Nanoparticles and Its Properties

Introduction:

The prefix 'nano' means a billionth ($10^{-9}$). The field of nanotechnology is the study of various structures of matter having dimensions of the order of a billionth of a meter. These particles are called nanoparticles. Nanotechnology is based on the fact that particles that are smaller than about $100 nm$ give rise to new properties of nanostructures built from them.

Particles that are smaller than the characteristic length for a particular phenomenon show different physical and chemical properties than particles of larger sizes. For example, mechanical properties, optical properties, conductivity, melting point, and reactivity have all been observed to change when particles become smaller than the characteristic length.

Gold and silver nanoparticles were used in window glass panes to obtain a variety of beautiful colors. Nanotechnology has a wide range of applications like producing lighter but stronger materials, constructing faster switches for computers, improving drug delivery to specific organs of the body, etc.

The radii of atoms and most of the molecules are less than a nanometer. Nanoparticles are generally considered to have a radius in the range of $1 nm$ to $100 nm$ which can have $25$ to $10^{6}$ atoms. A cluster of $1 nm$ radius has approximately $25$ atoms. This definition of nanoparticles based on size does not distinguish between molecules and nanoparticles as many organic molecules contain more than $25$ atoms.

Nanoparticles can be more appropriately defined as an aggregate of atoms, with a radius between 1 nm and 100 nm, with dimensions less than the characteristic length of some physical phenomena.

When particle size is less than the characteristic length of some physical phenomena, the particles show different properties. The nanoparticles show unique properties that change with their size. Classical mechanics is able to explain the properties of bulk materials but is unable to explain the properties of nanoparticles. Quantum mechanical principles have to be used to explain the properties of the nanoparticles.

Properties of Nanoparticles

As discussed earlier, the properties of nanoparticles are different from the bulk material. The properties of nanoparticles also vary with size and shape. Hence different properties can be obtained by changing the size and shape of the nanoparticles. Some of the properties of nanoparticles are as follows :

1) Optical properties: The color of nanoparticles is different from the bulk material. When a bulk material is reduced in size to a few hundred atoms, the energy band structure of the bulk material changes to a set of discrete energy levels. Atomic clusters of different sizes will have different energy level separations. As clusters of different sizes have different energy level separations, the color of the clusters (which are due to transitions between the energy levels) will depend on their size. Hence the size of the cluster can be altered to change the colour of a material. For example, gold in bulk form appears yellow but gold nanoparticles appear bright red in color. The medieval glass makers produced tinted glass with a beautiful variety of colors by dissolving metal particles like gold, silver, cobalt, iron, etc. Due to these metal nanoparticles, the glasses appear colored.

In semiconductor nanoparticles (which are used in quantum dots) there is a significant shift in the optical absorption spectra towards blue as the particle size is reduced.

2) Electrical properties: The resistivity in bulk matter is mainly due to the scattering of electrons by ions and crystal defects. In nanostructures, the resistivity mainly depends on scattering from the boundaries of nanoparticles when particle size becomes less than the mean free path between collisions. Thus smaller particle size increases the resistivity.

Various types of defects in the lattice also increase the resistivity by limiting the mean free path. However many nanostructures are too small to have internal defects.

Another effect of reduced size is the confinement of conduction electrons. In bulk conductors, the electrons move freely throughout the entire conductor. The situation changes when one or more dimensions of the conductor are made very small.

Consider a flat conducting plate with a large length and width but a small thickness in the range of a few nanometers. In this configuration, called a quantum well, the electron will be confined along one dimension but will move freely along the remaining two dimensions.

If a conducting wire has a long length but a very small diameter, the electrons can move freely along the length but will be confined in two mutually perpendicular transverse directions. This configuration is known as a quantum wire.

If all three dimensions of the conductor are in nanometer range, the configuration is called a quantum dot and the electron is confined in all three dimensions. Confinement of electrons to small dimensions leads to quantization of energy.
Coulomb Staircase
The level of doping in semiconductors gives rise to another important phenomenon. For typical doping levels of 1 donor impurity atom in $10^{8}$ atoms of semiconductor atoms, a quantum dot of $10^{7}$ semiconductor atoms would have an average of $10^{-1}$ electrons. In other words, on an average, one quantum dot in 10 will have a free electron. These result in the phenomena of single-electron tunneling and coulomb blockade. The conduction is due to the tunneling of electrons through the quantum dot. The electrons are blocked from tunneling except at discrete voltage change positions. This phenomenon is called coulomb blockade. The I-V characteristic shown in the above Figure is called the coulomb staircase.

