Chapter 2: Fundamental Principles of Nanomaterials

Synthesis Methods and Characterization Techniques

Learning Objectives

In this chapter, you will learn the fundamental synthesis techniques and characterization methods that form the foundation of nanomaterials research.

• ✅ Understand the differences between bottom-up and top-down approaches and master representative synthesis methods
• ✅ Master the principles and applications of major characterization techniques including TEM, SEM, and XRD
• ✅ Quantitatively understand size-dependent properties such as melting point depression, optical property changes, and superparamagnetism
• ✅ Understand the effects of surface and interface phenomena on nanomaterial properties
• ✅ Acquire methods for interpreting experimental data and criteria for selecting appropriate evaluation techniques
• ✅ Gain practical knowledge of synthesis and evaluation applicable in real research environments

2.1 Synthesis Methods for Nanomaterials

Nanomaterial synthesis methods are broadly classified into two approaches: Bottom-up and Top-down methods. These approaches differ fundamentally in the direction of material construction, and each has suitable application areas.

Bottom-up vs Top-down Methods

flowchart LR
    A[Atomic/Molecular Level] -->|Bottom-up| B[Nanostructures]
    C[Bulk Materials] -->|Top-down| B

    style A fill:#e1f5e1
    style C fill:#ffe1e1
    style B fill:#e1e5ff

Major Bottom-up Synthesis Methods

Chemical Vapor Deposition (CVD)

Principle

CVD is a technique that forms thin films or nanostructures on substrates by chemically reacting precursors in the gas phase. The typical process proceeds through the following stages:

1. Gas transport: Precursor gas is introduced into the reaction chamber
2. Surface diffusion: Gas molecules adsorb and diffuse on the substrate surface
3. Chemical reaction: Decomposition and reaction occur on catalyst surfaces or under high-temperature conditions
4. Nucleation and growth: Nanostructures form and grow
5. Byproduct removal: Gases produced by the reaction are exhausted

Representative Example: Carbon Nanotube (CNT) Synthesis

CNT synthesis by catalytic CVD uses metal nanoparticles such as iron (Fe), cobalt (Co), and nickel (Ni) as catalysts to decompose hydrocarbon gases (ethylene, methane, acetylene, etc.) at 800-1000°C.

C₂H₄ (g) → 2C (CNT) + 2H₂ (g)  [Catalyst: Fe/Co/Ni, 800-1000°C]

Representative Example: Graphene Synthesis

CVD on copper foil is an established method for synthesizing high-quality single-layer graphene over large areas. Methane gas is decomposed at high temperatures around 1000°C, and single-layer graphene grows through the catalytic action of the copper surface.

Advantages and Disadvantages

✅ Advantages:
- High crystallinity and high purity materials can be obtained
- Large-scale production possible through continuous processes
- Structural control possible through growth conditions (temperature, gas flow rate, pressure)
- Direct growth on substrates eliminates complex processes

❌ Disadvantages:
- High-temperature processes (500-1000°C or higher) required
- High equipment costs
- Precursor gases may be toxic or flammable
- Substrate materials limited (high-temperature resistance essential)

Solution-phase Synthesis Methods

Solution-phase synthesis produces nanomaterials through chemical reactions in solution and can be performed at relatively low temperatures (room temperature to ~300°C).

Sol-gel Method

Metal oxide nanoparticles and porous materials are synthesized using hydrolysis and condensation reactions of metal alkoxides.

Si(OC₂H₅)₄ + 4H₂O → Si(OH)₄ + 4C₂H₅OH  (Hydrolysis)
Si(OH)₄ → SiO₂ + 2H₂O                   (Condensation)

Applications: SiO₂, TiO₂, ZrO₂ nanoparticles, mesoporous silica

Hydrothermal Synthesis

In sealed vessels (autoclaves), aqueous solutions are reacted under high temperature and high pressure (100-300°C, several MPa). Thermodynamically stable crystalline phases can be obtained, and particle size and shape control is easy.

Applications: ZnO, TiO₂, zeolites, metal oxide nanorods

Co-precipitation

pH adjusting agents (NaOH, NH₃, etc.) are added to metal salt solutions to precipitate metal hydroxides, which are then calcined to obtain oxide nanoparticles.

