Chapter 1: Introduction to Nanomaterials

📖 Reading Time: 20-25 minutes 📊 Level: Beginner

Chapter 1: Introduction to Nanomaterials

The Nanoscale World and Size Effects

Learning Objectives

By studying this chapter, you will be able to:

1.1 What are Nanomaterials?

Definition of Nanoscale

The first step in understanding nanomaterials is to grasp what the "nano" scale actually means.

Nanometer (nm) is an extremely small unit of length, one billionth of a meter:

$$
1 \text{ nm} = 10^{-9} \text{ m} = 0.000000001 \text{ m}
$$

To understand this incredibly small scale, let's compare it with familiar sizes:

Object Size Nanometer Equivalent
Human height ~1.7 m 1,700,000,000 nm
Hair thickness ~80 μm 80,000 nm
Red blood cell ~7 μm 7,000 nm
Bacteria (E. coli) ~2 μm 2,000 nm
Virus (influenza) ~100 nm 100 nm
Typical nanomaterial size 1-100 nm 1-100 nm
DNA double helix diameter ~2 nm 2 nm
Water molecule ~0.3 nm 0.3 nm
Atom (carbon) ~0.15 nm 0.15 nm

Nanomaterials exist at a scale comparable to or smaller than viruses. At this scale, structures are formed by the assembly of several to thousands of atoms.

Definition of Nanomaterials

According to the International Organization for Standardization (ISO) technical specification ISO/TS 80004-1, nanomaterials are defined as follows:

Nanomaterial: Material with any external dimension, or internal structure, at the nanoscale (approximately 1 nm to 100 nm)

The critical point in this definition is the phrase "at least one dimension." This means that not all three dimensions need to be at the nanoscale; even if only one direction is nanoscale, it qualifies as a nanomaterial. This concept leads to the dimensional classification (0D, 1D, 2D, 3D) discussed later.

The key characteristics of nanomaterials are the following four:

  1. Dramatic increase in surface area/volume ratio: As size decreases, the proportion of surface atoms increases
  2. Emergence of quantum effects: When particle size becomes comparable to the electron wavelength, quantum mechanical effects become significant
  3. Size-dependent properties: Even with the same chemical composition, properties such as color, melting point, and catalytic activity change with size
  4. Unique optical properties: Novel optical properties absent in bulk materials appear, such as localized surface plasmon resonance in metal nanoparticles

Why are Nanomaterials Attracting Attention?

Bulk materials (conventional-sized materials) and nanomaterials can exhibit completely different properties even with the same chemical composition.

As a representative example, let's look at the size effect of gold (Au):

Particle Size Color Melting Point Characteristics
Bulk (ingot) Gold color (golden) 1,064°C Chemically stable, no catalytic activity
50-100 nm Blue-violet ~900-1,000°C Localized surface plasmon resonance
20-30 nm Red ~700-800°C Strong light absorption, bioimaging
5-10 nm Red-violet ~500-600°C High catalytic activity
2-3 nm Variable ~300-400°C Emergence of quantum effects

The same element, gold, exhibits such dramatic property changes depending on particle size. This size dependence is the fascination of nanomaterial research and the source of diverse application possibilities.

1.2 Size Effects and Surface/Interface Effects

Increase in Surface Area/Volume Ratio

One of the most important properties of nanomaterials is the dramatic increase in surface area/volume ratio.

As a simple example, consider a spherical particle with radius $r$.

$$
\frac{S}{V} = \frac{4\pi r^2}{\frac{4}{3}\pi r^3} = \frac{3}{r}
$$

From this equation, we see that as particle radius decreases, surface area/volume ratio increases. In other words, if size becomes 1/10, the surface area/volume ratio becomes 10 times larger.

Let's compare with specific numerical values:

Particle Diameter Surface Area/Volume Ratio Total Atoms (Au) Surface Atom Fraction
1 cm (10⁷ nm) 0.6 m⁻¹ ~10²² <0.001%
1 mm (10⁶ nm) 6 m⁻¹ ~10¹⁹ ~0.01%
100 μm (10⁵ nm) 60 m⁻¹ ~10¹⁶ ~0.1%
10 μm (10⁴ nm) 600 m⁻¹ ~10¹³ ~1%
1 μm (1000 nm) 6,000 m⁻¹ ~10¹⁰ ~10%
100 nm 60,000 m⁻¹ ~10⁷ ~20%
10 nm 600,000 m⁻¹ ~10⁴ ~40%
5 nm 1,200,000 m⁻¹ ~10³ ~60%
2 nm 3,000,000 m⁻¹ ~250 ~80%

In a 10 nm gold nanoparticle, approximately 40% of all atoms are on the surface. At 2 nm, an astonishing 80% of atoms are on the surface.

