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Articles 1 - 30 of 81
Full-Text Articles in Physical Sciences and Mathematics
Synthesis And Assessment Of Radiotherapy-Enhancing Nanoparticles, Hayden Winter
Synthesis And Assessment Of Radiotherapy-Enhancing Nanoparticles, Hayden Winter
Dissertations and Theses
Radiation Therapy (RT) is a common treatment for cancerous lesions that acts by ionizing matter in the affected tissue, causing cell death. The disadvantage of RT is that it is most often delivered via an external beam of radiation which must pass through healthy tissues to reach the target site, ionizing matter within healthy tissues as well. To address this drawback, techniques are being developed for increasing RT-induced cell death in a target tissue while minimizing cell death in surrounding tissues. This effect is known as radiation dose enhancement or RT enhancement.
The approach to RT enhancement studied in this …
Investigation Of Optical Second Harmonic Generation From Si (100) With Process Tailored Surface & Embedded Ag Nanostructures For Advanced Si Nonlinear Nanophotonics, Gourav Bhowmik
Legacy Theses & Dissertations (2009 - 2024)
The challenge of current microelectronic architecture in transmission bandwidth and power consumption can be potentially solved by using silicon photonics technologies that are compatible with modern CMOS fabrication. One of the critical active photonic devices for Si photonics is a Si based optical modulator. Most of the reported silicon modulators rely on the free carrier plasma dispersion effect. In those cases, a weak change of the refractive index obtained by carrier accumulation, injection or depletion is utilized in a Mach-Zehnder interferometer or a microring resonator to achieve intensity modulation, rendering them difficult for chip-level implementation due to a large footprint …
Exploring Gated Nanoelectronic Devices Fabricated From 1d And 2d Materials, Prathamesh A. Dhakras
Exploring Gated Nanoelectronic Devices Fabricated From 1d And 2d Materials, Prathamesh A. Dhakras
Legacy Theses & Dissertations (2009 - 2024)
One and two dimensional materials are being extensively researched toward potential application as ultra-thin body channel materials. The difficulty of implementing physical doping methods in these materials has necessitated various alternative doping schemes, the most promising of which is the electrostatic gating technique due to its reconfigurability. This dissertation explores the different fundamental devices that can be fabricated and characterized by taking advantage of the electrostatic gating of individual single-walled carbon nanotubes (SWNTs), dense SWNT networks and exfoliated 2D tungsten diselenide (WSe2) flakes.
Recent Advances In Continuous Models Of Electrochemical Supercapacitors, Hao-Tian Lu, Jing-Hong Zhou, Guang-Hua Ye, Xing-Gui Zhou
Recent Advances In Continuous Models Of Electrochemical Supercapacitors, Hao-Tian Lu, Jing-Hong Zhou, Guang-Hua Ye, Xing-Gui Zhou
Journal of Electrochemistry
Electrochemical capacitors (supercapacitors) have been developed as a new type of energy storage device with high energy and power densities, which have the advantages of both fast charging-discharging as traditional capacitors and high energy density as batteries. Notable improvements in their electrochemical performance have been achieved in recent years owing to the recent advances in understanding of charge storage mechanisms and the development of advanced nanostructured materials. Recently, modeling and simulation of these supercapacitors has been applied as a useful approach to better understand the working mechanisms of the supercapacitors by describing the concentrations and electric fields inside the capacitors. …
Enhanced Terahertz Emission From Quantum Dot By Graphene-Coated Nanoparticle, Edin Sijercic, P. T. Leung
Enhanced Terahertz Emission From Quantum Dot By Graphene-Coated Nanoparticle, Edin Sijercic, P. T. Leung
Physics Faculty Publications and Presentations
The terahertz (THz) emission from quantum dots in close proximity to graphene-coated nanoparticles is studied via phenomenological modeling with particular interest in the possibility of enhancement for such emission via the excitation of the graphene plasmons. It is shown that depending on various factors such as the damping factor and the Fermi level of the graphene, as well as the size and core material of the coated particle, such plasmonic-enhanced THz emission is indeed possible. This thus opens up a new pathway to provide intense THz sources for future applications.