Fe²⁺ + 2Fe³⁺ + 8OH⁻ → Fe₃O₄ + 4H₂O

Applications: Magnetic nanoparticles (Fe₃O₄, γ-Fe₂O₃), spinel-type oxides

Reduction Synthesis of Metal Nanoparticles

Metal nanoparticles are synthesized by reducing metal ions with reducing agents in the presence of protective agents (surfactants, polymers).

Representative Example: Gold Nanoparticle Synthesis by Turkevich Method

HAuCl₄ + C₆H₅O₇Na₃ → Au⁰ (nanoparticles) + oxidation products

Sodium citrate acts as both reducing agent and protective agent, yielding spherical gold nanoparticles of 10-50 nm. Size can be controlled by the concentration ratio of gold salt to citrate.

Gas-phase Synthesis Methods

Sputtering

Physical vapor deposition method where high-energy ions (typically Ar⁺) collide with target material, and ejected atoms are deposited on substrates. Performed in vacuum chambers and widely used for thin film and nanoparticle fabrication.

Features:
- Applicable to almost all materials (metals, oxides, nitrides, alloys)
- Precise control of deposition rate and particle size
- Uniform film thickness distribution
- Established industrial applications (semiconductors, displays, hard coatings)

Laser Ablation

Method where high-power pulsed laser irradiates solid targets, and gas-phase growth occurs from plasma generated by instantaneous evaporation.

Features:
- Applicable to high melting point materials and ceramics
- Stoichiometric composition preserved
- Narrow nanoparticle size distribution
- Suitable for small-scale research applications

Major Top-down Synthesis Methods

Mechanical Milling (Ball Milling)

High-speed rotation of hard balls mechanically pulverizes bulk materials to produce nanoparticles.

Process

1. Bulk material and hard balls (zirconia, stainless steel, WC, etc.) are placed in a container
2. High-speed rotation (200-600 rpm) imparts impact and friction energy
3. Repeated pulverization reduces particle size (typically several hours to several tens of hours)

Applications

• Metal and alloy nanoparticles
• Ceramic nanopowders
• Mechanical alloying
• Drug nanoparticles (improving pharmaceutical solubility)

Advantages and Disadvantages

✅ Advantages:
- Simple equipment with low cost
- Easy scale-up
- Applicable to wide range of materials

❌ Disadvantages:
- Broad particle size distribution (lacks uniformity)
- Crystal defects and amorphization occur
- Risk of contamination (wear from balls and container)
- Difficult shape control

Lithography

Patterns are formed on substrates using photomasks or beams, and nanostructures are created through etching or lift-off.

Photolithography

• Resolution: ~100 nm (5-7 nm with cutting-edge EUV lithography)
• Applications: Semiconductor integrated circuits, MEMS

Electron Beam Lithography (EBL)

• Resolution: <10 nm
• Direct writing with electron beam (mask-free)
• Suitable for R&D and prototyping (low throughput)

Nanoimprint Lithography (NIL)

• Physical transfer using molds
• Low cost, high throughput
• Biosensor and metamaterial applications

Etching

Dry Etching

Physical or chemical removal using plasma or ion beams. Anisotropic etching (selective in vertical direction) possible, standard technology for semiconductor processes.

Wet Etching

Chemical removal using chemical solutions. Basically isotropic etching, but anisotropic etching utilizing crystallographic orientation dependence is also possible (such as KOH etching of silicon).

2.2 Characterization Techniques

To accurately evaluate nanomaterial properties, it is essential to combine multiple analytical methods. Here we explain major techniques in morphology observation, structural analysis, compositional analysis, and optical property evaluation.

Morphology Observation Techniques

Transmission Electron Microscopy (TEM)

Principle

TEM transmits electron beams accelerated at 100-300 kV through thin specimen samples (thickness <100 nm) and detects transmitted or scattered electrons to form images. Since the electron wavelength is much shorter than visible light (400-700 nm) at approximately 2.5 pm for 200 kV accelerated electrons, atomic-level resolution can be achieved.

