Can you use both sides of a Peltier module to distill water? Using one side for heating and the other side for cooling. If so what type of Peltier module do you need and can you make it solar powered? Also do you need heatsinks, and how should it be placed? Do you need anything else besides the module? What type of power supply do you need?
solar panels are about 20% efficient, while thermal collectors are about 60% efficient. unless you can get a energy efficiency ratio 3 from the peltier you'll get better performance by just using the sun's heat directky to evaporate the water.
Admittedly the termerature difference between the condenser and the boiler will be fairly small so a high efficiencty may be possible, but peltiers have a failry high electrical resistance so the large current needed to move the large amount of heat will require a large peltier device to minimise the resistive losses.