Size EffectsSurface-to-Volume Ratio

Versus Shape

One of the most fundamental differences between nanomaterials and larger-scale materials is that nanoscale materials have an extraordinary ratio of surface area to volume.

Though the properties of traditional large-scale materials are often determined entirely by the properties of their bulk, due to the relatively small contribution of a small surface area,

For nanomaterials this surface-to-volume ratio is inverted, as we will see shortly.

As a result, the larger surface area of nanomaterials (compared to their volume) plays a larger role in dictating these materials’ important properties.

This inverted ratio and its effects on nanomaterials properties is a key feature of nanoscience and nanotechnology.

For these reasons, a nanomaterial’s shape is of great interest because various shapes will produce distinct surface-to-volume ratios and therefore different properties.

The expressions that follow can be used to calculate the surface-to-volume ratios in nanomaterialswith different shapes and to illustrate the effects of their diversity.

We start with a sphere of radius r. This is typically the shape of nanoparticles used in many applications. In this case, the surface area is given by

A = 4 π r2 and whereas the volume of a sphere is given by V= = (4 π r3 )/3

Thus, the surface-to-volume ratio of a sphere is given by A/ V =3/r

Next, consider a cylinder of radius r and height H—for example, a nanowire.

In this case, the volume V = πr2H, whereas the surface area A = 2πrH.

Thus, the surface-to-volume ratio is given by 2/r

The trend is similar to the sphere case, although the severe increase in surface-to-volume ratio occurs at larger critical dimensions.

Let’s now turn to a cube of side L. In this case, the volume and surface area of the cube are given by V = L3 and A = 6L2, respectively.

Therefore the surface-to volume ratio of a cube is given by 6/L

After stressing the importance of the increase in surface area in nanomaterials relative to traditional larger-scale materials, let us ask a question to ourselves:

how much of an increase in surface area will result?

For example: From a spherical particle of 10 μm to be reduced to a group of particles with 10 nanometers, assuming that the volume remains constant.

The volume of a sphere with 10 microns. gives V (10 μm) = 5.23 × 1011 nm3. We then calculate the volume of a sphere with 10 nm. , we get V (10 nm) = 523 nm3. Because the mass of the 10 micron particle is converted to a group of nanosized particles, the total volume remains the same.

Therefore, to calculate the number of nanosized particles generated by the 10 micron particle, we simply need to divide V (10 μm) by V (10 nm) in the form

Hence, we can conclude that one single particle with 10 microns can generate 1 billion nanosized particles with a diameter of 10 nm, whereas the total volume remains the same.

We are thus left with the task of finding the increase in surface area in going from one particle to 1 billion particles.

This can be done by first calculating the surface area of the 10 micron particle. Following gives A (10 μm) = 3.14 × 108 nm2. On the other hand, for the case of the 10 nm particle A (10 nm) = 314 nm2.

However, since we have 1 billion 10 nm particles, the surface area of all these particles amounts to 3.14 × 1011 nm2. This means an increase in surface area by a factor of 1000.

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SAMREEN

While going through some of your last lectures ,i got a doubt,may be its silly but i cud'nt find the resons.

As u say in nano-composite material,matrix can be of anything(micro or macro) and reinforcing material should be of nano scale and u also said in 2 D materials two dimension (Lx n Ly) are at any dimension just one in nano scale,

so my question is, how only the property of nano scale material dominates??other two phases in micro or macro scale but their property is not dominating, just because of nanomaterial surface to volume ratio they dominates over the property of other two micro-scale phases?

Face-centered cubic (FCC) structure. All 14 atoms are on the surface.

The smallest FCC nanoparticle that can exist: a cubo-octahedron. A bulk atom is at the center. Others are surface atoms

Surface Curvature

Surface curvature in two dimensions

For each surface atom there is an excess internal energy of ε/2 due to the absence of bonds

All solid materials have finite sizes.

As a result, the atomic arrangement at the surface is different from that within the bulk.

As shown in Figure , the surface atoms are not bonded in the direction normal to the surface plane.

Hence if the energy of each bond is ε/2 (the energy is divided by 2 because each bond is shared by two

atoms),

Then for each surface atom not bonded there is an excess internal energy of ε/2 over that of the atoms in the bulk.

