An interesting question . From my chemistry experience , i can say, electrical conductivity requires the movement of charged particles. Lead sulphate in solid state , electrostatic forces hold the ions together in a crystal lattice structure ( known as 3D interconnected ion network). Therefore, a solid compound is quite unlikely to conduct any electricity ,since ions are not free to move along...
I agree partially with the comment of Prof. Anoop Kumar Srivastava. We need the movement of charged particles to obtain electrical current. In electrolytes, the electrical conduction appears due to the movement of ions in the solvent (ionic conductivity). However, in solids the electrical conduction happens because of the movement of electrons (electronic conductivity). Therefore, solids can also be good electric conductors.
In this case, lead sulfate is a very bad electric conductor. Its electrical conductivity is 10^-6 S m-1 (Encyclopedia of Electrochemical Power Sources, p. 397). For this reason, discharged lead acid battery has greater inner resistance.
I am investigating lead-lead sulfate electrode charge discharge by impedance, and huge increase od tesistance is observed during discharge, transformation of lead to lead sulfate
Lead acid battery is amazing! It seems to be simple but indeed, it is very complex, even more than lithium ion battery…
The conductivity of the electrodes of lead acid battery is related to two processes, the conductivity of the solid phase (active material, additives, grid,…) and the conductivity of the liquid phase (electrolyte). During discharge process, the electrolyte concentration reduces (principally in the positive electrodes), reducing the electrolyte conductivity. Moreover, the deposition of lead sulfate also reduces the conductivity of the solid phase, because of its low electrical conductivity. Additionally, lead sulfate has high specific volume, and during discharge the porosity of electrodes reduces, reducing the electrolyte conductivity… and so on.
Since the discovery ( Gaston Planté , 1859) they are still in my opinion one of the best systems (based on "rocking chair" of sulfate), especially in recent time by combining with carbon based or what I am working on conducting polymers materials, to achieve higher energy and power.