A scaling law for properties of nano-structured materials

In this brief communication, we identify intrinsic length scales of several physical properties at the nano-scale and show that, for nano-structures whose characteristic sizes are much larger than these scales, the properties obey a simple scaling law. The underlying cause of the size-dependence of these properties at the nano-scale is the competition between surface and bulk energies. This law provides a yardstick for checking the accuracy of experimentally measured or numerically computed properties of nano-structured materials over a broad size range and can thus help replace repeated and exhaustive testing by one or a few tests.