human digestive track and relay valuable information out.
Monolayer and multilayer h-BN (Boron Nitride) film (2″×1″) grown in copper foil was purchased from Graphene Supermarket and used as received. Monolayer and bilayer graphene and MoS2 were grown in the lab with the following procedures:
For Graphene: CVD graphene sheets were produced with a procedure same as in Liu et al. See, Liu, P., et al., Layered and scrolled nanocomposites with aligned semi-infinite graphene inclusions at the platelet limit. Science, 2016. 353(6297): p. 364-367, which is incorporated by reference in its entirety. Briefly, copper foil (Alfa Aesar, 99.8%, 25 μm thick, for graphene growth) with a size of 2.0×2.2 cm was used as substrate, the copper was annealed at 30 sccm H2 gas flow (˜560 mTorr) for 30 min at 1000° C. and then 0.5 sccm (for single layer graphene) or 10 sccm (for bilayer graphene, see Tu, Z., et al., Controllable growth of 1-7 layers of graphene by chemical vapour deposition. Carbon, 2014. 73: p. 252-258., which is incorporated by reference in its entirety) methane was introduced for 15 min or 10 min, respectively. After that, the furnace was kept at 1000° C. for another 5 min and turned off. Cu foil was cooled down and removed out at room temperature.
For MoS2: Sapphire or SiO2 substrate (7.0 cm×1.7 cm) washed with acetone (5 min) and isopropyl alcohol (IPA, 5 min) was used in the growth of MoS2, MoCl5 powders (Sigma Aldrich, 99.99%, ˜4 mg) was loaded onto a SiO2/Si substrate and placed in the central part of the heating zone, the sulfur powder (Sigma Aldrich, 99.998%, ˜0.5 g) was added in a separate Al2O3 boat and placed at the upper stream side of the tube where the temperature was about 200° C. during the reaction. The sapphire or SiO2 substrate was placed at the downstream side 1 cm next to MoCl5. The tube was purged with 50-sccm Ar under vacuum for 30 min, then the furnace was heat to 850° C. in 30 min. The Ar flow kept at 50 sccm and the displayed pressure was about 1.13 torr. The tube was kept at the same temperature for another 10 min and then cooled down to room temperature naturally.
60 mg of black phosphorus dispersed in 20 mL EG and a tip sonicator with a power of (10% maximum power) sonicated the mixture for 10 hours with liquid cooling at 4° C. to get the exfoliated solution. This solution was centrifuged at 2000 rpm at room temperature for 20 min and the final dispersion of BP nanoflakes was obtained. To determine the concentration of BP nanoflakes, 1.5 g solution was sampled and filtered using 0.2 μm-sized PTFE syringe filter, and weighted the BP nanoflakes left on the filter after drying under vacuum overnight. The dispersion was diluted to solutions with different concentrations for the UV-Vis test. Spin coating was used to prepare samples of BP nanoflakes on SiO2/Si (or gold-coated) substrate for AFM, Raman spectroscopy, and X-ray photoelectron spectroscopy (XPS) test. A droplet of the dispersion was added on to a Holy-carbon grid and dried under vacuum to prepare the specimen for TEM.
In the fabrication, (1) pristine graphene, MoS2, or hBN grown by CVD method directly or alternatively, (2) functionalized graphene were used to produce Janus particles with a broken chemistry symmetry.
For (1), a PMMA layer was spin-coated around 230 nm onto the surface of the graphene/copper foil (or MoS2/SiO2) using 950PMMA A4 (MicroChem) at 3000 rpm for 1 min. The copper layer (or SiO2 layer) was etched out with ammonium persulfate (APS-100, TRANSENE CO INC) (or 1 M KOH solution at 80° C. for SiO2), and the left graphene (or MoS2)/PMMA film was rinsed with deionized water. Then Si/SiO2 substrate was picked up with the graphene side up (attaching the film from top side of the floating film on water) or a polydimethylsiloxane (PDMS) stamp (2.5×2.5 cm, 2 mm thickness) which has been attached to the graphene/PMMA layer already before the etching step.
For (2), a noncovalent functionalization strategy via π-π stacking was used to modify the graphene layer first before spin coating and etching. Specifically, the copper/graphene (single layer or bilayer) and a size of 2.0×2.2 cm was incubated in the dimethyl formamide (DMF) solution of functional molecules for 1 h and washed with fresh DMF, ethanol, and dried at room temperature (the washing step can remove those excess molecules which were not attached to the graphene surface). 2 mL DMF solution of 1-pyrenebutyric acid (97%, Sigma Aldrich), 1-aminopyrene (97%, Sigma Aldrich), 1,5-diaminonaphthalene (97%, Sigma Aldrich), or other functional molecules (2 mmol/L) was added into a 10 mL-beaker with copper foil, and mechanically shaken for 1 h, then the copper foil was removed out and rinsed with DMF and ethanol in sequence, with each of 30 s. After drying, following steps including spin-coating, etching, and transfer are the same as above. For characterization, the film was transferred onto Si/SiO2 substrate with the graphene side down and characterized with Raman spectroscopy with or without washing out the PMMA layer using acetone, to compare with the pristine graphene.
To functionalize the other side of the graphene film, in this step, methanol, a poor solvent of PMMA was used to prepare the solution of functional molecules. Functional molecules like 1-pyrenebutyric acid N-hydroxysuccinimide ester (95%, Sigma Aldrich) (4 mmol/L) and 1, 5-diaminonaphthalene were used in this step (1-pyrenebutyric acid N-hydroxysuccinimide ester dissolves in methanol at 80° C.). A few drops of the solution (˜0.5 mL) were added to overcover the surface of PMMA/graphene film on the SiO2/Si or PDMS substrate and the incubation time is 15 min. After that, the film was rinsed with fresh methanol for 30s to remove any residual functional molecules that are not attached to the graphene surface. After drying, the film is ready for the ink-jet printing in the next step. The SiO2/Si-supported film was characterized with Raman spectroscopy to confirm the functionalization.
4. Ink-Jet Printing of Polymer Latexes or their Composite Solution with Nanoparticles
In this step, polystyrene (PS) latex nanoparticles ink or its composite ink with various nanoparticles was printed onto Graphene A to generate a microspot array. Specifically, polystyrene (PS) latex solutions (Sigma Aldrich, PS or amine-modified PS, 0.10 μm or 0.05 μm mean particle size, 2.5 wt %) for example, were diluted with ethylene glycol (EG) to 1.2% (vol:vol=1:1), 0.83% (1:2), 0.50% (1:4), and 0.25% (1:9) as inks for the printing. The PS latex nanoparticles solution was also mixed with zinc oxide (ZnO) nanoparticle ink (2.5 wt. %, viscosity 10 cP, work function −4.3 eV, Sigma Aldrich) and further diluted with EG (VPS:VZnO:VEG=2:1:1) to prepare ZnO/PS ink; or iron oxide(II,III), magnetic nanoparticles solution (30 nm avg. part. size, 1 mg/mL, Sigma Aldrich) and dilute with EG (2:1:1) to prepare magnetic nanoparticle/PS ink; or the exfoliated BP solution (0.25 mg/mL, 1:1) to prepare BP/PS ink for printing. In the inkjet printing (MICROSYS, Cartesian Technologies) at room temperature, a ceramic printer needle was used and the printed ink volume is 1 nL for each dot, the space between the two adjacent dots is 500 μm, and the printing area is typically 1.5-2.0 cm in length and width. After printing, the ink was dried at room temperature overnight and further under house vacuum for 1 h. The printed dot array together with Si/SiO2 or PDMS-supported graphene/PMMA film was annealed at 120° C. for 10 min and cooled down to room temperature, and ready for the next step. The printer Fujifilm Dimatrix Materials Printer DMP-2850 was used and an ink volume of 10 pL or 1 pL was printed to prepare smaller-sized microspot with PS latex ink (1.25 wt %, 50 nm mean particle size, in mixture of water and ethylene glycol (1:1)).
Same as the preparation of graphene A above, (1) pristine 2D sheets or (2) functionalized 2D sheets was used to generate graphene B/PMMA film as the cover layer for stacking. Particularly, one-side functionalized graphene/PMMA film in step 4 was transferred onto a relatively larger Si/SiO2 wafer (5×5 cm) with graphene underneath. Drops of the solution of functional molecules such 1-pyrenebutyric acid N-hydroxysuccinimide ester, 1,5-diaminonaphthalene in methanol were added until the complete infusion of the solution into the underlying surface of the graphene/PMMA film. The film was incubated for 10 mins and after that, washed with fresh methanol, transferred back to the deionized water, and rinsed with water for 4 times with 10 mins each time. This film was floated in water and ready for the next step.
This stacking and liftoff procedure is the same for the pristine graphene or functionalized graphene. Specifically, the annealed graphene/PMMA film on SiO2 or PDMS substrate with the printed array of Step 6 severs as the bottom layer to pick up the cover layer of Step 6 from water. The two films with the sandwiched microspot array were dried at room temperature for 1 h and then annealed at 120° C. for 15 mins. After that, the films together with the substrate were placed into a 50-mL beaker with a magnetic stir bar, 15 mL of ethanol/water (4:1 in volume) was added, the beaker was sealed with paraffin and heated to 80° C. under magnetic stirring (1000 rpm) for 10 mins, after that, the solution was cooled down to room temperature, with visible, dark particles suspending in the solution. After standing overnight, these particles were settled down and the solution was replaced with fresh ethanol/water (4:1). The heating, stirring, settling down, and solution replacement procedure was repeated another two time to remove any residual PMMA in the solution or on the graphene surface and after that, these particles were stored in the solution and sampled out on to glass slide, SiO2 substrate, or ITO-coated glass via dropper for further characterizations or measurements.
7. Microparticles with Molybdenum Disulfide (MoS2) and Hexagonal Boron Nitride (hBN).
The preparation procedure is similar to that of graphene microparticles above. The only difference is the transfer of MoS2 sheet. Monolayer MoS2 grown on Si/SiO2 substrate was spin-coated with a thin PMMA layer and the MoS2/PMMA film was removed out from the SiO2 substrate using KOH solution (2 M in water) as etchant at 80° C. The film was rinsed with deionized water 5 times and used for the further printing and stacking to prepare microparticles with MoS2 surface. For hBN syncell, single layer or multi-layer CVD hBN film grown on copper foil was used, so the transfer and further preparation of hBN microparticles are the same as that of the graphene particles above.
The optical images of microparticles were acquired from ZEISS Axio Scope A1 with magnification of 5 and 20 times. The visualization of the liftoff process was also monitored the same microscope. Raman spectroscopy was performed on a Horiba Jobin Yvon LabRAM HR800 system using a 532 nm excitation laser, 10× objective lens with ˜10 μm diameter spot size, and 1800 lines/mm grating. The profile data of the microparticles were obtained with Tencor P-16 Surface Profilometer™ using a 2 um radius diamond tipped stylus Step height, with a measurement range of 20 Angstroms to 1 mm. Static water contact angle was measured by ramé-hart Model 590 goniometer. The transmittance of BP solution was measured with Shimadzu UV-3101PC Spectrophotometer at wavelength of 660 and 1176 nm, freshly exfoliated BP solution was used as stock solution and dilute with different times for the measurement.
