Some chemicals are capable of crystallizing in more than one geometry. These forms are called polymorphs, and are usually designated with Greek letters to indicate the order of discovery. Not surprisingly, the alpha form is usually the most stable, followed by the beta,... Polymorphs do occur in some semicrystalline polymers, something that is not as widely known in the polymer community as it should be, although being able to select for a particular polymorph can be difficult. Polypropylene is probably the best example (at least it is the largest volume polymer exhibiting polymorphism) - the beta form can be prepared simply with select nucleating agents such as dibenzylidene sorbitol. Polyvinylidene fluoride and polylactic acid are two other polymorphic polymers that I can name off the top of my head.
As with all crystalline structures, determining the geometry of the unit cell requires x-ray diffraction, although the various polymorphs usually show differing physical properties as well - melting temperatures, and in the case of polymers, differing mechanical properties.
So given this background, you might be able to quickly see that a research paper (open access) examining polymorphs in a small, nonpolymeric molecule, aspirin, with a nanoindentor could be easily adaptable to polymers, but only if you knew that polymers can also be polymorphic. In the study, the nanoindentation was performed on single crystals of the aspirin and even more specifically, on previously identified faces. As expected, the different crystals showed different mechanical properties.
Applying this test directly to polymers would be more challenging for two reasons. First, unless extreme steps are taken, any polymer will be polymorphic even when processed so as to produce a dominance of any one crystalline form. Second, unless extreme steps are again taken, the orientation of the crystals in the polymer will be oriented in numerous directions so that accessing a single face repeatedly would be quite a challenge.
Nonetheless, this work raises in my mind the idea that this approach certainly could be used to study the surface of a polymorphic polymer. After looking at different samples of pure isomorphs at different angles, you could then map the entirety of the surface to see if and where one particular crystal dominates.
As I do not have access to a nanoindentor, this is beyond my capabilities, but is anyone else up for the challenge?