Capacitor electrode surface roughness Does capacitor electrodes with high surface roughness provide increased capacitance over mirror polished ones?
Rough surface have more surface area than perfecly flat one,more surface equals more capacitance.
Imagine big air dielectric rf capacitor,would capacitance increase if I roughened the electrodes with something abrasive,like rubbing diamond particles against it?
What if I grew short carbon nanotubes on the electrodes? The carbon nanotubes will decrease the distance between electrodes very little since they are so small,but the surface area will increase big time,will that significanty increase capacitance?
 A: You can't use the surface area of a single electrode as the "area of the capacitor". A better approximation would be the area of a smooth surface you draw between the electrodes, in the volume of the dielectric.

A capacitor offers the chance for pairs of opposite charges to get close together without combining. This means their electric fields partially cancel out (an electric dipole). This reduced field then repels like charges less, allowing them to be packed closer together than would otherwise be 
possible for a given voltage — as expressed by $Q = CV$. The closer the separation between electrodes, the more the fields cancel out and the more capacitance you have.
Roughening the surfaces of a pair of parallel plates does nothing much to improve this, because it merely causes a small variation in the minimum distance the pairs of charges can approach — it is insignificant compared to the large distance between the plates.
However, if we make the entire structure of the capacitor "bumpy" — the two electrodes are shaped the same and much closer together than the size of the bumps, then this actually has a significant effect. The extreme case of such bumps, where the structure of the capacitor is actually folded back on itself, would be a common air-dielectric capacitor made up of alternating plates with bars connecting them to terminals. This is commonly thought of as many individual capacitors stacked up, but it is equally valid to think of it like a single parallel-plate capacitor that's been folded tightly back on itself.
The key is that for each point on the surface of one electrode, the other electrode is nearer to it, mostly, than the parts of the first electrode that you've brought closer together by roughening/folding it. As long as that is true, the field cancellation from the presence of the second electrode exceeds the repulsion of the like charges on the first electrode, and you've increased the capacitance.

A common case where literal roughening is used to increase capacitance is the electrolytic capacitor. In an electrolytic capacitor, there is one solid electrode, a dielectric consisting of an oxide layer on that electrode, and the electrolyte as the other electrode. Here, the electrolyte and the dielectric conform to the surface of the solid electrode, so the two electrodes are always very close together. 
Then, if you roughen or even puncture the surface of the solid electrode before you assemble the capacitor and form the dielectric layer, you've made a partially "folded" capacitor with more capacitance. (The reason this is better than actual folding, or rather rolling up more layers, is that you can fit more area per volume this way because the electrodes can only be so thin before they are not mechanically strong enough to hold together, or have areas that touch metal-to-metal and short out. An electrode can actually have many holes in it, forming a very 3-dimensional electrode all coated in dielectric oxide.)
Therefore, electrolytic capacitors do use a roughened structure to increase capacitance. 
