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1.
Langmuir ; 40(28): 14224-14232, 2024 Jul 16.
Artigo em Inglês | MEDLINE | ID: mdl-38940536

RESUMO

It is known that glow discharges with a water anode inject and form solvated electrons at the plasma-liquid interface, driving a wide variety of reduction reactions. However, in systems with a water cathode, the production and role of solvated electrons are less clear. Here, we present evidence for the direct detection of solvated electrons produced at the interface of an argon plasma and a water cathode via absorption spectroscopy. We further quantify their yield using the dissociative electron attachment of chloroacetate, measuring a yield of 1.04 ± 0.59 electrons per incident ion, corresponding to approximately 100% faradaic efficiency. Additionally, we estimate a yield of 2.09 ± 0.93 hydroxyl radicals per incident ion. Comparison of this yield with other findings in the literature supports that these hydroxyl radicals are likely formed directly in the liquid phase rather than by diffusion from the vapor phase.

2.
Adv Funct Mater ; 30(6)2020 Feb 05.
Artigo em Inglês | MEDLINE | ID: mdl-33828443

RESUMO

Silver nanofilament formation dynamics are reported for an ionic liquid (IL)-filled solid polymer electrolyte prepared by a direct-write process using a conductive atomic force microscope (C-AFM). Filaments are electrochemically formed at hundreds of xy locations on a ~40 nm thick polymer electrolyte, polyethylene glycol diacrylate (PEGDA)/[BMIM]PF6. Although the formation time generally decreases with increasing bias from 0.7 to 3.0 V, an unexpected non-monotonic maximum is observed ~ 2.0 V. At voltages approaching this region of inverted kinetics, IL electric double layers (EDLs) becomes detectable; thus, the increased nanofilament formation time can be attributed to electric field screening which hinders silver electro-migration and deposition. Scanning electron microscopy confirms that nanofilaments formed in this inverted region have significantly more lateral and diffuse features. Time-dependent formation currents reveal two types of nanofilament growth dynamics: abrupt, where the resistance decreases sharply over as little as a few ms, and gradual where it decreases more slowly over hundreds of ms. Whether the resistance change is abrupt or gradual depends on the extent to which the EDL screens the electric field. Tuning the formation time and growth dynamics using an IL opens the range of accessible resistance states, which is useful for neuromorphic applications.

3.
Langmuir ; 36(5): 1156-1164, 2020 Feb 11.
Artigo em Inglês | MEDLINE | ID: mdl-31995383

RESUMO

When a nonthermal plasma and a liquid form part of the same circuit, the liquid may function as a cathode, in which case electrons are emitted from the liquid into the gas to sustain the plasma. As opposed to solid electrodes, the mechanism of this emission has not been established for a liquid, even though various theories have attempted to explain it via chemical processes in the liquid phase. In this work, we tested the effects of the interfacial chemistry on electron emission from water, including the role of pH as well as the hydroxyl radical, the hydrogen atom, the solvated electron, and the presolvated electron; it was found that none of these species are critical to sustain the plasma. We propose an emission mechanism where electrons, generated from ionized water molecules in the uppermost monolayers of solution, are emitted into the plasma directly from the conduction band of the water.

4.
Small ; 14(39): e1802023, 2018 Sep.
Artigo em Inglês | MEDLINE | ID: mdl-30118585

RESUMO

Materials with reconfigurable optical properties are candidates for applications such as optical cloaking and wearable sensors. One approach to fabricate these materials is to use external fields to form and dissolve nanoscale conductive channels in well-defined locations within a polymer. In this study, conductive atomic force microscopy is used to electrochemically form and dissolve nanoscale conductive filaments at spatially distinct points in a polyethylene glycol diacrylate (PEGDA)-based electrolyte blended with varying amounts of ionic liquid (IL) and silver salt. The fastest filament formation and dissolution times are detected in a PEGDA/IL composite that has the largest modulus (several GPa) and the highest polymer crystal fraction. This is unexpected because filament formation and dissolution events are controlled by ion transport, which is typically faster within amorphous regions where polymer mobility is high. Filament kinetics in primarily amorphous and crystalline regions are measured, and two different mechanisms are observed. The formation time distributions show a power-law dependence in the crystalline regions, attributable to hopping-based ion transport, while amorphous regions show a normal distribution. The results indicate that the timescale of filament formation/dissolution is determined by local structure, and suggest that structure could be used to tune the optical properties of the film.

