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Why do the properties really change to an extreme level when they are made into nano size? I was wondering why the metal oxides become highly porous when they turn into nano in size.

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  • $\begingroup$ If these are two different questions, I suggest splitting them. $\endgroup$ – svavil Aug 17 '16 at 11:25
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Band gap pictures indeed vary tremendously with the size of the particle. Usual band gap computations of bulk materials rely on the Bloch's theorem, or on the nearly free electron approximation. These approximations work best when the bulk material is infinite, and break as long as it is sufficiently small.

For example, quantum dots have wide optical spectra because their band gaps are controlled by the particle size. An intuituve understanding of this fact may come as follows: electrons in the quantum dots are trapped in a small piece of the material (they can't go outside), so it's a lot like a particle in a 3D box. Indeed, the rough dependence of the band gap width on the size of the particle follows a $\sim L^{-2}$ law of the particle-in-a-box model.

Quantum confinement effect on the band gap of a quantum dot. By Jpailee (Own work) [CC BY-SA 3.0](http://creativecommons.org/licenses/by-sa/3.0), via Wikimedia Commons

Quantum confinement effect on the band gap of a quantum dot. By Jpailee (Own work) CC BY-SA 3.0, via Wikimedia Commons

Another example, with less intuitive explanations, can be graphene nanoribbons.

Band diagrams of graphene nanoribbons, [Stan et al, 2009](http://ieeexplore.ieee.org/ieee_pilot/articles/5076158/05117687/article.html#authors)

Band diagrams of graphene nanoribbons, Stan et al, 2009

Again, the wavefunctions of electrons in nanoribbons cannot be conventional Bloch waves; they are limited by the finite width of the nanoribbons, and the electron momentum is quantized in the transverse direction. Exact calculations are best done numerically. In general word, the presence of the edge changes the band diagram, because electrons can now propagate along the edge of the ribbon; new available states are introduced to the band diagram.

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