In addition, surface atoms will have more freedom to move and thus higher entropy.

. These two conditions are the origin of the surface free energy of materials.

For a pure material, the surface free energy γ can be expressed as,

= ES − TSS where ES is the internal energy, T is the temperature, and SS is thesurface thermal entropy. Equally important is the fact that the geometry of the surface, specifically its local curvature, will causea change in the system’s pressure.

These effects are normally called capillarity effects due to the fact that the initial studies were done infine glass tubes called capillaries.

To introduce the concept of surface curvature, consider the 2-D curve shown in Figure .

A circle of radius r just touches the curve at point C. The radius r is called the radius of curvature at C, whereas the reciprocal of the radius k = 1/ r is called the local curvature of the curve at C.

As shown in Figure , the local curvature may vary along the curve.

By convention, the local curvature is defined as positive if the surface is convex and negative if concave .

As the total energy (Gibbs free energy) of a system is affected by changes in pressure, variations in surface curvature will result in changes in the Gibbs free energy

Surface curvature in two dimensions

Concave and convex surface curvatures.

As the total energy (Gibbs free energy) of a system is affected by changes in pressure, variations in surface curvature will result in changes in the Gibbs free energy given by

the magnitude of the pressure difference increases as the particle size decreases, that is, as the localcurvature increases.

Therefore, at the nanoscale, this effect is very significant.

In addition, because the sign for the local curvature depends on whether the surface is convex or concave, the pressure inside the particle can be higher or lower than outside.

For example, if a nanoparticle is under atmospheric pressure, it will be subject to an extra pressure ΔP due to the positive curvature of the nanoparticle’s surface

Another important property that is significantly altered by the curvature effect is the equilibrium number of vacancies/defects?

SAMREEN: PART 2

A pure material or a compound with no defects in it. in “some way” ideal situations.

However, in fact, 100% pure materials and with no defects do not exist, although some materials can have small amounts of impurities and/or defects.

The origin of these defects is very diverse, ranging from atomic packing problems during processing to the formation of interfaces with poor atomic registry or the generation of defects during deformation.

On the basis of our discussion so far, you are probably thinking that the presence of defects is deleterious to materials.

In some cases that’s true, but in many cases defects are extremely beneficial.Some examples include:■ The presence of small amounts of carbon in iron (known as steel) makes possible the achievement of high strengths.■ The addition of 0.01% of arsenic can increase the conductivity of Si by 10,000 times.

■ Some defects called dislocations are responsible for plastic deformation in materials.

Q one more question, what is the relation between grain boundaries and defects? if defect is found in a material it will decreases some of its properties then how come it provides better stability to the material??

In general, we can classify the defects as point defects, linear defects, planar defects (interfacial defects), or volume defects (bulk defects), for which the scale of each class is shown in Figure

Let’s examine each class of defect in more detail.

The simplest point defect is called a vacancy, which is a lattice pointfrom which an atom is missing (see Figure).

Vacancies are introduced into a material during solidification or heat treatments or by radiation of atomic particles.

In fact, in a nuclear power plant, where radiation is continuously being produced, the monitoring of the formation of vacancies is crucial for the safety of the plant.

The presence of vacancies in a crystal is a necessity because the presenceof vacancies will increase the entropy (randomness) of the crystal.

In addition, the presence of a vacancy changes the stress field of the crystal.

the vacancy induces a tensile stress field around the neighboring atoms.

In addition, the equilibrium number of vacancies increases exponentially with temperature.

Typically, at room temperature, there is one vacancy per 1 million atoms, whereas at the melting temperature, there are 1000 vacancies per million atoms

A self-interstitial point defect can also form in materials. This occurs when an atom from the lattice goes into an interstitial position, a small space that is not usually occupied by any atom (see Figure).

The self-interstitial atom creates large distortions in the lattice because the initial available space is smaller than the atom dimensions.

In ionic structures, such as ceramic materials, because of neutrality,there are two types of point defects:

(1) the Schottky defect, which is a pair of defects formed by a vacancy of one cation and a vacancy of one anion (see Figure ), and

(2) the Frenkel defect, which is formed by a vacancy of one cation and a self-interstitial cation (Figure ) or a vacancy of one anion and a self-interstitial anion.

