A downhole filter comprising includes an open cell foam; and nanoparticles disposed in the open cell foam and exposed within pores of the open cell foam. A method of preparing the downhole filter includes combining a polyisocyanate and polyol to form a polymer composition; introducing nanoparticles into the polymer composition; and foaming the polymer composition to produce the downhole filter comprising an open cell foam having nanoparticles exposed within pores of the open cell foam. The nanoparticles can be derivatized with functional groups.