1) which of mechanical properties are affected?
2) How are they affected?
Rubber toughened epoxies is well researched topic.. this review article will be a god starting point
DOI:10.1080/15583720903048227
I agree with Sridhar, The review from Bagheri et al. is a really good place to start. Another paper available on researchgate is: "Synthesis of hairy acrylic core-shell particles as toughening agents for epoxy networks" from Hazot et al.
Please refer to the review articles in order to have detailed idea. Generally, the mechanical properties are studied in such cases.
Are you really asking about core-shell rubber Nanoparticles ? The area of acrylic core shell rubber particles is well trodden indeed, as others have suggested, and you can expect an increase in fracture toughness of the epoxy/adhesive, dependent on the volume fraction of the particles but possibly also their size or indeed particle size distribution . There will be a slight decrease in elastic modulus and a possible lowering of the yield stress compared to the control resin. I would direct you to the many papers by A J Kinloch et al.
I am personally not aware of any really nano- nano particles of this kind as commercially available; if they exist they are likely to have the effect of dramatic increase in the viscosity of the prepolymer in well dispersed state. Thus the processability would become the first issue; if successful then you may expect the same effects on mechanical properties as listed above. Again , recent reviews from Imperial College London (Kinloch, A Taylor et al) would be my first port of call.
Besides the predictions mentioned above, I think that dynamic modulus of elasticity of this nanocomposite will be changed (probably, increased) in comparison with pure epoxy rezin.
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