Synthesis And Characterization Of Mpims : Metallopolymers Of Intrinsic Microporosity, Kelly Walter
Synthesis And Characterization Of Mpims : Metallopolymers Of Intrinsic Microporosity, Kelly Walter
Legacy Theses & Dissertations (2009 - 2024)
Polymers of intrinsic microporosity (PIMs) are class of polymers known for high surface areas arising from their contorted and rigid backbone structures. While high surface area compounds are applicable in many fields, simultaneous solubility and conductivity in PIMs is still lacking. In general, the monomeric units that form the backbone, necessary to yield inefficient polymer strand packing and contortion, also break conjugation in the along the polymer backbone and therefore limit conductivity. It has been previously noted that extended conjugation and the addition of metal atoms (along the backbone) increases conductivity. We therefore sought to use a strategy whereby the …
Paracest Agents Encapsulated In Reverse Nano-Assembled Capsules (Racs): How Slow Molecular Tumbling Can Quench Cest Contrast, Annah Farashishiko, Jacqueline R. Slack, Mauro Botta, Mark Woods
Paracest Agents Encapsulated In Reverse Nano-Assembled Capsules (Racs): How Slow Molecular Tumbling Can Quench Cest Contrast, Annah Farashishiko, Jacqueline R. Slack, Mauro Botta, Mark Woods
Chemistry Faculty Publications and Presentations
Although paraCEST is a method with immense scope for generating image contrast in MRI, it suffers from the serious drawback of high detection limits. For a typical discrete paraCEST agent the detection limit is roughly an order of magnitude higher than that of a clinically used relaxation agent. One solution to this problem may be the incorporation of a large payload of paraCEST agents into a single macromolecular agent. Here we report a new synthetic method for accomplishing this goal: incorporating a large payload of the paraCEST agent DyDOTAM3+ into a Reverse Assembled nano-Capsule. An aggregate can be generated between …
Computational Optimization And Characterization Of Molecularly Imprinted Polymers, Jacob Jordan Terracina
Computational Optimization And Characterization Of Molecularly Imprinted Polymers, Jacob Jordan Terracina
Legacy Theses & Dissertations (2009 - 2024)
Molecularly imprinted polymers (MIPs) are a class of materials containing sites capable of selectively binding to the imprinted target molecule. Computational chemistry techniques were used to study the effect of different fabrication parameters (the monomer-to-target ratios, pre-polymerization solvent, temperature, and pH) on the formation of the MIP binding sites. Imprinted binding sites were built in silico for the purposes of better characterizing the receptor – ligand interactions. Chiefly, the sites were characterized with respect to their selectivities and the heterogeneity between sites.
Materials For Giant Spin Hall Effect Devices, Avyaya Jayanthinarasimham
Materials For Giant Spin Hall Effect Devices, Avyaya Jayanthinarasimham
Legacy Theses & Dissertations (2009 - 2024)
Studies presented in this thesis are an effort to control the growth of β W and explore
Exploring Magnetic Nanostructures Embedded Within Single-Crystal Silicon For Generation Of Spin-Polarized Carriers, Machara Krishna Girish Malladi
Exploring Magnetic Nanostructures Embedded Within Single-Crystal Silicon For Generation Of Spin-Polarized Carriers, Machara Krishna Girish Malladi
Legacy Theses & Dissertations (2009 - 2024)
Integrating magnetic functionalities with silicon holds the promise of developing, in the most dominant semiconductor, a paradigm-shift information technology based on the manipulation and control of electron spin and charge. Here, we demonstrate an ion implantation approach enabling the synthesis of a ferromagnetic layer within a defect free Si environment by exploiting an additional implant of hydrogen in a region deep below the metal implanted layer. Upon post-implantation annealing, nanocavities created within the H-implanted region act as trapping sites for gettering the implanted metal species, resulting in the formation of metal nanoparticles in a Si region of excellent crystal quality. …
Minimizing Corrosion Of Outdoor Metalworks Using Dispersed Chemically Stabilized Nanoclays In Polyvinylidene Fluoride Latex Coatings, Natasja Alexandria Swartz, Capri A. Price, Tami Lasseter Clare
