# Nanoparticle A **nanoparticle** is a discrete piece of matter whose three external dimensions all lie in the nanoscale, conventionally between about 1 and 100 nm.[^iso-1][^iso-2] Nothing inside it is new: a 5 nm grain of [[Gold|gold]] has the same face-centred cubic [[Crystal_structure|crystal structure]] and [[Electron_configuration|electron configuration]] as a gold ingot. What changes is the bookkeeping. Shrinking a sphere divides its area by the square of the scale factor and its volume by the cube, so the fraction of atoms at the surface, where bonds are unsatisfied, rises without limit. By 3 nm roughly half the atoms of a gold particle are surface atoms, and properties textbooks list as constants of the material — melting temperature, colour, catalytic activity, magnetic ordering — begin to depend on diameter. In the microsim below the reader sets one control, the particle diameter `D`, from 1 to 100 nm on a logarithmic slider, and a finite cluster is cut from the same lattice used on the [[Crystal_structure]] page. Surface atoms are coloured and counted against the shell approximation `f_surface ≈ 1 − (1 − 2·δ/D)³`, where `δ` is one atomic layer, and the [[Gibbs_free_energy|Gibbs]]–Thomson melting line `T_m(D) = T_m·(1 − 4·γ_sl/(ρ_s·ΔH_f·D))` is read out alongside it. On the gold preset the bulk melting point of 1337 K falls to about 1000 K at 3 nm. On the [[Materials_science]] flagship this page serves Part II, Fundamentals › Structure, in the section *Nanostructure*, where [[Microstructure|microstructure]] becomes fine enough that the surface, not the interior, sets the behaviour. ## Definitions The bounding numbers are conventions rather than physics. ISO/TS 80004-1 fixes the nanoscale as the length range from approximately 1 nm to 100 nm, and ISO/TS 80004-2 defines a *nano-object* as a discrete piece of material with one, two or three external dimensions in that range: a nanoparticle has all three, a nanofibre two and a nanoplate one.[^iso-1][^iso-2] IUPAC's 2012 recommendations are looser, admitting a particle of any shape with dimensions between 1 × 10⁻⁹ and 1 × 10⁻⁷ m.[^iupac2012] The word is stretched in both directions: it is used for a 2 nm gold cluster of a few hundred atoms, closer to a large molecule than to a solid, and for a 200 nm pigment grain that is not nanoscale at all. The lower bound is the interesting one. Below roughly 1 nm a particle has a countable structure, so that adding one atom changes it, and the language of a bulk phase with a surface stops working. Neighbouring terms are nested rather than synonymous. A [[Colloid|colloid]] is defined by behaviour in a medium, not size; soil scientists draw its boundary at 2 µm.[^soils-colloids][^atomsfirst-11] A [[Nanomaterials|nanomaterial]] is any material with nanoscale structure, and a [[Nanostructure|nanostructure]] is that arrangement itself. [[Quantum_dot|Quantum dots]] and [[Carbon_nanotube|carbon nanotubes]] are nano-objects the standards classify separately. ## History Nanoparticles were made and used long before they could be seen. The colours of gold ruby [[Glass|glass]] come from metal particles a few tens of nanometres across, and the first scientific account of them is Michael Faraday's 1857 Bakerian Lecture, in which he reduced gold chloride with phosphorus to obtain "beautiful ruby fluids", recognised the colour as belonging to finely divided gold rather than a dissolved compound, and saw the tint change when the particles aggregated.[^faraday1857] Gustav Mie supplied the theory in 1908 by solving [[Maxwell's_equations|Maxwell's equations]] exactly for scattering by a sphere, which explains why one metal gives red, purple or blue suspensions according to particle size.[^mie1908] The chemistry of making particles of a controlled size came later. Victor LaMer and Robert Dinegar set out in 1950 the burst-nucleation picture that still organises the subject: raise a solute above the [[Supersaturation|supersaturation]] threshold, let [[Nucleation|nucleation]] happen in one short burst, then let the nuclei grow while the concentration stays too low for new ones to form.[^lamer1950] John Turkevich and colleagues applied it to [[Gold|gold]] in 1951 with citrate reduction, and their recipe is still standard.[^turkevich1951] Wilhelm Ostwald had already described, in 1900, the coarsening that undoes monodispersity.[^ostwald1900] The size dependence the microsim shows was measured in 1976, when Philippe Buffat and Jean-Pierre Borel followed gold particles down to about 2 nm by [[Electron_diffraction|electron diffraction]] and found melting temperatures hundreds of kelvin below bulk, falling roughly as `1/D`.