Surface plasmon polaritons

Plasmons: Collective oscillations of the “free electron gas density” often at optical frequencies. The coupling of light to the metal nano particles produces resonances under specific conditions. The resonant interaction between them will localize the electromagnetic field near metal surface and drastically enhances the optical scattering phenomenon. The unique properties of the interface waves result from the frequency-dependent dispersion characteristics of metallic and dielectric materials. Thus, a dielectric–metallic interface can support surface plasmon polaritons (SPP). The momentum of a surface plasmon mode is greater than the momentum of propagation light modes of same frequency. There needs to be an Ex component of the field for a surface charge to exist. Hence SPs yield TM polarized fields. The EM fields of SPs are highly confined to the metal/dielectric interface. They evanescently decrease in strength away from the interface. The tangential and normal components of the SPP wave vector have imaginary parts even in a lossless system. Consequently, the amplitude of such an SPP should decrease in the direction of propagation and increase away from the interface.

Applications of SPP

Highly subwavelength radial miniaturization

Able to concentrate energy in wavelength volume

Strong dispersive properties mechanism for manipulating waves

Able to guide waves along the surface of a metal.

Dispersion of Surface plasmon polaritons

Surface plasmon polaritons (SPPs) are quasiparticles that are formed when light couples with electrons at the interface between a metal and a dielectric material. The dispersion of SPPs refers to the relationship between the frequency and wavevector of the SPPs, and it determines the behavior of the SPPs as they propagate along the interface.

In general, the dispersion of SPPs is described by a dispersion relation, which is a mathematical equation that describes the relationship between the frequency, wavevector, and other material parameters of the system. The dispersion of SPPs is influenced by several factors, including the metal used, the dielectric material, and the thickness of the metal film.

For instance, the dispersion of SPPs can be either positive or negative, depending on the combination of metal and dielectric material used. Positive dispersion means that the frequency of the SPPs increases with increasing wavevector, while negative dispersion means that the frequency decreases with increasing wavevector.

The dispersion of SPPs is important for several applications, such as surface-enhanced spectroscopies, photonics devices, and subwavelength imaging. The understanding of the dispersion of SPPs is crucial for the design and optimization of these applications.

Derivation of the dispersion equation

This relation is the basis for understanding of coupling of light to propagating surface plasmons, by using special approaches to match the wavevector. Surface plasmon polariton is a surface wave propagating along the metal dielectric interface or it is a coupled state between a photon and plasmon.

Incident Wave: E and H depends on Z-variable and time in the form of plane wave

Surface wave : EM wave energy concentrated at the interface (z direction)

and decay away from the interface, Surface ,

are independent on Y

-Amplitudes of Electric and magnetic fields along the x direction

The energy of polaritons is contributed by two parts. One part is pure EM energy accumulated in EM field and second part is energy of solid state.

Light couples with electron oscillations (Plasma oscillations in metal)

Therefore,

EM energy +kinetic energy of free electrons

Energy of resulting wave (SPP)

A plane wave has translational symmetry along z and Y directions

Without loss of generality we can assume that E and H are independent on Y. We need to find distribution of E an M Field.

I.e. Dependence of frequency of surface plasmon polariton on propagation constant kz

Using boundary conditions

We need to find dispersion equation of surface EM wave using from the fundamental Maxwell’s equations Maxwell’s equation

Equivalent to 6 scalar equations

A t the interface six components of electric and magnetic field can be divided into two sets

TM polariton i.e. connection between Hy, Ex, Ez component of EM field

TE polarization, TE polarization- Ey, Hx & Hz

In TM polarization only we can get non-trivial solution

Dispersion Equation

Helmholtz equation for Hy component of magnetic field

Ex and Ez in terms of magnetic field

Solution for Helmholtz equation in upper and lower medium

Upper medium

Lower medium

After applying boundary conditions x=0,

Continuity of tangential component of magnetic field

H1y (0) =H2y (0)

Continuity of tangential component of electric field

Substitute x=0 in the above equations

E1z (0) =E2z (0)

k1, k2 inverse penetration depths in medium1 and medium 2 respectively.

Substitute k1 & k2, k1= k2 =positive

Dispersion equation of SPP

This expression relates the wavenumber of the SPP along the propagation direction with the wavenumber of electromagnetic waves in vacuum k0. The unique properties of the interface waves result from the frequency-dependent dispersion characteristics of metallic and dielectric materials.

