For anything nanoscale, one needs to know that some of the most basic rules of interaction between objects have to be modified to take into account curvature, surface effects, and non-obvious, non-anisotropic/isotropic interactions. Once you get to the nanoscale, some things become less obvious; like coulombic interactions are additive to a extent, but London/VdW forces aren't. Also, VdW forces for example, have to be modified from the simple London equation to take into account things like "is it a Sphere-Sphere interaction? A sphere-cylinder interaction? A surface-surface interaction?" - there are different and subtle effects one needs to take into account for all those above, and it can be a bit mind-boggling.
Overall, a basic knowledge of Physics (thermodynamics; the concept of the partition function and ensembles) needs to be known. For most nanoscale objects in a system, you will deal with the chemical potential, so any thermodynamics relating to that would be useful. As for chemistry, a working knowledge of techniques, such as SEM, TEM, cryo-TEM (going more of a physics direction..) is useful, as all the energetics you will calculate of your system are going to come from those measurements.
Some knowledge of functional groups will be useful, as well as polymer chemistry. It will give you a good idea of what forces are dominating in the interaction between the nanoscale objects. Also, soft-matter (for example, biological membranes) are a popular area atm, so you might want to research into that. What are the main things that causes the different types of endocytosis to the cell, for example? What foreign nanoscale objects can bypass the barrier/ embed inside the membrane to cause nanotoxicity? (This is the whole area of nanotoxicology).
My point is, nanotechnology is a somewhat difficult field, since you need to have a good knowledge of just about..everything. But it's a fun and exciting field.
There are many CORE textbooks one needs to have:
Jacob S. Israelachvili - Intermolecular and Surface Forces - This is as close as one can get to the *bible* of nanoscale science. It explains in very good detail how one needs to modify rules for nanoscale interactions. It also gives a introductory but essential look at how the forces and the energies are calculated also.
Pathria and Beale - Statistical Mechanics - Probably the most comprehensive book on statistical mechanics, and will explain in excruciating detail the background for thermodynamics. I recommend coupling this book with a simpler book to make digesting easier. It starts from basic concepts like the derivation of the boltzmann coefficient and goes onto advanced concepts like Brownian motion and Fokker-Planck equations.