Atomic force microscopy (AFM) was performed using Asylum MFP-3D-BIO in tapping/AC mode with Si tips (Asylum, AC240TS). The scan rate was 0.7 Hz and scan angle was set to be 0°. Black phosphorus (BP) samples was prepared via spin-coating onto a plasma-treated SiO2/Si substrate. Scanning electron microscope was conducted on Zeiss Merlin High-resolution SEM, which is equipped with an in-lens energy selective backscatter detectors for back-scattered electron imaging and the visualization of regions of different composition. The BP/PS composite sample was prepared via mixing of 100 μL of PS latex nanoparticle dispersion (2.5 wt %) and 100 μL of BP dispersion in ethylene glycol (0.25 mg/mL) and drying on hot plate of 120° C. for 10 mins. Transmission Electron Microscopes (TEM) of BP nanoflakes was carried on JEOL 2010 Advanced High Performance TEM and BP nanoflakes were suspended on holy-carbon grid for the characterization. For the fluorescence imaging of MoS2 or graphene microparticles, the particles together with solvent were sampled and naturally dried on glass slides, a broadband supercontinuum white light source (NKT Photonics, SuperK EXTREME EXR-15) was attenuated with a neutral density filter. Fluorescence signal was filtered with band-pass and collected on a 512×512 pixel imaging area of electron multiplying charge coupled device (EMCCD) camera (Andor, iXon3). X-ray photoelectron microscopy (XPS, Kratos AXIS Ultra spectrometer with a monocromatized Al Kα source) was used to analyze the surface chemistry and compositions of various samples including microparticles with different 2D materials and different storage time, funtinalized graphene, BP nanoflakes, and others.
9. Study the Electrical Properties of Graphene Microparticles with Probe Station
A MATLAB code was written to execute commands over a semiconductor parameter analyzer (SPA) (Agilent E5262A Source Measure Units), which is used to query electrical information of the microparticles aided by a probe station. The microparticles were loaded into a probe station chamber and the electrical measurements were carried out in an ambient environment at room temperature with sweeping voltage rate was 50-100 mV/s. In general, the electrical properties of these 2D materials microparticles can be categorized into two major modes: in-plane mode and vertical (out-of-plane) mode. In the in-plane mode, the microparticles are placed onto an insulating surface (typically glass) with one of the 2D material (typically graphene) surfaces facing up, and the Tungsten (W) probe head gently placed on the material surface. In order to aid the process of locating a microparticle under the microscope atop the probe station, its location is separately located under an optical microscope and marked before it was placed in the probe station. In the vertical mode, vertical conductivities (or through-plane conductivity of the 2D material-composite vertical stack, i.e. Gr-PS/BP-Gr) are typically tested. In this case, a conductive substrate for the microparticle is needed to complete the probe-particle-substrate circuit. ITO substrate was selected for its robustness.
Microparticles G-MoS2 (0.07 wt %)/PS-G after a storage time of 2 months in the ethanol solution were used in the experiment. Specifically, a few droplets of microparticle solution were sampled and transferred it onto an ITO-coated glass. After drying the solvent under ambient conditions and further at vacuum for 1 h, the ITO/glass was placed with the deposited microparticles onto the probe station. A grid was drawn on the real-time image of the microparticles on the screen to facilitate the location of 12 spots on the microprobe (tip diameter=5 μm) for reading out and the write-in. A voltage sweeping of 0-0.15 V was first applied to read out the initial conductance status of the 12 spots and later selectively switching on 6 spots with a voltage sweeping of 0-5 V, and at the same time, keeping the other 6 spots unchanged. After this, the ITO/glass was removed out from the probe station and added ethanol solvent on to the surface to lift off the microparticles on the surface. Mechanical agitation was applied using fine glass tube or needles to assist the liftoff and the liftoff process was also visualized under the optical microscope. The microparticles will stay in the solution for 10 min after liftoff and is dried the solution under ambient conditions and further at vacuum again. The conductance of the twelve spots were read out on the probe station by applying a voltage sweeping of 0-0.15 V again. Here each microparticle has its own tails or shapes that differentiates it from others so that the same microparticle was identified before and after liftoff. The same grid was drawn to locate the spots with turning on treatment in previous so that the microprobe can read out the vertical conductance change of these same spots after liftoff for comparison.
Aerosolization of the dispersion of graphene microparticles was conducted with an airbrush (Master Airbrush G222 Pro SET, 0.5 mm set size) with a working pressure of 1.7 atm (25 psi) and distance of 30 cm. Specifically, 5 mL of microparticles (G-PS-G) solution was loaded and sprayed out using the air pressure generated by an air compressor (Master Airbrush Model C16 Black Mini Air Compressor). The microparticles together with the aerosolized solution were flying in air and collected by a board consisting of 21 (7×3) glass sides, which is 30 cm away from the airbrush. The microparticles collected by the glides have been further investigated with optical microscope for counting, morphology study, and position tracking, and Raman microscopy to study the graphene coverage.
If the collecting slides have a conductive surface, a thin ITO coating layer for example, the collected microparticles via either aerosolization or natural drying, with the substrate, can be placed onto the probe station for the direct writing-in and erasing-out of the digital memory, i.e., using the probe to switch on and off locally. If regular glass slides or other materials with an insulating surface were used, a contact transfer printing method that using an adhesive tape, e.g., conductive copper foil tape was applied to stick onto and transfer the particles out from the insulating surface to the desired copper foil tape. For the demonstration at a macroscopic level, G-PS/GOx (1 wt %)-G and G-PS/MoS2(0.07 wt %)-G particles fabricated via capillary printing with a diameter around 1-2 mm were used, with or without silver. The dispersion of the particles were sampled and dried on a glass slide, and then used both paper tape and conductive copper foil tape to conduct the contact transfer printing on a cm-sized area. In addition, the individual dried particles can also be picked up and transferred onto the tape via tweezers.
The mammalian digestive track corrosive environment was mimicked to test the chemical stability of G-PS-G, an in vitro protocol that was widely used as the test environment. Specifically, in a SBET (Simple Bioaccessibility Extraction Test) (see Oomen A G, Hack A, Minekus M, Zeijdner E, Cornelis C, Schoeters G, et al. Comparison of Five In Vitro Digestion Models To Study the Bioaccessibility of Soil Contaminants. Environ. Sci. Technol. 2002, 36(15): 3326-333, and Ruby M V, Davis A, Link T E, Schoof R, Chaney R L, Freeman G B, et al. Development of an in vitro screening test to evaluate the in vivo bioaccessibility of ingested mine-waste lead. Environ. Sci. Technol. 1993, 27(13): 2870-2877, each of which is incorporated by reference in its entirety), 100±0.5 mL extraction fluid (0.4 M glycine adjusted to pH 1.5 with concentrated HCl) was added to 1.0±0.5 g of dry weight of things to be digested. This mixture is rotated end-over-end at 37° C. at 30±2 rpm for 1 h. Similarly, G-PS-G microparticles placing on glass slides were treated with same acidic mixture overnight rather than 1 h.
Graphene microparticles (G-PS-G) were used with surface —NH2 functionalities for the demonstration. Briefly, the 1,5-diaminonaphthalene-functionalized microparticles in ethanol/water (4:1) solution were concentrated by centrifugation, a small droplet (about 0.1 mL) of the dispersion was sampled out with a large number of microparticles, added it to 2-mL gold nanoparticle solution (˜6.0E+12 particles/mL in citrate buffer, Sigma-Aldrich, 10 nm diameter), and incubated for 1 h. The microparticles were then separated from the solution via centrifugation. After three cycles of washing with fresh ethanol/water mixture and centrifugation, a droplet of the solution was finally retraced out with the dispersed microparticles and placing it on an ITO-coated glass. After drying overnight at vacuum overnight at room temperature, the surface conductivity of the microparticles and Raman spectra of 10 different microparticles were measured for a statistically study.
To demonstrate the ability to deploy these microparticles to function as stand-alone detectors in this practical scenario, both outer surfaces of the graphene layer of the microparticles were non-covalently functionalized with the nitrilotriacetic acid (NTA) ligand, and turn them into retractable sensor nodes for trace amounts of Zn2+ ions present in the ground soil, which is a crucial plant micronutrient that involves in many physiological functions of plants. Specifically, the microparticles were fabricated with polystyrene (PS)—Fe3O4 magnetic nanoparticle composite core, flanked by two double-layer graphene sheets on the top and bottom, following the standard procedure introduced previously. To functionalize the NTA ligand onto the outer surface of the graphene layers, a pyrene-containing linker, 1-pyrenebutyricacid-N-hydroxysuccinimide ester (Sigma Aldrich), then reacted with N,N-bis(carboxymethyl)-L-lysine hydrate (Sigma Aldrich) were used at room temperature, after adjusting the pH to 9.0, using an NHS ester amine-reactive cross-linking chemistry.
A. Strain Guided Fracture Propagation with Stochastic Seed Crack Formation
a. An Existing Model
There is an existing model on soft material fracturing within a strain field induced by curvature.
a. Model Derivation
There will be fluctuating tensile stretches in the graphene lattice once the PMMA layer is removed by the ethanol/water solution due to turbulent fluid flow. The primary purpose of this section is to estimate the strain distribution due to this random stretching/compressing of the free-standing graphene lattice by the external forces.
1. Consideration of a 2D Slice
To get started, a simple 2D slice is considered to find the relation between strain and elastic moduli of materials involved as well as their thickness, as informed by the vertical profile measurement of the microparticle (
This concave-down dough shape is captured by the sketched profile (
2F=EGrε2(r)2TGrw=ε1(r)EPMMAh(r)w+ε1(r)EGr2TGrw (9)
where F is the magnitude of force F, and ε1, ε2 are the material relative strain for Gr-BP/PS-Gr composite and Gr-Gr, respectively. Note PS was used to approximate the BP/PS composite, which is reasonable considering BP's low concentration within the PS matrix. This yields the following relationship:
which relates the relative strain outside the PS microspot to that within. Now that all is needed is to set an appropriate boundary condition to correctly evaluate the force F.
1. A Radially Symmetric 3D Model
By taking advantage of radial symmetry, one can easily generalize this 2D slice into a 3D model. It should be noted that since there is less and less material towards the middle of the microparticle, in order to withstand the same amount of force outward (which is clearly conserved), then materials closer to the center need to be stretched more, thereby having a larger strain. Without loss of generality, the center of the microparticle was set as the origin of the cylindrical coordinates, it then follows from Eq. (10) and the corresponding 3D force balance,
where ε2RF is defined as the relative strain at which force of magnitude F is applied to the ring of materials at radius RF. And if RF=250 μm and ε2RF=0.1% is set, and to approximate the dough shape of the microparticle, its vertical profile is approximated as:
where R0 is the radius of the PS microspot, which is set to 100 μm to the best estimation. This model yields a strain contour for the graphene materials that shows maximum strain built-up right outside the microspot (
a. Overview
A theoretical model that simulates the kinetic process involved in the first step of the autoperforation of bi-layer graphene during the microparticle fabrication process is developed. A mathematical model implemented in MATLAB allows us to predict the shape of the system after the first step as well as where the graphene sheets are most strained. A more thorough understanding of the mechanics of autoperforation, and how varying parameters affect the resultant shape, is crucial in order to be able to design customizable microparticles of different shapes, sizes, and materials.
b. Theoretical Considerations
1. A Kinetic Process
This model numerically solves the differential equations of motion that govern the auto-perforation process. The advantages of a kinetic model, as opposed to a thermodynamic—or equilibrium—model, are that it allows us to observe the kinetic trapped states during graphene folding. Additionally, there is an option in the model that allows graphene to tear once it reaches a certain specified strain.