[^buffat1976] ## Morphology and structure The sim's cluster is cut from the bulk lattice, and that is the right first picture: for most metals the interior of a nanoparticle larger than about 3 nm is an ordinary crystal, with the same [[Cubic_crystal_system|cubic]] unit cell and the coordination number of twelve that face-centred cubic packing gives.[^atomsfirst-10-6] What differs is the boundary. A truncated sphere cut from a lattice has a ragged surface of steps, edges and corners; a real particle relaxes toward a faceted shape that minimises total surface energy, so slowly grown gold and [[Silver|silver]] particles appear as truncated octahedra bounded by close-packed planes. Below about 5 nm the crystal itself becomes negotiable. Multiply twinned icosahedral and decahedral particles, which have no single lattice orientation and cannot be extended to a bulk crystal, compete because they expose more close-packed surface per atom. Shape is also engineered: rods, plates, cubes and hollow shells come from letting a capping agent bind one crystal face and slow its growth. Many particles are not one material. Core–shell particles carry a second phase grown over the first — a [[Semiconductor|semiconductor]] core inside a wider-[[Band_gap|band-gap]] shell, a magnetic core inside an inert oxide — the shell protecting the core and supplying the chemistry the surface needs. ### Variations The sim treats the particle as one sphere of one material because that is what its two equations assume. Real preparations have a distribution of sizes, and since both readouts vary as `1/D`, a spread of ±20 % in diameter spreads every size-dependent property with it. A "3 nm" sample is a claim about a mean. ## Nucleation and growth Making a nanoparticle is a race between making new particles and growing existing ones, and the size distribution is the outcome. [[Classical_nucleation_theory|Classical nucleation theory]] writes the free-energy cost of a spherical nucleus of radius `r` as a volume term that gains against a surface term that costs, `ΔG = −(4/3)·π·r³·Δg_v + 4·π·r²·γ`, which peaks at the critical radius `r* = 2·γ/Δg_v`.[^atomsfirst-11] Nuclei smaller than `r*` redissolve; those that pass it grow. Because `Δg_v` increases with [[Supersaturation|supersaturation]], a high supersaturation makes `r*` small and nucleation easy. LaMer's separation of the two stages follows from this. If solute is generated fast enough to overshoot the nucleation threshold, a burst of nuclei appears and consumes the excess so quickly that the concentration falls back below it; nucleation stops, and the surviving nuclei grow together for the rest of the reaction, which is what makes them nearly the same size.[^lamer1950] ### Ostwald ripening The curvature that sets `r*` also makes a finished suspension unstable. Solubility rises as radius falls, so a small particle is in equilibrium with a higher solute concentration than a large one; in a mixture the small dissolve and the large grow.[^ostwald1900] [[Ostwald_ripening]] is why suspensions need a capping agent or a surface charge to survive storage, and why a [[Catalysis|catalyst]] of small particles coarsens in service and loses activity. ### Two-step mechanism – autocatalysis model Where the classical picture fails, the kinetics are often better described by the two-step mechanism of Mark Watzky and Richard Finke: slow continuous nucleation `A → B` alongside fast autocatalytic surface growth `A + B → 2B`, in which existing particle surface converts the remaining precursor.[^watzky1997] It produces the sigmoidal conversion curves of transition-metal nanocluster syntheses, which burst nucleation alone cannot reproduce. ## Properties Every property that changes with size does so for one of two reasons: a growing share of the atoms are at the surface, or the particle has become comparable to some physical length — an electron's wavelength, a domain wall, the wavelength of light. The microsim's two readouts are the clearest cases of the first kind. ### Large surface-area-to-volume ratio For a sphere of diameter `D` and density `ρ` the specific surface area is `S = 6/(ρ·D)`, inversely proportional to diameter. Gold at 19.3 g/cm³ gives 3.1 m² per gram at `D` = 100 nm, 31 m²/g at 10 nm and 104 m²/g at 3 nm. The same geometry, applied to soil particles, is why the clay fraction of a soil carries almost all of its reactive surface.