I am experimenting with grafting multiple heartleaf philodendrons(philodendron cordatum) to the root of an oak tree(quercus). If the grafting is successful, the next step is to cut the root from the trunk, cap it, and place it in a long rectangular potter. The experiment to follow this will be to sustain the tree root with the philodendrons, and symbiotically use the philodendrons to sustain the tree root. Does anyone have experience in this type of experimental research and advice to provide?
I don't think this will work. Grafting will usually work between the same species and sometimes between the same genus. You're talking about grafting Philodendron cordatum to Quercus robur. The former is a tree from Europe, the latter a flowering plant from Brazil. They aren't compatible in the slightest. The graft will never take.
One possible route you might want to consider that may be more successful, but a lot more difficult, is using agrobacterium tumefaciens to infect a mix of cells from the two species. If you have a homogeneous mix of individual cells in culture, infect it with A. tumefaciens, the resulting gall will contain cells from both (incompatible) species. How they grow from there is unknown.