3) Magnetic properties: Magnetic properties are basically due to the orbital and spin motions of electrons around the nucleus. Every electron in an atom has spin and orbital magnetic moment which, when added, gives the total magnetic moment of the electron. The vector sum of all the moments of electrons gives the total moment of the atom. In most of the atoms, the net magnetic moment is zero.

However, atoms like iron, cobalt, and manganese, have a net magnetic moment. Crystals of these become atoms ferromagnetic when magnetic moments of all atoms are aligned in the same direction. The magnetic moment of magnetic nanoparticles is observed to be less than the value for perfect alignment of all moments. The net magnetic moment is observed to decrease with increasing temperature. This is due to thermal vibration of atoms in the cluster which disturbs the alignment of magnetic moments.
B-H Curve Ferromagnetic Material
In bulk ferromagnetic materials, the magnetic moment is less than the moment the material would have if every atomic moment were aligned in the same direction. This is due to the presence of 'domains' which are regions in which all atomic moments are in one direction but moments of different domains are in different directions. When bulk ferromagnetic materials are subjected to alternating magnetic fields, they show hysteresis for which the B-H curve is shown in the above Figure (a). In nanosized ferromagnetic particles, essentially consisting of a single domain, there is no hysteresis and the $B-H$ curve is as shown in the above Figure (b). These particles are called the superparamagnetic.

The saturation magnetization is observed to increase significantly on decreasing the particle size. Another interesting property of nanoparticles is that clusters made of up nonmagnetic atoms like rhenium show magnetic moment which increases with the decrease in particle size.

4) Structural properties: The structure of small nanoparticles can be entirely different from that of the bulk material. The crystal structure of large nanoparticles is observed to be the same as the bulk material but with different lattice parameters. As a result of the changed structure, the electronic structure changes which in turn leads to changes in optical properties and reactivity. (TWD)

5) Mechanical properties: Mechanical properties like hardness, elasticity, and ductility depend upon the bonds between atoms. Imperfections in the crystal structure and impurities result in changes in these properties. As the nanoparticles are highly pure and free from imperfections, they show different mechanical properties than the bulk material. It has been observed that Young's modulus decreases in metallic nanocrystals with a decrease in particle size. The yield stress has been observed to increase with the decrease in grain size in bulk materials with nanosized grains. Hence stronger materials can be produced by making materials with nanosized grains. The carbon nanotubes are estimated to be about 20 times stronger than steel.

Difference Between Prism Spectra and Grating Spectra

Prism Spectra

1.) Prism spectra are obtained by the phenomena of dispersion of light.

2.) Prism spectra have only one order.

3.) A prism spectrum is of bright intensity.

4.) In prism spectra, spectral colors overlap each other.

5.) Red color is dispersed least whereas violet color disperses the maximum.

6.) Prism spectrum depends upon the material of prism.

7.) The prism spectral lines are curved.

. Grating Spectra

1.) Grating spectra are obtained by the phenomena of diffraction of light.

2.) Grating spectra has more than one order.

3.) Grating spectra is of less intensity.

4.) In grating spectra, there is no overlapping of color.

5.) Red color diffracts the maximum whereas violet color diffracts the least.

6.) Grating spectra are independent of the material of grating.

7.) The grating spectral lines are almost straight.

Difference between interference and diffraction

Interference

1.) It is due to the superposition of two or more than two wavefronts coming from coherent sources.

2.) The intensity of all bright fringes are same

3.) Interference fringes either of the same size or decrease after moving away from the center.

4.) Dark fringes are usually perfectly dark.

5.) A minimum coherent source is needed.

Diffraction:

1.) It occurs due to secondary wavelets, originating from infinite different points of the same wavefronts.

2.) Central maxima of bright fringe is followed by either side maxima of decreasing intensity.

3.) Interference fringes are never of the same shape and size.

4.) Dark fringes are not perfectly dark.

5.) It is possible by either one or more than one source which need not be coherent.

