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:

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

Worked example: Armchair tube

Given: (6,6)

Find: Diameter and type.

Answer: 0.81 nm, metallic

Worked example: Zigzag tube

Given: (10,0)

Find: Type and gap.

Answer: Semiconducting, ~1.0 eV

Worked example: Composite stiffness

Given: 1 vol% graphene (1000 GPa) in epoxy (3 GPa), ideal

Find: Upper-bound E.

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 mg

Nanotubes 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

Applications

Key takeaways

Going further