An Arrhenius Argument to Explain Electrical Conductivity Maxima versus Temperature

Abstract

The existence of conductivity maxima in pure molten salt was interpreted by Grantham and Yosim to be due to ion association at low densities. Tödheide used a chloride-transfer shifting-equilibrium hypothesis to explain ion association in the case of bismuth trichloride. We have performed density-functional-theory based molecular dynamics simulations of the molten chlorides of Bi(III), Sn(II), and Hg(II), and Tödheide's hypothesis is not supported. Instead, the simulations imply a hopping barrier for ions between counterions, and we develop this concept into a density-dependent Arrhenius equation to explain the conductivity maxima.

The origin of the conductivity maximum in molten salts. II. SnCl2 and HgBr2

“…With the observation in simulation of a Grotthuss relay of Br − ions in the molecular liquid HgBr 2 , we now suggest that the "hopping" ideas we proposed earlier 23,24 be recast as density-dependent aspects of a general Grotthuss conductivity mechanism for all ions. A comparison with previous literature discussion of the Grotthuss mechanism of H + in aqueous media is then apt.…”

“…2,[17][18][19][20][21][22] However, we reported in 2012 the results of ab initio molecular dynamics (AIMD) simulations which showed that molten BiCl 3 is a network liquid with very little molecular character, and instead put forward a new theory to explain the conductivity maximum vs temperature. 23,24 The new theory attributed conductivity to atomic ions "hop[ping] from counterion to counterion," and used a density-dependent Arrhenius equation to ascribe the maximum to the competing effects of rising hopping opportunities (rising frequency factor A with thermal expansion) and diminishing hopping probability per opportunity (due to rising activation energy E a as the hopping distance increases with thermal expansion):…”