= Nanomaterial
A <nanomaterial> has constituent particles or structural features on the <nanoscale>, conventionally around $1$–$100\,\mathrm{nm}$. A collection of <nanoparticles> is one example; a bulk piece containing <nanoscale> internal structure can also be relevant. The scientific interest lies in how dimensions and interfaces affect behavior, rather than in treating $100\,\mathrm{nm}$ as a universal physical threshold.<About Nanotechnology by the National Nanotechnology Coordination Office>[definition and approximately 1–100 nm scale]{ref}
A simple geometric calculation explains one important effect. Suppose a fixed <volume> $V$ of solid is divided into identical spherical <nanoparticles> of radius $r$. Ignoring contact between particles, their number $N$ and total <surface area> $A$ are
$$
N=\frac{3V}{4\pi r^3},\qquad A=N4\pi r^2=\frac{3V}{r}.
$$
Reducing $r$ from $50\,\mathrm{nm}$ to $5\,\mathrm{nm}$ makes $1000$ times as many particles and ten times as much <surface area>, at the same total <volume>. More material is consequently close to an interface. Surface reactions and interactions with the surrounding medium can become much more influential; this geometric result alone does not guarantee a faster useful reaction or a more stable material.<What Is So Special about Nano? by the National Nanotechnology Coordination Office>[surface-area-to-volume discussion]{ref}
Size can also affect electronic behavior through <quantum confinement>. Which effect matters depends on the material, shape and environment. A useful comparison therefore holds composition fixed, measures particle dimensions with <electron microscopy>, and compares a chosen property across a size series. Such a comparison separates a size-dependent change from a change caused merely by using a different substance.<What Is So Special about Nano? by the National Nanotechnology Coordination Office>[size-dependent and quantum effects]{ref}
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