In one embodiment, an aerogel includes a layer of shaped particles having a particle packing density gradient in a thickness direction of the layer, wherein the shaped particles are characterized by being formed in an electrophoretic deposition (EPD) process using an impurity. In another embodiment, a method for forming a functionally graded porous nanostructure includes adding particles of an impurity and a solution to an EPD chamber, applying a voltage difference across the two electrodes of the EPD chamber to create an electric field in the EPD chamber, and depositing the material onto surfaces of the particles of the impurity to form shaped particles of the material. Other functionally graded materials and methods are described according to more embodiments.