Superconductors and its properties

Superconductivity

The property of a substance in which the electrical resistance of the substance is zero at very low temperatures. This property of substance is called superconductivity.

For certain substances, like mercury, the resistivity suddenly drops to zero at very low temperatures typically near the boiling point of liquid helium. Some metals, doped semiconductors, alloys and ceramics (i.e. these are insulators at room temperature and superconduct at higher temperatures than the metals) show superconductivity.

Temperature Dependence of Resistivity

In superconducting substances, the resistivity suddenly drops to zero at a particular temperature known as critical temperature ($T_{c}$) or transition temperature and remains zero below that as shown in Figure below.
Temperature Dependence  of Resistivity in Superconductor
The critical temperature for mercury is $4.2 K$. Below this critical temperature, mercury is superconducting whereas above this temperature it behaves like a normal conductor. Different superconducting materials have different critical temperatures but the nature of the variation in resistivity with temperature remains more or less similar.

Properties of Superconductors

1.) Zero electrical resistance:

The electrical resistivity of superconductors is zero at very low temperatures. The experimental testing of zero resistance was tried by connecting the substance at room temperature to a battery. A voltmeter was connected across the specimen to measure the electric potential difference across the specimen as shown in Figure below.
Zero Electrical Resistance of Superconductor Experiment
As the temperature of the substance gets lowered. It was observed that below a particular temperature (i.e. critical temperature), the electric potential difference across the substance suddenly dropped to zero.

2) Meissner effect:

When a substance is placed in a weak magnetic field and cooled below the critical temperature then this substance behaves like perfect diamagnets with zero magnetic induction. This phenomenon is called the Meissner effect.
Meissner Effect
The magnetic induction inside the substance in the normal state is given by, Superconductors

$B = \mu_{\circ} (H +M)$

where $H$ is the externally applied magnetic field and $M$ is the magnetization inside the substance.

When the temperature $T$ of the specimen is lowered below its critical temperature

$B= 0$

$M_{\circ}(H + M) = 0$

$H = - M$

The susceptibility $\chi$ is given by,

$\chi=\frac{M}{H}$

For diamagnetic substance $\chi=-1$

As the relative permeability

$\mu_{r}=1+\chi$

$\therefore \mu_{r}=0$

This indicates perfect diamagnetism.

Meissner effect cannot be explained by assuming that the superconductor is a perfect conductor with zero electrical conductivity. The electric field is given by,

$E=\frac{V}{l}$

$E=\frac{iR}{l}$

$E=\frac{iR}{l} \frac{A}{A}$

$E=\frac{RA}{l} \frac{i}{A}$

$E=\rho J$

Where

$\rho$ = Resistivity
$J$= Current density

If $\rho$ becomes zero for a finite current density $J$, then $E =0$.

From Maxwell's equations,

$\nabla \times \overrightarrow{E} = \frac{d \overrightarrow{B}}{dt}$

As $E=0$, $\frac{d \overrightarrow{B}}{dt} =0$

$\therefore \overrightarrow{B} = Constant$

$\therefore$ In a conductor the flux cannot change on cooling below the critical temperature. This contradicts the Meissner effects according to which the flux must reduce to zero and hence superconductor is not just a perfect conductor.

Due to the Meissner effect, superconductors strongly repel external magnets which leads to magnetic levitation.

3) Effect of magnetic field on superconductors :

Superconductivity is destroyed by sufficiently strong magnetic fields. The minimum value of the applied magnetic field required to destroy superconductivity is called the critical field $H_{c}$. and is a function of temperature. Above the critical temperature $T_{c}$, $H_{c} = 0$. Below the critical temperature, the variation of $H_{c}$, with temperature $T$ is as shown in Figure below and be represented by the equation
Effect of Magnetic Field on superconductor
$H_{c}=H_{\circ} \left[ 1- \left(\frac{T}{T_{c}}\right) \right]$

where $H_{\circ}$ is the critical field at absolute zero.

4) Persistent currents :

When a ring is placed in the magnetic field and the field is switched off, a current is induced in the ring. This induced current is called the persistent current.
Persistent Current
The magnitude of current remains constant even though there is no source of e.m.f. as the resistance of the superconducting ring is zero. These currents flowing in the ring produce magnetic fields that do not require any power supply to maintain a constant field.