[^soils-colloids] The sim counts atoms rather than area. Treating the outermost atomic layer of thickness `δ` as the surface, the surface fraction of a sphere is `f_surface ≈ 1 − (1 − 2·δ/D)³`. Taking `δ` = 0.29 nm, one nearest-neighbour spacing in gold, gives 1.7 % of atoms at the surface at `D` = 100 nm, 16 % at 10 nm, 31 % at 5 nm, 48 % at 3 nm and 64 % at 2 nm. A 10 nm gold sphere holds about 31,000 atoms with roughly 5,000 on the surface; a 3 nm sphere holds about 830 atoms with roughly 400 on it. The shell formula is a geometric idealisation — ILLUSTRATIVE below about 2 nm, where "surface" and "interior" stop being separable and the count depends on which facets the cluster exposes. ### Melting point depression A small particle melts below the bulk melting temperature because the surface it carries is expensive, and the smaller the particle the larger that cost is relative to the [[Enthalpy_of_fusion|enthalpy of fusion]] it must pay to melt. The homogeneous-melting form of the Gibbs–Thomson relation is `T_m(D) = T_m·(1 − 4·γ_sl/(ρ_s·ΔH_f·D))`, a straight line in `1/D` whose slope is fixed by one characteristic length, `d₀ = 4·γ_sl/(ρ_s·ΔH_f)`. The sim's gold preset takes `T_m` = 1337 K and reaches about 1000 K at `D` = 3 nm, which implies `d₀` ≈ 0.76 nm, a little over two atomic diameters.[^presets-cn] Reading the same line elsewhere gives 1327 K at 100 nm — a 10 K depression, undetectable in practice — then 1236 K at 10 nm, 1135 K at 5 nm and 832 K at 2 nm. The curve is flat across most of the slider and collapses in its last decade, which is why `D` is a logarithmic control. Buffat and Borel's measurements follow this shape down to a few nanometres, below which the transition broadens and a single melting temperature stops being well defined.[^buffat1976] ### Quantum mechanics effects The second kind of size effect needs no surface. When a particle becomes smaller than the natural extent of an electron–hole pair, the carriers are confined, their allowed energies spread apart, and the optical [[Band_gap|band gap]] widens as the particle shrinks. This makes a [[Quantum_dot|quantum dot]] of one composition emit across the visible spectrum by diameter alone — a different mechanism from the [[Absorbance|absorption]] resonance of a metal particle, which Mie's theory handles classically.[^mie1908] ### Ferromagnetic and ferroelectric effects Ordering that depends on cooperation between many unit cells also weakens with size. Below a critical diameter a [[Ferromagnetism|ferromagnetic]] particle can no longer support a domain wall and becomes a single domain; smaller still, thermal energy flips its whole moment faster than a measurement can follow. [[Ferroelectricity|Ferroelectric]] order is suppressed in the same way, and the [[Curie_temperature|Curie temperature]] falls with particle size. ## Production Routes divide into breaking things down and building them up. Mechanical milling, grinding a powder with hard media, is the crudest top-down method and the one that scales; it is limited by contamination from the media and by a floor on the size it reaches. [[Selective_laser_melting|Laser]] ablation goes smaller by vaporising a target and letting the vapour condense. Bottom-up routes give better control. Inert-gas condensation evaporates a metal into a low-pressure gas, where collisions cool the vapour and particles nucleate and grow before collection on a cold surface; residence time sets the size. Pyrolysis of a precursor in a flame produces oxide particles by the tonne, and is how commercial fumed [[Silicon_dioxide|silica]] and [[Ceramic|ceramic]] powders are made. Wet-chemical synthesis — the Turkevich citrate route and its descendants — reduces a dissolved salt in the presence of a capping agent, and gives the finest control over size and shape because the agent can be chosen to bind particular crystal faces.[^turkevich1951] A bare particle is rarely the product. Functionalisation attaches molecules to the surface: thiols on gold, silanes on oxides, citrate for an electrostatic charge. The coating stops aggregation and [[Ostwald_ripening|ripening]], and supplies the chemistry the application needs. ## Characterization Because size is the variable that matters, measuring it is the central problem, and no one method covers the range. Electron microscopy images individual particles and gives shape as well as size, but counts only what was on the grid. [[X-ray_crystallography|X-ray]] line broadening gives a volume-weighted mean size for the crystalline domains through the Scherrer relation of 1918: the width of a [[Powder_diffraction|powder diffraction]] peak varies inversely with the size of the coherently diffracting region.