A Schottky defect and a Frenkel defect.

So far we have only discussed defects in pure solids or compounds.

However, as mentioned before, impurities must exist. Even if the metal is almost (99.9999%) pure, there are still 1023 impurities in 1 m3.

Therefore the following question arises:

Where do the impurities go?

That all depends on the impurity and the host material.

The final result will be a consequence of (1)the kind of impurity,

(2) the impurity concentration, and

(3) the temperature and pressure.

However, in general, impurities can go to a substitutional site, that is, a site occupied by the host atom. In this case they will be called substitutional atoms. Or impurities can go to an interstitial site and will be called interstitial atoms (different from self-interstitials).

Whether the impurities go to a substitutional or interstitial site will depend on (1) atomic size, (2) crystal structure, (3) electronegativity, and (4) valence electrons.

With respect to atomic size, interstitial atoms are small compared with host atoms.

Example 1: In covalent bonded materials, substitutional atoms can create a unique imperfection in the electronic structure if the impurity atom is from a group in the periodic table other than that of the host atoms.

An example is the addition of As or P (Group V) in Si (Group IV; see Figure ).

Only four of five valence electrons of these impurities can participate in the bonding, because thereare only four possible bonds with neighboring atoms.

The extra nonbonding electron is loosely bound to the region around the impurity atom in a weak electrostatic interaction.

Thus the binding energy of this electron is relatively small, in which case it becomes a free or conducting electron

Addition of phosphorous, having five valence electrons, to silicon leads to an increase in electrical conductivity due to an extra bonding electron.

Example 2: In polymers, the addition of impurities can also have significant consequences.

For example, natural rubber becomes cross-linked when small amounts of sulfur (5%) are added.

As a result, the mechanical properties change dramatically.

Natural rubber has a tensile strength of 300 psi, whereas vulcanized rubber (sulfur addition) has a tensile strength of 3000 psi.

Now let’s discuss another class of defects called linear defects.

These defects, also called dislocations, are the main mechanism in operation when a material is deformed plastically.

Currently, several techniques are available for the direct observation of dislocations.

The transmission electron microscope (TEM) is probably the most utilized in this respect

Let’s look at the simplest case, the edge dislocation.

Imagine the following sequence of events: (1) take a perfect crystal, (2) make a cut in the crystal, (3) open the cut, and (4) insert an extra plane of atoms (see Figure).

The end result is an edge dislocation. These dislocations are typically generated during processing or in service, if subjected to enough stress.

The presence and motion of dislocations dictate whether materials are ductile or brittle. Because metals can easily generate and move dislocations, they are ductile.

On the other hand, ceramic materials have a high difficulty in Nucleating and moving dislocations due to the covalent/ionic character of thebonds, and they are therefore brittle.

One of the important parameters related to dislocations is the knowledge of the amount of dislocation length per unit volume. This is called the dislocationdensity and is given by

Sequence of events leading to the formation of an edge dislocation

where LD is the total length of dislocations and V is the volume.

Another class of defects is that of interfacial defects.

Among these, we’ll first discuss the free surfaces.

All solid materials have finite sizes.

As a result, the atomic arrangement at the surface is different from within the bulk.

Typically, surface atoms form the same crystal structure as in the bulk, but the unit cells have slightly larger lattice parameters.

In addition, surface atoms have more freedom to move and thus have higher entropy.

We can now understand that different crystal surfaces should have different energies, depending onthe number of broken bonds.

The second type of interfacial defect is the grain boundary.

This boundary separates regions of different crystallographic orientation.

The simplest form of a grain boundary is called a tilt boundarybecause the misorientation is in the form of a simple tilt about anAxis.

We know that grain boundaries have also an interfacial energy dueto the disruption of atomic periodicity.

However, will they have higher or lower energies than free surfaces?

The answer is lower energies.

This is because grain boundaries exhibit some distortion in the type of bonds they form, but there are no absent bonds.

Most of the materials utilized in our daily lives are polycrystalline materials.

This means that the materials are composed of many crystalswith different orientations, separated by grain boundaries (seeFigure).

It turns out that this network of grains significantly

affects several of the material properties.

In 1959, Physics Nobel Laureate Richard Feynman gave a talk at Caltech on the occasion of the American Physical Society meeting. The talk was entitled, “There’s Plenty of Room at the Bottom.”