5.
Electrophoresis ; 2018 Feb 27.
Artigo em Inglês | MEDLINE | ID: mdl-29484678

RESUMO

Exosomes carry microRNA biomarkers, occur in higher abundance in cancerous patients than in healthy ones, and because they are present in most biofluids, including blood and urine, these can be obtained noninvasively. Standard laboratory techniques to isolate exosomes are expensive, time consuming, provide poor purity, and recover on the order of 25% of the available exosomes. We present a new microfluidic technique to simultaneously isolate exosomes and preconcentrate them by electrophoresis using a high transverse local electric field generated by ion-depleting ion-selective membrane. We use pressure-driven flow to deliver an exosome sample to a microfluidic chip such that the transverse electric field forces them out of the cross flow and into an agarose gel which filters out unwanted cellular debris while the ion-selective membrane concentrates the exosomes through an enrichment effect. We efficiently isolated exosomes from 1× PBS buffer, cell culture media, and blood serum. Using flow rates from 150 to 200 µL/h and field strengths of 100 V/cm, we consistently captured between 60 and 80% of exosomes from buffer, cell culture media, and blood serum as confirmed by both fluorescence spectroscopy and nanoparticle tracking analysis. Our microfluidic chip maintained this recovery rate for more than 20 min with a concentration factor of 15 for 10 min of isolation.

6.
Phys Chem Chem Phys ; 19(20): 13010-13021, 2017 May 24.
Artigo em Inglês | MEDLINE | ID: mdl-28480933

RESUMO

The elucidation of catalyst surface-plasma interactions is a challenging endeavor and therefore requires thorough and rigorous assessment of the reaction dynamics on the catalyst in the plasma environment. The first step in quantifying and defining catalyst-plasma interactions is a detailed kinetic study that can be used to verify appropriate reaction conditions for comparison and to discover any unexpected behavior of plasma-assisted reactions that might prevent direct comparison. In this paper, we provide a kinetic evaluation of CH4 activation in a dielectric barrier discharge plasma in order to quantify plasma-catalyst interactions via kinetic parameters. The dry reforming of CH4 with CO2 was studied as a model reaction using Ni supported on γ-Al2O3 at temperatures of 790-890 K under atmospheric pressure, where the partial pressures of CH4 (or CO2) were varied over a range of ≤25.3 kPa. Reaction performance was monitored by varying gas hourly space velocity, plasma power, bulk gas temperature, and reactant concentration. After correcting for gas-phase plasma reactions, a linear relationship was observed in the log of the measured rate constant with respect to reciprocal power (1/power). Although thermal catalysis displays typical Arrhenius behavior for this reaction, plasma-assisted catalysis occurs from a complex mixture of sources and shows non-Arrhenius behavior. However, an energy barrier was obtained from the relationship between the reaction rate constant and input power to exhibit ≤∼20 kJ mol-1 (compared to ∼70 kJ mol-1 for thermal catalysis). Of additional importance, the energy barriers measured during plasma-assisted catalysis were relatively consistent with respect to variations in total flow rates, types of diluent, or bulk reaction temperature. These experimental results suggest that plasma-generated vibrationally-excited CH4 favorably interacts with Ni sites at elevated temperatures, which helps reduce the energy barrier required to activate CH4 and enhance CH4 reforming rates.

7.
ACS Appl Mater Interfaces ; 16(22): 28367-28378, 2024 Jun 05.
Artigo em Inglês | MEDLINE | ID: mdl-38769612

RESUMO

Formation of C-N containing compounds from plasma-catalytic coupling of CH4 and N2 over various transition metals (Ni, Pd, Cu, Ag, and Au) is investigated using a multimodal spectroscopic approach, combining polarization-modulation infrared reflection-absorption spectroscopy (PM-IRAS) and optical emission spectroscopy (OES). Through sequential experiments utilizing CH4 and N2 nonthermal plasmas, we minimize plasma-phase reactions and identify key intermediates for C-N coupling on metal surfaces. Results show that simultaneous CH4 and N2 exposure with plasma stimulation produces surface C-N species. However, N2-CH4 sequential exposure does not lead to C-N species formation, while CH4-N2 sequential exposure reveals the presence of CHx surface species and CN radical species as key precursors to C-N species formation. From further analysis using X-ray photoelectron spectroscopy and liquid chromatography-mass spectrometry, the influence of exposure conditions on the degree of nitrogen incorporation and the nature of C-N species formed were revealed. The work highlights the importance of surface chemistry and exposure conditions in surface C-N coupling with plasma stimulation.