This increase in surface atoms leads to the following dramatic property changes:

Influence of Surface Energy

In nanoparticles, surface energy has a major impact on the overall material properties.

A representative phenomenon is melting point depression. Nanoparticles melt at temperatures lower than bulk materials.

This phenomenon is known as the Gibbs-Thomson effect and can be approximated by the following equation:

$$
T_m(r) = T_{m,\text{bulk}} \left(1 - \frac{2\gamma V_m}{r \Delta H_f}\right)
$$

Where:
- $T_m(r)$: Melting point of particle with radius $r$
- $T_{m,\text{bulk}}$: Melting point of bulk material
- $\gamma$: Surface energy (surface tension)
- $V_m$: Molar volume
- $\Delta H_f$: Enthalpy of fusion
- $r$: Particle radius

Experimental data for gold nanoparticle melting points:

Particle Diameter Melting Point Depression from Bulk
Bulk 1,064°C 0°C
100 nm ~1,050°C ~14°C
50 nm ~1,020°C ~44°C
20 nm ~950°C ~114°C
10 nm ~850°C ~214°C
5 nm ~650°C ~414°C
2 nm ~350°C ~714°C

A 2 nm gold nanoparticle melts at a temperature more than 700°C lower than bulk gold. This property is utilized in developing low-temperature sintering materials and thermally responsive materials.

Enhancement of Catalytic Activity

The increase in surface area/volume ratio leads to dramatic enhancement of catalytic activity.

Let's consider platinum (Pt) catalysts as an example:

Relationship between platinum particle size and catalytic activity:

Pt Particle Size Surface Area (per gram) Relative Catalytic Activity Cost Efficiency
Bulk plate ~1 m²/g 1× 1×
10 μm powder ~0.1 m²/g 2× 2×
100 nm powder ~10 m²/g 50× 50×
10 nm nanoparticles ~100 m²/g 500× 500×
3 nm nanoparticles ~300 m²/g 1,500× 1,500×

3 nm platinum nanoparticles exhibit 1,500 times the catalytic activity of bulk platinum plates. This means 1,500 times the performance can be extracted from the same mass of platinum, significantly contributing to reducing the use of rare metals.

1.3 Quantum Effects and Quantum Confinement

Emergence of Quantum Effects

When particle size reaches the nanoscale, quantum mechanical effects that cannot be explained by classical physics become significant.

The key to understanding quantum effects is the de Broglie wavelength. All particles have wave-like properties, and their wavelength $\lambda$ is given by:

$$
\lambda = \frac{h}{p} = \frac{h}{mv}
$$

Where:
- $h$: Planck's constant ($6.626 \times 10^{-34}$ J·s)
- $p = mv$: Momentum (mass × velocity)
- $m$: Particle mass
- $v$: Particle velocity

Let's calculate the de Broglie wavelength of an electron at room temperature (300 K):

$$
\lambda = \frac{h}{m_e v} \approx \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 1.17 \times 10^5} \approx 6.2 \text{ nm}
$$

The de Broglie wavelength of an electron is approximately 6 nm. When particle size becomes comparable to or smaller than this wavelength, electrons behave as "waves confined within the particle," and quantum effects become important.

Quantum Confinement Effect

The quantum confinement effect is a phenomenon where electrons or holes (positive charge carriers) are confined in a narrow space, causing their energy states to become discrete.

As the simplest model, consider a one-dimensional infinite potential well. The energy levels of a particle confined in a box of length $L$ are:

$$
E_n = \frac{n^2 h^2}{8mL^2} \quad (n = 1, 2, 3, \ldots)
$$

Where:
- $n$: Quantum number
- $h$: Planck's constant
- $m$: Particle mass
- $L$: Box length (particle size)

Important conclusions can be drawn from this equation:

  1. Energy is discrete: Only specific values ($E_1, E_2, E_3, \ldots$) are allowed, not continuous values
  2. A minimum energy (ground state) exists: $E_1 = \frac{h^2}{8mL^2}$, which is not zero
  3. Energy gap depends on size:

$$
\Delta E = E_2 - E_1 = \frac{3h^2}{8mL^2} \propto \frac{1}{L^2}
$$

As particle size decreases, the energy gap increases.