NANO STRUCTURES

1. Introduction

Nanotechnology deals with the physiochemical, optical, electrical, and mechanical properties of materials whose size and shape are engineered at the nanoscale. Nanomaterials (NMs) have gained prominence in technological advancements due to their tunable physical, chemical, and biological properties with enhanced performance over their bulk counterparts.

NMs are categorized depending on their size, composition, shape, and origin. The ability to predict the unique properties of NMs increases the value of each classification.

Nano structures refer to materials or objects that have dimensions in the nanometer scale, which is about 1 to 100 nanometers. Nanoscale materials and structures exhibit unique properties that are different from those of their bulk counterparts due to the high surface-to-volume ratio, quantum size effects, and the confinement of electrons in small dimensions.

Nano structures can be made from various materials such as metals, ceramics, polymers, and composites. They can be prepared using various techniques such as top-down (for example, etching and lithography) and bottom-up (for example, self-assembly and chemical synthesis) approaches.

Nano structures have a wide range of applications, including in electronics, energy, biomedical, and environmental fields. For example, they can be used to improve the performance of batteries, create more efficient solar cells, or develop new drug delivery systems.

It's worth noting that while nano structures have the potential to bring significant benefits, they also pose potential health and environmental risks due to their small size and large surface area, which can make them more reactive and easier to penetrate biological membranes. Therefore, it's important to carefully consider the potential benefits and risks of nano structures in their design, synthesis, and use.

The nanomaterials have at least one dimension of 1–100 nm. The nanomaterials exist in single, aggregated, or fused forms with several shapes such as tubular, spherical, and irregular. The most common types of nanomaterials are nanofibers, nanotubes, quantum dots, and nanosheets.

Nanoparticles (NPs)

• Smaller in structures but larger than QDs, usually ranging from 8 to 100 nanometers.

• Exhibit behaviors between those bulk materials and atoms or molecules.

• Possess unexpected optical properties as their size allows for quantum confinement effects.

Low-dimensional nanomaterials with a size of 1–100 nm exhibit the distinctive features responding to their specific characteristics. Their features depend on the synthesis routes (top-down or bottom-up procedures) and the growth methods in solid, liquid, vapor and hybrid phases. Products are finally classified into 0D, 1D, 2D, or 3D dimensional materials based on their sizes in each dimension (x, y, or z) measured in nanoscale size range. This classification is highly dependent on the electron movement along the dimensions in the NMs.

(i) Zero-dimensional nanomaterials: Here, all dimensions (x, y, z) are at nanoscale, i.e., no dimensions are greater than 100 nm. It includes nanospheres and nanoclusters. The electrons are confined in all directions. The electrons are not allowed to move anywhere in the system. The consequence of this confinement in space is the quantization of their energy and momentum. In this case they are subjected to principles of quantum mechanical motion rather than classical mechanics. The motion of electrons in the confined space can be modeled by the motion of a particle in a potential well with infinite walls. The most common representation of zero-dimensional NMs are NPs.

Nanoparticles are of interest because of the new properties (such as chemical reactivity and optical behavior) that they exhibit compared with larger particles of the same materials.

For example, titanium dioxide and zinc oxide become transparent at the nanoscale, however, are able to absorb and reflect UV light, and have found application in sunscreens.

Nanoparticles can also be arranged into layers on surfaces, providing a large surface area and hence enhanced activity, relevant to a range of potential applications such as catalysts.

• Fullerene - Composed of at least 60 atoms of carbon, wrapped-up graphene-buckyball

• A cage-like carbon cluster, made up of 12 pentagons and 20 hexagons, five-and six-membered ring patterns.

• C60is the most stable and spherical in shape, diameter of C60 fullerene is about 0.7 nm

•

C60 fullerene is a type of nano structure that is made of carbon atoms and has a spherical shape. It is one of the simplest and best-studied fullerenes, a family of carbon-based nanostructures that also includes other shapes, such as tubes and ellipsoids. C60 fullerene was first synthesized in 1985, and since then it has been extensively studied for its unique physical and chemical properties.

One of the key properties of C60 fullerene is its high stability and resistance to chemical reactions. This makes it useful as a component in a variety of applications, including as a lubricant, a scavenger of free radicals, and a building block for the synthesis of other nanostructures.