2. Spring Force
The 2D sheet is broken down into a square lattice with nodes representing material points, each node accounting for the mass of all the materials within that unit lattice. Each node experiences a spring force from each of its four neighbors. For a material with linear elasticity, such as PMMA, this force FLS is:
F
LS
=EεA
0 (1)
where E is the Young's modulus of the relevant material, E is the strain, and A0 is the cross sectional area of the section. However, graphene is known to have a nonlinear elasticity, and the non-linear spring force a node feels from one of its neighbors, FNLS is:
F
NLS=(Eε+Dε2)A0 (2)
where D is a third order elastic modulus to account for the non-linearity, and typical values for EGr and DGr are 1.0 TPa and −2.0 TPa, respectively. In this model, the material connecting the nodes is a two-layer composite of PMMA and graphene, which is modeled as two parallel springs, giving the total spring force FS:
F
S=(EGrε+DGrε2)TGrL0+(EPMMAε)TPMMAL0 (3)
where TGr and TPMMA are the thicknesses of the graphene and PMMA layer, respectively, and L0 mesh size perpendicular to the force direction.
3. Van Der Waals Force
Van der Waals forces are weak intermolecular forces that arise due to permanent and induced dipole moments in molecules. Each particle in this model experiences attractive van der Waals forces towards the bottom sheet of graphene, and also to the polystyrene pellet. The potential for the surface-surface interaction (per unit area), W, is given by,
and the corresponding van der Waals force, FvdW, is
where H is the Hamaker constant, and δ is the distance between the two interacting surfaces. The surface-surface interaction is the most appropriate for this model (as opposed to an atom-surface or sphere-surface interaction), since the discretization of the graphene sheet produces planar units with large aspect ratios.
4. Capillary Interaction
Capillary forces (i.e. water-graphene attractive interactions) play a large role in many graphene folding and transfer applications. However, the exact nature and magnitude of the capillary interaction between water and graphene is not well understood, and is the topic of many different studies. The binding energy Wadh for water on bilayer graphene is 58.9±1.9 mJ·m−2. Further, the maximum traction reported by one study is σm≈90 MPa. This traction due to capillary forces is crucial to the first step of the auto-perforation process.
5. Gravity
Gravity acts on all particles, given by Newton's second law, Fg=mg, where g is the acceleration of gravity, and m is the mass of one node. The mass of one node is found by dividing the total mass of the system by the number of nodes in the system:
where ρGr and ρPMMA refer to material densities, and N is the number of nodes in the system.
6. Viscous Dissipation
The Reynolds number is a non-dimensional number that represents the ratio of inertial to viscous forces in a fluid. The Reynolds number of the composite folding system, Re, at 20° C. is given by:
where μ is the dynamic viscosity of the liquid, and ν is the velocity of a given node. The Re<<1 means that viscous effects cannot be ignored. Therefore, a Stokes' drag force Fd acting opposite to sheet's downward velocity is included:
F
d=6πμRv (8)
where R is the Stokes' radius (approximated as the thickness of the PMMA support layer). The graphene sheet does not actually fall through water, the Stokes' drag is meant to account for the fact that water is displaced.
c. Model Implementation
1. Nodes and Springs
The structure of this model is an extended system of nodes and springs. For a square mesh with n nodes on a side, there are a total of n2 nodes total, and 2n(n−1) springs since n(n−1) springs are initially parallel to each of the x and they directions. Note that if the nodes are contained in a 2D array, the ordered pair (i,j) is equivalent to (row, column). Additionally, the nodes are numbered from 1 to n2, starting with (1, 1) and ending with (nx, ny). This is because the ordinary differential equation (ODE) solvers work with 1D vectors of variables. However, it is much more concise and efficient to work with these variables in a 2D array, and then convert it to a 1D vector right before calling the ODE solver. These naming conventions are needed in order to precisely define the relationship between the 1D and 2D representations.
2. Periodic Boundary Conditions
This model utilizes a periodic boundary condition. This means that the “unit cell” modeled behaves as if it was repeated infinitely on all sides. Specifically, edge nodes are nodes with i=1, i=nx, j=1, or j=ny. Most nodes have four springs attached to them, but these edge nodes only have two or three. The periodic boundary condition is achieved by modifying the forces felt by edge nodes so that the “missing” forces are taken from the opposite side of the unit cell. For example, node (i, ny) has no neighbor to the right; there is no node (i, ny+1). The spring force node (i, ny) feels to the right is then the same force that node (i, 1) feels to the right. In the code, this is implemented by using logic to determine if a node is an edge node, and if so substituting the missing forces with forces from the opposite edge. The periodic boundary condition has the effect of fixing the edge nodes in the x-y plane. This is because the edge treatment described above treats opposite edge nodes as the same point—when the unit cell is repeated, the edges overlap. Intuitively, this also makes sense because in an infinitely extended grid of microparticles, the edge nodes lie exactly halfway between two microparticles.
d. Results Summary
The output of this model is the shape of the graphene/PMMA sheet during and after the folding process. This section is intended to show results obtained from the model and in this example, a 250×250 mesh is used, with an aspect ratio of 1:100 (microcylinder height to radius). This level of resolution is needed in order to observe the shape of the resulting profile in the region near the edge of the polystyrene pellet.
Using the native values of the materials (250 nm thick PMMA and 0.67 nm bilayer graphene composite) and the appropriate microspot form factor, a maximum of 0.78% relative strain was obtained within the composite film right outside of the microspot edge, which hence forth shall be referred to as the “folding strain” (
This model is adapted from the seminal work by Stewart and Williams et. al. in the Hewlett-Packard laboratories, where an equivalent circuit model consisting of a rectifier in parallel with a memristor is constructed (
I=I
m
+I
r
=w
nβ sin h(αV)+χ{exp(γV)−1} (13)
which is chosen more for its simplicity and ability to reproduce the I-V behavior than as a detailed physics model. In the first term, Im, which represents a flux-controlled memristor, β sin h(αV) is the approximation used for the ON state of the memristor, which is essentially electron tunneling through a thin residual barrier; α and β are fitting constants that are used to characterize the ON state, and w is the state variable of the memristor. In this case w is proportional to the applied electric field. The second term in Eq. (13), Ir, represents the I-V character for the rectifier, and χ and γ are the fitting constants used to characterize the net electronic barrier when the memristor is switched OFF. The exponent n of the state variable is used as a free parameter in the model, which is adjusted to modify the switching between the ON and OFF states of the device to be consistent with the experimental observations. A large n is typically interpreted as evidence for a highly nonlinear dependence of the effective vacancy drift velocity on the voltage applied to the device.
In order not to limit the scope of search space for the curve fitting, nonlinear programming was used to locate the minimum of the unconstrained multivariable objective function. The objective functions themselves are simply sums of least square differences between the I-V curves derived from Eq. (13) and experimental data. This semi-empirical model is capable of fitting, to great success, all the I-V behaviors for the two-terminal memristors tested, and some of the fits are shown here as an example (
Experimental data are represented as solid red lines, and model fits as black dashed lines.
These fittings yield parameters that can provide deeper insights toward each memristor element. For instance, a closer inspection of the fitting parameters (Table 4) for data presented in
If the left term Im=wn sin h(αV) is compared with the α values, it is observed an increase of α as the memristor is switched from an OFF state to an ON state. Mathematically, the smaller α is, the further along in the V-axis does the Im start to kink up, meaning the more voltage it requires to turn the memristor ON. As more charges are put into the memristor, the memristor is closer to its ON state, which coincides with the experimental observation. If the second term Ir=χ{exp(γV)−1} that characterizes the rectifier component is focused on, this is just a recast of the Shockley diode equation, where χ is known as the reverse bias saturation current (or OFF state current), and γ is just the inverse product of the ideality factor and the thermal voltage. In the first run, the reverse bias saturation current is notably smaller and the diode is much closer to ideal. Both of these observations agrees with the fact that the memristor is initially in the OFF state.
Reduction in machine size down to micrometers will dramatically decrease their fabrication cost, along with yielding the possibility to explore environments that are too small or too dangerous for humans or larger robots. To date, the development of such machines was hindered by both energy-thirsty electronics and limited, on-board energy storage capacity. Disclosed herein is a syncell, a micrometer-size particle capable of changing their electronic state. Compared to the state-of-the-art millimeter-size robots, the syncell's size shrinkage is enabled by developments in 2D materials that considerably reduce operational power requirements. The syncell state machine (100×100×5 μm3, making them invisible to the human eye) is composed of a power source, a switch, and a memory element that form a closed electronic circuit. This circuit remains operational even after travelling inside a turbulent droplet a distance of 0.6 m in air. Syncells successfully detect analytes while in air and store this information in the memory using power harvested by a photodetector. This layout represents a concept of aerosolizable electronics with particles that can be dispersed in air while having active electronics on-board. To facilitate syncell collection, syncell standoff detection was realized with on-board retroreflectors. These aerosolizable electronics will allow rapid and cheap monitoring of viruses, bacteria, and fumes that spread over large areas.
Today there are two main tendencies in the field of micromachines: micro/nanoparticles and biorobotics. Decades of chemical synthesis have led to the development of complex core-shell particles with multifunctional capabilities that are widely used for drug delivery, biosensing, imaging, etc. See, Bao, G., S. Mitragotri, and S. Tong, Multifunctional Nanoparticles for Drug Delivery and Molecular Imaging. Annual Review of Biomedical Engineering, 2013. 15(1): p. 253-282, which is incorporated by reference in its entirety. Although micro- and nanoparticles are relatively simple to synthesize, they are significantly limited in their integration capability with conventional electronics and their development of complex logical operations. Biorobotics based on genetic engineering, in turn, was able to harness bacterial life and viruses to create micromachines. See, Smanski, M. J., et al., Synthetic biology to access and expand nature's chemical diversity. Nat Rev Micro, 2016. 14(3): p. 135-149, and Ravi, S. K. and S. C. Tan, Progress and perspectives in exploiting photosynthetic biomolecules for solar energy harnessing. Energy & Environmental Science, 2015. 8(9): p. 2551-2573, each of which is incorporated by reference in its entirety. Nevertheless, genetic engineering is also limited by intrinsic cell architecture and design. As an alternative, micro-scale electrical systems can be made from scratch with their architecture being optimized to the application at hand.