Measurable Parameters

Typical Resolution: 0.2-0.5 nm (point resolution), <0.1 nm (cutting-edge instruments)

Applications

1. Size and shape evaluation of gold nanoparticles
   - Measure >50 particles to evaluate size distribution as histogram
   - Quantify uniformity with standard deviation (SD) or coefficient of variation (CV = SD/mean × 100%)

2. Structural analysis of carbon nanotubes
   - Determine number of layers (single-wall SWCNT, multi-wall MWCNT)
   - Measure diameter and length
   - Evaluate defect density

3. Crystallinity evaluation of quantum dots
   - Identify crystal structure from HRTEM lattice images
   - Measure crystallographic plane spacing (e.g., CdSe (111) plane = 0.35 nm)

Scanning Electron Microscopy (SEM)

Principle

SEM scans a finely focused electron beam (probe diameter 1-10 nm) across the sample surface and detects emitted secondary or backscattered electrons to image surface morphology.

Differences from TEM

Applications

1. Morphology observation of nanowires and nanorods
   - Measure length and diameter
   - Calculate aspect ratio (length/diameter)
   - Evaluate orientation

2. Pore structure of nanoporous materials
   - Pore size distribution
   - Surface roughness

3. Dispersion state of nanocomposites
   - Nanoparticle distribution in matrix
   - Presence of agglomeration

Atomic Force Microscopy (AFM)

Principle

AFM brings a sharp cantilever probe (tip radius 10-100 nm) close to the sample surface and images surface morphology by detecting probe displacement due to interatomic forces (van der Waals forces, electrostatic forces, etc.) through laser reflection.

Measurement Modes

• Contact Mode: Probe scans in contact with sample (high resolution but risk of sample damage)
• Tapping Mode: Probe intermittently contacts with resonant vibration (suitable for soft samples)
• Non-contact Mode: Detects electrostatic forces without contact (ultrahigh resolution)

Features

✅ Advantages:
- No vacuum required (measurement in air or liquid)
- Applicable to insulators and conductors
- Quantitative height information (Z-direction resolution <0.1 nm)

❌ Disadvantages:
- Slow scanning speed (several minutes to tens of minutes per image)
- Limited measurement range (typically <100 μm square)
- Image degradation due to probe wear

Applications

• Determine graphene layer number (identify interlayer distance 0.34 nm by height measurement)
• Structural observation of DNA and proteins
• Surface roughness evaluation of thin films (calculate Ra, RMS)

Structural Analysis Techniques

X-ray Diffraction (XRD)

Principle (Bragg's Law)

Diffraction peaks appear due to X-ray interference at crystal lattice planes. Bragg's law expresses the diffraction condition with the following equation:

$$
n\lambda = 2d\sin\theta
$$

Where:
- $n$: Diffraction order (integer)
- $\lambda$: X-ray wavelength (0.154 nm for Cu Kα)
- $d$: Lattice plane spacing
- $\theta$: Incident angle (Bragg angle)

Crystal Structure Identification

Crystal phases are identified by comparing diffraction patterns (2θ vs intensity) with standard databases (ICDD PDF, COD).

Example: Gold nanoparticles (FCC structure)
- (111) plane: 2θ ≈ 38.2°
- (200) plane: 2θ ≈ 44.4°
- (220) plane: 2θ ≈ 64.6°
- (311) plane: 2θ ≈ 77.5°

Crystallite Size Estimation (Scherrer Equation)

Nanocrystal particle size can be estimated from the full width at half maximum (FWHM) of diffraction peaks:

$$
D = \frac{K\lambda}{\beta\cos\theta}
$$

Where:
- $D$: Crystallite size (nm)
- $K$: Shape factor (0.9 for spherical particles)
- $\beta$: Physical broadening of FWHM (radians) = measured FWHM - instrumental broadening
- $\theta$: Bragg angle

Note: The Scherrer equation gives crystallite size (coherent scattering region), which may differ from particle size (such as polycrystalline structures where one particle consists of multiple crystallites).

