The constant phase element was invented to help describe the behaviour of certain types of chemical system which resisted being described using conventional circuit elements, This is not surprising as the sorts of phenomena that need CPEs to describe them occur in places that look nothing like electrical or electronic circuits.

So sadly I don't think you can answer what a CPE is in a physical sense, like pointing to such and such a structure and exclaiming 'Behold! A CPE!'

You will certainly need CPEs and Warburg elements to model the behaviour of DSC during Electrochemical Impedance Spectroscopy. But equally well, you certainly won't need them at all if you are examining the behaviour at very low frequencies or DC.

Best wishes with your research!

Thank you Mr. Maine, for your answer and the wishes.