Thomas-Fermi dielectric function

Dielectric constant, relation to susceptibility, 110. See also Dielectric susceptibility Dielectric function Fermi-Thomas, 378 Lindhard, 378... 

The calculations were subsequently extended to moderate surface charges and electrolyte concentrations.8 The compact-layer capacitance, in this approach, clearly depends on the nature of the solvent, the nature of the metal electrode, and the interaction between solvent and metal. The work8,109 describing the electrodesolvent system with the use of nonlocal dielectric functions e(x, x ) is reviewed and discussed by Vorotyntsev, Kornyshev, and coworkers.6,77 With several assumptions for e(x,x ), related to the Thomas-Fermi model, an explicit expression6 for the compact-layer capacitance could be derived ... 

Use of Eq. (17-6) and the dielectric function of Eq. (16-31) corresponds to the accurate screening calculation. Use of Eq. (17-6) with Eq. (16-30) corresponds to the use of the Fermi-Thomas approximation throughout this is presumed to be less accurate, though apparently it has not been tested except in Problem 17-1. 

By comparing the expression for the dielectric function in the Thomas-Fermi case, Eq. (2.110), with the general result of the exponentially screened potential, Eq. (2.101), we conclude that this approximation corresponds to an exponentially screened potential of the form given in Eq. (2.99) with the Thomas-Fermi screening inverse length l]... 

In this equation, n is the conduction electron density, Ep the Fermi energy and kp the radius of the Fermi sphere. e(Q) given by (4.159) is also known as the Lindhard dielectric constant [4.69]. For Q 0, the quantity in the square brackets is equal to 1 and e(Q) then reduces to the Thomas-Fermi dielectric function [4.69],... 

In the static limit and for the case of a Thomas-Fermi dielectric function [35], f q) = 1 + qjji/q, we find... 

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