Chapter 2: Fundamental Principles of Nanomaterials

We will organize the top-down/bottom-up synthesis methods and "what to observe" in key characterization techniques. Experience basic analysis of XRD and SEM images using Python.

💡 Supplement: XRD is the "fingerprint of crystals," SEM is the "photograph of surfaces." Fixing preprocessing and threshold settings improves reproducibility.

Synthesis Methods and Characterization Techniques

Learning Objectives

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

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

2.1 Synthesis Methods for Nanomaterials

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

Bottom-Up vs Top-Down

Major Bottom-Up Synthesis Methods

Chemical Vapor Deposition (CVD)

Principle

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

1. Gas-phase transport: Precursor gases are 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 the catalyst surface or under high-temperature conditions
4. Nucleation and growth: Nanostructures form and grow
5. By-product removal: Gases generated 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 monolayer graphene over large areas. Methane gas is decomposed at high temperatures around 1000°C, and monolayer graphene grows through the catalytic action of the copper surface.

Advantages and Disadvantages

✅ Advantages: - High crystallinity and high purity materials can be obtained - Continuous process enables mass production - Structure control possible through growth conditions (temperature, gas flow rate, pressure) - Direct growth on substrate eliminates complex processes

❌ Disadvantages: - High-temperature process (500-1000°C or higher) required - High equipment cost - Precursor gases may be toxic or flammable - Limited substrate materials (high-temperature resistance required)

Liquid-Phase Synthesis Methods

Liquid-phase synthesis is a method that produces nanomaterials through chemical reactions in solution, characterized by implementation at relatively low temperatures (room temperature to ~300°C).

Sol-Gel Method

This method synthesizes oxide nanoparticles and porous materials using hydrolysis and condensation reactions of metal alkoxides.

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

Application examples: SiO₂, TiO₂, ZrO₂ nanoparticles, mesoporous silica

Hydrothermal Synthesis

This method reacts aqueous solutions under high-temperature, high-pressure conditions (100-300°C, several MPa) in a sealed container (autoclave). Thermodynamically stable crystal phases are obtained, and particle size and shape control is easy.

Application examples: ZnO, TiO₂, zeolites, metal oxide nanorods

Co-precipitation

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

Fe²⁺ + 2Fe³⁺ + 8OH⁻ → Fe₃O₄ + 4H₂O

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

Reduction Synthesis of Metal Nanoparticles

This method reduces metal ions with reducing agents and synthesizes metal nanoparticles 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, producing spherical gold nanoparticles of 10-50 nm. Size can be controlled by the concentration ratio of gold salt and citrate.

Gas-Phase Synthesis Methods

Sputtering

This physical deposition method bombards a target material with high-energy ions (typically Ar⁺), depositing the ejected atoms onto a substrate. Implemented in a vacuum chamber, it is 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

This method irradiates a solid target with high-power pulsed laser, causing gas-phase growth from plasma generated by instantaneous evaporation.

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

Major Top-Down Synthesis Methods

Mechanical Milling (Ball Milling)

This method produces nanoparticles by mechanically pulverizing bulk materials through high-speed rotation of hard balls.

Process

1. Load bulk material and hard balls (zirconia, stainless steel, WC, etc.) into a container
2. Apply impact and friction energy through high-speed rotation (200-600 rpm)
3. Particle size decreases through repeated pulverization (typically several to tens of hours)

Application Examples

• 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 a wide range of materials

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

Lithography

This method forms patterns on a substrate using photomasks or beams, creating nanostructures 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 (no mask required)
• Suitable for R&D and prototyping (low throughput)

Nanoimprint Lithography (NIL)

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

Etching

Dry Etching

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

Wet Etching

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

2.2 Characterization Techniques

To accurately evaluate the properties of nanomaterials, it is essential to combine multiple analytical methods. Here, we explain major technologies in each category: morphology observation, structural analysis, compositional analysis, and optical property evaluation.

Morphology Observation Techniques

Transmission Electron Microscopy (TEM)

Principle

TEM passes an electron beam accelerated at 100-300 kV through a thin specimen (thickness <100 nm), detecting transmitted and scattered electrons to form images. Since the electron wavelength is much shorter (~2.5 pm for 200 kV accelerated electrons) than visible light (400-700 nm), atomic-level resolution can be achieved.

