Relativity and the Lead-Acid Battery

Abstract

The energies of the solid reactants in the lead-acid battery are calculated ab initio using two different basis sets at non-relativistic, scalar relativistic, and fully relativistic levels, and using several exchange-correlation potentials. The average calculated standard voltage is 2.13 V, compared with the experimental value of 2.11 V. All calculations agree in that 1.7-1.8 V of this standard voltage arise from relativistic effects, mainly from PbO2 but also from PbSO4. PACS numbers: 82.47.Cb,82.60.Cx,31.15.ae,31.15.aj,31.15.es Keywords: lead, lead battery, relativity, relativistic effectsThe lead battery is an essential part of cars, and has numerous other applications. This well-known invention is now 150 years old [1,2]. About 75% of the World lead production and a turnover of about 30 billion USD are due to these batteries. Although there are electrochemical simulations starting from the given thermodynamical data[3, 4], we are not aware of any ab initio ones for the lead battery. This is in stark contrast to other rechargeable batteries, such as the modern lithium-ion based systems, where they abound. The problem is difficult enough to be a theoretical challenge, and there is the additional fascination that, Pb being a heavy-element, relativistic effects on its compounds could play an important role, as qualitatively found a long time ago [5][6][7][8]. For metallic lead, see [9][10][11].The discharge reaction of the lead-acid cell isThe electronic structures of both and β-PbO 2 [15-17] have been theoretically studied earlier. Especially, the metallic conductivity of the β-PbO 2 , making the large currents possible, was shown to be an impurity, conduction-band effect, attributed to donor impurities at oxygen sites [16][17][18][19]. The alloying of the Pb electrode is also important in practice, but is not discussed here, because the minute amounts of other elements do not affect the EMF of the cell.The construction of the lead-acid battery[20] has a positive lead dioxide electrode, a negative electrode of metallic lead, and a sulfuric acid electrolyte. The discharge reaction between a Pb(IV) and a Pb(0) produces 2 Pb(II), in form of solid PbSO 4 . The experimental thermodynamics of the reaction are well-known [21].The three solids can be treated with existing solid-state theories, such as density functional theory (DFT), because the bonding mechanism in the investigated species is dominated by covalent interactions where DFT is expected to provide reliable results. Adequately simulating the liquid phase in multiple relativistic regimes is beyond current state of the art, however. We avoid this problem by introducing the known energy ∆E(2) for the experimental reactionWe can use this empirical relationship because only light elements and only S(VI) occur in eq. (2), whose contribution to relativistic effects are small. Combining the equations (1) and (2) givesThe voltages for the lead-acid battery reaction may then be calculated from the reaction energieswhere we use calculated ∆E(3) values and experimenta...

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