Debye-Hiickel length

In the non-linear differential equation Eq. (43), k is related to the inverse Debye-Hiickel length. The method briefly outlined above is implemented, e.g., in the pro-... 

When Di > i>2, the effective Debye—Hiickel length X (which now depends on ip(x)) is larger than that obtained for the Poisson—Boltzmann equation. Consequently, the diffuse double layer is larger in the vicinity of a charged surface, as predicted earlier.4 7 9 However, when V2 > Vi (small counterions), X < X and the diffuse double layer is compressed. The effect is proportional to the ionic strength and is, in general, small for typical electrolyte concentrations, since n(v — v[Pg.337]

When the electrolyte concentration is increased, the range of the double layer decreases dramatically (the Debye-Hiickel length decreases) and the magnitude of the surface potential also decreases. In the linear approximation, ]f(x) = iJj(c E)cxp( — (x-dB)/X) (for x>dB) and the second right-hand-side term of Eq. (48) becomes ... 

Figure 1. The dependence of the characteristic decay lengths A i, A2 of the system on the Debye Hiickel length Ad (Am = 14.9 A Ah = m = 1.67 A).

When plotted as functions of where j is the separation distance through water and >.dh is the Debye-Hiickel length, the Hamaker constants H calculated for both kinds of salts collapsed on a single curve, that can be very well represented by [14] ... 

Firstly, the physical origin of the empirical parameter x is not known. As suggested by Petrache et. al [13], it might simply represent a correction due to the interlamelar salt deficit (compared to the salt concentration in reservoir). However, since the Debye-Hiickel length is inverse proportional to the square root of the ionic strength, to account for the value x = 0.2 the... 

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. 

Haymet also studied 2 2 electrolytes. Here, even at 0.1 mol dm", the association with dimers is 10-20% (Fig. 3.52). The dependence of dimer and trimer formation on z+z in Fig. 3.53 is for a constant value of the Debye-Hiickel length, 1 /k. 

We deduce for an expression which coincides (in the limit case of negligible interaction between nearest neighbors) with the reciprocal of the characteristic Debye-Hiickel length. Following current methods we establish the relation between x and the given experimental results. We study the... 

This length is called the Debye-Hiickel length. Therefore the electrostatic field is... 

The basic parameter in a model of such processes is the Debye-Hiickel length / == kT... 

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