Disclosed herein is a catalyst which comprises a silica core having an outer surface and a mesoporous silica shell having an outer surface and an inner surface with the inner surface being inside the outer surface of said mesoporous silica shell proximate to and surrounding the outer surface of said silica core. Wherein the outer surface of the mesoporous silica shell has openings leading to pores within the mesoporous silica shell which extend toward the outer surface of said silica core. The catalyst also includes catalytically active metal nanoparticles positioned within the pores proximate to said core, wherein the catalytic metal nanoparticles comprise about 0.0001 wt % to about 1.0 wt % of the catalyst. Also disclosed are methods of making the catalyst and using it to carry out a process for catalytically hydrogenolysizing a polyolefinic polymer.