8.
ACS Appl Mater Interfaces ; 16(4): 4561-4569, 2024 Jan 31.
Artigo em Inglês | MEDLINE | ID: mdl-38240076

RESUMO

Polycrystalline Ni, Pd, Cu, Ag, and Au foils exposed to nonthermal plasma (NTP)-activated N2 are found to exhibit a vibrational feature near 2200 cm-1 in polarization-modulation infrared reflection-absorption spectroscopy (PM-IRAS) observations that are not present in the same materials exposed to N2 under nonplasma conditions. The feature is similar to that reported elsewhere and is typically assigned to chemisorbed N2. We employ a combination of temperature-dependent experiments, sequential dosing, X-ray photoelectron spectroscopy, isotopic labeling, and density functional theory calculations to characterize the feature. Results are most consistent with a triatomic species, likely NCO, with the C and O likely originating from ppm-level impurities in the ultrahigh-purity (UHP) Ar and/or N2 gas cylinders. The work highlights the potential for nonthermal plasmas to access adsorbates inaccessible thermally as well as the potential contributions of ppm-level impurities to corrupt the interpretation of plasma catalytic chemistry.

9.
Artigo em Inglês | MEDLINE | ID: mdl-39163018

RESUMO

In response to the escalating demand for flexible devices in applications such as wearables, sensors, and touch panels, there is a need for innovative fabrication approaches for devices made from nanomaterial-based inks. Subsequent to ink deposition, a pivotal stage in device manufacturing typically involves high-temperature sintering, posing challenges for heat-sensitive substrates. Nonthermal plasma jet sintering utilizing an atmospheric pressure dielectric barrier discharge (DBD) plasma jet enables sintering at room temperature and standard pressure, facilitating the sintering of printed nanoparticle films without compromising substrate or film surface integrity. However, determining optimal plasma jet sintering conditions can be challenging due to multiple processing variables with intricate interrelationships. This work employed Bayesian optimization (BO) and machine learning (ML) to identify optimal values for seven primary plasma jet sintering variables. Optimization yielded a 99.2% increase in the measured electrical conductivity for plasma jet-sintered indium tin oxide (ITO) films after five rounds of experiments. Moreover, the optimal sintering conditions achieved an electrical conductivity that was 81.4% of conventional furnace sintering at 300 °C, but was three times faster and with a peak substrate temperature below 47 °C. This result demonstrates the prospect of applying BO to optimize processing techniques for emerging low-temperature requirements.

10.
J Am Chem Soc ; 135(44): 16264-7, 2013 Nov 06.
Artigo em Inglês | MEDLINE | ID: mdl-24144120

RESUMO

Plasmas (gas discharges) formed at the surface of liquids can promote a complex mixture of reactions in solution. Here, we decouple two classes of reactions, those initiated by electrons (electrolysis) and those initiated by gaseous neutral species, by examining an atmospheric-pressure microplasma formed in different ambients at the surface of aqueous saline (NaCl) solutions. Electrolytic reactions between plasma electrons and aqueous ions yield an excess of hydroxide ions (OH(-)), making the solution more basic, while reactions between reactive neutral species formed in the plasma phase and the solution lead to nitrous acid (HNO2), nitric acid (HNO3), and hydrogen peroxide (H2O2), making the solution more acidic. The relative importance of either reaction path is quantified by pH measurements, and we find that it depends directly on the composition of the ambient background gas. With a background gas of oxygen or argon, electron transfer reactions yielding excess OH(-) dominate, while HNO2 and HNO3 formed in the plasma and by the dissolution of nitrogen oxide (NOx) species dominate in the case of air and nitrogen. For pure nitrogen (N2) gas, we observe a unique coupling between both reactions, where oxygen (O2) gas formed via water electrolysis reacts in the bulk of the plasma to form NOx, HNO2, and HNO3.