Application Example

XRD measurement results for gold nanoparticles:
(111) peak: 2θ = 38.2°, FWHM = 0.8° = 0.0140 rad

Crystallite size calculation:
D = (0.9 × 0.154 nm) / (0.0140 × cos(19.1°))
  = 0.1386 / 0.0132
  ≈ 10.5 nm

Raman Spectroscopy

Principle

When laser light irradiates a sample, scattered light with energy changed by molecular vibration (Raman scattered light) is generated. By measuring this energy shift (Raman shift, unit: cm⁻¹), molecular vibrational modes and crystal structures can be identified.

Evaluation of Graphene and CNTs

For carbon-based nanomaterials, the following characteristic peaks are observed:

Defect Density Evaluation

The D/G intensity ratio ($I_D/I_G$) increases with higher defect density.

• Perfect graphene: $I_D/I_G \approx 0$
• High-quality CVD graphene: $I_D/I_G < 0.1$
• Defective graphene: $I_D/I_G > 0.5$

Single-layer Graphene Identification

Layer number can be distinguished by 2D band shape:
- Single-layer: 2D band is a single sharp peak, $I_{2D}/I_G > 2$
- Bilayer: 2D band separates into four Lorentzian functions
- Multilayer: 2D band broadens, $I_{2D}/I_G < 1$

Compositional Analysis Techniques

X-ray Photoelectron Spectroscopy (XPS)

Principle

X-rays irradiate the sample, and the kinetic energy of photoelectrons emitted by the photoelectric effect is measured. The binding energy ($E_B$) of photoelectrons is determined by the following equation:

$$
E_B = h\nu - E_K - \phi
$$

Where $h\nu$ is X-ray energy, $E_K$ is photoelectron kinetic energy, and $\phi$ is work function.

Surface Chemical Composition

Since XPS provides information from several nm (approximately 5-10 nm) of the surface, it is suitable for surface chemical composition analysis. Atomic % of detected elements can be quantified.

Chemical State Analysis

Since binding energy changes with chemical bonding state for the same element (chemical shift), oxidation states and bonding forms can be identified.

Example: Surface modification evaluation of gold nanoparticles
- Au 4f₇/₂ peak (Au⁰): 84.0 eV
- Au-S thiol bond Au: 84.4 eV (0.4 eV shift)
- S 2p peak: 162 eV (thiol bond)

Energy Dispersive X-ray Spectroscopy (EDX/EDS)

Principle

Characteristic X-rays emitted from samples by electron beam irradiation are measured for energy to identify elements. Since each element has unique X-ray energies, qualitative and quantitative analysis is possible.

Elemental Mapping

In SEM/TEM-EDX, two-dimensional maps of elemental distribution can be obtained by detecting X-rays while scanning the electron beam.

Applications

• Quantify composition ratio of alloy nanoparticles (Au-Ag, Pt-Pd)
• Confirm core-shell nanoparticle structure (e.g., visualize Fe, Si, O distribution in Fe₃O₄@SiO₂ by elemental mapping)
• Elemental dispersion in nanocomposites

Note: Detection sensitivity for light elements (H, He, Li, Be, B, C, N, O) is low, and quantification accuracy also decreases.

Optical Property Evaluation

UV-Vis Absorption Spectroscopy

Principle

Ultraviolet-visible light (wavelength 200-800 nm) is irradiated on the sample, and the intensity of transmitted or reflected light is measured. Absorbance ($A$) follows the Lambert-Beer law:

$$
A = \varepsilon c l
$$

Where $\varepsilon$ is molar extinction coefficient, $c$ is concentration, and $l$ is path length.

Light Absorption Properties

Electronic states and optical band gaps can be evaluated from absorption spectra of nanomaterials.

Observation of Plasmon Resonance

Metal nanoparticles exhibit characteristic absorption peaks due to collective oscillation of free electrons (Localized Surface Plasmon Resonance, LSPR).

Example: Gold nanoparticles
- Particle size 10-50 nm (spherical): λmax ≈ 520 nm (red-purple)
- Increasing particle size → red shift
- Shape change (rod, star) → multiple peaks

Band Gap Estimation (Tauc plot)

The band gap ($E_g$) of semiconductor nanoparticles is determined from the absorption edge using a Tauc plot:

$$
(\alpha h\nu)^{1/n} = B(h\nu - E_g)
$$

Where $\alpha$ is absorption coefficient, $h\nu$ is photon energy, $n$ is transition type (2 for direct transition, 1/2 for indirect transition), and $B$ is a constant.