This is why semiconductor nanoparticles (quantum dots) change color with size.

Emission Color Control in Semiconductor Quantum Dots

Quantum dots (QDs) are semiconductor nanoparticles where the bandgap (forbidden gap) changes with size, allowing control of emission color.

Example of CdSe (cadmium selenide) quantum dots:

Particle Diameter Bandgap Emission Color Emission Wavelength Application Example
Bulk 1.74 eV Infrared ~710 nm -
10 nm 1.85 eV Red ~670 nm Red QLED
6 nm 2.00 eV Orange ~620 nm Display
4 nm 2.25 eV Yellow-green ~550 nm Bioimaging
3 nm 2.50 eV Green ~495 nm Green QLED
2 nm 2.75 eV Blue ~450 nm Blue QLED

As particle diameter decreases from 10 nm to 2 nm, the bandgap increases from 1.85 eV to 2.75 eV, and the emission color changes from red to blue.

This can be explained by the Brus equation (simplest approximation form):

$$
E_g(r) = E_{g,\text{bulk}} + \frac{h^2}{8r^2}\left(\frac{1}{m_e^} + \frac{1}{m_h^}\right) - \frac{1.8e^2}{4\pi\epsilon\epsilon_0 r}
$$

Where:
- $E_g(r)$: Bandgap of quantum dot with radius $r$
- $E_{g,\text{bulk}}$: Bandgap of bulk semiconductor
- $m_e^$, $m_h^$: Effective mass of electron and hole
- $e$: Electron charge
- $\epsilon$: Dielectric constant
- Second term: Energy increase due to quantum confinement ($\propto 1/r^2$)
- Third term: Energy decrease due to Coulomb interaction ($\propto 1/r$)

Major applications of quantum dots:

  1. QLED (Quantum dot LED displays): Commercialized by Samsung, Sony; color reproducibility improved by 150% over conventional displays
  2. Bioimaging: Brighter than fluorescent dyes, less photobleaching
  3. Solar cells: Multi-junction solar cells with theoretical efficiency improvement (possibility to exceed Shockley-Queisser limit)
  4. Quantum information technology: Candidate material for quantum bits

Localized Surface Plasmon Resonance in Metal Nanoparticles

Metal nanoparticles exhibit a unique optical phenomenon called localized surface plasmon resonance (LSPR).

Plasmons are collective oscillations of free electrons in metals. In nanoparticles, the electron cloud oscillates due to the electric field of light, and resonance occurs at specific wavelengths.

LSPR in gold nanoparticles:

Particle Size/Shape LSPR Wavelength Observed Color Application
10-20 nm spherical ~520 nm Red Biosensing
50 nm spherical ~530 nm Red-violet Photothermal therapy
100 nm spherical ~570 nm Blue-violet SERS substrate
Nanorod (3:1 aspect ratio) ~650 nm, ~520 nm Blue-green Imaging
Nanoshell (Au/SiO₂) ~800 nm Transparent (near-infrared) Cancer hyperthermia

LSPR application examples:

  1. Biosensing: Antibodies modified on gold nanoparticles; LSPR wavelength shifts upon target molecule binding (detection limit: pM order)
  2. Surface-Enhanced Raman Scattering (SERS): Raman signal enhanced by 10⁶-10¹⁴ times; single-molecule detection possible
  3. Cancer hyperthermia: Near-infrared light (high tissue penetration) heats gold nanoparticles to selectively kill cancer cells
  4. Color filters: Plasmonic color filters with controlled LSPR wavelength

1.4 Classification of Nanomaterials

Nanomaterials are classified based on how many dimensions are at the nanoscale.

