The Dielectric Constant as a Function of Displacement

The best-known empirical expression for eA as a function of EA2 is Grahame s.117,130 Its differential form with vector notation dropped, an with n2 isotropic and constant is  

Buckingham s incremental dielectric constant. The corresponding integral dielectric constant sA = Aa/Ea given by Booth s equation124 is the integral of Eq. (42) between the limits 0 and EA, divided by EA. Its value depends on the value of m, and is  

Equation (45) has the same form as Eq. (42) with m = 1, but it represents the integral dielectric constant. The value of 

In intense fields, L(xA) approaches (1 - 1/xa), and it is easily verified by calculation that(3/xA)(l - l/xA) in Eq. (46) coincides closely with (1 + 2xA2/15) = (1 + 2bEA2)-l/2 from Eq. (42) for xA 2.5-3.0. Thus Grahame s Eq. (42) with m = 0.5 may act as an excellent replacement for Booth s expression (Eq. 35) for the integral dielectric constant to simplify calculation, if necessary. It also suggests a function which may be used to mimic L(xA)  

Electron Transfer Reactions With and Without Ion Transfer 215 

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