Cubic millimeter-size devices, called “smart dust”, are the smallest dispersed electronic devices reported to date. See, Seo, D., et al., Wireless Recording in the Peripheral Nervous System with Ultrasonic Neural Dust. Neuron, 2016. 91(3): p. 529-539, which is incorporated by reference in its entirety. While the initial concept was developed more than 15 years ago, further progress was hindered by the lack of efficient energy storage technologies. Indeed, light-weight batteries do not provide enough power, often forcing small robots to rely on external energy harvesting. To this end, some versions of smart dust harvested energy from electromagnetic wireless radiation, limiting the devices' operation to a distance of a few meters. See, Seo, D., et al., Wireless Recording in the Peripheral Nervous System with Ultrasonic Neural Dust. Neuron, 2016. 91(3): p. 529-539, which is incorporated by reference in its entirety. Unfortunately, this approach cannot be scaled down, due to receiver size limitations. See, Seo, D., et al., Model validation of untethered, ultrasonic neural dust motes for cortical recording. Journal of Neuroscience Methods, 2015. 244: p. 114-122, which is incorporated by reference in its entirety. Alternative energy harvesting techniques (chemical power harvesting, bacteria-produced power, ultrasound, magnetic field and light) are continuously being developed, delivering microwatts of power on the micrometer scale but, so far, have had little to no success in powering energy-thirsty electronics (usually requiring milliwatts). See, Zebda, A., et al., Single Glucose Biofuel Cells Implanted in Rats Power Electronic Devices. Scientific Reports, 2013. 3: p. 1516, Kim, H. and M. J. Kim, Electric Field Control of Bacteria-Powered Microrobots Using a Static Obstacle Avoidance Algorithm. IEEE Transactions on Robotics, 2016. 32(1): p. 125-137, Servant, A., et al., Controlled In Vivo Swimming of a Swarm of Bacteria-Like Microrobotic Flagella. Advanced Materials, 2015. 27(19): p. 2981-2988, and Chang, S. T., et al., Remotely powered self-propelling particles and micropumps based on miniature diodes. Nat Mater, 2007. 6(3): p. 235-240, each of which is incorporated by reference in its entirety.
In a micrometer-size electronic state machines, or a “syncell” (an allusion to the biological term synthetic cell—minimal cell), the issue of energy deficiencies is circumvented using novel 2D devices that require only microwatts, or even nanowatts, of power. Built from 2D materials, these devices are only a few atoms thick, enabling a high integration density. Note that 2D devices are still in their infancy: Most publications to date demonstrate individual 2D devices fabricated on flat silicon wafers. See, Wang, Q. H., et al., Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat Nano, 2012. 7(11): p. 699-712, Radisavljevic B, et al., Single-layer MoS2 transistors. Nat Nano, 2011. 6(3): p. 147-150, Lopez-Sanchez, O., et al., Ultrasensitive photodetectors based on monolayer MoS2. Nat Nano, 2013. 8(7): p. 497-501, Cheng, R., et al., Electroluminescence and Photocurrent Generation from Atomically Sharp WSe2/MoS2 Heterojunction p-n Diodes. Nano Letters, 2014. 14(10): p. 5590-5597, and Lopez-Sanchez, O., et al., Light Generation and Harvesting in a van der Waals Heterostructure. ACS Nano, 2014. 8(3): p. 3042-3048, each of which is incorporated by reference in its entirety. Here, a complete electronic circuit composed of 2D devices is assembled, forming a 2D state machine that is operational when lifted-off of silicon.
Large area monitoring of various bacteria, spores, smokes, dust, and fumes is an important task, which currently requires a lot of resources. See, Hansen, M. C. and T. R. Loveland, A review of large area monitoring of land cover change using Landsat data. Remote Sensing of Environment, 2012. 122: p. 66-74, which is incorporated by reference in its entirety. In one implementation, satellite scanning can rapidly cover large areas, but it is costly and indirect (this translates into limited applicability). On-ground sensor installation is labor-intensive and can often be slow in comparison to analyte distribution. Employing a fleet of flying sensors (e.g., drones) is again associated with high costs. As an alternative, the concept of aerosolizable electronics is introduced. Syncells dispersed in the air carrying 2D electronic devices that remain operational even in flight. Air drag calculations demonstrate that these syncells will have <1 cm/s sedimentation speed (
Due to their high aspect ratio, micrometer-scale 2D materials have low mechanical stability that limits their application off-substrate. To circumvent this, a syncell base that plays a role of the carrier substrate for 2D devices was designed. The syncell base material is a critical choice: It should remain stable during various fabrication stages (2D material transfer, patterning, lift off, etc.) that often require development steps in different solvents. Using the SU-8 photoresponsive polymer, it can be processed with micrometer precision and becomes very stable after crosslinking. Conventional photolithography allows syncell bases' fabrication in different shapes and sizes that can be targeted for different designs and applications (
To demonstrate the performance of the electrical circuit on the syncell base, an electrical state machine was designed with elements of combinational logic. To this end, three components have been chosen: a power source, a switch, and a memory element that are implemented by a photodetector, a chemiresistor, and a memristor, respectively (
The performance of electronic devices changes when they are removed from a native substrate due to the imposed stretch and strain, however 2D materials possess higher strain limits as compared to the conventional III-V materials. See, Salvatore, G. A., et al., Wafer-scale design of lightweight and transparent electronics that wraps around hairs. Nature Communications, 2014. 5: p. 2982, and Akinwande, D., N. Petrone, and J. Hone, Two-dimensional flexible nanoelectronics. Nature Communications, 2014. 5: p. 5678, each of which is incorporated by reference in its entirety. To explore the performance of the devices, syncells were tested in three configurations: (1) as-fabricated on the silicon substrate, (2) after liftoff, and (3) after spraying using a nebulizer across a 0.6 m distance in a 0.15 m diameter tube (
To test individual components, separate syncells were fabricated with isolated devices. The first component is the photodetector, serving as a photocell: It converts light into electrical current that, in turn, can be used to power other 2D components. The 2D photodetector is made of a p-n photodiode comprised of MoS2 and WSe2 monolayers with golden electrodes in a 90° configuration with the minimal distance of ˜10 μm (
The second component is the chemiresistor. It consists of a MoS2 monolayer that changes its electrical conductance upon molecular adsorption (
The third component is a memristor. It needs to operate with voltages harvested by the photodetector. To date, most memristors operate in the 1-3 V range (far higher than what the photocell can harness). See, Hao, C., et al., Liquid-Exfoliated Black Phosphorous Nanosheet Thin Films for Flexible Resistive Random Access Memory Applications. Advanced Functional Materials, 2016. 26(12): p. 2016-2024, Wang, W., et al., MoS2 memristor with photoresistive switching. Scientific Reports, 2016. 6: p. 31224, and Sangwan, V. K., et al., Gate-tunable memristive phenomena mediated by grain boundaries in single-layer MoS2. Nat Nano, 2015. 10(5): p. 403-406, each of which is incorporated by reference in its entirety. Only one example satisfies the requirements (see, Bessonov, A. A., et al., Layered memristive and memcapacitive switches for printable electronics. Nat Mater, 2015. 14(2): p. 199-204, which is incorporated by reference in its entirety): A MoS2 memristor fabricated between gold and silver electrodes (
Once assembled together, the developed components form a state machine. To operate reliably, the microcircuit has to meet specific energy and power requirements. The first one has already been briefly mentioned and satisfied by the choice of the appropriate memristor: Generated photodetector voltage c has to exceed the threshold memristor voltage Vth. The second criterion is that the memristor should not change its state if there is only an analyte. To this end, all devices were covered except the chemiresistor with a hBN monolayer, ensuring that no chemical reaction is happening with them (
where Rph is the photodetector resistance. After the reaction with the analyte, the chemiresistor decreases its resistance to Rchƒ. This allows the memristor to change its state from RmOFF to RmON, which again can be assessed through the Ohm's law:
For memristor to change its state, the following has to be satisfied: RmON>RmOFF, yielding:
Equations (3) and (5) set requirements for the circuit design. In case of TEA, Rchƒ can maximally reach ≈Rchin/2, so MoS2 size should be carefully chosen to satisfy Eqs. (3) and (5).
To demonstrate state machine operations, syncells were fabricated with three components assembled in one closed circuit (
To further strengthen the demonstration, conductive carbon nanotube ink (0.2 g/l) was used as the analyte. For these experiments, the bare syncell substrate was used instead of MoS2 as the chemiresistor. SU-8 is an insulating material (sheet resistance ˜10 pS), and its low conductance significantly strengthens condition of Eq. (3), while adsorbed carbon nanotubes form a percolated network with conductivities on the order of μS (
Researchers have identified several important closed systems from which it is difficult to extract information or interface electronics within an inaccessible interior. See Lillesand, T., Kiefer, R. W. & Chipman, J. Remote Sensing and Image Interpretation. 1, 1-59 (2014), which is incorporated by reference in its entirety. Examples include oil and gas conduits, chemical and biosynthetic reactors, porous geological materials for upstream oil and mining exploration and the human digestive tract. See Brunete, A., Hernando, M., Torres, J. E. & Gambao, E. Heterogeneous multi-configurable chained microrobot for the exploration of small cavities. Automat. Constr. 21, 184-198 (2012), Murvay, P.-S. & Silea, I. A survey on gas leak detection and localization techniques. J. Loss Prevent. Process Ind. 25, 966-973 (2012), Rajtar, J. M. & Muthiah, R. Pipeline Leak Detection System for Oil and Gas Flowlines. J. Manufact. Sci. Eng. 119, 105-109 (1997), Gavrilescu, M. & Tudose, R. Z. Residence time distribution of the liquid phase in a concentric-tube airlift reactor. Chem. Eng. Proces. 38, 225-238 (1999), Kurt, S. K., Gelhausen, M. G. & Kockmann, N. Axial Dispersion and Heat Transfer in a Milli/Microstructured Coiled Flow Inverter for Narrow Residence Time Distribution at Laminar Flow. Chem. Eng. Tech. 38, 1122-1130 (2015), Tan, X., Sun, Z. & Akyildiz, I. F. Wireless Underground Sensor Networks: MI-based communication systems for underground applications. IEEE 57, 74-87 (2015), and Yamate, T., Fujisawa, G. & Ikegami, T. Optical Sensors for the Exploration of Oil and Gas. J. Lightwave Technol. 35, 3538-3545 (2017), each of which is incorporated by reference in its entirety. Several methods to probe such systems exist, but they are either indirect or very limited in their applicability. At the same time, fully autonomous electronic chips have been limited to the millimetre-range, which remains too large for addressing the above applications. See Kalantar-Zadeh, K. et al. A human pilot trial of ingestible electronic capsules capable of sensing different gases in the gut. Nat. Electronics 1, 79-87 (2018), and Costello, B. P. J. d. L., Ledochowski, M. & Ratcliffe, N. M. The importance of methane breath testing: a review. J. Breath Res. 7, 024001 (2013), each of which is incorporated by reference in its entirety. To this end, it was demonstrate that CSMs can be injected into a pipeline system, probe it, and then be successfully retrieved to deliver the captured information.