Minimizing Corrosion Of Outdoor Metalworks Using Dispersed Chemically Stabilized Nanoclays In Polyvinylidene Fluoride Latex Coatings, Natasja Alexandria Swartz, Capri A. Price, Tami Lasseter Clare
Chemistry Faculty Publications and Presentations
Nanoclays are small enough to appear optically transparent, yet they have large surface-to-volume and high aspect ratios that can significantly inhibit water diffusion when incorporated into protective coatings. Clear coatings, which minimally affect the aesthetics of metalworks, are commonly applied to outdoor metalworks, such as sculptures, to prevent and slow corrosion. In recent years, waterborne clear coatings, rather than solvent-based clear coatings, are increasingly used in many applications to reduce the quantity of volatile organic components in the formulation, yet the performance of dry films produced from waterborne colloidal suspensions is generally poorer. In this work, we aim to improve …
Expanding The Versatility Of Nano Assembled Capsules As Platform Of Potential High Payload Mri Contrast Agents, Annah Farashishiko
Expanding The Versatility Of Nano Assembled Capsules As Platform Of Potential High Payload Mri Contrast Agents, Annah Farashishiko
Dissertations and Theses
Magnetic resonance imaging (MRI) has become a powerful clinical modality in diagnostic medicine. It is non-invasive and offers high spatial and temporal resolution. The goal of molecular imaging is to reveal the pathophysiology underlying the observed anatomy and diagnose diseases. The detection of pathological biomarkers can lead to early recognition of diseases and improved monitoring for recurrence. Clinically available contrast agents are limited in their discrimination of contrast between tissues and they tend to have very high detection limits. Because biomarkers are very low in concentration there is a need for high payload deposition of contrast agent (CA) and targeted …
A Novel Methodology For Spatial Damage Detection And Imaging Using A Distributed Carbon Nanotube-Based Composite Sensor Combined With Electrical Impedance Tomography, Hongbo Dai, Gerard J. Gallo, Thomas Schumacher, Erik T. Thostenson
A Novel Methodology For Spatial Damage Detection And Imaging Using A Distributed Carbon Nanotube-Based Composite Sensor Combined With Electrical Impedance Tomography, Hongbo Dai, Gerard J. Gallo, Thomas Schumacher, Erik T. Thostenson
Civil and Environmental Engineering Faculty Publications and Presentations
This paper describes a novel non-destructive evaluation methodology for imaging of damage in composite materials using the electrical impedance tomography (EIT) technique applied to a distributed carbon nanotube-based sensor. The sensor consists of a nonwoven aramid fabric, which was first coated with nanotubes using a solution casting approach and then infused with epoxy resin through the vacuum assisted resin transfer molding technique. Finally, this composite sensor is cured to become a mechanically-robust, electromechanically-sensitive, and highly customizable distributed two-dimensional sensor which can be adhered to virtually any substrate. By assuming that damage on the sensor directly affects its conductivity, a difference …
Novel Two-Dimensional Devices For Future Applications, Pratik Agnihotri
Novel Two-Dimensional Devices For Future Applications, Pratik Agnihotri
Legacy Theses & Dissertations (2009 - 2024)
The scalability of field effect transistor has led to the monumental success of complementary metal-oxide-semiconductor (CMOS) technology. In the past, device scaling was not the major issue to a greater extent. Recently with current technology nodes, transistor characteristics show signs of reduced performance due to short channel effects and other issues related to device scaling. Device designers look for innovative ways to enhance the transistor performance while keeping up with device miniaturization. Successful inventions include the development of tri-gate technology, gate all around (GAA) field effect transistors, silicon-on-insulator substrate, and high-k dielectrics. These developments have enabled the device scaling that …