Assuntos
Gases/química , Cloreto de Sódio/química , Pressão Atmosférica , Elétrons , Concentração de Íons de Hidrogênio , Soluções , Propriedades de Superfície , Água/química
11.
Lab Chip ; 23(2): 285-294, 2023 01 17.
Artigo em Inglês | MEDLINE | ID: mdl-36524732

RESUMO

Ribonucleoproteins (RNPs), particularly microRNA-induced silencing complex (miRISC), have been associated with cancer-related gene regulation. Specific RNA-protein associations in miRISC complexes or those found in let-7 lin28A complexes can downregulate tumor-suppressing genes and can be directly linked to cancer. The high protein-RNA electrostatic binding affinity is a particular challenge for the quantification of the associated microRNAs (miRNAs). We report here the first microfluidic point-of-care assay that allows direct quantification of RNP-associated RNAs, which has the potential to greatly advance RNP profiling for liquid biopsy. Key to the technology is an integrated cation-anion exchange membrane (CEM/AEM) platform for rapid and irreversible dissociation (k = 0.0025 s-1) of the RNP (Cas9-miR-21) complex and quantification of its associated miR-21 in 40 minutes. The CEM-induced depletion front is used to concentrate the RNP at the depletion front such that the high electric field (>100 V cm-1) within the concentration boundary layer induces irreversible dissociation of the low KD (∼0.5 nM) complex, with ∼100% dissociation even though the association rate (kon = 6.1 s-1) is 1000 times higher. The high field also electrophoretically drives the dissociated RNA out of the concentrated zone without reassociation. A detection limit of 1.1 nM is achieved for Cy3 labelled miR-21.


Assuntos
MicroRNAs , Microfluídica , Neoplasias , Humanos , Regulação da Expressão Gênica , Microfluídica/instrumentação , MicroRNAs/química , Ribonucleoproteínas/química
12.
ACS Nano ; 17(10): 9388-9404, 2023 05 23.
Artigo em Inglês | MEDLINE | ID: mdl-37071723

RESUMO

Extracellular nanocarriers (extracellular vesicles (EVs), lipoproteins, and ribonucleoproteins) of protein and nucleic acids mediate intercellular communication and are clinically adaptable as distinct circulating biomarkers. However, the overlapping size and density of the nanocarriers have so far prevented their efficient physical fractionation, thus impeding independent downstream molecular assays. Here, we report a bias-free high-throughput and high-yield continuous isoelectric fractionation nanocarrier fractionation technique based on their distinct isoelectric points. This nanocarrier fractionation platform is enabled by a robust and tunable linear pH profile provided by water-splitting at a bipolar membrane and stabilized by flow without ampholytes. The linear pH profile that allows easy tuning is a result of rapid equilibration of the water dissociation reaction and stabilization by flow. The platform is automated with a machine learning procedure to allow recalibration for different physiological fluids and nanocarriers. The optimized technique has a resolution of 0.3 ΔpI, sufficient to separate all nanocarriers and even subclasses of nanocarriers. Its performance is then evaluated with several biofluids, including plasma, urine, and saliva samples. Comprehensive, high-purity (plasma: >93%, urine: >95% and saliva: >97%), high-yield (plasma: >78%, urine: >87% and saliva: >96%), and probe-free isolation of ribonucleoproteins in 0.75 mL samples of various biofluids in 30 min is demonstrated, significantly outperforming affinity-based and highly biased gold standards having low yield and day-long protocols. Binary fractionation of EVs and different lipoproteins is also achieved with similar performance.


Assuntos
Líquidos Corporais , Vesículas Extracelulares , Saliva/metabolismo , Ribonucleoproteínas , Líquidos Corporais/química , Vesículas Extracelulares/metabolismo , Lipoproteínas/análise , Lipoproteínas/metabolismo
13.
Phys Rev Lett ; 109(22): 224301, 2012 Nov 30.
Artigo em Inglês | MEDLINE | ID: mdl-23368125

RESUMO

A planar surface acoustic wave on a solid substrate and its radiated sound into a static liquid drop produce time-averaged, exponentially decaying acoustic and electric Maxwell pressures near the contact line. These localized contact-line pressures are shown to generate two sequences of hemispherical satellite droplets at the tens of microns and submicron scales, both obeying self-similar exponential scaling but with distinct exponents that correspond to viscous dissipation and field leakage length scales, respectively. The acoustic pressure becomes dominant when the film thickness exceeds (1/4π) of the surface acoustic wave wavelength and it affects the shape and stability of the mother drop. The Maxwell pressure of the nanodrops, which exceeds ten atmospheres, is sensitive to the contact angle.

