7 Quantum Confinement-Size effects and properties of nanostructures
S.S. islam
Nanoscale
The macroscopic properties of any material (e.g., melting and boiling point, etc.) can be measured by examining the sample in conventionally convenient quantities under standard lab conditions. These quantities can vary for different materials as well as the purpose of investigations. One of the most often defined quantity is ‘mole’ such that one mole of any substance consists 6.022 x 1023 molecules. Thus, if any property of one mole of the substance is measure, this value usually represents the average value of 6.022 x 1023 molecules of that substance. It is often deduced that this value remains same regardless of the size of the group of molecules under investigation. However, this does not hold for all materials. That is, as the size of the material is decreased to reach nanoscale, the same material may demonstrate radically different properties. In other words, materials start demonstrating size dependent properties after reaching the nano-dimensions. This happens because matter at nanoscale does not follow Newtonian principles and quantum mechanics needs to be applied to describe the behavior of materials. This is explained for gold in Module-1 of this unit.
What kind of small is this?
Nanoscaled materials are considered to be consisting of clusters of atoms/molecules, not the single atoms/ molecules. For instance, 8 hydrogen atoms or 3.5 gold atoms placed adjacent forming a row become one nanometre long. In this regard, the size of nanomaterials is intermediate to a single atom or molecule, and their bulk forms. At these dimensions, matter exhibits novel properties. Therefore, nanomaterials offer the following opportunities:
- They can be used to improve existing materials as well as to produce new materials with exceptional properties.
- As nanomaterials have the size resembling that of the largest molecules present in nature (such as proteins, DNA, etc.), they can be integrated into a device to interact with these molecules.
Physics at Nanoscale
Owing to their nanoscaled dimensions, nano materials are dimensionally more close to individual atoms and molecules than to the bulk materials, and therefore, their behavior is described using quantum mechanics. Quantum mechanics is the scientific model employed to describe the motion and energy of individual atoms and electrons. The significant quantum effects and the properties relevant at nanoscale are described below:
1. At nanoscale, electromagnetic forces dominate whereas the gravitational forces are negligible
Since the mass of nanoscaled objects becomes very small, gravitational force, which scales linearly with the mass of the particles, becomes negligible.
Since electromagnetic force is independent of the mass of the particles, and is determined by the charge and distance of the particles, it is strong even for the nanosized particles. As an example, between two protons, electromagnetic force is 1036 times stronger than the gravitational force between them.
2. Wave-particle duality
For extremely small objects having very low mass (e.g. electron), wave nature becomes pronounced. Thus an electron exhibits wave-like properties and its position can be described by the wave probability function.
3. Tunneling
Tunneling is an extremely important consequence in nanoscaled materials. As per classical physics, an object can pass a potential barrier if its energy is greater than that of the barrier. Thus, if the object has energy lower than the barrier potential, the object cannot cross the barrier. In this case, there is zero probability of locating the object on other side of the potential barrier (see Figure 1). As per quantum physics, the object can tunnel through the barrier. Also, the thickness of the barrier is crucial in determining the tunneling probability of the particle. That is, the thickness of the barrier should be of the order of particle’s wavelength. Thus, even if the object energy is lower than the potential of the barrier, there is a finite probability of locating the particle at the other side of the barrier.
Figure 1 Schematic illustration of tunneling across a potential barrier.
Tunneling is an important quantum effect and forms the basic principle of scanning tunneling microscope (STM) used to image the nanostructured materials.
4. Quantum Confinement
In nanostructured materials, including metals, electrons are not free to move within the material, but are confined in space.
5. Quantization of energy
The electrons in the nanomaterials do not have continuous energy bands; rather they exist only at some discrete energy states. This is effect called the quantization of energy, and is most pronounced in quantum dots.
6. Random molecular motion assumes importance
Above absolute zero, the molecules move owing to their kinetic energy. This motion is described as the random molecular motion and occurs in materials at a temperature above 0K. In bulk materials, this movement can be neglected in comparison to the size of the object; therefore do not influence object’s movement. However, in nanoscaled objects, these motions are comparable to the particles’ dimensions and thus affect their behavior.
7. Larger surface area to volume ratio
Nanomaterials possess very large surface areas. The smaller the object is, the larger the surface area to volume ratio. Large surface-to-volume ratio is an extremely important characteristic of a nanoparticle. This property is described in detail in the subsequent sections.
8. Energy of confined electrons
In nano-crystals, the energy levels of electrons do not remain continuous as is the case with bulk materials. Rather, owing to the confined electron wave functions, they become discrete resulting in finite DoS. These effects appear when the dimensions of the potential well approach de Broglie wavelength of electrons resulting in change in energy levels. The effect is described as Quantum confinement and consequently, the nano-crystals are often called quantum dots or QDs. These effects influence the electrical, optical as well as mechanical behaviour of material. Depending on the QD size, confined electrons have higher energy than the electrons in bulk materials. This shift in energy (Figure 2), is given by:
here, represents the principal quantum number; ℎ is Planck’s constant; is effective mass and is the radius of the QD.
Figure 2 Variation of energy with size of the quantum dot (QD).