In addition to its stability, C60 fullerene has also been shown to have interesting electronic properties, which make it useful as a material in electronic devices, such as field-effect transistors and photovoltaic cells. It can also act as a host for other species, such as metal atoms and molecules, leading to the formation of functional materials with novel properties. Overall, C60 fullerene is an important example of a nano structure that has been well studied and has numerous potential applications.

Quantum dots

Nanoparticles of semiconductors (quantum dots) were theorized in the 1970s and initially created in the early 1980s. If semiconductor particles are made small enough, quantum effects come into play, which limit the energies at which electrons and holes (the absence of an electron) can exist in the particles. As energy is related to wavelength (or color), this means that the optical properties of the particle can be finely tuned depending on its size. Thus, particles can be made to emit or absorb specific wavelengths (colors) of light, merely by controlling their size.

Recently, quantum dots have found applications in composites, solar cells and fluorescent biological labels (for example to trace a biological molecule) which use both the small particle size and tunable energy levels.

(ii) One-dimensional nanomaterials: Here, two dimensions (x, y) are at nanoscale and the other is outside the nanoscale. This leads to needle shaped nanomaterials. It includes nanofibers, nanotubes, nanorods, and nanowires.

Nanowires

Nanowires are ultrafine wires or linear arrays of dots, formed by self-assembly. They can be made from a wide range of materials. Semiconductor nanowires made of silicon, gallium nitride and indium phosphide have demonstrated remarkable optical, electronic and magnetic characteristics (for example, silica nanowires can bend light around very tight corners).

Nanowires have potential applications in high-density data storage, either as magnetic read heads or as patterned storage media, and electronic and opto-electronic nanodevices, for metallic interconnects of quantum devices and nanodevices.

The preparation of these nanowires relies on sophisticated growth techniques, which include self-assembly processes, where atoms arrange themselves naturally on stepped surfaces, chemical vapor deposition (CVD) onto patterned substrates, electroplating or molecular beam epitaxy (MBE). The ‘molecular beams’ are typically from thermally evaporated elemental sources.

(iii) Two-dimensional nanomaterials: Here, one dimension (x) is at nanoscale and the other two are outside the nanoscale. The 2D nanomaterials exhibit platelike shapes. It includes nanofilms, nanolayers and nano coatings with nanometer thickness. Due to their high anisotropy and chemical functions, two-dimensional (2D) nanomaterials have attracted increasing interest and attention from various scientific fields, including functional electronics, catalysis, supercapacitors, batteries, and energy materials. In the biomedical field, 2D nanomaterials have made significant contributions to the field of nanomedicine, especially in drug/gene delivery systems, multimodal imaging, biosensing, antimicrobial agents and tissue engineering.

2D nanomaterials are considered to be the thinnest nanomaterials due to their thickness and dimensions on macroscale/nanoscale. These nanomaterials have a layered structure with strong in-plane bonds and weak van der Waals (vdW) between layers. These ultrathin nanomaterials can be produced from laminated precursors described in the following sections. Although the ideal state is a single layer, but often these nanosheets are composed of few layers (less than ten layers). In recent years, 2D nanomaterials such as graphene, hexagonal boron nitride (hBN), and metal dichalcogenides (MX2) have attracted a lot of attention due to their satisfactory properties and widespread uses in the electronics, optoelectronics, catalysts, energy storage facilities, sensors, solar cells, lithium batteries, composites, etc.

Inspired by the unique optical and electronic properties of graphene, 2D layered materials – as well as their hybrids – have been intensively investigated in recent years, driven by their potential applications mostly for nanoelectronics.

The broad spectrum of atomic layered crystals includes transition metal dichalcogenides (TMDs), semiconducting dichalcogenides, monoatomic buckled crystals, such as black phosphorous (BP or phosphorene), and diatomic hexagonal boron nitride (h-BN).

This class of materials can be obtained by exfoliation of bulk materials to small scales, or by epitaxial growth and chemical vapor deposition (CVD) for large areas.

Such atomically thin, single- or few-layer crystals are featured with strong intralayer covalent bonding and weak interlayer van der Waals bonding, resulting in superior electrical, optical and mechanical properties.

(iv) Three-dimensional nanomaterials: These are the nanomaterials that are not confined to the nanoscale in any dimension. These materials have three arbitrary dimensions above 100 nm. No dimension at the nanoscale, all dimensions at the macroscale. The bulk (3D) nanomaterials are composed of a multiple arrangement of nano size crystals in different orientations. It includes dispersions of nanoparticles, bundles of nanowires and nanotubes as well as multi nano layers (polycrystals) in which the 0D, 1D and 2D structural elements are in close contact with each other and form interfaces.

