What requirements do the cathode and anodes have to have? What make one metal good and the other not as good? What characteristics do they need?
Thanks
The first most obvious problem is not reacting with the electrolyte. So if you want more than 1.2V from the anode, you have to use something other than water. (Lithium cells use something weird like diethyl carbonate plus something ionic dissolved in it.) After that, a whole mess of complex and mucky chemistry gets involved: free energy (kinetics: how fast it reacts, under various conditions), surface activity, oxidation products and how well they adhere (you need an adherent oxidation product for it to be rechargeable; lead metal forms adherent lead sulfate in the lead-acid battery, but zinc does not, hence little of the zinc hydroxide byproduct can be reversed in an alkaline cell -- and this is part of the reason why they are not rechargeable), the list goes on.
Really good batteries are hard to design because the chemistry and materials science are all very complex; they're often discovered as much by accident as by intent. You might have some vague idea of a starting point, like, let's use lithium metal because it's got the most voltage -- and then just try a thousand variations of electrolyte, carrier, cathode and so on, and hope that you'll find something useful.
Just for playing around, the biggest drawback is internal resistance. Yes you can put two hunks of dissimilar metal in vinegar and measure a voltage, but that doesn't mean it's useful. To minimize resistance, and therefore maximize the amount of power that can be drawn from the cell, you need to get the electrodes as close together as possible (usually, using a soaked, permeable membrane to prevent the electrodes from shorting out!), the area as large as possible (which is why spiral wound structures are so popular, using long, thin sheets of metal for the electrodes), and the electrolyte as conductive as is practical.
Electrolyte examples:
The dry cell uses ammonium chloride, which dissolves something like 40% strength in water. Sodium chloride saturates at 25%, and potassium chloride around 33%.
The alkaline cell uses something like 20% KOH, a strong base.
The lead-acid cell uses 20-40% sulfuric acid, as its name implies.
All of these are pretty strong (near saturation), and good ionic conductors.
In the case of sulfuric acid, both the pure substance and the solution are liquids, so any strength from 0% to 100% could be made. But as it happens, it's most conductive (most strongly ionized) around this strength. Sulfuric acid can give up multiple ions when it dissolves, so it can make a more conductive solution, but only when dissolved sufficiently. This, despite being weaker in solution!
Tim