Perhaps the main contributor to the properties of nanomaterials is due to the large reduction of scale. For a cubic structure the surface area is 6*d*d, while the volume is d*d*d. Thus, the ratio of surface to volume will be 6/d. This implies that with reduction in scale of d the surface dependent features will begin to outweigh the volume/bulk dependent characteristics. Surface dependent features generally imply some form of energy/material exchange with the environment. For example: these may include photonic interactions such as surface plasmon resonance, explaining why nanoparticles of different sizes and shapes often exhibit different colors in solution.
I agree with all the aspects treated before, but it is necessary to mention that the increase size to volume ratio also leads to a higher reactivity due to a higher number of active sites, in the case of catalysts for example these is a very important factor.
As far as metal nanoparticles and catalysis are concerned, shape can be even more important than size. This is particularly visible for small particles. Specific shape creates unique type of metal centers on the corners and edges of the particle. For example, cubic particles are much more active than spherical particles of the same size. This is a new type of chemical reactivity that is available only in nano-and subnano-regions. For catalysis it is often crucial, see for instance our short review: http://dx.doi.org/10.1021/om201120n
Higher surface ratio, more interfaces and active sites are most common factors. Another factor I want to complement is the orientation. When the nanomaterials are oriented aligned such as ZnO or TiO2 nanorod arrays, they will show enhanced properties like field emission or photocatalyst. And the oriented align of nano building blocks in hierachical biomineral structures such as nacre and tooth enamel will trap cracks and enhance the toughness. Besides, the metal nanoparticles sometimes has surface plasmonic polarization (SPP), and the arrays of these particles will show special optical and electronic properties.
High surface area, shapes and orientation are main factors. The availability of surface electrons and orientation for reactions in high surface area mainly differentiate the nano materials behavior. Same as the case in absorption and transmittance of light which varies from size to size and shape to shape.
both the size and surface "ACTIVE" site are two major reasons for the catalytic behavior. and they follow in different research area. maybe for the nano synthesizers, the size, morphology is more important. and the surface chemists and physician, the active sites. anyway, for a catalyst, it ultimately related to the adsorption/desorption of reactants and products.
due to the very high area/mass or area to volume ratio of nanoparticle, the fraction of atoms on the surface are very high. This leads to increase the reactivity of nanoparticles and their interactions with other nanoparticles or with surroundings.