This question is too vague.. many factors govern the type and extent of interactions between metal oxides and polymer matrix. Please be more specific.
It depends on the nanofiller and on the polymer used. In the case of nanoclays usually secondary forces play a major role, but if you use silane or other coupling agents or reactive surfactants, chemical bonds may also form. In the case of organically modified nanoclays the quaternary long aliphatic chanin amines attach to the clay surface by ionic bond, while the "tail phase" exhbits van der waals bonding with the polymer. In the case of carbon nanotubes or graphenes you usually have secondary bonding, unless the nanofillers are chemically modified. Please specify the systems you are actually interested in.
If your nanoparticles are passivated with surfactant, the interaction should be van der waals force between the polmerchain of the polymer and surfactant. Plz refer to my paper: Granular magnetoresistance in cobalt/poly (3-hexylthiophene, 2, 5-diyl) hybrid thin films prepared by a wet chemical method, Applied Physics Letters 95, 082509 (2009), or more detail: Cobalt-based magnetic nanocomposites: fabrication, fundamentals and applications, Journal of Physics D: Applied Physics 44, 393001 (2011) (end of part 2 and part 4).
If your precursor nanoparticles are bare particles, and if your polymer has some free functional groups, nanoparticle can form coordination bonds.
The detailed bonding between oxide nano particles and polymer is very fundamental topic. you may find some meaningful information in the research paper on dye-sensitized solar cell, which has many such orgnic-inorgnic interfaces.
It's all depends on the nature of the functional groups on org and inorg materials. Shirkavand cited a good article where u can find the answer(s). U can also refer the review article published in Angew Chem Int Ed http://www.chem.toronto.edu/staff/GAO/flashed/courses_files/extensive%20meso%20review.pdf
That depends of the kind of polymer used and metal oxide, the interaction will be the same present between functional groups exposed in the polymer and the oxide. Medium conditions where is carried out the process are of relevance, variables like pH, temperature, presence of other agents etc. You can change this interaction via "functionalization" of surfaces using "linkers" to change this interaction to a desire one, like covalent, ionic, salt, van der Waals etc.
As most of the answers say, it depends on the nature of the polymer matrix and the filler. For example, if the matrix is a carboxylated polymer, ionic bonds can be formed i.e. ionomers, where the cation from the metal oxide can interact with the anion in the carboxylic group. Hydrogen bonds are also susceptible to be formed in that case.
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