Exponential screening

Slater s rules have been refined to improve their match with experimental data. One relatively simple refinement is based on the ionization energies for the elements hydrogen through xenon, and it provides a calculation procedure similar to that proposed by Slater. A more elaborate method incorporates exponential screening and provides energies that are in closer agreement with experimental values. ... 

With some modifications the model matrix elements (18) may also be applied to ionized systems. It appears reasonable to generalize the exponential screening function as follows ... 

Hre addition of salt to polyelectrolyte solutions lowers the penalty due to cormterion redistribution, thus promoting phase separation. At high salt concentrations, the electrostatic interactions between charged monomers are exponentially screened, leading to the renormalization of the second virial... 

In a salt solution the electrostatic interactions are exponentially screened over distances larger than the Debye screening length. In this case the simulations may be significantly speed up by considering electrostatic interactions between only those monomers that are within a cutoff distance r uf The choice of the cutoff distance is dictated by the desired accuracy. 

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]... 

If K = T, h 1, which gives /h < 1. Thus, the mean square amplitude is much less than the interplane separation, h. The double layer interaction has completely screened out the undulation force In this case, the Helfrich interaction is not only much weaker than the double layer disjoining pressure (Eqn. III.ll), but is exponentially screened as well. However, with added electrolyte, as soon as the Debye screening length becomes significantly smaller than the interplanar spacing, the Helfrich interaction switches back on. It is precisely this effect which Safinya et al. used to pin down the Helfrich force. 

Slit pores and nanotubes. The simplest model of a porous electrode is a slit-like pore similar to the one shown on Fig. 4. The main difference with planar electrodes is that the multi-layered structure cannot be formed anymore. Instead, the ions are surrounded on both sides by the electrified walls. As discussed in the methods, Kondrat et al. have shown that it results in an exponential screening of... 

Here, Uo=H.13 eV and y O.373 The constant and exponential screening factors were introduced in Ref. 37 in order to produce a soliton charge distribution in agreement with experimental XPS-data. The inter-site distance rnm in Eq. (8) is calculated using the the optimized geometry of the polymer chain. 

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