Measurable Parameters

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

Application Examples

1. Size and shape evaluation of gold nanoparticles - Measure 50 or more particles to evaluate size distribution with histograms - 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 interplanar 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) over the sample surface, detecting emitted secondary electrons or backscattered electrons to image surface morphology.

Differences from TEM

Application Examples

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 or absence of aggregation

Atomic Force Microscopy (AFM)

Principle

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

Measurement Modes

• Contact mode: Scan with probe in contact with sample (high resolution but risk of sample damage)
• Tapping mode: Probe resonantly vibrates with intermittent contact (suitable for soft samples)
• Non-contact mode: Detect electrostatic forces without contact (ultra-high resolution)

Features

✅ Advantages: - No vacuum required (atmospheric and liquid measurements possible) - Measurable regardless of insulator or conductor - Quantitative height information (Z-direction resolution <0.1 nm)

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

Application Examples

• Determine number of graphene layers (identify interlayer distance of 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 radiation) - $d$: lattice plane spacing - $\theta$: incident angle (Bragg angle)

Crystal Structure Identification

The diffraction pattern (2θ vs intensity) is compared with standard databases (ICDD PDF, COD) to identify crystal phases.

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)

The particle size of nanocrystals 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 structure 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 a sample is irradiated with laser light, scattered light with energy changed by molecular vibrations (Raman scattered light) is generated. By measuring this energy shift (Raman shift, unit: cm⁻¹), molecular vibration modes and crystal structures can be identified.

Evaluation of Graphene and CNT

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

Defect Density Evaluation

The larger the D/G intensity ratio ($I_D/I_G$), the higher the defect density.

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

Monolayer Graphene Identification

The number of layers can be distinguished by the shape of the 2D band: - Monolayer: 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

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

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

where $h\nu$ is the X-ray energy, $E_K$ is the kinetic energy of photoelectrons, and $\phi$ is the work function.

Surface Chemical Composition

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

Chemical State Analysis

Even for the same element, binding energy changes depending on the chemical bonding state (chemical shift), enabling identification of oxidation states and bonding forms.

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

This method measures the energy of characteristic X-rays emitted from the sample by electron beam irradiation to identify elements. Since each element has a unique X-ray energy, 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.

Application Examples

• Compositional ratio quantification of alloy nanoparticles (Au-Ag, Pt-Pd)
• Structure confirmation of core-shell nanoparticles (e.g., visualize distribution of Fe, Si, O 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 quantitative accuracy also decreases.

Optical Property Evaluation

UV-Vis Absorption Spectroscopy

Principle

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

$$ A = \varepsilon c l $$

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

Light Absorption Properties

From the absorption spectrum of nanomaterials, electronic states and optical band gaps can be evaluated.

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) - Increase in particle size → red shift - Shape change (rod, star) → multiple peaks

Band Gap Estimation (Tauc Plot)

The band gap ($E_g$) of semiconductor nanoparticles can be obtained from the absorption edge using a Tauc plot:

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

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

Plot $(αh\nu)^2$ vs $h\nu$ (for direct transition) or $(αh\nu)^{1/2}$ vs $h\nu$ (for indirect transition), extrapolate the linear portion, and 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 dot (diameter 3 nm): $E_g$ = 2.4 eV (λ ≈ 520 nm) → blue shift due to quantum confinement effect

Fluorescence Spectroscopy

Principle

The sample is irradiated with excitation light, and the wavelength and intensity of fluorescence emitted from the fluorescent substance are measured. Fluorescence at longer wavelengths than the excitation light is observed (Stokes shift).

Luminescence 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 of luminescence efficiency of fluorophores, expressed as the ratio of the number of emitted photons to the number of 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 are due to increased surface area/volume ratio, quantum size effects, surface energy contributions, etc.

Melting Point Depression

Gibbs-Thomson Effect

The melting point ($T_m(r)$) of nanoparticles decreases with decreasing particle size ($r$). 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 larger. Surface atoms have weaker bonds than internal atoms, making them thermally unstable and lowering the melting point.

Example of Gold Nanoparticles

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 have confirmed 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) of 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 becomes maximum, 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, it shifts to longer wavelengths (red shift) due to increased damping.