Chemistry at Nanoscale
Since a nanoparticle is essentially a cluster of atoms/molecules, all forms of bindings relevant in chemistry, are relevant at nanoscale as well. These are described below:
1. Intramolecular bonding
These are also called chemical interactions and cause a change in the chemical structure of the molecule. Examples are ionic, metallic, and covalent bonding.
2. Inter-molecular bonding
These are the physical interactions causing no change in chemical structure of molecule. Examples are ion-ion bonds, ion-dipole bonds, van der Waals bonds, hydrogen bonds, hydrophobic bonds, repulsive interactions, etc.
Nanomaterials are formed of a variety of molecules joined together or large molecules which take 3D structures via inter-molecular bonding (such as macromolecules). Thus nanoscience includes supramolecular chemistry as well. Additionally, intermolecular bonding plays a significant role in these macromolecules.
- Intermolecular bondings include hydrogen and van der Waals interactions. Such bonds are individually weak. However, when they are present in large numbers, their total energy can be very large. As an example, a DNA molecule (cross-section = 2nm) has numerous hydrogen bonds holding the two helixes together. These interactions assume great significance in nanomaterials as their surface area is very large and numerous small forces apply on very large areas.
- Intermolecular bonds are essential to the structure of macromolecules (e.g., proteins). They form their specific 3D structure which has specific biological functions. Any disturbance to these bonds may permanently affect their structure which in turn may deteriorate their working.
- Hydrophobic effect is another significant intermolecular interaction in nanoscience. This process is fundamentally driven by entropy. This property can be described as the ability of non-polar molecules (such as oil) to exist as clusters in water.
Molecules as “Devices”
Macromolecules, in nanoscience, are frequently described as “devices”. These devices can trap or release a certain species under specific conditions (e.g. pH). When molecules function as devices, bonds may also be device components. The application of molecules including molecular switches, actuators, and electronic wires is an important area of investigation.
Material Properties at Nanoscale
Surface Properties
Surface properties influence the physical and chemical properties of all the materials whether they are in bulk or nanoscale form. Surface performs several functions such as they manage inflow or outflow of materials or energy; they can work as catalysts, etc. The science which investigates the chemical, physical and biological properties of surface is termed as surface science. Generally, the surface is regarded as the interface, since it acts as a boundary between the material and its surroundings.
Nanomaterials possess large surface areas. This can be understood as follows: when the bulk material is repeatedly divided into smaller and smaller pieces, total volume, of all the pieces taken together, does not change while the surface area considerably increases. Thus, the surface-area to volume ratio is greatly enhanced (see Figure 3).
Figure 3 Schematics illustration of increase in surface-to-volume ratio with reduction in size.
Importance of surface atoms
The chemical groups present at the surface/interface of a material influence its properties (e.g., catalysis, electronic conduction, adhesion, gas storage, etc.). Since in nanomaterials, majority of atoms are present at their surface, they exhibit enhanced surface activities. This makes nanomaterials particularly useful in catalytic reactions, detection reactions including sensing of a specific compound, etc. which require physical adsorption of particular species at material’s surface.
Additionally, properties like melting point are also affected by the size of the particle. Nanosized particles of a material have lower melting point than their bulk forms. This is because it is easy to remove the surface atoms as they are in contact with fewer atoms of the material, thus the energy required to overcome the inter-molecular forces holding the atoms is low leading to lower melting point. As an example, bulk CdSe melts at 1678K whereas a 3nm CdSe crystal melts at 700K.
Shape also matters
For a given volume, the surface area also depends upon material’s shape, e.g., (Figure 4), between a sphere and cube with equal volumes, the surface area of cube is larger. Consequently, apart from the size, shape of the material is also significant.
Figure 4 Shape affects the surface area.
Surface Energy
Atoms or molecules existing at the interface (or surface) differ from the same atoms/molecules present in the interior or bulk of the material. This applies to all materials. Surface atoms or molecules have increased reactivities and are highly prone to form clusters. Thus, the surface atoms are unstable and possess higher surface energies.
As mentioned earlier, the majority atoms of a nanomaterial are surface atoms. This causes high energies of the nanomaterials. Since, high energy systems strive to lose their energy, by any process; nanomaterials are inherently unstable. There are a variety of ways with which a nanomaterial can minimize its high surface energy. Agglomeration is a natural way to decrease the surface energy (as it strongly depends on the surface area, which can be greatly decreased via clustering). As shown in Figure 5, by clubbing two boxes of similar surface areas, the overall surface area of the clubbed box is highly reduced, thereby also decreasing the surface energy.
Figure 5 Surface energy of two isolated cubes is more than that of the two agglomerated cubes.
Thus, nanoparticles intrinsically tend to agglomerate. From their application point of view, agglomeration is undesirable. To reduce this tendency nanoparticles, a surfactant may be used.