Classification by Dimensionality

graph TD
    A[Nanomaterials] --> B[0-Dimensional<br/>0D]
    A --> C[1-Dimensional<br/>1D]
    A --> D[2-Dimensional<br/>2D]
    A --> E[3-Dimensional<br/>3D]

    B --> B1[Nanoparticles<br/>Nanoparticles]
    B --> B2[Quantum Dots<br/>Quantum Dots]
    B --> B3[Fullerenes<br/>Fullerenes]

    C --> C1[Carbon Nanotubes<br/>CNT]
    C --> C2[Nanowires<br/>Nanowires]
    C --> C3[Nanofibers<br/>Nanofibers]

    D --> D1[Graphene<br/>Graphene]
    D --> D2[Transition Metal Dichalcogenides<br/>TMDCs]
    D --> D3[Nanosheets<br/>Nanosheets]

    E --> E1[Nanoporous Materials<br/>Nanoporous materials]
    E --> E2[Nanocomposites<br/>Nanocomposites]
    E --> E3[Nanocrystalline Materials<br/>Nanocrystalline materials]

    style A fill:#e1f5ff
    style B fill:#fff4e1
    style C fill:#ffe1f5
    style D fill:#e1ffe1
    style E fill:#f5e1ff

Classification criteria:

0-Dimensional Nanomaterials (0D)

Nanoparticles

Quantum Dots

Fullerenes

1-Dimensional Nanomaterials (1D)

Carbon Nanotubes (CNTs)

Carbon nanotubes are structures formed by rolling graphene sheets (hexagonal lattice of carbon atoms) into cylindrical shapes.

Classification:
1. Single-walled carbon nanotubes (SWCNT): Composed of one graphene sheet
- Diameter: 0.4-3 nm
- Electronic properties: Metallic or semiconducting depending on rolling direction
- Strength: Tensile strength ~100 GPa (100 times that of steel)

  1. Multi-walled carbon nanotubes (MWCNT): Multiple graphene sheets concentrically layered
    - Diameter: 10-100 nm
    - Electronic properties: Primarily metallic
    - Conductivity: Higher than copper (up to 10⁷ S/m)

Key properties:

Property Value Comparison
Tensile strength 50-100 GPa 50-100 times steel
Young's modulus ~1 TPa Comparable to diamond
Electrical conductivity Up to 10⁷ S/m Close to copper (6×10⁷ S/m)
Thermal conductivity ~3,000 W/m·K Exceeds diamond (2,200 W/m·K)
Current density Up to 10⁹ A/cm² 1,000 times copper

Applications:
- Composite materials: Lightweight high-strength materials (aerospace, sports equipment)
- Electronic devices: CNT transistors (CNT-FETs), transparent conductive films
- Energy storage: Lithium-ion battery electrodes, supercapacitors
- Sensors: Gas sensors, biosensors

Nanowires

Nanofibers

2-Dimensional Nanomaterials (2D)

Graphene

Graphene is a two-dimensional sheet with thickness of approximately 0.34 nm (one atomic layer of carbon) where carbon atoms are arranged in a hexagonal lattice. In 2004, Andre Geim and Konstantin Novoselov isolated it by mechanical exfoliation and received the Nobel Prize in Physics in 2010.

Remarkable properties:

Property Value Comparison
Electrical conductivity ~10⁸ S/m About 100 times copper
Electron mobility 200,000 cm²/V·s (room temperature) More than 100 times silicon
Tensile strength 130 GPa About 200 times steel
Young's modulus 1 TPa Comparable to diamond
Thermal conductivity 5,000 W/m·K About 12 times copper (400 W/m·K)
Optical transmittance 97.7% (monolayer) Nearly transparent
Specific surface area 2,630 m²/g (theoretical) More than twice activated carbon

Application fields:
1. Electronics: Graphene FETs (high-speed transistors), transparent conductive films, flexible electronics
2. Energy: Lithium-ion battery electrodes (3× capacity improvement), supercapacitors (10× energy density)
3. Composite materials: Graphene/polymer composites (strength and conductivity improvement)
4. Sensors: Chemical sensors, biosensors (single-molecule detection possible)
5. Transparent conductive films: Touch panels, solar cells (expected as ITO replacement)

Transition Metal Dichalcogenides (TMDCs)

Nanosheets

3-Dimensional Nanomaterials (3D)

Nanoporous Materials

Nanocomposites

Nanocrystalline Materials

1.5 Application Areas of Nanomaterials

Nanomaterials are bringing innovation to various fields by exploiting their unique properties.