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

Applications

• Biosensing (detection of wavelength shift due to antibody-antigen binding)
• Photothermal therapy (PTT): near-infrared light absorption → heat generation → cancer cell destruction
• Surface-enhanced Raman scattering (SERS): 10⁶-10⁸ times signal enhancement by plasmon enhancement effect

Band Gap Changes in Semiconductor Quantum Dots

Quantum Confinement Effect

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

Brus Equation (Effective Mass Approximation Model)

The band gap ($E_g(r)$) of quantum dots 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 masses of electron and hole - $\varepsilon$: relative permittivity

Second term (positive): energy increase due to quantum confinement (main term) Third term (negative): energy decrease due to Coulomb interaction (correction term)

Size-Emission Color Relationship (CdSe Quantum Dots)

CdSe properties: - $E_g(\infty)$ = 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 example of particle size and band gap:

Applications

• Bioimaging: near-infrared emitting quantum dots (700-900 nm) with high tissue penetration
• Displays: fabrication of red, green, blue primary colors by size adjustment (QLED TV)
• Solar cells: absorption of light in a wide wavelength range with multiple sizes of 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 size ($d_c$) at which superparamagnetism emerges 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)

Example of Magnetite (Fe₃O₄)

• $K$ = 1.1 × 10⁴ J/m³
• Critical particle size 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 remanent magnetization) - Less prone to aggregation (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: guidance 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

The smaller the grain size, the higher the grain boundary density, and dislocation movement is inhibited at grain boundaries, causing material hardening.

Inverse Hall-Petch Effect (< 10 nm)

When grain size becomes 10 nm or less, grain boundary sliding becomes dominant, causing softening instead. 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 nanocomposite

2.4 Surface and Interface Effects

In nanoparticles, the surface area/volume ratio ($S/V$) increases rapidly. 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/volume ratio becomes 10 times larger.

Proportion of Surface Atoms

At a particle size of 3 nm, about 1/3 of the atoms are on the surface, and the contribution of surface energy cannot be ignored.

Surface Energy and Surface Tension

Surface Energy

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

Representative surface energy values (room temperature):

Metals have high surface energy, making nanoparticles prone to aggregation.

Surface Functionalization

Surface modification is an important technology for controlling the dispersibility, stability, and functionality of nanoparticles.

Modification with Organic Molecules

Thiol Compounds (Gold Nanoparticles)

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

Representative examples: - Alkanethiol (HS-(CH₂)ₙ-CH₃): hydrophobization - Mercaptoundecanoic acid (HS-(CH₂)₁₀-COOH): hydrophilization, 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: - Protein adsorption suppression (stealth effect) - Avoidance of recognition by immune system - Delayed renal excretion

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. Improved dispersibility - Electrostatic repulsion (introduction of charged groups: -COO⁻, -NH₃⁺) - Steric repulsion (osmotic pressure of polymer chains)

2. Prevention of aggregation - DLVO theory: electrostatic repulsion vs van der Waals attraction - Increase repulsive force through modification

3. Functionalization - Bioconjugation: antibody, DNA, peptide immobilization - Targeting: folic acid, RGD peptide - Stimuli responsiveness: pH responsiveness, temperature responsiveness

Summary

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

1. Bottom-up and top-down approaches differ in construction direction, and various methods such as CVD, liquid-phase synthesis, and lithography are selectively used according to application

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 include nanoscale-specific phenomena such as melting point depression (Gibbs-Thomson effect), LSPR, quantum confinement effect, and superparamagnetism

4. Surface and interface effects govern the stability and functionality of nanoparticles, 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 the 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 the Scherrer equation
• UV-Vis spectrum analysis and plasmon resonance peak detection
• Visualization of size-band gap relationship for quantum dots
• Introduction to nanomaterial property prediction using machine learning

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

Exercises

Problem 1: Selection of Synthesis Method

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

(a) Want to synthesize 100 mg of monodisperse gold nanoparticles with a particle size of 5 nm (b) Want to form nanodot patterns (pitch 100 nm) with controlled arrangement on a semiconductor substrate (c) Want to mass-produce (1 kg or more) 10 nm magnetic nanoparticles (Fe₃O₄) at low cost (d) Want to synthesize monolayer graphene over a large area (10 cm square) on copper foil

Problem 2: XRD Analysis

In XRD measurement of gold nanoparticles, the diffraction peak of the (111) plane 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 of (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

Answer the following questions about CdSe quantum dots (particle size 4.0 nm).

(a) Calculate the band gap increase from bulk (ΔEg) using only the second term (quantum confinement term) of Brus's equation. (b) Estimate the emission wavelength of this quantum dot. (c) How will the emission wavelength change if the particle size is changed to 3.0 nm?

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

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