This class can contain bulk powders, dispersions of nanoparticles, bundles of nanowires, and nanotubes as well as multi-nanolayers.

These changes arise through systematic transformation in density of electronic energy levels as a function of size, and these changes result in strong variations in the optical and electrical properties with size.

Exceptionality Of Metal Nanoparticles

Different Types Of Nanoparticles

Nanoparticles are tiny particles with sizes between 1 and 100 nanometers. There are various types of nanoparticles, including:

· Metal nanoparticles

· Semiconductor nanoparticles

· Magnetic nanoparticles

· Carbon nanoparticles

· Polymeric nanoparticles

· Lipid nanoparticles

· Ceramic nanoparticles

Each type has unique properties that make them useful in various fields of science and technology.

Metal nanoparticles: These are nanoparticles made from metals such as gold, silver, platinum, and copper. Metal nanoparticles have unique physical and chemical properties that make them useful in a wide range of applications such as medical diagnostics, drug delivery, and catalysis.

Semiconductor nanoparticles: e.g., cadmium selenide, zinc oxide, and silicon. used in electronics, solar cells, and biological imaging.

Magnetic nanoparticles:

o Made from magnetic materials such as iron oxide and cobalt,

o used in biomedical applications such as drug delivery and magnetic resonance imaging (MRI)

Carbon nanoparticles:

o e.g., carbon nanotubes and graphene,

o used in electronics, energy storage, and water purification.

Polymeric nanoparticles:

o e.g., synthetic or natural polymers such as polystyrene, polyethylene glycol, and chitosan,

o used in drug delivery and gene therapy.

Lipid nanoparticles: phospholipids and cholesterol

Ceramic nanoparticles:

o Ceramic materials such as alumina, silica, and titania,

o used in catalysis, electronic materials, and biomedical applications.

Metal nanoparticles overview

Metal nanoparticles (MNPs) are tiny particles made from metal atoms with dimensions in the range of 1 to 100 nanometers. These particles have unique physical, chemical, and electronic properties that differ from those of the bulk metal material. The surface area-to-volume ratio of metal nanoparticles is very high, which makes them highly reactive and can enhance their properties in certain applications such as electronics, catalysis, biomedical engineering, and materials science.

MNPs can be made from a variety of metals, including gold, silver, platinum, copper, iron, and more. In recent years, the use of metal nanoparticles in medicine has received significant attention due to their unique properties, such as high biocompatibility, tunable surface chemistry, which make them useful for drug delivery, medical imaging, and cancer therapy.

Physical properties of metal nanoparticles

MNPs have unique physical properties that differ from their bulk metal counterparts since their size and shape can be precisely controlled during synthesis. The physical properties of metal nanoparticles are highly tunable. The size and shape of the nanoparticles affect their electronic, optical, and magnetic properties.

Because of their higher surface area-to-volume ratio they become more reactive and enhance their properties in specific applications.

MNPs can exhibit unique colors and fluorescence properties. for example, Au NPs exhibit a characteristic red color due to their plasmonic properties. Some MNPs, such as iron, cobalt, and nickel, exhibit magnetic properties that can be exploited in applications such as magnetic data storage and biomedical imaging.

The melting point of metal nanoparticles can be lower than that of the bulk metal due to the presence of surface defects and lattice distortions.

The surface chemistry of MNPs can be tuned by modifying their surface with ligands or coatings, which can affect their properties in applications such as catalysis and drug delivery.

Synthesis/Preparation of metal nanoparticles

Chemical reduction method: In this method, a reducing agent is used to reduce metal ions into nanoparticles. For example, sodium borohydride is commonly used to reduce metal ions such as gold, silver, and platinum to form nanoparticles.

In Electrochemical method, metal ions are reduced electrochemically to form nanoparticles. The size and shape of the nanoparticles can be controlled by adjusting the voltage and current during the electrochemical process.

In Microwave-assisted method: In this method, metal ions are mixed with a reducing agent and then exposed to microwave radiation. The heat generated by the microwave radiation promotes the reduction of the metal ions to form nanoparticles.

Green synthesis method, here the plant extracts or other natural sources are used as reducing agents to prepare metal nanoparticles. This method is considered environmentally friendly as it avoids the use of harsh chemicals and solvents.