Plot $(αh\nu)^2$ vs $h\nu$ (for direct transitions) or $(αh\nu)^{1/2}$ vs $h\nu$ (for indirect transitions), and extrapolate the linear portion to read $E_g$ from the intersection with the horizontal axis.

Application Example: CdSe quantum dots
- Bulk CdSe band gap: $E_g$ = 1.74 eV (λ ≈ 710 nm)
- Quantum dots (diameter 3 nm): $E_g$ = 2.4 eV (λ ≈ 520 nm) → blue shift due to quantum confinement effect

Fluorescence Spectroscopy

Principle

Excitation light irradiates the sample, and the wavelength and intensity of fluorescence emitted from fluorescent materials are measured. Fluorescence with longer wavelength than excitation light is observed (Stokes shift).

Emission Properties of Quantum Dots

Semiconductor quantum dots (CdSe, CdTe, InP, PbS, carbon dots, etc.) exhibit size-dependent emission colors.

Size-Emission Color Relationship (CdSe Quantum Dots)

Quantum Yield (QY)

An indicator representing emission efficiency of fluorophores, defined as the ratio of emitted photons to absorbed photons:

$$
QY = \frac{\text{Number of emitted photons}}{\text{Number of absorbed photons}} \times 100\%
$$

High-quality quantum dots: QY = 50-90%

Applications: Bioimaging, displays (QLED), solar cells

2.3 Size-dependent Properties

At the nanoscale, unique properties not seen in bulk materials emerge. These arise from increased surface area-to-volume ratio, quantum size effects, and contributions of surface energy.

Melting Point Depression

Gibbs-Thomson Effect

The melting point of nanoparticles ($T_m(r)$) decreases with decreasing particle radius ($r$). This is described by the Gibbs-Thomson equation:

$$
T_m(r) = T_m(\infty) \left(1 - \frac{4\sigma_{sl}}{\rho \Delta H_f r}\right)
$$

Where:
- $T_m(\infty)$: Bulk melting point (K)
- $\sigma_{sl}$: Solid-liquid interface energy (J/m²)
- $\rho$: Density (kg/m³)
- $\Delta H_f$: Enthalpy of fusion (J/kg)
- $r$: Particle radius (m)

Physical Interpretation

In nanoparticles, the proportion of surface atoms increases, and the contribution of surface energy becomes significant. Surface atoms have weaker bonding than interior atoms, making them thermally unstable and lowering the melting point.

Gold Nanoparticle Example

Bulk melting point of gold (Au): $T_m(\infty)$ = 1337 K (1064°C)

Parameters:
- $\sigma_{sl}$ = 0.132 J/m²
- $\rho$ = 19300 kg/m³
- $\Delta H_f$ = 6.3 × 10⁴ J/kg

Relationship between particle size and melting point:

Experimental Data

Actual measurements confirm by differential scanning calorimetry (DSC) that the melting point of 2-5 nm gold nanoparticles decreases to 600-900°C.

Changes in Optical Properties

Localized Surface Plasmon Resonance (LSPR) in Metal Nanoparticles

Principle

When light is incident on metal nanoparticles, free electrons oscillate collectively, causing a resonance phenomenon (plasmon resonance). At this resonance frequency, light absorption is maximized, and a strong absorption band appears.

The plasmon resonance frequency ($\omega_p$) of spherical metal nanoparticles is approximated by the Drude-Sommerfeld model:

$$
\omega_p = \sqrt{\frac{ne^2}{m^* \varepsilon_0}}
$$

Where $n$ is electron density, $e$ is elementary charge, $m^*$ is effective mass, and $\varepsilon_0$ is vacuum permittivity.

Size Dependence

LSPR peak wavelength of gold nanoparticles (spherical):

As particle size increases, increased damping causes a shift to longer wavelengths (red shift).

Shape Dependence

Non-spherical particles exhibit multiple plasmon resonance modes due to anisotropy.

Example: Gold nanorods
- Transverse mode: Short axis direction, ~520 nm
- Longitudinal mode: Long axis direction, 600-1200 nm (varies with aspect ratio)

As aspect ratio (length/diameter) increases, the longitudinal mode shifts to longer wavelengths and can be tuned to the near-infrared region.

