Nanoscale - Surface-To-Volume Ratio



Surface atoms in nanoscale things act differently from their bulk atoms. 



Consider the ratio of surface area A to volume V of a nanostructure to determine whether surface or bulk effects prevail. 





The ratio A/V of three solids in the shapes of a sphere, a cube, and a right-square pyramid is compared in Table. 

It demonstrates that this ratio scales as 1/r, where r is a linear size measure. 

All regular, basic constructions are found to scale in the same way. 

Even for a complex structure, if a single size parameter can be identified (for example, by enclosing the structure within a sphere of radius r), the same scaling holds roughly. 


Physically, the 1/r scaling means that the ratio A/V rises as the size of a three-dimensional structure decreases. 



In the example illustrated in Figure, the dramatic impact on surface area can be observed. 




The cube A has 1 m sides and a 6 m2 surface area. 

Each cube has a surface area of 6 cm2 when split into smaller 1 cm cubes (part B), however there are 106 of them, resulting in a total surface area of 600 m2. 

If cube A (part C) were cut into 1 nm cubes, the total surface area would be 6000 km2. 

Despite the fact that the overall volume stays the same in all three instances, the collective surface area of the cubes is significantly enhanced. 



A significant increase in the area of surfaces (or interfaces) may result in completely new electrical and vibrational states for each surface. 


Indeed, surface effects are responsible for melting that begins at the surface (pre-melting) and for a compact object's lower melting temperature (as compared to its bulk equivalent). 

Furthermore, significant changes in the thermal conductivity of nanostructures may be ascribed in part to increased surface area. 



A nanowire's thermal conductivity, for example, may be considerably lower than that of the bulk material, whereas carbon nanotubes have a much greater thermal conductivity than diamonds. 


Even though bulk gold is chemically inert, it exhibits significant chemical reactivity in the form of a nano size cluster, which is an example of surface effects. 

This is due in part to the number of surface atoms that act like individual atoms in a gold nanocluster. 

Bulk silver, on the other hand, does not react well with hydrochloric acid. 

The electrical structure of the surface states has been ascribed to the strong reactivity of silver nanoparticles with hydrochloric acid. 



An increase in surface area affects mechanical and electrical characteristics in addition to thermal and chemical properties. 


Indium arsenide (InAs) nanowires, for example, show a monotonic reduction in mobility as their radius approaches 10 nm. 

The low-temperature transport results clearly indicate that mobility deterioration is caused by surface roughness scattering. 



Furthermore, the existence of surface charges and a decreased coordination of surface atoms may result in a very high stress that is far outside the elastic regime. 


Charges on the polar surfaces of thin zinc-oxide (ZnO) nanobelts may spontaneously form rings and coils, which is unusual. 

Unexpected nanoscale phenomena like shape-based memory and pseudo elasticity may be explained by a high surface area and the associated surface effects. 

Young's modulus of films thinner than 10 atomic layers, for example, is found to be 30% lower than the bulk value. 

All of these findings suggest that increasing the surface-to-volume ratio is essential for nanoscale things.





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