Tailoring The Optical Properties Of Silicon With Ion Beam Created Nanostructures For Advanced Photonics Applications, Perveen Akhter
Tailoring The Optical Properties Of Silicon With Ion Beam Created Nanostructures For Advanced Photonics Applications, Perveen Akhter
Legacy Theses & Dissertations (2009 - 2024)
In today’s fast life, energy consumption has increased more than ever and with that the demand for a renewable and cleaner energy source as a substitute for the fossil fuels has also increased. Solar radiations are the ultimate source of energy but harvesting this energy in a cost effective way is a challenging task. Si is the dominating material for microelectronics and photovoltaics. But owing to its indirect band gap, Si is an inefficient light absorber, thus requiring a thickness of solar cells beyond tens of microns which increases the cost of solar energy. Therefore, techniques to increase light absorption …
Analysis Of An Electrospun Nanofiber Device Applicable To Limb Salvage: Mass Loss, Morphological Changes, And Quantification Of Antibiotic Release, Caitlin Quinn
Honors Theses
The creation of an electrospun nanofiber embedded with two antibiotics that will be used to prevent infection while also stimulating bone regeneration will be explored. The nanofiber will contain an aminoglycoside and a glycopeptide, and it is sought to deliver a sustained release of antibiotics for up to 12 weeks. To determine release rate, nanofiber samples are immersed in 10.0 mL of MiliQ water (MQ), incubated at 37°C, assayed at specific time intervals, and then analyzed using ultra performance liquid chromatography in tandem with mass spectrometry. A hydrophilic interaction liquid chromatography (HILIC) method utilizing ultra-performance liquid chromatography (UPLC) in tandem …
Optical And Sensing Properties Of Various Shaped Gold Nanoplates And Highly Controlled Asymmetric Gold Nanoplate/Nanosphere Coupled Assemblies., Aiqin Fang
Electronic Theses and Dissertations
With the development of a strategy to correlate the dark-field light scattering spectra of individual nanostructures with scanning electron microscopy (SEM) and atomic force microscopy (AFM) images of the same nanostructures, we were able to investigate several interesting optical properties of Au nanoplates (NPs) and asymmetrically-coupled Au nanospheres (NSs) attached to Au NPs with a high level of control. The light scattering spectra of the NP/NS coupled structures depend strongly on the location of NS attachment on the NP. Attachment of multiple NSs at the edge/vertex sites leads to a unique synergistic effect. In contrast to the uniform distribution of …
Metal-Semiconductor-Metal (Msm) Photodetectors With Plasmonic Nanogratings, Narottam K. Das, Ayman Karar, C L Tan, Mikhail Vasiliev, Kamal Alameh, Yong Tak Lee
Metal-Semiconductor-Metal (Msm) Photodetectors With Plasmonic Nanogratings, Narottam K. Das, Ayman Karar, C L Tan, Mikhail Vasiliev, Kamal Alameh, Yong Tak Lee
Mikhail Vasiliev
We discuss the light absorption enhancement factor dependence on the design of nanogratings inscribed into metal-semiconductor-metal photodetector (MSM-PD) structures. These devices are optimized geometrically, leading to light absorption improvement through plasmon-assisted effects. Finite-difference time-domain (FDTD) simulation results show ~50 times light absorption enhancement for 850 nm light due to improved optical signal propagation through the nanogratings. Also, we show that the light absorption enhancement is strongly dependent on the nanograting shapes in MSM-PDs.
Optical Metrology For Directed Self-Assembly Patterning Using Mueller Matrix Spectroscopic Ellipsometry Based Scatterometry, Dhairya J. Dixit
Optical Metrology For Directed Self-Assembly Patterning Using Mueller Matrix Spectroscopic Ellipsometry Based Scatterometry, Dhairya J. Dixit
Legacy Theses & Dissertations (2009 - 2024)
The semiconductor industry continues to drive patterning solutions that enable devices with higher memory storage capacity, faster computing performance, lower cost per transistors, and higher transistor density. These developments in the field of semiconductor manufacturing along with the overall minimization of the size of transistors require cutting-edge metrology tools for characterization.