Applications

• Biosensing (detecting wavelength shift from antibody-antigen binding)
• Photothermal therapy (PTT): Near-infrared light absorption → heat generation → cancer cell destruction
• Surface-enhanced Raman scattering (SERS): 10⁶-10⁸ fold signal enhancement from plasmon enhancement effect

Band Gap Changes in Semiconductor Quantum Dots

Quantum Confinement Effect

When semiconductor nanoparticle size becomes smaller than the exciton Bohr radius ($a_B$), the motion of electrons and holes is spatially confined, and energy levels become discrete. As a result, the band gap expands, and absorption/emission wavelengths blue shift.

Brus Equation (Effective Mass Approximation Model)

The band gap of quantum dots ($E_g(r)$) is described by the following equation:

$$
E_g(r) = E_g(\infty) + \frac{\hbar^2 \pi^2}{2r^2} \left(\frac{1}{m_e^} + \frac{1}{m_h^}\right) - \frac{1.8e^2}{4\pi\varepsilon\varepsilon_0 r}
$$

Where:
- $E_g(\infty)$: Bulk band gap
- $\hbar$: Planck constant/2π
- $r$: Quantum dot radius
- $m_e^, m_h^$: Effective mass of electron and hole
- $\varepsilon$: Relative permittivity

Second term (positive): Energy increase from quantum confinement (main term)
Third term (negative): Energy decrease from Coulomb interaction (correction term)

Size-Emission Color Relationship (CdSe Quantum Dots)

CdSe property values:
- $E_g(\infty)$ = 1.74 eV
- $m_e^$ = 0.13 $m_0$
- $m_h^$ = 0.45 $m_0$
- $\varepsilon$ = 10.2
- Exciton Bohr radius: $a_B$ = 5.6 nm

Calculation examples of particle size and band gap:

Applications

• Bioimaging: Near-infrared emitting quantum dots with high tissue penetration (700-900 nm)
• Displays: Create RGB primary colors by size tuning (QLED TV)
• Solar cells: Absorb broad wavelength range with multiple-sized quantum dots

Changes in Magnetic Properties

Superparamagnetism

Principle

When ferromagnetic nanoparticles become smaller than a critical size, thermal energy ($k_B T$) exceeds magnetic anisotropy energy ($KV$), and the magnetization direction frequently reverses. This state is called superparamagnetism.

Critical Size

The critical particle diameter ($d_c$) for superparamagnetism emergence is determined by the following condition:

$$
KV \approx 25 k_B T
$$

Where:
- $K$: Magnetic anisotropy constant (J/m³)
- $V = \frac{\pi d^3}{6}$: Particle volume
- $k_B$: Boltzmann constant (1.38 × 10⁻²³ J/K)
- $T$: Temperature (K)

Magnetite (Fe₃O₄) Example

• $K$ = 1.1 × 10⁴ J/m³
• Critical particle diameter at room temperature ($T$ = 300 K):

$$
d_c \approx \left(\frac{150 k_B T}{\pi K}\right)^{1/3} \approx 15 \text{ nm}
$$

Characteristics of Superparamagnetism

✅ Advantages:
- Magnetization becomes zero when magnetic field is turned off (no remanence)
- Less prone to agglomeration (no magnetic attraction)
- Easy redispersion

❌ Disadvantages:
- Zero coercivity (unsuitable for magnetic recording)

Medical Application: MRI Contrast Agent

Superparamagnetic iron oxide nanoparticles (SPION) are used as T₂ contrast agents for MRI.

Example: Feridex® (iron oxide nanoparticles, particle size 4-6 nm)
- Improved biocompatibility with dextran coating
- Detection of lesions in liver and spleen

Other applications:
- Magnetic hyperthermia (cancer treatment): Heat generation in alternating magnetic field
- Drug delivery: Guided to target site by magnetic field

Mechanical Properties

Size Strengthening Effect (Hall-Petch Relationship)

Hall-Petch Relationship

The yield stress ($\sigma_y$) of polycrystalline materials increases with decreasing grain size ($d$):

$$
\sigma_y = \sigma_0 + \frac{k}{\sqrt{d}}
$$

Where $\sigma_0$ is friction stress and $k$ is a material constant.

