Nanomaterials: Carbon, 2D Materials, Nanoparticles & Composites
The building blocks of nanotechnology. Learn carbon nanomaterials (fullerenes, carbon nanotubes with chirality (n,m), graphene and its extraordinary properties), 2D materials beyond graphene (h-BN, MoS₂, MXenes), metal and metal-oxide nanoparticles, quantum dots, nanowires, porous materials (MOFs, zeolites, mesoporous silica), polymer nanocomposites, dendrimers and liposomes — with Python for CNT diameter, chirality and metallic/semiconducting character, and graphene's areal density.
Nanomaterials come in a remarkable variety: single-atom-thick sheets, hollow tubes, cages of 60 carbon atoms, crystalline frameworks with more internal surface than a football field per gram.
Their structure at the atomic level determines electrical, mechanical, optical and chemical behaviour — for example, how a graphene sheet is rolled decides whether a nanotube is a metal or a semiconductor.
An analogy
Graphene is chicken wire made of carbon atoms. Roll the chicken wire into a tube and you get a nanotube; how you roll it (straight or on a slant) decides whether electricity flows like in a metal or like in a semiconductor.
Carbon nanomaterials
Carbon's nano family:
- Fullerenes (C₆₀ 'buckyballs') — 0D cages
- Carbon nanotubes — single- and multi-walled; tensile strength ~50–100 GPa, excellent conductors
- Graphene — one atom thick, ~1 TPa modulus, mobility up to ~10⁵ cm²/V·s, 97.7% optical transparency
- Carbon dots, nanodiamonds, carbon nanofibres
- Graphene oxide / reduced GO for scalable coatings and composites
2D materials and nanoparticles
Beyond graphene: hexagonal boron nitride (insulator), transition-metal dichalcogenides like MoS₂ (semiconductors with direct gap in monolayers), phosphorene, MXenes (conductive carbides for energy storage). Van der Waals heterostructures stack them like LEGO. Metal nanoparticles (Au, Ag, Pt, Pd) for catalysis, sensing and antimicrobials; oxides (TiO₂, ZnO, SiO₂, Fe₃O₄ magnetic particles) for photocatalysis, UV blocking, imaging and separation.
Porous and soft nanomaterials
Metal–organic frameworks (MOFs) and covalent organic frameworks with surface areas > 5000 m²/g for gas storage and carbon capture; zeolites and mesoporous silica for catalysis and drug loading. Soft nanomaterials: liposomes and lipid nanoparticles, polymeric micelles, dendrimers, DNA origami — central to nanomedicine.
Nanocomposites and properties engineering
Adding a few percent of nanofillers (CNTs, graphene, nanoclay, nanosilica) can raise stiffness, strength, conductivity, barrier or flame resistance of polymers — if the fillers are well dispersed and bonded (surface functionalisation). Percolation thresholds for conductivity can be < 0.1 wt% for CNTs. Challenges: agglomeration, cost, scalable production and consistent quality.
Formulas
- CNT diameter:
d = a·√(n² + nm + m²)/π - Chiral angle:
θ = arctan(√3·m/(2n + m)) - Metallic rule:
(n − m) mod 3 = 0 → metallic; otherwise semiconducting - Semiconducting CNT gap:
E_g ≈ 0.8 eV·nm/d - Rule of mixtures (composite):
E_c = V_f·E_f + (1 − V_f)·E_m
Worked example: Armchair tube
Given: (6,6)
Find: Diameter and type.
- 0.246√108/π
- (6 − 6) mod 3 = 0
Answer: 0.81 nm, metallic
Worked example: Zigzag tube
Given: (10,0)
Find: Type and gap.
- 10 mod 3 = 1 → semiconducting
- d = 0.78 nm → 0.8/0.78
Answer: Semiconducting, ~1.0 eV
Worked example: Composite stiffness
Given: 1 vol% graphene (1000 GPa) in epoxy (3 GPa), ideal
Find: Upper-bound E.
- 0.01 × 1000 + 0.99 × 3
Answer: 13 GPa (real values much lower due to dispersion)
Carbon nanotube chirality and graphene density
import math
# Carbon nanotube (n, m): diameter, chiral angle and metallic/semiconducting rule
a = 0.246 # graphene lattice constant (nm)
for n, m in ((10, 10), (17, 0), (18, 0), (13, 6)):
d = a * math.sqrt(n * n + n * m + m * m) / math.pi
theta = math.degrees(math.atan(math.sqrt(3) * m / (2 * n + m)))
kind = "metallic" if (n - m) % 3 == 0 else "semiconducting"
extra = f", band gap ~ {0.8/d:.2f} eV" if kind == "semiconducting" else ""
print(f"({n},{m}): d = {d:.2f} nm, chiral angle {theta:.1f} deg, {kind}{extra}")
# Graphene: carbon atoms per cm2 and mass of 1 m2
atoms_per_nm2 = 2 / (math.sqrt(3) / 2 * a**2)
print(f"graphene: {atoms_per_nm2:.1f} atoms/nm2, 1 m2 weighs {atoms_per_nm2*1e18*12*1.6605e-27*1e6:.2f} mg")
# (10,10): d = 1.36 nm, chiral angle 30.0 deg, metallic
# (17,0): d = 1.33 nm, chiral angle 0.0 deg, semiconducting, band gap ~ 0.60 eV
# (18,0): d = 1.41 nm, chiral angle 0.0 deg, metallic
# (13,6): d = 1.32 nm, chiral angle 18.0 deg, semiconducting, band gap ~ 0.61 eV
# graphene: 38.2 atoms/nm2, 1 m2 weighs 0.76 mgNanotubes of almost identical diameter can be metals or semiconductors depending on chirality — a single index change from (17,0) to (18,0) flips the behaviour. Separating them by type is a key manufacturing challenge for CNT electronics. A square metre of graphene weighs under a milligram yet could support a cat, according to a famous estimate.
Common mistakes
- Wrong: Assuming all CNTs conduct like metals. — Right: Two-thirds of random SWCNTs are semiconducting.
- Wrong: Expecting bulk composites to match nanofiller properties. — Right: Dispersion and interfaces limit performance.
- Wrong: Calling multilayer flakes 'graphene'. — Right: Specify layer number; properties change quickly.
Applications
- Batteries: CNT conductive additives in Li-ion electrodes.
- Composites: Graphene-enhanced sports goods and coatings.
- Carbon capture: MOFs for CO₂ adsorption.
- Transparent electrodes: Silver nanowires and graphene.
Key takeaways
- Carbon: fullerenes, CNTs, graphene.
- (n − m) mod 3 = 0 → metallic CNT.
- 2D materials, nanoparticles, MOFs, soft nanocarriers.
- Nanocomposites need dispersion and interfaces.
Going further
- Van der Waals heterostructures: Twisted bilayer graphene and moiré physics.
- CNT sorting: Density-gradient and polymer wrapping separation.
- Reticular chemistry: Designing MOFs for targeted adsorption.