The properties of matter can change with scale. The size-dependent properties refers to properties affected by the dramatic increase in the surface-to-volume ratio that occurs as the size of the material approaches the nanoscale such as time between changes of state (solid to liquid or liquid to gas), rate of reaction, function as a catalyst, etc. The time to freeze or melt is decreased because more surface area is exposed to heat energy allowing a faster transition to occur.
An easy way to visualize the increase in surface area is to imagine a block of something, say a cube of sugar, and counting the 6 exposed surfaces. Cut that block in half and you now have twice the number of surfaces exposed for half the volume, 6 surfaces to half the volume or 12 surfaces spread over the original volume. Cut each piece in half again and you have twice again the number of surfaces with a quarter of the volume, 24 surfaces over the original volume. As this continues you can quickly see the dramatic increase in the ratio of surface area to volume.
Did you know that the interesting changes in surface dominant properties at the nanoscale are being explored for novel applications as catalysts in the chemical and energy production industries? You can learn more about nanotechnology by using the experiments and trying the interactive fact sheet available at wonderville.ca.