14.
iScience ; 25(8): 104653, 2022 Aug 19.
Artigo em Inglês | MEDLINE | ID: mdl-35958027

RESUMO

The extracellular RNA communication consortium (ERCC) is an NIH-funded program aiming to promote the development of new technologies, resources, and knowledge about exRNAs and their carriers. After Phase 1 (2013-2018), Phase 2 of the program (ERCC2, 2019-2023) aims to fill critical gaps in knowledge and technology to enable rigorous and reproducible methods for separation and characterization of both bulk populations of exRNA carriers and single EVs. ERCC2 investigators are also developing new bioinformatic pipelines to promote data integration through the exRNA atlas database. ERCC2 has established several Working Groups (Resource Sharing, Reagent Development, Data Analysis and Coordination, Technology Development, nomenclature, and Scientific Outreach) to promote collaboration between ERCC2 members and the broader scientific community. We expect that ERCC2's current and future achievements will significantly improve our understanding of exRNA biology and the development of accurate and efficient exRNA-based diagnostic, prognostic, and theranostic biomarker assays.

15.
Anal Chem ; 83(8): 3017-23, 2011 Apr 15.
Artigo em Inglês | MEDLINE | ID: mdl-21417427

RESUMO

The novel effects resulting from the entrainment of low mobility ions during alternating current (ac) electrospray ionization are examined through mass spectrometry and voltage/current measurements. Curious phenomena such as pH modulation at high frequencies (>150 kHz) of an applied ac electric field are revealed and explained using simple mechanistic arguments. Current measurements are utilized to supplement these observations, and a simplified one-dimensional transient diffusion model for charge transport is used to arrive at a scaling law that provides better insight into the ac electrospray ionization process. Moreover, because of the different pathway for ion formation in comparison to direct current (dc) electrospray, ac electrospray (at frequencies >250 kHz) is shown to reduce the effects of ionization suppression in a mixture of two molecules with different surface activities.


Assuntos
Espectrometria de Massas por Ionização por Electrospray/métodos , Citocromos c/análise , Concentração de Íons de Hidrogênio , Mioglobina/análise , Compostos de Amônio Quaternário/análise , Propriedades de Superfície
16.
Anal Chem ; 83(9): 3260-6, 2011 May 01.
Artigo em Inglês | MEDLINE | ID: mdl-21456580

RESUMO

A surface acoustic wave-based sample delivery and ionization method that requires minimal to no sample pretreatment and that can operate under ambient conditions is described. This miniaturized technology enables real-time, rapid, and high-throughput analysis of trace compounds in complex mixtures, especially high ionic strength and viscous samples that can be challenging for conventional ionization techniques such as electrospray ionization. This technique takes advantage of high order surface acoustic wave (SAW) vibrations that both manipulate small volumes of liquid mixtures containing trace analyte compounds and seamlessly transfers analytes from the liquid sample into gas phase ions for mass spectrometry (MS) analysis. Drugs in human whole blood and plasma and heavy metals in tap water have been successfully detected at nanomolar concentrations by coupling a SAW atomization and ionization device with an inexpensive, paper-based sample delivery system and mass spectrometer. The miniaturized SAW ionization unit requires only a modest operating power of 3 to 4 W and, therefore, provides a viable and efficient ionization platform for the real-time analysis of a wide range of compounds.

