Step 1: Understanding the Concept:
The term "nano-materials" refers to materials that are structured at the nanoscale. The prefix "nano-" implies a scale of nanometers (\(1 \text{ nm} = 10^{-9} \text{ m}\)). The definition is based on the size at which the material's properties begin to differ significantly from those of its bulk counterpart, often due to quantum effects or a high surface-area-to-volume ratio.
Step 2: Detailed Explanation:
By international convention (e.g., ISO/TS 80004), a nanomaterial is defined as a material with any external dimension in the nanoscale, or having an internal structure or surface structure in the nanoscale. The nanoscale is defined as the length range from approximately 1 to 100 nanometers.
Therefore, the characteristic length that defines a material as a "nano-material" is typically considered to be less than 100 nm in at least one dimension. The other options represent larger length scales that are generally considered to be in the micro- or sub-micron range, where bulk properties usually dominate.
Step 3: Final Answer:
The standard and widely accepted definition for the characteristic length of nano-materials is less than 100 nm.