Energy Sector

Lithium-ion Batteries (LIB)

Fuel Cells

Solar Cells

Electronics Sector

Semiconductor Devices

Displays

Medical and Biomedical Sectors

Drug Delivery Systems (DDS)

Imaging

Biosensors

Environmental and Catalysis Sectors

Water Treatment

Air Purification

CO₂ Reduction

Materials and Structural Sectors

Composite Materials

Coatings

1.6 Market and Future Prospects of Nanomaterials

Global Market Size

The market for nanomaterials and nanotechnology is rapidly expanding.

Market size and growth rate by sector (2023-2030 forecast):

Sector 2023 Market Size 2030 Forecast Annual Growth Rate (CAGR)
Nanoelectronics $45 billion $85 billion 9.5%
Nanomedicine/Drug Delivery $38 billion $72 billion 10.2%
Nanoenergy (Batteries/Solar Cells) $32 billion $68 billion 11.3%
Nanocomposites $27 billion $51 billion 9.8%
Nanocatalysts/Environmental Materials $18 billion $34 billion 9.4%
Others (Coatings, Cosmetics, etc.) $40 billion $70 billion 8.2%
Total $200 billion $380 billion 9.8%

Major market expansion drivers:
1. Electric vehicle (EV) adoption: High-performance battery demand
2. 5G/6G communication: High-frequency devices, transparent conductive films
3. Renewable energy: Solar cells, fuel cells, energy storage
4. Personalized medicine: Drug delivery, biosensors
5. Carbon neutrality policies: CO₂ reduction catalysts, lightweight materials

Major Research Countries and Regions

Publication ranking (nanomaterials field, 2022):

  1. China: 72,000 papers (35%)
  2. United States: 38,000 papers (18%)
  3. India: 22,000 papers (11%)
  4. South Korea: 14,000 papers (7%)
  5. Japan: 12,000 papers (6%)
  6. Germany: 11,000 papers (5%)
  7. Iran: 9,000 papers (4%)
  8. United Kingdom: 8,000 papers (4%)

Top patent-filing companies (2018-2022 cumulative):

  1. Samsung Electronics (South Korea): 3,200 patents
  2. LG Chem (South Korea): 2,800 patents
  3. BASF (Germany): 2,100 patents
  4. IBM (United States): 1,900 patents
  5. Intel (United States): 1,700 patents
  6. Toray (Japan): 1,500 patents
  7. Panasonic (Japan): 1,400 patents
  8. 3M (United States): 1,300 patents

1. Sustainable Nanomaterials

2. Multifunctional Nanomaterials

3. Computational and AI-Driven Nanomaterial Design

4. Nano-Bio Convergence

1.7 Safety and Ethical Issues of Nanomaterials

With the rapid development of nanomaterials, consideration of their safety and ethical aspects is becoming increasingly important.

Safety Concerns

Potential risks:

  1. Biological effects
    - Cytotoxicity: Oxidative stress due to reactive oxygen species (ROS) generation
    - Lung effects: Inhaled nanoparticles reaching deep lungs, risk of inflammation and fibrosis
    - Barrier penetration: Possibility of crossing blood-brain barrier, placenta
    - Accumulation: Long-term accumulation in liver, spleen

High-risk examples:
- CNTs: Asbestos-like shape, risk of pulmonary fibrosis
- Silver nanoparticles: Accumulation in liver cells, cytotoxicity due to silver ion release
- Titanium dioxide (TiO₂) nanoparticles: Classified by IARC (International Agency for Research on Cancer) as Group 2B (possibly carcinogenic to humans)

  1. Environmental effects
    - Impact on aquatic ecosystems: Toxicity to algae, fish
    - Impact on soil microorganisms: Decreased activity of nitrogen-fixing bacteria
    - Bioconcentration: Possibility of concentration through food chain

  2. Occupational exposure
    - Manufacturing site risks: Inhalation, skin contact
    - Waste disposal: Dispersion during incineration, leaching from landfills

Current status of risk assessment:

Regulations and Guidelines

Major regulatory agencies and regulations:

  1. European Union (EU)
    - REACH regulation (Registration, Evaluation, Authorization and Restriction of Chemicals): Nanomaterials covered, special registration requirements
    - Cosmetics regulation: Labeling obligation for nanomaterial-containing products ("nano" notation in ingredient name)
    - Food regulation: Approval system for novel foods containing nanomaterials

  2. United States
    - FDA (Food and Drug Administration): Guidance for nanomaterial-containing products (2014)
    - EPA (Environmental Protection Agency): Environmental risk assessment of nanomaterials
    - NIOSH (National Institute for Occupational Safety and Health): Recommended occupational exposure limits