To illustrate, a model pipeline section was fabricated, into which gaseous ammonia was injected. Ammonia is a highly toxic gas used as a fertilizer in agriculture and as a refrigerant in the chemical industry. See Kalantar-Zadeh, K. et al. A human pilot trial of ingestible electronic capsules capable of sensing different gases in the gut. Nat. Electronics 1, 79-87 (2018), and Farra, R. et al. First-in-Human Testing of a Wirelessly Controlled Drug Delivery Microchip. Sci. Trans. Med. (2012), each of which is incorporated by reference in its entirety. It is also one of the most dangerous compounds to be transported through pipelines. See Timmer, B., Olthuis, W. & Berg, A. Ammonia sensors and their applications—a review. Sens. Actuat. B 107, 666-677 (2005), which is incorporated by reference in its entirety. To probe the pipeline internally, CSMs were first injected within the system (
Soot nanoparticles emitted by diesel engines, industrial emissions, and power plants pose health, climate, and environmental risks. See Cho, B. et al. Charge-transfer-based Gas Sensing Using Atomic-layer MoS2. Sci. Rep. 5, 8052 (2015), which is incorporated by reference in its entirety. Aerosolized micro- and nanoparticles can travel thousands of kilometres before sedimentation (see Bernstein, J. A. et al. Health effects of air pollution. J. Allergy Clin. Imm. 114, 1116-1123 (2004), which is incorporated by reference in its entirety), making it challenging to predict soot distribution and impact. To date, the large area monitoring of soot remains an economically inviable task. To this end, CSMs as dispersed, printed devices can potentially cover large areas to successfully detect soot, remaining virtually invisible to the naked eye, but otherwise easily detectable on a surface (see below). In this case, aerosolization allows CSMs to be rapidly printed over a specific area of interest as intact, functional, autonomously powered devices.
To demonstrate the monitoring of undesirable particulates from surface dispersed CSMs, the nebulized CSMs were deposited over an area of 0.6×0.6 m2. Next, 2 g/l of Printex XE2-B soot was loaded into a separate nebulizer and sprayed over three distinct locations (
To efficiently detect the location of CSMs at standoff distances, a distinct batch was fabricated, where the CSM base consisted of a retroreflector design. The design follows that of Switkes et al. as 100 μm-size retroreflector for low intensity laser (10 mW/cm2) reflected light from distances of up to 1 km. See Grob, B., Schmid, J., Ivleva, N. P. & Niessner, R. Conductivity for Soot Sensing: Possibilities and Limitations. Anal. Chem. 84, 3586-3592 (2012), and Switkes, M., Ervin, B. L., Kingsborough, R. P., Rothschild, M. & Sworin, M. Retroreflectors for remote readout of colorimetric sensors. Sens. Actuat. B 160, 1244-1249 (2011), each of which is incorporated by reference in its entirety. CSM retroreflectors were fabricated using SU-8 coated with 100 nm Ag designed in the checkered shape that allows them to reflect light back to the source from angles up to 60° (
The capability of grafting autonomous electronic circuits are capable of logical operation and information storage onto sub-millimetre-sized particles, forming what is termed Colloidal State Machines (CSMs). These particles can undergo aerosolization while carrying functional electronics on-board capable of interaction with the environment. With a thickness of 1.24 μm and weight of ˜1.4 g/m2, this CSM design represents one of the thinnest and lightest circuits produced to date. See Switkes, M., Ervin, B. L., Kingsborough, R. P., Rothschild, M. & Sworin, M. Retroreflectors for remote readout of colorimetric sensors. Sens. Actuat. B 160, 1244-1249 (2011), which is incorporated by reference in its entirety. In this design, the on-board circuit forms a state machine with two inputs (chemical and optical) and one output comprised of a memristor. Owing to the usage of 2D materials, CSM requires only 30 nW to irreversibly record events, granting it the ability to be powered from the energy harvested by the on-board 2D photodiode (30-100 nW). The results of chemical sensing are irreversibly stored in the memory (inducing memristor conductivity changes of up to 150 times). Furthermore, the addition of integrated retroreflectors allows the dispersed CSMs to be rapidly (<1 ms/frame) detected by a laser-scanning system. Colloidal state machines may find applications in a wide range of areas, including biosensing (e.g., within the human digestive tract), large-area sensing, confined space monitoring (e.g., chemical and biosynthetic reactors, oil and gas conduits), and aerospace programs.
Batteries typically have 0.1 nW/μm3 with energy capacities of 1 nJ/μm. See Spellings, M. et al. Shape control and compartmentalization in active colloidal cells. Proceedings of the National Academy of Sciences 112, E4642-E4650 (2015), and Ferrari, S. et al. Latest advances in the manufacturing of 3D rechargeable lithium microbatteries. Journal of Power Sources 286, 25-46 (2015), each of which is incorporated by reference in its entirety. Basic electronic devices, like a quartz oscillator and a radio frequency identification (RFID) tag made from conventional III-V electronics, consume approximately 100 nW and 10 μW, respectively. A sub-millimeter battery with 100×100×100 μm3 dimensions should provide a power of 100 μW and store energy of 1 mJ, which is enough to power the above mentioned devices for 165 min and 100 sec, respectively. To ensure longer operational times, early attempts at autonomous microsystems often rely on external energy harvesting. In particular, some versions of smart dust harvested energy from wireless electromagnetic radiation, limiting the device operation to a distance of just a few meters. See Seo, D. et al. Wireless Recording in the Peripheral Nervous System with Ultrasonic Neural Dust. Neuron 91, 529-539 (2016), which is incorporated by reference in its entirety. Unfortunately, this approach does not appear capable of downward scaling, due to receiver size limitations. See Seo, D., Carmena, J. M., Rabaey, J. M., Maharbiz, M. M. & Alon, E. Model validation of untethered, ultrasonic neural dust motes for cortical recording. Journal of Neuroscience Methods 244, 114-122 (2015), which is incorporated by reference in its entirety. Alternative energy harvesting techniques, such as chemical power harvesting, bacteria-produced power, ultrasound, magnetic field and light, are continuously being developed. See Zebda, A. et al. Single Glucose Biofuel Cells Implanted in Rats Power Electronic Devices. Scientific Reports 3, 1516 (2013), Kim, H. & Kim, M. J. Electric Field Control of Bacteria-Powered Microrobots Using a Static Obstacle Avoidance Algorithm. IEEE Transactions on Robotics 32, 125-137 (2016), Servant, A., Qiu, F., Mazza, M., Kostarelos, K. & Nelson, B. J. Controlled In Vivo Swimming of a Swarm of Bacteria-Like Microrobotic Flagella. Advanced Materials 27, 2981-2988 (2015), and Chang, S. T., Paunov, V. N., Petsev, D. N. & Velev, O. D. Remotely powered self-propelling particles and micropumps based on miniature diodes. Nat Mater 6, 235-240 (2007), each of which is incorporated by reference in its entirety. They deliver between 0.1 and 10 nW/(100×100 μm2) of power, which to date is not enough for conventional electronic needs. Fortunately, 2D material devices are predicted to bypass these difficulties, having a number of advantages, such as low-power performance as compared to Si (<0.5 V), acceptable gate control with subthreshold swings <<60 mV/dec, and large turn on currents (>103 μA/μm). See Ionescu, A. M. & Riel, H. Tunnel field-effect transistors as energy-efficient electronic switches. Nature 479, 329-337 (2011), and Fiori, G. et al. Electronics based on two-dimensional materials. Nat Nano 9, 768-779 (2014), each of which is incorporated by reference in its entirety. Most recent publications focus on individual 2D devices, while no integration of power harvesting and usage has been demonstrated yet. See Wang, Q. H., Kalantar-Zadeh, K., Kis, A., Coleman, J. N. & Strano, M. S. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat Nano 7, 699-712 (2012), Radisavljevic B, Radenovic A, Brivio J, Giacometti V & Kis A. Single-layer MoS2 transistors. Nat Nano 6, 147-150 (2011), Lopez-Sanchez, O., Lembke, D., Kayci, M., Radenovic, A. & Kis, A. Ultrasensitive photodetectors based on monolayer MoS2. Nat Nano 8, 497-501 (2013), Cheng, R. et al. Electroluminescence and Photocurrent Generation from Atomically Sharp WSe2/MoS2 Heterojunction p-n Diodes. Nano Letters 14, 5590-5597 (2014), and Lopez-Sanchez, O. et al. Light Generation and Harvesting in a van der Waals Heterostructure. ACS Nano 8, 3042-3048 (2014), each of which is incorporated by reference in its entirety. Moreover, these efforts tend to describe 2D devices on flat silicon wafers, while their performance on substrates of high curvature is less understood.
CVD graphene sheets were produced as follows: briefly, copper foil (Alfa Aesar, 99.8%, 25 μm thick, for graphene growth) with a size of 2.0×2.2 cm was used as substrate, the copper was annealed at 30 sccm H2 gas flow (˜560 mTorr) for 30 min at 1000° C. and then 0.5 sccm (for single layer graphene) or 10 sccm (for bilayer graphene. See Tu Z, Liu Z, Li Y, Yang F, Zhang L, Zhao Z, et al. Controllable growth of 1-7 layers of graphene by chemical vapour deposition. Carbon 2014, 73: 252-258, which is incorporated by reference in its entirety.) methane was introduced for 15 min or 10 min, respectively. After that, the furnace was kept at 1000° C. for another 5 min and turned off. Cu foil was cooled down and removed out at room temperature.
Sapphire or SiO2 substrate (7.0 cm×1.7 cm) washed with acetone (5 min) and isopropyl alcohol (IPA, 5 min) was used in the growth of MoS2, MoCl5 powders (Sigma Aldrich, 99.99%, ˜4 mg) was loaded onto a SiO2/Si substrate and placed in the central part of the heating zone, the sulfur powder (Sigma Aldrich, 99.998%, ˜0.5 g) was added in a separate Al2O3 boat and placed at the upper stream side of the tube where the temperature was about 200° C. during the reaction. The sapphire or SiO2 substrate was placed at the downstream side 1 cm next to MoCl5. The tube was purged with 50-sccm Ar under vacuum for 30 min, then the furnace was heat to 850° C. in 30 min. The Ar flow kept at 50 sccm and the displayed pressure was about 1.13 torr. The tube was kept at the same temperature for another 10 min and then cooled down to room temperature naturally.
60 mg of Black phosphorus was well grounded before being dispersed in 20 mL EG and a tip sonicator (10% maximum power) was used to sonicate the resulted mixture for 10 hours with liquid cooling at 4° C. The obtained solution was centrifuged at 2000 rpm at room temperature for 20 min to produce the final dispersion of BP nanoflakes. To determine the concentration of BP nanoflakes, we sampled 1.5 g solution and filtered it using a 0.2 μm-sized PTFE syringe filter, and weighted the BP nanoflakes left on the filter after drying under vacuum overnight. The dispersion was diluted to solutions with different concentrations to collect the UV-Vis absorption. The spin coating was used to prepare samples of BP nanoflakes on SiO2/Si (or gold-coated) substrate for AFM, Raman spectroscopy, and X-ray photoelectron spectroscopy (XPS). A droplet of the dispersion was added on to a Holy-carbon grid and dried under vacuum to prepare the specimen for TEM.
For other 2D nanoflakes or nanoparticles, single layer graphene oxide dispersion in water (500 mg/L), molybdenum disulfide (MoS2) pristine flakes in solution (1-8 monolayers, 18 mg/L), and MoS2 ultrafine powder (˜90 nm) were purchased from Graphene Supermarket and used as received. Ethylene glycol (Sigma Aldrich, 99.8%) was used to further disperse MoS2 ultrafine powder for the ink application.