Physical Interpretation

As grain size decreases, grain boundary density increases, and dislocation movement is inhibited at grain boundaries, causing material hardening.

Inverse Hall-Petch Effect (< 10 nm)

When grain size becomes less than 10 nm, grain boundary sliding becomes dominant, and conversely softening occurs. This phenomenon is called the inverse Hall-Petch effect.

Application Examples

• Nanocrystalline metals: Grain size 10-100 nm, 2-5 times the strength of bulk
• Superhard tool materials: WC-Co nanocomposites

2.4 Surface and Interface Effects

In nanoparticles, the surface area-to-volume ratio ($S/V$) increases dramatically. For spherical particles:

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

When particle size becomes 1/10, the surface area-to-volume ratio increases 10 times.

Proportion of Surface Atoms

At particle size 3 nm, approximately one-third of atoms exist on the surface, and the contribution of surface energy cannot be ignored.

Surface Energy and Surface Tension

Surface Energy

Energy required to create a surface, expressed as energy per unit area (J/m²) or force per unit length (N/m).

Representative surface energy values (room temperature):

Since metals have high surface energy, they become prone to agglomeration upon nanoparticle formation.

Surface Functionalization

Surface modification is an important technique for controlling nanoparticle dispersibility, stability, and functionality.

Modification with Organic Molecules

Thiol Compounds (Gold Nanoparticles)

Thiol groups (-SH) form strong Au-S bonds (bonding energy ~200 kJ/mol) with gold surfaces.

Representative examples:
- Alkanethiol (HS-(CH₂)ₙ-CH₃): Imparts hydrophobicity
- Mercaptoundecanoic acid (HS-(CH₂)₁₀-COOH): Imparts hydrophilicity, bioconjugation
- Thiolated DNA/peptides: Biosensing applications

Silane Coupling Agents (Oxide Nanoparticles)

Silane coupling agents (R-Si(OR')₃) react with hydroxyl groups (-OH) on oxide surfaces to form covalent bonds.

Representative examples:
- APTES (3-aminopropyltriethoxysilane): Amino group introduction
- MPTMS (3-mercaptopropyltrimethoxysilane): Thiol group introduction
- GPTMS (3-glycidyloxypropyltrimethoxysilane): Epoxy group introduction

Applications: Surface modification of TiO₂, SiO₂, Fe₃O₄ nanoparticles

Polymer Coating

PEG Modification (Polyethylene Glycol)

PEG modification is a standard method for improving biocompatibility and extending blood circulation time.

Effects:
- Suppression of protein adsorption (stealth effect)
- Avoidance of recognition by immune system
- Delayed excretion from kidneys

Applications: Drug delivery systems (DDS), in vivo imaging

Surfactants

Amphiphilic molecules (with hydrophilic head and hydrophobic tail) enable stable dispersion of nanoparticles in water.

Representative examples:
- Citrate (reducing agent and protective agent in gold nanoparticle synthesis)
- CTAB (cetyltrimethylammonium bromide): Gold nanorod synthesis
- Triton X-100, Tween 20: Nonionic surfactants

Purposes of Surface Modification

1. Improving Dispersibility
   - Electrostatic repulsion (introducing charged groups: -COO⁻, -NH₃⁺)
   - Steric repulsion (osmotic pressure of polymer chains)

2. Preventing Agglomeration
   - DLVO theory: Electrostatic repulsion vs van der Waals attraction
   - Increase repulsive force through modification

3. Imparting Functionality
   - Bioconjugation: Antibody, DNA, peptide immobilization
   - Targeting: Folic acid, RGD peptide
   - Stimuli-responsiveness: pH-responsive, temperature-responsive

Summary

In this chapter, we have learned the fundamental synthesis techniques, characterization methods, and size-dependent properties that form the foundation of nanomaterials research.

