On the dielectric constant of dilute solutions of polar molecules in non-polar solvents

Abstract

Summary. — The dielectric constant e of an extremely dilute solution of a polar substance in a non-polar solvent is studied for the following model system : a simple cubic lattice with each site occupied either by an A molecule with polarizatbiliy αA or by a B molecule with polarizability αB and permanent dipole µ. This model is solved exactly to the first order in the mole fraction xB of B, leading to the quantity (dε/dxB)0. This same quantity is evaluated by means of the approximate theories of Debye and Onsager, and it is observed that, on replacing a lattice sum by a continuum integral, the exact formula for (dε/dxB)0 reduces to the Onsager expression. For the particular model system studied here, the Debye and Onsager approximations deviate in opposite directions from the exact value of (dε/dxB) o but the discrepancies are however slight in both cases. This suggests that permanent dipole moments evaluated from the dielectric constant of dilute solutions by means of the approximate formulae of either Debye or Onsager, are reliable within a few percents.