  3. Japan
    - Ministry of Economy, Trade and Industry: Guidelines for appropriate management of nanomaterials
    - Ministry of Health, Labour and Welfare: Evaluation under Chemical Substances Control Law
    - Ministry of the Environment: Environmental impact assessment of nanomaterials

Safe handling:

Ethical and Social Issues

1. Technology divide

2. Transparency and information disclosure

3. Responsible Research and Innovation (RRI)

Nanomaterial safety assessment projects in Japan:

Summary

In this chapter, we learned the fundamentals of nanomaterials. Here is a summary of the key points:

  1. Nanoscale: The extremely small world of 1-100 nm. About 10 times the size of water molecules, comparable to viruses.

  2. Size effects: Dramatic increase in surface area/volume ratio (40% of atoms are on the surface at 10 nm). Physical property changes occur, such as melting point depression, enhanced catalytic activity, and increased reactivity.

  3. Quantum effects: When particle size becomes comparable to the electron de Broglie wavelength (~6 nm), quantum confinement effects emerge. In semiconductor quantum dots, bandgap and emission color can be controlled by size.

  4. Classification by dimensionality: 0-dimensional (nanoparticles, quantum dots), 1-dimensional (CNTs, nanowires), 2-dimensional (graphene, TMDCs), 3-dimensional (nanoporous materials, nanocomposites). Properties and applications differ by dimensionality.

  5. Wide range of applications: Energy (batteries, fuel cells, solar cells), electronics (transistors, displays), medicine (drug delivery, imaging), environment (catalysts, water treatment), materials (composites, coatings), and many other fields.

  6. Rapidly growing market: From $200 billion in 2023 to $380 billion in 2030 (annual growth rate 9.8%). China and the United States lead in research.

  7. Safety and ethics: Risk assessment of biological and environmental impacts is important. Regulatory development, safe handling, and responsible research and development are required.

Nanomaterials are a fascinating field where the simple parameter of size brings about dramatic property changes. Further development from basic science to practical applications is expected in the future.

Preview of Next Chapter

In the next chapter (Chapter 2: Fundamental Principles of Nanomaterials), we will study the following topics to gain a deeper understanding of the phenomena learned in this chapter:

We will aim for more quantitative understanding using mathematical formulas.

Exercises

Problem 1: Calculation of Size Effects

For a spherical gold (Au) nanoparticle with a diameter of 10 nm, calculate the following:

(a) Calculate the surface area/volume ratio.

(b) Assuming the atomic radius of gold is 0.144 nm, estimate the total number of atoms in this particle (Hint: The unit cell volume of gold's face-centered cubic lattice is approximately 0.068 nm³, with 4 atoms per unit cell).

(c) Estimate the number of surface atoms and calculate the fraction of surface atoms (Hint: Assume the surface atomic layer as a shell with thickness 0.3 nm).

Problem 2: Quantum Confinement Effect

Explain how the bandgap changes when the size of a CdSe quantum dot decreases from 6 nm to 2 nm. Also, describe the change in emission color. Qualitatively explain the change in energy levels from the perspective of quantum confinement effects.

Problem 3: Classification of Nanomaterials

Classify the following nanomaterials as 0-dimensional, 1-dimensional, 2-dimensional, or 3-dimensional:

(a) Single-walled carbon nanotube (diameter 1 nm, length 10 μm)

(b) Graphene sheet (thickness 0.34 nm, lateral size 1 mm × 1 mm)

(c) CdSe quantum dot (diameter 5 nm)

(d) MOF (metal-organic framework, crystal size 100 μm, pore size 1 nm)

(e) Silver nanowire (diameter 50 nm, length 20 μm)

(f) Fullerene C₆₀ (diameter approximately 0.7 nm)