In this lecture, Feynman said:

What I want to talk about is the problem of manipulating and controlling things on a small scale … What are the limitations as to how small a thing has to be before you can no longer mold it? How many times when you are working on something frustratingly tiny like your wife’s wrist watch have you said to yourself, “If I could only train an ant to do this!” What I would like to suggest is the possibility of training an ant to train a mite to do this … A friend of mine (Albert R. Hibbs) suggests a very interesting possibility for relatively small machines. He says that, although it is a very wild idea, it would be interesting in surgery if you could swallow the surgeon. You put the mechanical surgeon inside the blood vessel and it goes into the heart and “looks” around. It finds out which valve is the faulty one and takes a little knife and slices it out.

Sequence of images showing the various levels of scale. (Adapted from Interagency Working Group on Nanoscience, Engineering and Technology, National Science and Technology Council Committee on Technology, “Nanotechnology: Shaping the World Atom by Atom.” Sept.1999.)

A green leaf is composed of chloroplasts inside which photosynthesis occurs.

Photosynthesis is in fact an excellent example of the role of nanostructures in theworld’s daily life.

Leaves contain millions of chloroplasts, which make a green plant green .

Inside each chloroplast, hundreds of thylakoids contain light-sensitive pigments.

These pigments are molecules with nanoscale dimensions that capture light (photons) and direct them to the photo reaction centers.

At every reaction center, there are light-sensitive pigments that execute the actual photon absorption. When this happens, electrons become excited, which triggers a chain reaction in which water and carbon dioxide are turned into oxygen and sugar

What is so special about nanotechnology?

First, it is an incredibly broad, interdisciplinary field. It requires expertise in physics, chemistry,materials science, biology, mechanical and electrical engineering, medicine, and their collective knowledge.

Second, it is the boundary between atoms and molecules and the macro world, where ultimately the properties are dictated by the fundamental behavior of atoms.

Third, it is one of the final great challenges for humans, in which the control of materials at the atomic level is possible. So, are nanoscience and nanotechnology real, are they still fiction?

in the episode “Evolution” of Star Trek, a boy releases “nanites,” which are robots at the nanoscale fabricated to work in living cells. These machines end up evolving into intelligent beings that gain control the starship Enterprise.

In the book Queen of Angels, humans with psychological problems can be treated by an injectionof nanodevices.

These fictional ideas could become reality if in the future we become able to control matter at the atomic or molecular level. Yet, some skeptical questions may arise, such as:

■ Are molecular entities stable?■ Are quantum effects an obstacle to atomic manipulation?■ Is Brownian motion a significant effect in nanocomponents?■ Are friction and wear relevant for nanocomponents?

The answer to the first question is yes. The human population is the best living example

Each human being contains approximately 1027 atoms that are reasonably stable, and due to cellular multiplication, the human body is able to build itself using molecular mechanisms.

With respect to the quantum effects, the uncertain atomic position (Δx) can be estimated from classical vibrational frequency calculations.

Earth’s clock of life. (Adapted from Peter D. Wardand Donald Brownlee, The Life and Death ofPlanet Earth: How the New Science of AstrobiologyCharts the Ultimate Fate of Our World,

Times Book Publisher, 2003.)

Window from Chartres Cathedral. The intensecolors of many Medieval stained-glass windowsresulted from nanosized metal oxide particlesadded to the glass during the fusion process

The Lycurgus cup looks green when light shines on it but red when a light shinesinside it. The cup contains gold nanoparticles.

(Courtesy of the British Museum.)

Detail of Feathered Serpent from a wall paintingat Cacaxtla, Mexico. (Courtesy of Barbara Fash,

Peabody Museum, Harvard University.)

The Kurakuen house in Nishinomya City, Japan,designed by Akira Sakamoto Architect andAssociates, uses a photocatalytic self-cleaningpaint—one of the many architectural productsbased on nanomaterials. (Courtesy of JapanArchitect.

The hierarchy of electrical behavior. The interesting ones are in the darker colored boxes, with examples of materials and applications

A bar chart of modulus. The chart reveals the difference in stiffness between the families.

A bubble chart of modulus and density. Families occupy discrete areas of the chart.