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A nanoparticle formed from several crystallographic domains joined by twin boundaries. Low-energy external facets can compensate the internal boundary and elastic-strain cost; fivefold motifs cannot extend as an unstrained periodic bulk crystal.

A processable dispersion of nanoparticles with a solvent and any stabilizers or binders. For a metallic printed conductor, drying, ligand removal and consolidation must turn the deposited particles into a connected low-resistance structure without damaging the substrate.

Brownian motion is the fluctuating motion of a suspended particle produced by thermal molecular collisions. Using the standard Brownian displacement conventions, in a uniform fluid without external drift, mean displacement is zero but mean-square displacement grows with time. For overdamped diffusion, $⟨\Delta x^2⟩=2Dt$ in one coordinate and $⟨|\Delta \mathbf{r}{|}^2⟩=6Dt$ in three dimensions, with $D=k_{B}T/\zeta$ and Stokes friction $\zeta =6\pi \eta a$ for a no-slip sphere.

Brownian transport brings nanoparticles into encounters and allows them to explore configurations during self-assembly. Reversible interactions permit rearrangement toward low-free-energy structures; interactions that are too strong can instead trap disordered aggregates. Thermal fluctuations also oppose localization in shallow traps. The symbol $\zeta$ avoids confusing friction with an unrelated chemical potential.

Interpreting the nominal size as diameter $d=10\mathrm{nm}$, fluid viscous dominance requireswith ${\rho }_f$ in $\mathrm{kg}{\mathrm{m}}^{-3}$. The liquid density is not supplied, so the conventional fluid-Reynolds crossover is not numerically fixed. As an explicitly additional illustrative assumption, ${\rho }_f=870\mathrm{kg}{\mathrm{m}}^{-3}$ gives $\mathrm{Re}=1$ near $69\mathrm{m}{\mathrm{s}}^{-1}$; ordinary much slower nanoparticle motion is well within the viscous regime.

If instead the supplied gold density is inserted into the dimensionless ratio ${\rho }_{p}Ud/\eta$, that ratio reaches one at $3.0\mathrm{m}{\mathrm{s}}^{-1}$. It is not the fluid Reynolds number. Including the spherical Stokes prefactor, the particle relaxation criterion ${\tau }_{p}U/d=1$ occurs at $54\mathrm{m}{\mathrm{s}}^{-1}$. These quantify different inertia comparisons. The wording's speed direction is reversed: viscous dominance is obtained by making speed sufficiently small. If 10 nm denotes radius, the length-based thresholds halve.

A tightly focused laser produces a strong intensity gradient. A small polarizable particle experiences a gradient force toward increasing intensity when the real polarizability has the appropriate positive sign; radiation pressure from scattering and absorption pushes predominantly along the beam. A high-numerical-aperture objective creates lateral confinement and a sufficiently strong opposing axial gradient for a three-dimensional optical trap. Equilibrium is generally shifted from the intensity maximum by radiation pressure.

For a Rayleigh sphere, $\alpha =4\pi {ϵ}_m{a}^3({ϵ}_p-{ϵ}_m)/({ϵ}_p+2{ϵ}_m)$ in an absolute-permittivity convention, and ${\mathbf{F}}_{\mathrm{grad}}\simeq \frac{1}{4}\mathrm{Re}\alpha \nabla |E{|}^2$ for peak complex field amplitude. Near a stable point, $F_x\simeq -k_{x}x$; the trap depth must exceed thermal fluctuations sufficiently to retain the particle. Viscous drag opposes motion, Brownian forcing produces fluctuations, and gravity/buoyancy are normally small at this scale.

For absorbing gold, use its complex wavelength-dependent permittivity: scattering, absorption and heating can frustrate trapping. The existence of an ideal dielectric gradient-force trap does not guarantee stable trapping of every metal nanoparticle at every wavelength or power.^[ref]

Use floating-catalyst chemical vapor deposition to form a continuous suspended network. Introduce a carbon feed together with a volatile catalyst precursor into a hot gas-flow reactor. Catalyst nanoparticles nucleate in the gas stream; tubes grow while moving through the reaction zone and assemble into an interconnected aerogel.

Withdraw that network continuously, collect it on a rotating spindle, and consolidate or twist it into a fiber. Long tubes, suitable number density and adequate overlap allow the network to transmit the drawing force without breaking into isolated clumps. The take-up rate must be matched to network production; collection is not simply a geometrically scaled version of a substrate carpet.

The catalyst and tubes form in the flowing gas, and the product is drawn directly from a growing aerogel. This differs both from a supported carpet and from later spinning of a separately prepared nanotube dispersion. The original demonstration combined CVD synthesis with continuous product withdrawal from the furnace.^[ref]

Use a shaped nickel particle or nanowire as both sacrificial template and reducing agent. gold grows where nickel is consumed, allowing gold-coated particles, porous shells and, with suitable removal of the remaining nickel, hollow gold nanostructures. The original template controls the overall shape; the balance of dissolution, deposition and diffusion controls wall thickness and porosity.

A hollow product is not guaranteed simply by writing the reaction: deposition may seal a solid nickel core, whereas defects can maintain access to the interior and permit further replacement. Controlled composition and transport can give a progression from core–shell to porous or hollow structures. This is useful for high-surface-area electrodes, catalytic surfaces and plasmonic structures, while avoiding an electrical lead to every individual nanoparticle.