Electrochemical preparation of Metal nanoparticles

Electrochemical methods are widely used for the preparation of metal nanoparticles due to their simplicity, scalability, and ability to control the size and shape of the nanoparticles. The electrochemical methods for the preparation of metal nanoparticles can be classified into two categories: anodic and cathodic methods.

Anodic methods: In anodic methods, the metal ions are reduced at the electrode surface to form metal nanoparticles. Anodic stripping voltammetry (ASV) is an example of an anodic method used to prepare metal nanoparticles. In ASV, the metal ions are first adsorbed onto the electrode surface and then reduced to form metal nanoparticles.

Cathodic methods: In cathodic methods, the metal ions are reduced at the cathode surface to form metal nanoparticles. Cathodic reduction can be carried out in the presence of a stabilizing agent, such as a surfactant or polymer, to prevent the aggregation of nanoparticles. Electrochemical deposition (ECD) is an example of a cathodic method used to prepare metal nanoparticles. In ECD, a metal salt solution is electrolyzed using an appropriate cathode material to form metal nanoparticles.

Both anodic and cathodic methods can be used to prepare metal nanoparticles with a high degree of control over their size and shape. The electrochemical methods also offer the advantage of being scalable and easy to perform. The choice of method depends on the specific metal, the desired size and shape of the nanoparticles, and the intended application.

Photochemical Methods for the Preparation Of Metal Nanoparticles

Photochemical methods are another popular approach for the preparation of metal nanoparticles. These methods involve the use of light to drive the reduction of metal ions to form nanoparticles. The photochemical methods can be divided into two categories: direct and indirect photochemical methods.

In direct photochemical methods, the metal ions are reduced (in the presence of a reducing agent) directly by a photochemical reaction induced by UV light Which lead to the formation of metal nanoparticles.

In indirect photochemical methods, a photosensitive metal precursor is first synthesized, which upon exposure to light, undergoes a chemical transformation to form the metal nanoparticles.

Photochemical methods offer several advantages over other synthesis methods, including the ability to prepare metal nanoparticles at low temperatures, high yields, and good control over the size and shape of the nanoparticles. Moreover, photochemical methods are eco-friendly as they do not require any harsh reducing agents or high temperatures. However, these methods require a high-intensity light source, and the synthesis process can be time-consuming.

Surface Plasmon Resonance

Surface plasmon resonance (SPR) is a phenomenon that occurs when light hits a metal surface and creates oscillations of electrons on the surface called surface plasmons. The surface plasmons interact with the incident light and cause a reduction in the reflected light intensity at a specific angle, known as the resonance angle.

Origin Of SPR

MNPs exhibit surface plasmon resonance because of their unique optical properties, which arise due to the interaction of light with free electrons on the surface of the nanoparticles.

In a metal nanoparticle, the electrons are confined to a small volume, and their energy levels are quantized, leading to discrete energy levels. When light is incident on the nanoparticle, the electrons absorb photons and get excited to higher energy levels. This excitation leads to a collective oscillation of the free electrons on the surface of the nanoparticle, known as a surface plasmon.

The surface plasmon resonance of a metal nanoparticle occurs when the frequency of the incident light matches the resonant frequency of the collective oscillation of the electrons. This leads to a sharp peak in the absorption or scattering spectrum of the nanoparticle at a particular wavelength, which is characteristic of the size, shape, and composition of the nanoparticle.

Metal nanoparticles are commonly used in biosensing applications because of their unique optical properties. The localized surface plasmon resonance (LSPR) of metal nanoparticles can be tuned by changing their size, shape, and composition, allowing for sensitive detection of biomolecules such as proteins, DNA, and viruses. LSPR-based biosensors are highly sensitive and specific, making them useful for a wide range of applications in medical diagnostics, environmental monitoring, and food safety. SPR is commonly used as a label-free analytical technique to study the interaction between biomolecules such as proteins, DNA, and antibodies. It is particularly useful for determining the binding affinity and kinetics of biomolecular interactions.

In an SPR experiment, one of the interacting partners is immobilized on a metal surface, typically gold, while the other partner is injected in solution over the surface. As the molecules bind and dissociate, the refractive index at the metal surface changes, resulting in a shift in the resonance angle. By measuring the shift in the resonance angle, the binding kinetics and affinity can be calculated.

SPR is widely used in drug discovery, biomolecular interaction studies, and medical diagnostics. It is a powerful tool for understanding the molecular mechanisms of biological processes and for developing new drugs and diagnostic tests.