Answer Examples ### Answer to Problem 1 **(a) Surface area/volume ratio** Radius $r = 5$ nm = $5 \times 10^{-9}$ m $$ \frac{S}{V} = \frac{3}{r} = \frac{3}{5 \times 10^{-9}} = 6 \times 10^8 \text{ m}^{-1} $$ **Answer: $6 \times 10^8$ m⁻¹ = 600,000 m⁻¹** **(b) Total number of atoms** Particle volume: $$ V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (5 \times 10^{-9})^3 = 5.24 \times 10^{-25} \text{ m}^3 = 524 \text{ nm}^3 $$ Unit cell volume: $V_{\text{cell}} = 0.068$ nm³, 4 atoms per unit cell $$ \text{Total atoms} = \frac{V}{V_{\text{cell}}} \times 4 = \frac{524}{0.068} \times 4 \approx 30,800 \text{ atoms} $$ **Answer: Approximately 30,000 atoms** **(c) Fraction of surface atoms** Surface shell volume (outer radius 5 nm, inner radius 4.7 nm): $$ V_{\text{shell}} = \frac{4}{3}\pi (5^3 - 4.7^3) = \frac{4}{3}\pi (125 - 103.8) = 88.9 \text{ nm}^3 $$ Surface atom number: $$ N_{\text{surface}} = \frac{88.9}{0.068} \times 4 \approx 5,230 \text{ atoms} $$ Surface atom fraction: $$ \frac{N_{\text{surface}}}{N_{\text{total}}} = \frac{5,230}{30,800} \approx 0.17 = 17\% $$ **Answer: Surface atoms approximately 5,200, fraction approximately 17%** (Note: More rigorous calculations would consider coordination numbers, but here we use a simplified shell model) --- ### Answer to Problem 2 **Bandgap change**: Due to the quantum confinement effect, as particle size decreases, the spacing between energy levels increases. In the one-dimensional infinite well model: $$ E_n \propto \frac{1}{L^2} $$ Therefore, when size decreases from 6 nm to 2 nm (1/3), the energy level spacing increases approximately 9 times ($(1/3)^{-2} = 9$). Since this quantum confinement energy is added to the bulk CdSe bandgap (1.74 eV): - **6 nm quantum dot**: Bandgap approximately 2.00 eV → **Orange emission** (wavelength approximately 620 nm) - **2 nm quantum dot**: Bandgap approximately 2.75 eV → **Blue emission** (wavelength approximately 450 nm) **Energy level change**: As particle size decreases, the motion of electrons and holes is strongly restricted, and the ground state energy increases. This causes the maximum energy of the valence band to decrease and the minimum energy of the conduction band to increase, resulting in bandgap expansion. **Emission color change**: Shifts from orange → yellow-green → green → blue toward shorter wavelengths. --- ### Answer to Problem 3 | Nanomaterial | Classification | Reason | |--------------|---------------|---------| | (a) Single-walled CNT | **1-dimensional** | Diameter 1 nm (nanoscale), length 10 μm (macroscale) | | (b) Graphene sheet | **2-dimensional** | Thickness 0.34 nm (nanoscale), lateral dimensions 1 mm (macroscale) | | (c) CdSe quantum dot | **0-dimensional** | All directions are 5 nm (nanoscale) | | (d) MOF | **3-dimensional** | Overall crystal is 100 μm (macro) but contains 1 nm pores (nanostructure) internally | | (e) Silver nanowire | **1-dimensional** | Diameter 50 nm (nanoscale), length 20 μm (macroscale) | | (f) Fullerene C₆₀ | **0-dimensional** | All directions are approximately 0.7 nm (nanoscale) |

References

  1. Roduner, E. (2006). Size matters: why nanomaterials are different. Chemical Society Reviews, 35(7), 583-592. DOI: 10.1039/B502142C

  2. Burda, C., Chen, X., Narayanan, R., & El-Sayed, M. A. (2005). Chemistry and properties of nanocrystals of different shapes. Chemical Reviews, 105(4), 1025-1102. DOI: 10.1021/cr030063a

  3. Alivisatos, A. P. (1996). Semiconductor clusters, nanocrystals, and quantum dots. Science, 271(5251), 933-937. DOI: 10.1126/science.271.5251.933

  4. Brus, L. E. (1984). Electron–electron and electron‐hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state. The Journal of Chemical Physics, 80(9), 4403-4409. DOI: 10.1063/1.447218

  5. Maier, S. A. (2007). Plasmonics: Fundamentals and Applications. Springer Science & Business Media. DOI: 10.1007/0-387-37825-1

  6. Nel, A., Xia, T., Mädler, L., & Li, N. (2006). Toxic potential of materials at the nanolevel. Science, 311(5761), 622-627. DOI: 10.1126/science.1114397

← Back to Series Contents | Next Chapter: Fundamental Principles of Nanomaterials →

← Back to Series Index