Debye-Hiickel screening constant

Cell Model Debye-Hiickel Screening Constant... 

In order to treat the combined effects of added salt and dielectric boundaries on a manageable level, we use screened Debye-Hiickel (DH) interactions between all charges. In the presence of a dielectric interface, the Green s function can in general not be calculated in closed form [114] except for (i) a metallic substrate (with a substrate dielectric constant e =oo) and (ii) for e =0 (which is a fairly accurate approximation for a substrate with a low dielectric constant). For two unit charges at positions r and r one obtains for the total electrostatic interaction including screening and dielectric boundary effects... 

Here, T is the absolute temperature, e is the bulk dielectric constant of the solvent, P is the number of phosphate charges, k is the inverse of the Debye screening length, kB is the Boltzmann constant, qna is the renormalized charge, the interaction between the charges is screened Debye-Hiickel potential, and — j b is the distance between a pair of charges labeled i and /... 

The forth issue is the increase in the repulsion between bilayers at short distances. In Fig. 1, the osmotic pressure is plotted as a function of separation distance (data from Ref. [13]) for no added salt, for l M KC1 and for 1 M KBr. They reveal an increase in repulsion at short separation distances upon addition of salt. While the relatively small difference between 1 M KC1 and 1 M KBr can be attributed to the charging of the neutral lipid bilayers by the binding of Br (but not C.1-) [14], the relatively large difference between no salt and 1 M KCl is more difficult to explain. Even a zero value for the Hamaker constant (continuous line (2) in Fig. 1), in the 1 M KCl case, is not enough to explain the increase in repulsion, determined experimentally. The screening of the van der Waals interaction, at distances of the order of three Debye-Hiickel lengths (about 10 A) should lead, according to Petrache et al. calculations, to a decrease of only about 30% of the Hamaker constant (from 1.2kT to about 0.8kT, see Fig. 5C of Ref. [14]). Therefore, an additional mechanism to increase the hydration repulsion or the undulation force (or both) upon addition of salt should exist to explain the experiments. 

Dielectric properties describe the polarization, P, of a material as its response to an applied electric field E (bold symbols indicate vectors) [1—3], In the field of solution chemistry, the discussion of dielectric behavior is often reduced to the equilibrium polarization, Pq = So(s — V) Eq (eq is the electric field constant), of the isotropic and nonconducting solvent in a static field, Eq. Characteristic quantity here is the static relative permittivity (colloquially dielectric constant ), , which is a measure for the efficiency of the solvent to screen Coulomb interactions between charges (i.e., ions) embedded in the medium. As such, enters into classical electrolyte theories, like Debye-Hiickel theory or the Bom model for solvation free energy [4, 5] and is used... 

Figure 42 The ratio of the Debye-Hiickel potential due to a finite straight line charge (Eq. [368], C = oo) to that of an infinite line charge (Eq. [364]) as a function of the perpendicular distance (in A) from the center of the finite line charge for several different lengths (L — 5,10,20,50 A) listed at the right a Debye screening constant of kd = 0.132 A was used, corresponding to 0.1 M monovalent salt and 0.02 M divalent salt.

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