17.
ACS Appl Mater Interfaces ; 13(47): 56242-56253, 2021 Dec 01.
Artigo em Inglês | MEDLINE | ID: mdl-34786947

RESUMO

Nonthermal plasmas (NTPs) produce reactive chemical environments, including electrons, ions, radicals, and vibrationally excited molecules, that can drive chemistry at temperatures at which such species are thermally inaccessible. There has been growing interest in the integration of conventional catalysis with reactive NTPs to promote novel chemical transformations. Unveiling the full potential of plasma-catalytic processes requires a comprehensive understanding of plasma-catalytic synergies, including characterization of plasma-catalytic surface interactions. In this work, we report on a newly designed multimodal spectroscopic instrument combining polarization-modulation infrared reflection-absorption spectroscopy (PM-IRAS), mass spectrometry, and optical emission spectroscopy (OES) for the investigation of plasma-surface interactions such as those found in plasma catalysis. In particular, this tool has been utilized to correlate plasma-phase chemistry with both surface chemistry and gas-phase products in situ (1) during the deposition of carbonaceous surface species via NTP-promoted nonoxidative coupling of methane and (2) during subsequent activation of surface deposits with an atmospheric pressure and temperature argon plasma jet on both nickel (Ni) and silicon dioxide (SiO2) surfaces. For the first time, the activation of carbonaceous surface species by a NTP on Ni and SiO2 surfaces to form hydrogen gas and C2 hydrocarbons was directly observed, where both PM-IRAS and OES measurements suggest that they may form through different pathways. This unique tool for studying plasma-surface interactions could enable more rational design of plasma-stimulated catalytic processes.

18.
ACS Appl Mater Interfaces ; 13(39): 47244-47251, 2021 Oct 06.
Artigo em Inglês | MEDLINE | ID: mdl-34546717

RESUMO

Atmospheric pressure nonthermal plasmas hold great promise for applications in environmental control, energy conversion, and material processing. Even at room temperature, nonthermal plasmas produce energetic and reactive species that can initiate surface modifications at a plasma-surface interface, including thin-film nanoparticle assemblies, in a nondestructive and effective way. Here, we present the plasma-activated sintering of aerosol jet printed silver thin films on substrates ranging from glass to delicate materials including blotting paper, fruits, and flexible plastic. We characterize the microstructural evolutions and electrical properties of printed films along with the electrical, thermal, and optical properties of an argon plasma jet. We demonstrate an electrical conductivity as high as 1.4 × 106 S/m for printed films sintered under atmospheric conditions in which the surface temperature stays below 50 °C. These results highlight a future direction where additive manufacturing of electronic devices can be achieved on flexible and low-melting-point materials under ambient conditions without requiring additional thermal processing by utilizing nonthermal plasmas.

19.
J Chem Phys ; 132(10): 104111, 2010 Mar 14.
Artigo em Inglês | MEDLINE | ID: mdl-20232951

RESUMO

Equilibrium molecular dynamics combined with the Green-Kubo formula can be used to calculate the thermal conductivity of materials such as germanium and carbon. The foundation of this calculation is extracting the heat current from the results and implementing it into the Green-Kubo formula. This work considers all formulations from the literature that calculate the heat current for the Tersoff potential, the interatomic potential most applicable to semiconductor materials. The formulations for the heat current are described, and results for germanium and carbon are presented. The formulations are compared with respect to how well they capture the physics of the Tersoff potential and how well the calculated value of the thermal conductivity reflects the experimentally measured value.

20.
Front Chem ; 7: 216, 2019.
Artigo em Inglês | MEDLINE | ID: mdl-31024900

RESUMO

In situ fabrication of nanostructures within a solid-polymer electrolyte confined to subwavelength-diameter nanoapertures is a promising approach for producing nanomaterials for nanophotonic and chemical sensing applications. The solid-polymer electrolyte can be patterned by lithographic photopolymerization of poly(ethylene glycol) diacrylate (PEGDA)-based silver cation (Ag+)-containing polyelectrolyte. Here, we present a new method for fabricating nanopore-templated Ag nanoparticle (AgNP) arrays by in situ photopolymerization using a zero-mode waveguide (ZMW) array to simultaneously template embedded AgNPs and control the spatial distribution of the optical field used for photopolymerization. The approach starts with an array of nanopores fabricated by sequential layer-by-layer deposition and focused ion beam milling. These structures have an optically transparent bottom, allowing access of the optical radiation to the attoliter-volume ZMW region to photopolymerize a PEGDA monomer solution containing AgNPs and Ag+. The electric field intensity distribution is calculated for various ZMW optical cladding layer thicknesses using finite-element simulations, closely following the light-blocking efficiency of the optical cladding layer. The fidelity of the polyelectrolyte nanopillar pattern was optimized with respect to experimental conditions, including the presence or absence of Ag+ and AgNPs and the concentrations of PEGDA and Ag+. The self-templated approach for photopatterning high-resolution photolabile polyelectrolyte nanostructures directly within a ZMW array could lead to a new class of metamaterials formed by embedding metal nanoparticles within a dielectric in a well-defined spatial array.

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