A conventional example tells that when we bring two pieces of some materials with different work functions in contact electrons start to flow from material with lower work function into material with higher work function. However this penetration of electrons from one material (let say metal) into another happen for a small, near-contact distance (typically few nanometers).
In this regard I have a questions:
1) How much energy approximately is released when electrons penetrate from one material into another? Is it an exothermic process at all?
2) Does amount of energy released increases when we increase contact surface of two metals with different work functions? Let say we take two extremely thin (a few nanometers) and extremely large (a few square miles) sheets of different metals with large difference in work functions and bring them in contact. Will electron penetration from one material to another happen through the entire volume of both material (thanks to how thin they are)? And if yes, how much energy would be released in this case?
3) Typically a supercapacitor electrodes are made of homogenous materials (such as carbon or graphene). Is there any sense to make them out of different materials with different work functions? Can we expect that by bringing electrons from material (electrode) with higher work function to material (electrode) with lower work function we need to spend some additional energy and therefore would be able to save and store this energy?