If titania nanotube arrays are coated with material and I want to check whether the tubes are coated completely, what technique would be the best to use?
I would suggest you can do a TEM or SEM for it with an insitu EDX. It will tell you if your nanotubes are coated with the required material and how the spread of the coating is.
For EDX measurement coupled with SEM, when identifying composition, one has to keep in mind that the minimum surface to be measured is 3micrometers by 3 micrometers (at least for the one we use) - so for top should be ok, but for the cross-section view depends on the length of nanotubes.
If coating can be easily seen with SEM, you can check the spreading of the coating on top and also on cross-section images. If you want to get a really good cross-section you can also perform ion-milling.
If you cannot get good quality view of the coating with SEM, for sure you will get with TEM. Furthermore, if your coating material can be easily identified in XPS - you can perform a sputter-depth profile and see the quantity of coating on the whole length of nanotubes.
You can also use TGA to do thermal analysis on the material, if the coating and the nanotubes have different degradation temperature. And based on the weight lost and the density of the coating, calculate back for its volume. Then measure the thickness of your coating using SEM or TEM to compared it with the volume you calculated. If two values match pretty well, you might have a complete and even coating on the tubes.
This is more general if you have a large amount of coated tubes.
Inverse Gas Chromatography is a powerful tool to gather information on the surface and can nicely be used in your case. The comparison between the surface energy and the nanoroughness before and after coating will enable you to know if your coating is complete or not.
I believe you can use N2 or mercury porosimetry depending on the diameter of your nanotubes and find the difference between the specific areas of the coated and uncoated nanotubes. This way you can calculate the volume of the coating material.