A procedure reported in literature was adopted for the noncovalent functionalization via π-π stacking. Generally, the copper foil with graphene (single layer or bilayer) and a size of 2.0×2.2 cm was incubated in the dimethyl formamide (DMF) solution of functional molecules for 1 h and washed with fresh DMF, ethanol, and dried at room temperature (the washing step can remove those excess molecules which were not attached to the graphene surface). Specifically, 2 mL DMF solution of 1-pyrenebutyric acid (97%, Sigma Aldrich), 1-aminopyrene (97%, Sigma Aldrich), 1,5-diaminonaphthalene (97%, Sigma Aldrich), or other functional molecules (2 mmol/L) was added into a 10 mL-beaker with copper foil, and mechanically shaken for 1 h, then the copper foil was removed out and rinsed with DMF and ethanol in sequence, with each of 30 s. After drying, the copper foil was spin-coated with a PMMA layer around 230 nm using 950PMMA A4 (MicroChem) at 3000 rpm for 1 min. The copper layer was etched out with ammonium persulfate (APS-100, TRANSENE CO INC) and the left graphene/PMMA film was rinsed with deionized water. For characterization, the film was transferred onto Si/SiO2 substrate with the graphene side down and characterized with Raman spectroscopy with or without washing out the PMMA layer using acetone, to compare with the pristine graphene. For further fabrication and modification, the film was picked up with Si/SiO2 substrate with the graphene side up or a polydimethylsiloxane (PDMS) stamp (2.5×2.5 cm, 2 mm thickness) has been attached to the graphene/PMMA layer before the etching step.
In this step, methanol, a poor solvent of PMMA, was used as the only solvent to prepare the solution of functional molecules or rinse in this step. Functional molecules like 1-pyrenebutyric acid N-hydroxysuccinimide ester (95%, Sigma Aldrich) (4 mmol/L) and 1,5-diaminonaphthalene were used in this step (a heating to 80° C. is required to dissolve like 1-pyrenebutyric acid N-hydroxysuccinimide ester in methanol). A few drops of the solution were added to overcover the surface of the SiO2 wafer or PDMS-supported PMMA/graphene film and the incubation time is 15 min. After that, the film was rinsed with fresh methanol for 30 s to remove any residual functional molecules which were not attached to the graphene surface. After drying, the film is ready for the ink-jet printing in the next step. The SiO2-supported film can be characterized with Raman spectroscopy, while the PDMS-supported film can be transferred to another piece of Si/SiO2 wafer for characterization via washing out the PMMA layer.
(6). Ink-Jet Printing of Polymer Latexes or their Composite Solution with Nanoparticles
Polymer latex, polystyrene (PS) latex (Sigma Aldrich, amine-modified polystyrene, fluorescent orange, 0.1 μm mean particle size, 2.5 wt %) for example, were diluted with ethylene glycol (EG) to 1.25% (vol:vol=1:1), 0.83% (1:2), 0.50% (1:4), and 0.25% (1:9) as inks for the printing. The PS latex was also composting with zinc oxide (ZnO) nanoparticle ink (2.5 wt. %, viscosity 10 cP, work function −4.3 eV, Sigma Aldrich) and further diluted with EG (vol:vol:vol=2:1:1), iron oxide(II,III), magnetic nanoparticles solution (10 nm avg. part. size, 5 mg/mL in H2O, Sigma Aldrich) and further dilute with EG (vol:vol:vol=9:2: 7), or exfoliated black phosphorus solution (vol:vol=1:1) to prepare functional inks for the printing. In the inkjet printing at room temperature using a MICROSYS printer, from Cartesian Technologies, a ceramic printer needle was used and the printed ink volume is 1 nL for each dot, the spacing between the two adjacent dots is 500 μm, and the printing area is typically 1.5-2.0 cm in length and width. After printing, the ink was dried at room temperature overnight and further under house vacuum for 1 h. This Si/SiO2 or PDMS-supported graphene/PMMA film with the printed dot array was annealed at 120° C. for 10 min and cooled down to room temperature, and ready for the next-step use. A printer from Fujifilm Dimatrix Materials (Printer DMP-2850) was also used and n ink volume of 10 pL or 1 pL was printed to prepare smaller-sized microspot with PS latex ink (1.2 wt %, 50 nm mean particle size, in a mixture of water and ethylene glycol (1:1)).
For the printing of conductive silver microspot array, silver dispersion (nanoparticle, 30-35 wt. % for printing on plastic films, Sigma-Aldrich) was diluted with ethylene glycol/water mixture (1:1 in volume) for 200 times as nanoink and the MICROSYS printer for the printing, with a printing volume of 1 nL. In addition to the use of printers above to print the microparticles, the contact printing was done with a capillary tube with an ink volume around 0.5 μL by hand, with this, larger spots were printed with a diameter about 1 mm. The sequential printing of silver microspot array and capillary contact printing allow users to print polymer or its composite particles with separated silver spots. As a simple demonstration, the silver microspot array was first printed with an ink volume of 1 nL for each spot a space of 500 μm for the two adjacent dots, and annealed at 120° C. for 10 mins. The polymer or its composite spots were printed by capillary contacting to cover the silver array, further annealing at 130° C. for 10 mins is applied to enhance the bonding between the two materials.
To prepare the second piece of graphene/PMMA film (which will be used as the cover layer during the stacking process), a modified fabrication procedure was adopted. Particularly, one-side functionalized graphene/PMMA film in step 4 was transferred onto a relatively larger Si/SiO2 wafer (5×5 cm), and drops of the functional molecule (i.e., 1-pyrenebutyric acid N-hydroxysuccinimide ester, 1,5-diaminonaphthalene) solution in methanol were added onto the wafer until the complete infusion of the solution into the underlying surface of the graphene/PMMA film. The film was incubated for 10 mins and after that, washed with fresh methanol, transferred back to the deionized water, and rinsed with water for 4 times with 10 mins each time. This film was left in water and ready for the next step.
The annealed graphene/PMMA film on SiO2 or PDMS substrate in Step 7 severing as the bottom layer to pick up the cover layer in Step 5 from water. The two films with the sandwiched PS or its nanocomposite dots were dried at room temperature for 1 h and then annealed at 120° C. for 15 mins. After that, the films together with the substrate were placed into a 50-mL beaker with a magnetic stir bar, 10-15 mL of ethanol/water (4:1 in volume) was added, the beaker was sealed with paraffin and heated to 80° C. under stirring for 10 mins, after that, the solution was cooled down to room temperature and water for 12 h, with visible, dark particles suspending in the solution. After standing overnight, these particles were settled down and the solution was replaced with fresh ethanol/water (4:1). The heating, stirring, settling, and solution replacement procedure was repeated another two time to remove any residual PMMA in the solution or on the graphene surface and after that, these particles were stored in the solution and fishing out on to glass slide, SiO2 substrate, or ITO-coated glass via pipette for further characterization or measurement.
(9). The Preparation of 2D Syncell Particles with CVD Graphene without Functionalization
The preparation of syncell particles with pristine graphene as outer layer is simpler and faster than the above procedure to prepare the syncell particles with two-side functionalized graphene. Briefly, graphene (A) was transferred onto PMMA with either PDMS or Si/SiO2 as substrate, the film with graphene layer up. The film was printed with PS or PS/nanoparticles dot array, and annealed at 120° C. for 10 mins. The other layer of graphene (B layer) was transferred to PMMA. This film was floated in water and stacked onto graphene A to form the sandwich. The stacked two graphene/polymer films with PS dots (or PS nanocomposite dots) dried at room temperature overnight and then annealed at 120° C. for 10 mins. The further liftoff operation was the same as above.
(10). The Preparation of 2D Syncell Particles with Molybdenum Disulfide (MoS2) and Hexagonal Boron Nitride hBN (Syncell)
The preparation procedure is similar that in (9). The only difference is the transfer of MoS2 sheet. MoS2 grown on Si/SiO2 substrate was spin-coated with a thin PMMA layer (same as above) and the MoS2/PMMA film was liftoff from the SiO2 substrate with KOH solution (2 M in water) as etchant at 80° C. The film was rinsed with deionized water 5 times and used for the further printing, stacking, and liftoff, to prepare MoS2 syncell. For hBN syncell, single layer or multi-layer hBN film grown on grown on copper foil produced by CVD method was purchased from Graphene Supermarket, the transfer and further preparation of syncell particles are the same as that of the graphene syncell particles above.
The optical images of microparticles were acquired from ZEISS Axio Scope Al with a magnification of 5 and 20 times. The visualization of the liftoff process was also monitored the same microscope. A temperature controlled microscopic stage from Linkam Scientific was coupled to the microscope system for heating up solution during the liftoff. Raman spectroscopy was performed on a Horiba Jobin Yvon LabRAM HR800 system using a 532 nm excitation laser, 10× objective lens with ˜10 μm diameter spot size, and 1800 lines/mm grating. The profile data of the microparticles were obtained with Tencor P-16 Surface Profilometer™ using a 2 um radius diamond tipped stylus Step height, with a measurement range of 20 Angstroms to 1 mm. Static water contact angle was measured by ramé-hart Model 590 goniometer. The transmittance of BP solution was measured with Shimadzu UV-3101PC Spectrophotometer at a wavelength of 660 and 1176 nm. Freshly exfoliated BP solution was used as a stock solution and dilute at different times for the measurement. NanoSight LM10 (Malvern) was used for the rapid and accurate analysis of the size distribution and population of BP nanoparticles from 10 nm to 2000 nm in diameter using single particle tracking.
Atomic force microscopy (AFM) was performed using Asylum MFP-3D-BIO in tapping/AC mode with Si tips (Asylum, AC240TS). The scan rate was 0.7 Hz, and scan angle was set to be 0°. Black phosphorus (BP) samples was prepared via spin-coating onto a plasma-treated SiO2/Si substrate. Scanning electron microscope was conducted on Zeiss Merlin High-resolution SEM, which is equipped with an in-lens energy selective backscatter detectors for back-scattered electron imaging and the visualization of regions of different composition. For SEM observation, the BP/PS composite sample was prepared via mixing of 100 μL of PS latex nanoparticle dispersion (2.5 wt %) and 100 μL of BP dispersion in ethylene glycol (0.25 mg/mL) and drying on the hot plate of 120° C. for 10 min. Transmission Electron Microscopes (TEM) of BP nanoflakes was carried on JEOL 2010 Advanced High-Performance TEM, and BP nanoflakes were suspended on a holy-carbon grid for the characterization. For the fluorescence imaging of MoS2 or graphene microparticles, the particles together with solvent were sampled and naturally dried on glass slides, a broadband supercontinuum white light source (NKT Photonics, SuperK EXTREME EXR-15) was attenuated with a neutral density filter. Fluorescence signal was filtered with band-pass filters and collected on a 512×512-pixel imaging area of electron multiplying charge coupled device (EMCCD) camera (Andor, iXon3). X-ray photoelectron microscopy (XPS, Kratos AXIS Ultra spectrometer with a monochromatized Al Kα source) was used to analyze the surface chemistry and compositions of various samples including microparticles with different 2D materials, functionalized graphene, BP nanoflakes, and others.