[^scherrer1918] Light scattering in suspension returns a hydrodynamic diameter including coating and adsorbed solvent, so it reads larger than the electron-microscope core. Gas adsorption measures specific surface area directly, and comparing it against `S = 6/(ρ·D)` tests whether the particles are separate: a measured area well below the value implied by the imaged diameter means they have [[Sintering|sintered]] together. ## Health and safety The hazard argument follows the same geometry as the rest of the page. A fixed mass broken into smaller particles presents more surface, so more of it is available to react, dissolve or adsorb biological molecules: one gram of gold delivers 3 m² of surface as 100 nm spheres and 104 m² as 3 nm spheres. Small particles also deposit differently in the airway, because below about 100 nm their transport is dominated by [[Diffusion|diffusion]] rather than inertia, and they reach the deep lung. Nanoparticles are not new to the environment — combustion, volcanic activity and sea spray have always produced them, and they are a component of ambient [[Air_pollution|air pollution]]. What is new is deliberate production at scale. Toxicity depends on composition, solubility, shape and coating as much as on size, so blanket statements about "nanoparticles" as a class are not useful.[^health-cn] ## Regulation Regulation runs into the definition problem first. Chemical legislation identifies a substance by composition, which does not distinguish a nanoparticle from the bulk material, so regulators have had to add a size criterion. The European Commission's recommended definition of a nanomaterial is framed on the number-based particle size distribution, requiring a stated fraction of particles to have one or more external dimensions in the 1–100 nm range; it was revised in 2022.[^eu-rec] Because the criterion counts particles rather than mass, a material can qualify while its nanoscale fraction contributes almost nothing to its weight — and measuring the distribution well enough to decide is itself difficult. ## Applications Most uses exploit one of the two size effects. Catalysis uses the surface fraction directly: dispersing a precious metal as nanoparticles on a support puts most of an expensive element where reactant molecules reach it, which is why [[Heterogeneous_catalysis|heterogeneous catalysts]] are made this way.[^atomsfirst-11] Reinforcement disperses hard particles through a [[Polymer|polymer]] or a metal so the interfacial area transfers load and pins [[Dislocation|dislocations]], the mechanism of [[Precipitation_hardening|precipitation hardening]] at a finer scale. Optical and magnetic uses exploit the second. Quantum dots serve as size-tuned emitters; metal particles give pigments whose tint is set by diameter, as in Faraday's ruby fluids; oxide particles a few tens of nanometres across absorb ultraviolet while staying transparent to visible light, which puts them in sunscreens. In every case the specification is a diameter — the argument for making diameter the sim's only control. ## See also - [[Nanostructure]] - [[Gold]] — the element variant of this sim, the ruby fluids of Faraday's 1857 lecture - [[Nanomaterials]] - [[Colloid]] - [[Nanotechnology]] - [[Ostwald_ripening]] - [[Quantum_dot]] - [[Surface_science]] ## References [^iso-1]: International Organization for Standardization. *ISO/TS 80004-1, Nanotechnologies — Vocabulary — Part 1: Core vocabulary* (the nanoscale as the length range from approximately 1 nm to 100 nm) (edition and clause to pin). [^iso-2]: International Organization for Standardization. *ISO/TS 80004-2, Nanotechnologies — Vocabulary — Part 2: Nano-objects* (nano-object, nanoparticle, nanofibre, nanoplate) (edition and clause to pin). [^iupac2012]: Vert, M.; Doi, Y.; Hellwich, K.-H.; Hess, M.; Hodge, P.; Kubisa, P.; Rinaudo, M.; Schué, F. (2012). "Terminology for biorelated polymers and applications (IUPAC Recommendations 2012)." *Pure and Applied Chemistry* 84 (2): 377–410 (DOI to pin). [^faraday1857]: Faraday, M. (1857). "The Bakerian Lecture: Experimental Relations of Gold (and Other Metals) to Light." *Philosophical Transactions of the Royal Society of London* 147: 145–181 (DOI to pin). [^mie1908]: Mie, G. (1908). "Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen." *Annalen der Physik* 330 (3): 377–445 (DOI to pin). [^lamer1950]: LaMer, V. K.; Dinegar, R. H. (1950). "Theory, Production and Mechanism of Formation of Monodispersed Hydrosols." *Journal of the American Chemical Society* 72 (11): 4847–4854 (DOI to pin). [^turkevich1951]: Turkevich, J.; Stevenson, P. C.; Hillier, J. (1951). "A study of the nucleation and growth processes in the synthesis of colloidal gold." *Discussions of the Faraday Society* 11: 55–75 (DOI to pin). [^ostwald1900]: Ostwald, W. (1900). "Über die vermeintliche Isomerie des roten und gelben Quecksilberoxyds und die Oberflächenspannung fester Körper." *Zeitschrift für physikalische Chemie* 34: 495–503 (pages to pin). [^buffat1976]: Buffat, Ph.; Borel, J.