Two-Dimensional Chalcogenides : Material Synthesis And Nano-Device Applications, Robin Bay Jacobs-Gedrim
Two-Dimensional Chalcogenides : Material Synthesis And Nano-Device Applications, Robin Bay Jacobs-Gedrim
Legacy Theses & Dissertations (2009 - 2024)
Low-dimensional nanostructures exhibit distinct properties from their bulk counterparts. Here the synthesis of novel low-dimensional nanostructures is demonstrated using both top down and bottom up processes and their properties are investigated. Two-dimensional (2D) binary sesquichalcogenides are introduced as a viable material platform for phase change random access memory, photodetection, and the investigation of topological insulator surface states. An exponential relationship is observed between layer thickness and energy consumption during switching of 2D phase change devices, ultra-high responsivity in 2D photoresistors, and surface-rich conduction in 2D topological insulator nanoplates. Additionally, methods for the assessment of chemical purity, stoichiometry, and dimensions of …
Characterization Of Metallic And Semimetallic Oxide Nanoparticles In Industrial Wastewater And Associated Toxicity, Gary Roth
Legacy Theses & Dissertations (2009 - 2024)
Engineered nanomaterials (ENMs) play an increasing role in manufacturing and consumer products. Currently, there is no standard approach to studying ENM toxicity, and a growing body of literature suggests that ENMs may have toxicity differing from similar compounds in bulk or dissolved form. I examined ENMs used in the semiconductor manufacturing process called chemical-mechanical planarization (CMP) for their properties, removal in the wastewater treatment system (WWT), in-vitro toxicity, and location post-inhalation in-vivo. It was found that ENMs in CMP slurries have morphology determined by their elemental composition, but assessment of size and concentration can differ substantially between accepted techniques. Particles …
Enhanced Electrocatalytic Efficiency Of C/Mwnts For Methanol Oxidation Using Ni Deposited On Mwnts, Murat Farsak, Gülfeza Kardaş
Enhanced Electrocatalytic Efficiency Of C/Mwnts For Methanol Oxidation Using Ni Deposited On Mwnts, Murat Farsak, Gülfeza Kardaş
Turkish Journal of Chemistry
The power density of direct methanol fuel cells (DMFCs) can be changed by using different anode materials. Especially porous materials are preferred for the anode. In the present study, multiwall carbon nanotubes were first injected into graphite. Then, by depositing nickel, a catalyst was prepared for use as the anode material of the DMFC. This catalyst was named Ni@MWNTs. The oxidation of methanol and some kinetic parameters were investigated in KOH solution. Cyclic voltammetry was used for the electrochemical measurements. Kinetic parameters of the methanol oxidation were determined at different temperatures, scan rates, and concentrations of methanol. The surface morphologies …
Enzyme-Based Nitric Oxide Releasing Thin Films And Scaffolds, Mutha Merenna Nuwan Bhagya Gunasekera
Enzyme-Based Nitric Oxide Releasing Thin Films And Scaffolds, Mutha Merenna Nuwan Bhagya Gunasekera
ETD Archive
Nitric oxide synthase enzyme (NOS) embedded in thin films and scaffolds, when exposed to a solution of its substrate arginine, a source of reducing equivalents, and other required ingredients of the NOS reaction, can release fluxes of nitric oxide (NO). The latter is a molecule known to counteract platelet aggregation, and thus can prevent the thrombosis cascade on the surfaces of implantable medical devices. Therefore NO antithrombogenic regimens such as active coatings and embedded scaffolds have the potential to increase the lifespan of implantable biomaterials. Layer-by-layer electrostatic adsorption allows for assembly of multi-component protein/polyelectrolytes nanostructured films. Electrospun fiber matrices may …
Fundamental Studies Of Supported Graphene Interfaces : Defect Density Of States In Graphene Field Effect Transistors (Fets) And Ideal Graphene - Silicon Schottky Diodes, Dhiraj Sinha
Legacy Theses & Dissertations (2009 - 2024)
The physics of transport in atomically thin 2D materials is an active area of research, important for understanding fundamental properties of reduced dimensional materials and for applications. New phenomena based on graphene may include properties of topologically protected insulators. Applications of these materials are envisioned in electronics, optoelectronics and spintronics.
Growth And Characterization Of Graphene On Cuni Substrates, Parul Tyagi
Growth And Characterization Of Graphene On Cuni Substrates, Parul Tyagi
Legacy Theses & Dissertations (2009 - 2024)
Graphene is a single layer of sp2 bonded carbon atoms that crystallizes in the honeycomb structure. Because of its true two-dimensional structure, it has very unique electrical properties, including a very high carrier mobility that is symmetric for holes and electrons. To realize these unique properties, it is important to develop a method for growing graphene films with uniform thickness and low defect density. One of the most popular methods of growth is by chemical vapor deposition on Cu substrates, because it is self-limited. However many applications require the growth of graphene films that are more than one atomic layer …
