The Dielectric Constant of Water and the Saturation Effect

TLDR

The study extends Onsager and Kirkwood theories to derive expressions for the dielectric constant at high electric field strengths. The authors applied the extended theories to water, deriving simple formulas that incorporate the Langevin function and specific numerical factors for the Onsager and Kirkwood methods. The resulting formula predicts a reduction of the dielectric constant due to saturation, becoming significant for fields exceeding 10^6 V cm⁻¹.

Abstract

The Onsager and Kirkwood theories of polar dielectrics are extended to give expressions for the dielectric constant at high field strengths. The theory is applied in detail to water and simple formulas for the dielectric constant in terms of well-known quantities are obtained. The results of the calculation are embodied in the formula ε=n2+απN0(n2+2)μνEL(βμν(n2+2)EkT),where n is the optical refractive index, N0 the number of molecules per unit volume, μv the dipole moment of the water molecule, E is the field strength, and T the absolute temperature. L(x) is the usual Langevin function, and α and β are numerical factors which have the following values (a) Onsager method α=4/3, β=1/2.(b) Kirkwood method α=28/3√73, β=√73/6.From these formulas it is shown that the reduction of the dielectric constant due to the saturation effect is of importance for fields greater than 106 volts per cm.