5) Isotope effect :

According to observations, the critical temperature of superconductors varies with isotopic mass. The critical temperature is smaller for larger isotopic mass. This phenomenon is called the isotope effect.

The relation between critical temperature $T_{c}$ and isotopic mass $M$ is given by,

$T_{c}M^{a} = Constant$

For most of the materials $a =\frac{1}{2}$

$\therefore T_{c}M^{\frac{1}{2}} = Constant$

$\therefore T_{c} \propto M^{-\frac{1}{2}} $

As lattice vibrations are reduced for larger isotopic masses, the isotope effect indicates that superconductivity is due to the interaction between electrons and lattice vibrations.

6) Critical Current:

All the current-carrying conductor produces a magnetic field around it. Similarly, When current flows through a superconducting wire, a magnetic field is produced around it. If the current in the superconducting wire is increased, the magnetic field intensity just outside it will increase and reach the critical field $H_{c}$. If the current is increased beyond this value, the wire will be subjected to a magnetic field exceeding the critical field due to which the superconducting state will be destroyed and then it will revert to its normal state. The maximum current that a superconductor can carry without reverting back to its normal state is known as critical current.

The magnetic induction due to a wire of radius $r$ just outside it is

$B=\frac{\mu_{\circ}i}{2 \pi r}$

$\mu_{\circ} H=\frac{\mu_{\circ}i}{2 \pi r}$

$H=\frac{i}{2 \pi r}$

If the critical current in $_{c}$, and critical field is $H_{c}$, ,

$H_{c}=\frac{i_{c}}{2 \pi r}$

$i_{c}=2 \pi r H_{c}$

Types of Superconductors

There are two types of superconductors based on the difference in magnetization exhibited by them. These are known as Type-I (or soft) and Type-II (or hard) superconductors.

1) Type-I Superconductors (Soft superconductors):

The magnetization curve for a Type-I -M superconductor is shown in Figure below. Type-I superconductors show the complete Meissner effect when the applied magnetic field H is less than the critical field $H_{c}$.
Type - I Superconductor
The magnetization in the superconductor is proportional to the applied field and the superconductors behave like perfect diamagnet.

For $H > H_{ç}$, the magnetization is negligible and the superconductor becomes a normal conductor. Pure elements show such magnetization curves. The values of $H_{c}$, are very low.

2) Type-II Superconductors (Hard superconductors)

The magnetization curve for a type-II superconductor is shown in Figure below.
Type - II Superconductor
There are two critical field $H_{c1}$ and $H_{c2}$ in Type-II superconductors that characterize it. Upto the lower critical field $H_{c1}$, the superconductor is perfectly diamagnetic and flux is completely ejected out from the superconductor. The magnetization in the superconductor is proportional to the applied field. Between $H_{c1}$ and $H_{c2}$, the Meissner effect is incomplete but electrically it is a superconductor but not magnetically. This state is called the mixed state or the vortex state.

The values of $H_{c}$ may be $100$ times or higher than the critical field $H_{c}$, for type-I superconductors.

Above the higher critical field $H_{c2}$ the superconductor becomes a normal conductor.

Type-II superconductors are usually alloys or transition metals with high values of electrical resistivity in the normal state.

High-Temperature Superconductors

Kamerlingh Onnes discovered superconductivity in mercury in 1911 with a critical temperature of $4.2 K$. The research was then focussed on materials with larger critical temperatures so that the phenomenon could become commercially viable.

But, till about 1986, the highest critical temperatures were observed to be nearly $20 K$. In 1986, an oxide of lanthanum, barium, and copper ($La_{1.85} Ba_{0.15} CuO_{4}$) was observed to have a critical temperature of $36 K$. In 1987, an oxide of yttrium, barium and copper ($YBa_{2}Cu_{3},0_{7}$) was found to have a critical temperature of $90 K$ and then an oxide of thallium, barium, calcium and copper($Tl_{2}Ba_{2}Ca_{2}Cu_{3}O_{10}$) was found to have a critical temperature of $120 K$.

The presence of parallel sheets of $CuO_{2}$ is the main feature of high-temperature superconductors.. Efforts are going on to find superconductors with critical temperatures near room temperature.

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