The Dielectric Constant at High Field Strengths

Booth73 used Frolich s108 modification of the Onsager expressions101 for the cavity field in non-associated polar liquids, and corresponding modifications of Kirkwood s equation for associated polar media. Booth s assumptions in deriving Eq. (28) for the Kirkwood case are important to determine the validity of his final expressions. He used the Onsager-Frolich cavity field ratio 

3ea/(2ea + n2) as the value for qA = FA/EA in the Langevin function, pointing out that the cavity field expression would be exact only if ea = e0, i.e., Ea is everywhere small and constant. To make the calculation tractable, he assumed the validity ofEq. (30), and that ea n2, so that Eq. (30) became  

The reaction field is small and independent of EA and FA, so he put FA Fa = qAEA = (3/2)Fa for simplicity. Using Frolich s Lorentz cavity with the dipole in an n2 medium108  

Their equations for the Onsager theory put i2 in the Langevin function, instead of one A inside and one outside. However, die error is not serious since the calculations and graphs are correct 

If the Langevin function in Eq. (35) is expanded to the second term, we obtain  

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A. D. Buckingham, /. Chem. Phys., 25, 428 (1956). Theory of the Dielectric Constant at High Field Strengths. 

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