1. Bottom-up and top-down methods differ in construction direction, and various techniques such as CVD, solution synthesis, and lithography are used according to applications

2. For characterization, it is important to comprehensively evaluate using multiple analytical methods such as TEM (morphology and internal structure), XRD (crystal structure), and UV-Vis (optical properties)

3. Size-dependent properties such as melting point depression (Gibbs-Thomson effect), LSPR, quantum confinement effect, and superparamagnetism emerge as nanoscale-specific phenomena

4. Surface and interface effects dominate nanoparticle stability and functionality, and appropriate surface modification can control dispersibility, biocompatibility, and targeting

5. Quantitative understanding is important, and properties can be predicted and evaluated using equations such as Scherrer equation, Brus equation, and Hall-Petch relationship

Preview of Next Chapter

In the next chapter (Chapter 3), you will learn practical analysis methods for nanomaterial data using Python. Specifically, the following themes will be covered:

• Statistical analysis of nanoparticle size distribution and histogram creation
• Crystallite size estimation from XRD data using Scherrer equation
• UV-Vis spectral analysis and plasmon resonance peak detection
• Visualization of size-band gap relationship in quantum dots
• Introduction to machine learning for nanomaterial property prediction

Let's master the basics of data-driven nanomaterials research using actual experimental data and Python code.

Exercises

Problem 1: Selection of Synthesis Methods

Select the optimal nanomaterial synthesis method for the following purposes and explain the reasons.

(a) Synthesize 100 mg of monodisperse gold nanoparticles with particle size 5 nm
(b) Form alignment-controlled nanodot patterns (pitch 100 nm) on semiconductor substrates
(c) Large-scale production (1 kg or more) of 10 nm magnetic nanoparticles (Fe₃O₄) at low cost
(d) Synthesize single-layer graphene on copper foil over large area (10 cm square)

Problem 2: XRD Analysis

In XRD measurement of gold nanoparticles, the (111) plane diffraction peak was observed at 2θ = 38.2° with FWHM = 1.2°. Estimate the crystallite size using the Scherrer equation.

Given Information:
- Cu Kα radiation: λ = 0.154 nm
- Shape factor: K = 0.9
- Bragg angle for (111) plane: θ = 19.1°
- Instrumental physical broadening: 0.1° (included in FWHM)

Calculation Steps:
1. Calculate physical broadening (β)
2. Convert β to radians
3. Substitute into Scherrer equation to calculate crystallite size

Problem 3: Size-dependent Properties

For CdSe quantum dots (particle size 4.0 nm), answer the following questions.

(a) Using only the second term (quantum confinement term) of Brus equation, calculate the band gap increase from bulk (ΔEg).
(b) Estimate the emission wavelength of this quantum dot.
(c) If the particle size is changed to 3.0 nm, how does the emission wavelength change?

Given Information:
- Bulk band gap of CdSe: Eg(∞) = 1.74 eV
- Electron effective mass: me = 0.13 m₀
- Hole effective mass: mh = 0.45 m₀
- Planck constant: ℏ = 1.055 × 10⁻³⁴ J·s
- Electron mass: m₀ = 9.109 × 10⁻³¹ kg
- Elementary charge: e = 1.602 × 10⁻¹⁹ C

References

1. Cao, G. & Wang, Y. (2011). Nanostructures and Nanomaterials: Synthesis, Properties, and Applications (2nd ed.). World Scientific. DOI: 10.1142/7885

2. Buffat, P. & Borel, J.-P. (1976). Size effect on the melting temperature of gold particles. Physical Review A, 13(6), 2287-2298. DOI: 10.1103/PhysRevA.13.2287

3. 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

4. Link, S. & El-Sayed, M. A. (1999). Size and Temperature Dependence of the Plasmon Absorption of Colloidal Gold Nanoparticles. The Journal of Physical Chemistry B, 103(21), 4212-4217. DOI: 10.1021/jp984796o

5. Gupta, A. K. & Gupta, M. (2005). Synthesis and surface engineering of iron oxide nanoparticles for biomedical applications. Biomaterials, 26(18), 3995-4021. DOI: 10.1016/j.biomaterials.2004.10.012

6. Ferrari, A. C. & Basko, D. M. (2013). Raman spectroscopy as a versatile tool for studying the properties of graphene. Nature Nanotechnology, 8(4), 235-246. DOI: 10.1038/nnano.2013.46

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