First-Principles Study Of The Electric Field Effect On The Water-Adsorbed Rutile Titanium Dioxide Surface, Abraham L. Hmiel
First-Principles Study Of The Electric Field Effect On The Water-Adsorbed Rutile Titanium Dioxide Surface, Abraham L. Hmiel
Legacy Theses & Dissertations (2009 - 2024)
TiO2 is a semiconducting material that has been used extensively in many industrial applications, and recently has become a candidate for photocatalytic water splitting, fuel cell anode support materials, sensors, and other novel nanodevices. The interface of TiO2 with water, historically well-studied but still poorly understood, presents a ubiquitous environmental challenge towards the ultimate practical usefulness of these technologies. Ground-state density functional theory (DFT) calculations studying the characteristics of molecular adsorption on model surfaces have been studied for decades, showing constant improvement in the description of the energetics and electronic structure at interfaces. These simulations are invaluable in the …
Assessing Different Zeolitic Adsorbents For Their Potential Use In Kr And Xe Separation, Breetha Alagappan
Assessing Different Zeolitic Adsorbents For Their Potential Use In Kr And Xe Separation, Breetha Alagappan
UNLV Theses, Dissertations, Professional Papers, and Capstones
Separation of Kr from Xe is an important problem in spent nuclear fuel fission gas management. The energy intensive and expensive cryogenic distillation method is currently used to separate these gases. In this thesis, we have carried out the research into appropriate sorbents for the separation of Kr and Xe using pressure swing adsorption. We have examined zeolites using gas adsorption studies as they have the potential to be more cost effective than other sorbents. Zeolites are microporous aluminosilicates and have ordered pore structures. The pores in zeolites have extra-framework cations are substantially free to move. The mobility of cations …
Multi-Level Surface Enhanced Raman Scattering Using AgoX Thin Film, Ming Lun Tseng, Chia Min Chang, Bo Han Cheng, Pin Chieh Wu, K. S. Chung, M. K. Hsiao, H. W. Huang, D. W. Huang, Hai-Pang Chiang, P.T. Leung, D. P. Tsai
Multi-Level Surface Enhanced Raman Scattering Using AgoX Thin Film, Ming Lun Tseng, Chia Min Chang, Bo Han Cheng, Pin Chieh Wu, K. S. Chung, M. K. Hsiao, H. W. Huang, D. W. Huang, Hai-Pang Chiang, P.T. Leung, D. P. Tsai
Physics Faculty Publications and Presentations
Ag nanostructures with surface-enhanced Raman scattering (SERS) activities have been fabricated by applying laser-direct writing (LDW) technique on silver oxide (AgOx) thin films. By controlling the laser powers, multi-level Raman imaging of organic molecules adsorbed on the nanostructures has been observed. This phenomenon is further investigated by atomic-force microscopy and electromagnetic calculation. The SERS-active nanostructure is also fabricated on transparent and flexible substrate to demonstrate our promising strategy for the development of novel and low-cost sensing chip.
Efficient Pbs/Cds Co-Sensitized Solar Cells Based On Tio2 Nanorod Arrays, Yitan Li, Lin Wei, Xiya Chen, Ruizi Zhang, Xing Sui, Yanxue Chen, Jun Jiao, Liangmo Mei
Efficient Pbs/Cds Co-Sensitized Solar Cells Based On Tio2 Nanorod Arrays, Yitan Li, Lin Wei, Xiya Chen, Ruizi Zhang, Xing Sui, Yanxue Chen, Jun Jiao, Liangmo Mei
Physics Faculty Publications and Presentations
Narrow bandgap PbS nanoparticles, which may expand the light absorption range to the near-infrared region, were deposited on TiO₂ nanorod arrays by successive ionic layer adsorption and reaction method to make a photoanode for quantum dot-sensitized solar cells (QDSCs). The thicknesses of PbS nanoparticles were optimized to enhance the photovoltaic performance of PbS QDSCs. A uniform CdS layer was directly coated on previously grown PbS-TiO₂ photoanode to protect the PbS from the chemical attack of polysulfide electrolytes. A remarkable short-circuit photocurrent density (approximately 10.4 mA/cm²) for PbS/CdS co-sensitized solar cell was recorded while the photocurrent density of only PbS-sensitized solar …
Light-Matter Interactions Of Plasmonic Nanostructures, Jennifer Reed
Light-Matter Interactions Of Plasmonic Nanostructures, Jennifer Reed
Electronic Theses and Dissertations
Light interaction with matter has long been an area of interest throughout history, spanning many fields of study. In recent decades, the investigation of light-matter interactions with nanostructures has become an intense area of research in the field of photonics. Metallic nanostructures, in particular, are of interest due to the interesting properties that arise when interacting with light. The properties are a result of the excitation of surface plasmons which are the collective oscillation of the conduction electrons in the metal. Since the conduction electrons can be thought of as harmonic oscillators, they are quantized in a similar fashion. Just …