Reactions where surface properties are important
1. Catalysis
Catalysts are substances which enhance the rate of a chemical reaction without being consumed. Naturally occurring catalysts, often termed as enzymes, are highly efficient and produce the desired end products with minimal energy utilization. Artificial catalysts are usually produced by fixing metal particles over oxide surfaces. These are not energy efficient. The active surface of a catalyst is very important in catalyzing processes, since higher surface implies higher surface activity. As the size of the catalyst is reduced, its active surface increases. In addition to this, organization of active sites is also crucial. Since, both these features can be engineered in nanotechnology, it holds great potential to enhance catalyst design. Additionally, nanoparticles in catalysis will drastically reduce the quantity of the material needed, thereby benefitting both economically as well as environmentally.
2. Detection/Sensing
The detection of a specific chemical or biological species from a mixture is the basic principle of operation of sensing devices (e.g., chemical sensors, biosensors, and microarrays). Similar to catalysis, sensing is also a surface/interface phenomenon. The rate, specificity and accuracy of this reaction can be greatly enhanced by nanomaterials. Enhanced surface area in nanomaterials provides more active sites available for detection resulting in rapid detection. Also, the detection limit is also lowered. Further, as the nanomaterials with specific surface behaviors can be easily designed at molecular level, the active sites on the material surface can act as “locks” to detect specific molecules. Nanomaterials provide more detection sites in the same device, all of which can be engineered to detect a specific analyte/species. Therefore, nanotechnology can greatly enhance the detections capabilities in miniaturized devices.
Electrical Properties
Quantum confinement and its effect on electrical properties of materials
Quantum confinement results in increase in the energy bandgap of the material (see Figure 6). Additionally, at nanoscale dimensions as the energy levels become quantized. Thus, the band overlap in metals disappears and a bandgap emerges. Thus, some metals behave as semiconductors at nanoscale.
Figure 6 Schematic comparison of the bandgap in the bulk semiconductor, a quantum dot and a single atom.
The increase in bandgap energy implies that more energy can be absorbed by the material. Higher energies mean shorter wavelengths (or blue shift). A nanomaterial will emit the fluorescent light of higher wavelength resulting in blue shift. By adjusting the size of the nanoparticle, its absorption and emission can be tuned over a wide wavelength range.
Optical Properties
The energy levels in nanoscaled semiconductors are quantized, splitting the conduction and valance bands. This discretizes the conduction as well as valance bands. Since charge can only be transferred across these discrete levels, only specific wavelengths can be absorbed. This results in monochromatic emissions from nanostructured semiconductors.
Figure 7 Ten distinguishable emission colours of ZnS-capped CdSe quantum dots excited by a near UV lamp.
Since the energy gap of the material is increased due to quantum confinement, more energy can be absorbed by it. Higher energy means shorter wavelength (blue shift). By tuning the size of the semiconductor nanocrystal, its bandgap can be controlled. Thus, the wavelength absorbed/emitted light by the crystal can also be tuned. Consequently, same material (such as CdSe) can emit different colors depending on its size (Figure 7).
From white to transparent materials
High-protection sunscreens appear white due to scattering of visible light by them. Most of them have ZnO and TiO2 particles having dimensions of ~200 nm. When visible light interacts with these clusters, all of its wavelengths get scattered and combine to appear white coloured (Figure 8).
Figure 8 Scattering curves for 100 nm and 200 nm ZnO clusters.
When the dimension of the cluster is decreased down to ~100nm, maximum scattering occurs ~200nm, shifting the curve towards shorter wavelengths, which are not in visible range. Thus the same material appears transparent after reduction in size.
Magnetic Properties
Magnetic properties of the material can also be altered by nanostructuring. The magnetization curve of a material can be adjusted by controlling its size, resulting in soft or hard magnets with enhanced properties. Generally, the magnetic behavior of a material depends upon its structure and temperature. For experiencing a magnetic field, the material must have a finite nonzero spin. The transition size of classically expected magnetic domains is ~1μm. With decreasing the size of the magnet, surface atoms form a significant portion of the total number of atoms. This greatly enhances surface effects, and in turn the quantum confinement assumes significance. As the size of these domains is reduced to nanoscale, the materials exhibit novel properties because of quantum confinement, like the giant Magnetoresistance effect (GME). This is a fundamental nano-effect which is now being used in modern data storage devices.
Mechanical Properties
Depending on the structure, some nanomaterials can exhibit exceptional mechanical properties. One such material is carbon nanotubes (CNTs), which are extremely small tubes having the same honeycomb structure of graphite (bulk), but with different properties than it (Figure 9). CNTs can be 100 times stronger than steel but six times lighter.
Figure 9 Various types of CNTs.
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References & Suggested Reading:
- T. Pradeep, A Textbook of “Nanoscience and Nanotechnology”, McGraw Hill Education, 2012.
- https://nanoyou.eu/
- https://www.nano.gov/nanotech-101/special
- http://www.bfr.bund.de/en/questions_and_answers_on_nanotechnology-8568.html
- https://www.hindawi.com/journals/jnm/si/163450/
- https://utsa.influuent.utsystem.edu/en/publications/nanomaterial-properties-size-and-shape-dependencies
- https://pdfs.semanticscholar.org/0f15/1448f1f0fa98b949678545e261f26bad4ae8.pdf
- Huang, Bing, et al. “Construction and properties of structure-and size-controlled micro/nano-energetic materials.” Defence technology 9.2 (2013): 59-79.