Static screening

The next step to include electron-electron correlation more precisely historically was the introduction of the (somewhat misleading) so-called local- field correction factor g(q), accounting for statically screening of the Coulomb interaction by modifying the polarizability [4] ... 

In the early phases of the war in the Southwest Pacific Area commanders who considered area screening as a means of concealing airfields from enemy air attack ran up against several serious problems. These included not only a lack of a suitable means for static screening and a shortage of smoke materials but also a scarcity in shipping, both within the immediate area and from the United States to SWPA. If smoke was to be used the means and material would have to be devised locally. 

In the second of his two well-known papers (of 1976) devoted to the dynamics of entangled polymer solutions, de Gennes used a "two-fluid model" to determine the effects of hydrodynamic interactions. Among the many results reported in this paper are two of particular interest to us here, viz., (1) that these interactions are not screened in the static, long wavelength limit and (2) that static screening does occur provided that the wavelength is less than the radius of the polymer chain. 

Indeed, it can be seen from the second line of Eq. (37) that static screening occurs only if both of the conditions and... 

A second very fundamental objection to the existence of static screening is especially convincing when applied to the steady flows of homogeneous solutions. It relies upon the principle of Galilean invariance, according to which the form of the linear equations of motion of the medium (composite of solvent and solute) should be unchanged when the velocity is everywhere increased by an additive constant. This principle would be violated if these equations included a uniformly... 

Clearly, we are just scratching the surface of the Rouse, Rouse-Zimm and related models here. One additional point we wish to make is that, as Freed and Edwards showed, in the presence of a background of other molecules the hydrodynamics interactions are screened, with a real space screening distance This introduces another effective cutoff in eq. 2.26. We do not have time to trace the consequences of this. We will, however, raise the question, which has received much attention in the literature, of whether I// and the static screening distance scales are the same (have the same power law dependence on concentration). Also we will point out that with a p-independent cutoff, the spectrum of relaxation, and consequently various properties, becomes Rouse-like. 

In order to take into account the screening of the charges, an exponential factor is contained in the numerator in Eqs. (4) and (5). Since only one single column of polymer chains (see Fig. 1) is included in this calculations, all polymer chains appear at the same vertical distance from the impurities and from each other. Therefore, we need not to take into account explicitly any distance dependence of screening perpendicular to the chains. Instead we introduce the static screening parameters and 62 in Eqs. (4) and (5) above. The values of these parameters, i=l. 5 and 2=1.8, are those derived in Ref. 25 for the screening perpendicular to a metallic chain at distances d and V3d, respectively. These screening parameters are also shown below to reproduce the external potential used in Ref. 25. 

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