-P. (1976). "Size effect on the melting temperature of gold particles." *Physical Review A* 13 (6): 2287–2298. https://doi.org/10.1103/PhysRevA.13.2287 [^watzky1997]: Watzky, M. A.; Finke, R. G. (1997). "Transition Metal Nanocluster Formation Kinetic and Mechanistic Studies. A New Mechanism When Hydrogen Is the Reductant: Slow, Continuous Nucleation and Fast Autocatalytic Surface Growth." *Journal of the American Chemical Society* 119 (43): 10382–10400 (DOI to pin). [^scherrer1918]: Scherrer, P. (1918). "Bestimmung der Größe und der inneren Struktur von Kolloidteilchen mittels Röntgenstrahlen." *Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse* 1918: 98–100 (pages to pin). [^atomsfirst-10-6]: Flowers, P.; Neth, E.; Robinson, W. et al. *Chemistry: Atoms First*, 2nd ed. (2019), OpenStax, Ch. 10 Liquids and Solids, §10.6 Lattice Structures in Crystalline Solids (unit cells, face-centred cubic packing, coordination number 12), pp. 475–544 (page to pin). https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^atomsfirst-11]: Flowers, Neth & Robinson (2019), Ch. 11 Solutions and Colloids, pp. 545–596 (dispersions, colloids, surfactants and the surface area of divided matter; catalysis on dispersed solids) (page to pin). [^soils-colloids]: Canadian Society of Soil Science. *Digging into Canadian Soils: An Introduction to Soil Science* (2021), Ch. 5, p. 175–176 (soil colloids are particles below 2 µm; Table 5.1 gives 22.6 cm²/g of specific surface for the sand fraction of a clay loam, which matches `S = 6/(ρ·d)`; the printed silt and clay rows of that table do not, and are not used here). https://open.umn.edu/opentextbooks/textbooks/digging-into-canadian-soils-an-introduction-to-soil-science [^eu-rec]: European Commission. Commission Recommendation on the definition of nanomaterial, 2011/696/EU (18 October 2011), revised by the Commission Recommendation of 10 June 2022 (2022/C 229/01) (Official Journal citation and clause to pin). [^presets-cn]: *Citation needed.* The gold preset (bulk `T_m` = 1337 K, about 1000 K at `D` = 3 nm) is supplied by the M8 sim row; the characteristic length `d₀` ≈ 0.76 nm quoted here is derived from those two preset numbers, not measured. A tabulated solid–liquid interfacial energy `γ_sl` and enthalpy of fusion for gold, with their source, would let `d₀` be computed independently and checked against Buffat and Borel's data.[^buffat1976] [^health-cn]: *Citation needed.* The statements that deposition below about 100 nm is diffusion-dominated, and that toxicity tracks composition, solubility, shape and coating rather than size alone, are standard in the inhalation-toxicology literature but are not carried by any Portal Book; a review or an occupational-hygiene guidance document should be pinned here before this section is promoted beyond draft. ## Further reading - Flowers, P.; Neth, E.; Robinson, W. et al. *Chemistry: Atoms First*, 2nd ed. (2019), OpenStax — Ch. 10 Liquids and Solids (§10.6, the lattice the sim's cluster is cut from) and Ch. 11 Solutions and Colloids. - Canadian Society of Soil Science. *Digging into Canadian Soils: An Introduction to Soil Science* (2021) — Ch. 5, for the specific-surface argument applied to natural colloids. - Buffat, Ph.; Borel, J.-P. (1976), *Physical Review A* 13: 2287 — the measurement behind the melting-point readout. ## External links - Open Textbook Library entries for the two Portal Books cited above are linked in the footnotes. - The Wikipedia pair's *External links* section is the place to look for current nanoparticle databases and inventories; none is reproduced here until its URL has been checked. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Nanoparticle.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Nanoparticle* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Nanoparticle.html" data-title="Nanoparticle"></div> *Built from `MICROSIM_GUIDE/specs/sims/Nanoparticle.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Nanoparticle) : [Wikitube](https://en.wikitube.io/wiki/Nanoparticle) · pinned revision [1373365903](https://en.wikipedia.org/w/index.php?oldid=1373365903) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Materials_science]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Materials_science row M8 · sim pending (matter/Nanoparticle).*