To study the electrical properties of microparticles with the probe station, a MATLAB code was written to execute commands over a semiconductor parameter analyzer (SPA) (Agilent E5262A Source Measure Units), which is used to query electrical information of the microparticles aided by a probe station. The microparticles were loaded into a probe station chamber, and the electrical measurements were carried out in an ambient environment at room temperature with sweeping voltage rate was 50-100 mV/s. In general, the electrical properties of these graphene microparticles can be categorized into two major modes: in-plane mode and vertical (out-of-plane) mode. In the in-plane mode, the microparticles are placed onto an insulating surface (typically glass) with one of the 2D material (typically graphene) surfaces facing up, and the Tungsten (W) probe head gently placed on the material surface. To aid the process of locating a microparticle under the microscope atop the probe station, its location is separately located under an optical lens and marked before it was placed in the probe station. In the vertical mode, vertical conductivities (or through-plane conductivity of the 2D material-composite vertical stack, i.e. Gr-PS/BP-Gr) are typically tested. In this case, a conductive substrate for the microparticle is needed to complete the probe-particle-substrate circuit. ITO substrate was selected for its robustness.
1. Fabrication
To define polymer syncell bases, the first photolithography step was performed using the negative photoresist SU-8 2002 on SiO2/Si wafer (
The fourth photolithography step with a LOR30B sacrificial layer and Shipley S1805 was used to define the structure of subsequent MoS2 film. The MoS2 film was deposited using a modified Langmuir-Blodgett method, where the MoS2 film was collected at an ethanol-hexane interface. See, Bessonov, A. A., et al., Layered memristive and memcapacitive switches for printable electronics. Nat Mater, 2015. 14(2): p. 199-204, which is incorporated by reference in its entirety. To form the top oxide layer, the structure was annealed at 200° C. for 2 h. The lift off process was performed in Remover PG at 80° C. The fifth photolithography with a LOR30B sacrificial layer and Shipley S1805 was used to define 100 nm-thick silver electrical contacts. The lift off process was performed in Remover PG at 80° C. A monolayer hBN (patterned in 50 μm wide stripes) was then transferred on top. Since hBN is transparent, its alignment on the syncell is very challenging. To this end, hBN was transferred with S1850 photoresist in order to help visualize the structure (the photoresist was removed afterwards). Finally, syncells were coated with a PMMA layer for support and lifted off the substrate using KOH solution. To disperse syncells, the PMMA was dissolved in acetone.
Retroreflectors were fabricated using SU-8 photolithography with subsequent evaporation of 100 nm silver.
2. Methods
2D Materials.
Large-area MoS2 films were grown by a chemical vapor deposition (CVD) process described elsewhere. See, Yu, Y., et al., Controlled Scalable Synthesis of Uniform, High-Quality Monolayer and Few-layer MoS2 Films. Scientific Reports, 2013. 3: p. 1866, which is incorporated by reference in its entirety. Briefly, solid 0.5 g S and 4 mg MoCl5 were used as precursors, and a 2×1 cm2 300 nm SiO2/Si wafer piece was used as a growth substrate in a vacuum tube quartz furnace. The system was filled with 50 sccm Ar for 1 h with subsequent growth at 850° C. under 2 Torr pressure for 10 min and a 30 min temperature ramp. As-grown MoS2 films were coated with polystyrene and peeled from the substrate—taking advantage of the surface-energy-assisted method. See, Gurarslan, A., et al., Surface-Energy-Assisted Perfect Transfer of Centimeter-Scale Monolayer and Few-Layer MoS2 Films onto Arbitrary Substrates. ACS Nano, 2014. 8(11): p. 11522-11528, which is incorporated by reference in its entirety. Continuous films of hBN and WSe2 monolayers were purchased from Graphene Supermarket and 6Carbon, respectively.
Characterization.
Raman and photoluminescence measurements were performed using a Raman spectrometer HR-800 (Horiba BY) with 532 nm laser. Height profiles were measured using a CCi HD optical profiler. Electrical resistance measurements were performed in the ARS PSF-10-1-4 Cryogenic Probe Station using micromanipulators as probes (7×, Micromanipulator). Conductance measurements were performed by scanning the voltage from −0.1 to 0.1 V.
Aerosol Experiments.
All aerosol experiments were performed with a Master Airbrush G22 nebulizer in a closed tube in the laminar flow hood. Syncells (dispersed in 80% water/20% ethanol) were sprayed under 2-15 psi pressure from a 300 μm nozzle. The second nebulizer was used to spray analyte droplets in the orthogonal direction (
Standoff Detection.
Standoff syncell detection was performed using a setup with galvanized mirrors, a 532 nm laser, and a photodetector (H10330a-25,HAMAMATSU).
3. In-Flight Analysis
To further understand syncell in-flight behavior, rigorous mathematical calculations were performed on different aerosol aspects. The nebulizer provides 2-15 psi pressure over a 2 cm long tube with a diameter of 0.3 mm. This impulse provides initial droplet speeds of 7-100 m/s, which are rapidly slowed down due to the air drag. Time until the full stop in the horizontal direction is called relaxation time and can be calculated from the equation of motion:
where ν is the particle speed, ρair is the air density, ρparticle particle density, Cd drag coefficient and D the particle characteristic length. Travelled distance in the horizontal direction can be calculated by integrating the solution to Eq. (6). As will be shown in the following, drying time is much longer than the relaxation time; therefore, the particle can be treated as being a liquid droplet for relaxation calculations.
Droplets with 100-300 μm have relaxation times on the order of microseconds, with higher speeds increasing particle drag and, consequently, shortening relaxation time (
The drying process consists of two distinct parts. While evaporating, the droplet loses energy at the expense of its temperature. This happens until it reaches an equilibrium temperature where convective heat flux from the surroundings matches to energy lost due to evaporation. The time that it takes for the droplet to stabilize its temperature is called the cooling time. In the second part, the droplet temperature is stable while the diameter decreases. The time required for complete droplet evaporation is called the lifetime.
Cooling time can be calculated from a droplet energy balance (see Holterman, H. J., Kinetics and Evaporation of Water Drops in Air, in Institute of Agricultural and Environmental Engendering. 2003, which is incorporated by reference in its entirety):
where cp is the specific heat (water: cp=4180 J kg−1 K−1), h is the heat of evaporation (water: h=22.6 105 J/kg), b and ξ are special parameters (see below), psat is the saturated vapor pressure, and γ is a constant (˜67 Pa/K).
After the droplet temperature stabilizes, its diameter change can be approximated as in Holterman (2003):
where ML is the molecular weight of the evaporating liquid (water: 0.018 kg/mole), Dvapor is the average diffusion coefficient for vapor molecules in the saturated film around the drop, T is the average absolute temperature, Tw is the wet-bulb temperature (ΔT=T−Tw), Re is Reynold's number, Sc is Schmidt's number, and R is the gas constant (8.31 J mol−1 K−1). Solving this yields the expression for the droplet lifetime:
where q0 and q1 are parameters defined later in the text.
Numerical calculations showed that cooling time decreases with droplet speed, as vapor pressure decreases with speed, leading to faster evaporation and cooling. Interestingly, the droplet stops much faster compared to the cooling time (
Sedimentation speed is calculated from the equilibrium condition, where the drag on a particle is equal to the buoyant force FB:
F
B=−½ρairACdν2. (10)
For spherical objects under low Reynold's numbers, calculation follows the famous Stokes' law. However, dried syncell has a non-spherical shape and can possibly move into a non-Stokes regime. To account for this, the drag coefficient needs to be modified.
Correction factors were introduced for non-spherical particles. In the Stokes regime, the syncell will preferentially fall with the drag parallel to the axis of symmetry (α is aspect ratio) (see, Byron, M. L., The rotation and translation of non-spherical particles in homogeneous isotropic turbulence. arXiv:1506.00478, 2015, which is incorporated by reference in its entirety):
while in the non-linear regime, the syncell will rotate—having the following ƒ:
The projected syncell is also different for Stokes and nonlinear regimes:
Surface area:
Shape factor:
C
shape=1+1.5(Asurf−1)1/2+6.7(Asurf−1). (16)
Next, a corrected Reynolds number and a corrected drag coefficient are:
The drag coefficient is given by the product of the corrected drag coefficient and the shape factor: Cd=Cd*Cshape.
Relaxation Time.
The drag coefficient for the relaxation time calculations is approximated using the following empirical formula:
with constants a=24, b=0.32 and c=0.52, where Re stands for the Reynolds number:
with ηair being the dynamic air viscosity.
Cooling Time.
The droplet energy balance is:
P
evap
=P
ambient
+P
cooling. (21)
The required power to evaporate a volume dV during a small time interval dt is equal to:
The power withdrawn from the syncell for water evaporation is equal to:
The heat withdrawn from ambient air (temperature Td) by a drop at temperature T′ can be expressed as:
P
ambient=α(Td−T′), (24)
where α is a heat transfer coefficient that can be determined from the steady-state evaporation rate. This yields:
where:
with constants b0=7.5 and b1=237.3 and psat, the saturated vapor pressure (empirical formula for water):
p
sat=610.7 107.5T/(T+237.3). (28)
and Tw is the wet bulb temperature that can be related to relative humidity (RH) by the following empirical formula (again for water):
T
w
=T−((a0+a1T)+(b0+b1T)RH+(c0+c1T)RH2), (29)
with constants: a0=5.11, a1=0.43 K−1, b0=−0.047, b1=−0.0059 K−1, c0=−4×10−5 and c1=1.66×10−5K−1.
Lifetime.
For lifetime calculations, the average diffusion coefficient for vapor molecules in the saturated film around the drop can be calculated using the empirical formula derived for water:
D
vapor=21.2*10−6*(1+0.0071(T−273)). (30)
Schmidt's number is a dimensionless quantity relating the viscous transport of a material to its diffusive transport:
This yields the following formula:
where a and b are constants depending only on ambient conditions and liquid properties:
Solving this yields:
where
with r0≈64.65 s−0.5 and s0≈−1.117×10−3 m s−0.5.
4. MoS2/TEA Binding Analysis
The reaction between MoS2 and TEA can be summarized as follows:
introducing the binding constant kƒ, the association constant kb, and the irreversible constant ki.
To extract these binding constants, MoS2 resistance changes previously measured are fitted by Perkins et al. (
5. State Machine Operation: Power Balance
A successful state machine should not change its state when there is no chemical, even under light illumination. Therefore, the following criteria should be met:
which sets the boundary for the initial chemiresistance:
In this case RmOFF>>Rph and ε/Vth≈2, transforming Eq. (42) into Rchin>RmOFF. The larger the value of RmOFF, the stronger criteria Eq. (42) becomes.
After reaction with an analyte, chemiresistor decreases its resistance to Rchƒ. This allows the voltage across the memristor to reach Vth, changing its resistance:
After liftoff and aerosolization, CSMs can occasionally be bent because of the following reasons: (1) turbulent forces during propulsion, (2) collision during landing, or (3) capillary forces during drying (
F
r
≈mβR, (45)
where m is CSM mass and β CSM rotational acceleration. During propulsion, CSM experience turbulent flow, meaning that β can be approximated as
where ω is CSM angular frequency. Taking the nebulizer tube length to be 2 cm long, CSM acceleration is estimated as 103 m/s2 and Fr=10−8 N.
Capillary forces Fc during drying can be calculated as:
F
c
=σl, (46)
where σ is water surface tension and l is water perimeter length over which CSM bending occurs. Taking σ=0.1 N/m and l=10−4 m, Fc=10−5 N.
The bending force (Fb) for CSM is calculated as:
where w is the CSM width (50 μm), h CSM thickness (1 μm), d bending displacement, E SU-8 Young's modulus (2·109 Pa), and L bending length (50 μm). For minimal displacement of d=1 μm, Fb˜10−6 N. These forces may fluctuate a lot due to nonlinear effects and CSM aggregation, however, capillary forces appear to be the most probable reason for CSM deflection, which is visible in
Strain Guided Fracture Propagation with Stochastic Seed Crack Formation
a. An Existing Model
There is an existing model on soft material fracturing within a strain field induced by curvature. See Mitchell N P, Koning V, Vitelli V, Irvine W T M. Fracture in sheets draped on curved surfaces. Nat. Mater. 2017, 16(1): 89-93, which is incorporated by reference in its entirety. Conforming materials to rigid substrates with Gaussian curvature—positive for spheres and negative for saddles—has proven a versatile tool to guide the self-assembly of defects such as scars, pleats, folds, blisters, and liquid crystal ripples. It has been shown that curvature can likewise be used to control material failure and guide the paths of cracks. A simple analytical model has been proposed to capture crack behavior at the onset of propagation, while a two-dimensional phase-field model with an added curvature term successfully captures the crack's path. Because the curvature-induced stresses are independent of material parameters for isotropic brittle media, these results apply across scales, particularly on the nanometer scale for the generation of microparticles reported thereof.
b. Crack Response to Curvature Stresses and Formulation in Terms of Curvature Potential
Consider the stresses induced by curvature and their interaction with the crack tip in a flat sheet. Stresses generated in the bulk of a material become concentrated near a crack tip. In turn, a crack extends when the intensity of stress concentration exceeds a material-dependent, critical value. Expressed mathematically, in the local coordinates of the crack tip (r, θ), the stress in the vicinity of the tip takes the form
where ƒijI,II are universal angular functions. The factors KI and KII measure the intensity of tensile and shear stress concentration at the crack tip, respectively, and are known as stress intensity factors. Thus, the Griffith length, ac, is the length of the crack at which the intensity of stress concentration reaches the critical value, Kc. In curved plates or sheets, the near-tip stress fields display the same singular behavior as in Eq. (48), but the values of the stress intensity factors are governed by curvature.
Curving a flat sheet involves locally stretching and compressing the material by certain amounts at each point. According to the rules of differential geometry, this stretching factor, controlled by the field Φ(ρ), is determined by an equation identical to the Poisson equation of electrostatics, with the Gaussian curvature, G(ρ), playing the role of a continuous charge distribution
∇2Φ(ρ)=−G(ρ) (49)
As the sheet equilibrates, its elasticity tends to oppose this mechanical constraint, giving rise to stress. The isotropic stress from curvature is then related to the potential via
σkkG=EΦ (50)
where E is the Young's modulus, and the stress components are determined by integrals of the curvature potential. It has been reported previously that positive (negative) curvature promotes local stretching (compression) of an elastic sheet, leading to the enhancement (suppression) of crack initiation. Variations in the potential Φ(ρ) steer the crack path, with the form determined from the curvature distribution.
Curvature not only governs the critical length for fracture initiation, but also the direction of a crack's propagation. For cracks inclined with respect to the bump, the cracks change direction as they begin to propagate, kinking at the onset of crack growth and curving around the bump. Cracks kink and curve towards the azimuthal direction because a decaying curvature potential, Φ(ρ), creates a local stress asymmetry. As a result, the crack relieves more elastic energy by deflecting towards the azimuthal direction. Analytical prediction of the kink angle, θk, has previously been made by selecting the direction of maximum hoop stress asymptotically near the crack tip.
Given knowledge of the stress field of an uncracked sheet on a curved surface, the stress intensity factors (KI, KII) for a crack on that curved surface has been calculated previously. See Zhang P, Ma L, Fan F, Zeng Z, Peng C, Loya P E, et al. Fracture toughness of graphene. Nat. Commun. 2014, 5: 3782, which is incorporated by reference in its entirety. These quantities measure the intensity of tensile and shear stress concentration at the crack tip. The stress intensity factors for each seed crack position and orientation follow from integrating the infinite-plane Westergaard solution over the crack length
where and
are the tensile and shear stresses, respectively, in the crack's local x-y coordinate system. The tilde distinguishes
from σij(ρ,ϕ), which is a function of the material coordinate system rather than the crack coordinate system and is therefore a different function of its arguments, despite being the same physical quantity. Here a is the crack length, and by selecting the direction of maximum hoop stress (
) at the crack tip as the direction of crack propagation, the kink angle at the onset of propagation takes the form
where η=KII/KI and if a crack whose length is relatively small compared to the length scale over which the stress fields vary, that is,
the expression for η simplifies, because
K
I=√{square root over (πa)}(σρρ(ρ*)sin2(β)+σϕϕ(ρ*)cos2(β) (53)
K
II=√{square root over (πa)}{σϕϕ(ρ*)−σρρ(ρ*)}sin(β)cos(β) (54)
where the inclination angle β is the angle of the seed crack with respect to the radial direction. Since KII vanishes for radial and azimuthal cracks (β=0, π/2), these cracks do not kink, while for intermediate values of β, that is, for β mod
the shear stress on the crack, measured by KII, will be nonzero. Therefore, if the crack grows, it will kink at the onset of propagation.
For azimuthal seed cracks (β=π/2), there is no kink because the loading is mode I (tensile) for small seed cracks, but as the crack grows, the asymmetric stresses from curvature direct the crack in a continuous arc. The Griffith length (ac) of a crack is the length at which the energy released by extending the crack exceeds the fracture energy. This corresponds to the condition that the intensity of stress concentration in some direction
where
σyy(ρ*)=σρρ(ρ*)sin2(β)+σϕϕ(ρ*)cos2(β) (56)
σxy(ρ*)={σϕϕ(ρ*)−σρρ(ρ*)}sin(β)cos(β) (57)
If small cracks were considered, expressions for the kink angle and Griffith length are in terms of the curvature potential Φ(ρ). For any rotationally symmetric curvature distribution G(ρ), it has been shown that the ratio of the stress intensity factors of a small crack centered at ρ* is
where
is the average value of the curvature potential in the region enclosed by the circle of radius ρ*. Thus, the quantity Φ−Ω appearing in Eq. (58) is the difference between the local value of the potential Φ(ρ*) and the value of the potential averaged from the center to the location of the crack, and this quantity can be readily identified as the local stress asymmetry.
For the crack to propagate, the tractions along the crack faces must be positive. Therefore, the sign of this stress asymmetry determines whether the crack kinks towards the radial or azimuthal direction. For a crack in a potential “well” (where Φ increases with radial distance), the crack kinks toward the radial direction (with respect to the center of the well). For a crack in a potential “dome” or “peak” (where Φ decreases with radial distance), the crack kinks toward the azimuthal direction. Note this in turn establishes the guiding principle that directs crack propagation along “maximum hoop strain” that has been exploited to great effect in this work.
The Griffith length for the small crack can likewise be computed from a symmetric curvature potential, Φ(ρ), via
F(
Note that the curvature potential measures the local isotropic compression
This implies that crack growth tends to be suppressed in regions where Φ<0 and stimulated where Φ>0. A local stress asymmetry, however, can play an important role in attenuating this generalization. A curvature potential which increases with radial distance (a potential “well”) preferentially stimulates the growth of cracks which are oriented along the radial direction, so that the Griffith length of a radial crack in a potential well is smaller than that of an azimuthal crack centered the same distance ρ* from the minimum of Φ. Conversely, potentials, which decrease with distance from the center preferentially, stimulate the growth of cracks oriented along the azimuthal direction.
c. Estimation of the Griffith Length for Free-Standing Graphene
The minimum seed crack needed for run-away fracture propagation on freestanding graphene is estimated using Eq. (60) and (61). First, it is needed to figure out what function form each term takes on. In terms of the universal angular functions, coordinate transformation is performed (from local Cartesian to global Polar) for mode I as such
Recall that
ƒθθI={right arrow over (e)}θ· ·{right arrow over (e)}θ (66)
and
{right arrow over (e)}
θ=−sin(θ){right arrow over (e)}x+cos(θ){right arrow over (e)}y (67)
where a universal function angular function tensor was defined with the following form
If is a symmetric tensor (i e. ƒijI=ƒjiI) it follows that
ƒθθI(
Similarly, mode II is calculated,
ƒθθII(
given that
In terms of the other parameter values, the critical stress intensity factor for monolayer graphene, Kc, has recently been experimentally measured to be 4.0±0.6 MPa·m1/2 (see Zhang P, Ma L, Fan F, Zeng Z, Peng C, Loya P E, et al. Fracture toughness of graphene. Nat. Commun. 2014, 5: 3782, which is incorporated by reference in its entirety) and the Young's modulus of graphene, E, is approximately 1 TPa (see Lee G-H, Cooper R C, An S J, Lee S, van der Zande A, Petrone N, et al. High-Strength Chemical-Vapor-Deposited Graphene and Grain Boundaries. Science 2013, 340(6136): 1073-1076, which is incorporated by reference in its entirety); as for Φ, it is just the curvature potential (or lattice strain), which according to the simulation in the above sections, is estimated to be around 1% at the point of maximum strain. With these, all possible values of β's can be scanned over and
e. Kinetic Monte-Carlo Simulation of Crack Propagation
A kinetic Monte-Carlo model (rejection KMC method) is created to simulate the stochastic crack initiation and propagation. To monitor the fracture path at the micrometer level, 2D square lattice is used to capture the birds-eye geometry of the graphene-polystyrene-graphene ink-jet printed array. Crack initiation is assigned randomly with a given probability over the entire graphene lattice at each iteration step. Transition rates for continued propagation at each of the four possible directions are then calculated and executed accordingly. Upon the creation of the 2D lattice, the key iteration steps can be summarized generically as following:
1. Set the time to t=0.
2. Choose an initial state k.
3. Get the number Nk of all possible transition rates, from state k into state i.
4. Find the propagation event to carry out i by uniformly sampling from the Nk transitions above.
5. Accept the event with probability ƒki=rki/r0, where r0 is a suitable upper bound for rki.
6. If accepted, update the current state from k to i.
7. Get a new uniform random number u′ from 0 to 1. 8. Update the time with t=t+Δt, where Δt=(Nkr0)−1ln(l/u′).
9. Return to step 3.
Three example simulation results are shown (
If the crack formation can be zoomed in and compared with microscopy results, the simulation seems to corroborate well with experimental observations (
Other embodiments are within the scope of the following claims.
This application is a continuation which claims priority to International Application No.: PCT/US2018/39876, filed Jun. 27, 2018, which claims the benefit of prior U.S. Provisional Application No. 62/525,752, filed on Jun. 28, 2017, which is incorporated by reference in its entirety.
| Number | Date | Country | |
|---|---|---|---|
| 62525752 | Jun 2017 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | PCT/US2018/039876 | Jun 2018 | US |
| Child | 16114185 | US |
