Debye-Hiickel profiles

Now we see that if k is large enough and a small enough then i(r) will become negative for small r before the truncation arises at r = cr. This is, of course, impossible and we must either abandon the use of the linearized DH (Debye-Hiickel) approach altogether or eliminate the negative portion of the coion density profile. 

Hole Correction of the Debye-Hiickel Coion Density Profile The DHH Theory... 

Rudhardt and Leiderer were the first to use TIRM for the experimental investigation of depletion potentials. They measured the interaction potential between charged polystyrene spheres and a glass wall in solutions of polyethyleneoxide with different concentrations up to a number density of p = O.lp. Hie experimental potential profiles were perfectly described by a superposition of an electrostatic repulsion in the Debye-Hiickel-Detjaguin approximation, a gravitational contribution, and a depletion part of the Asakura-Oosawa type. 

A number of new approximate, but accurate, analytical results are also presented here the most significant ones are (1) the extension of Gouy-Chapman theory to mixed electrolyte solutions whereby an effective counterion valence is introduced, (2) two approximate potential profiles for curved surfaces (one of them new) are generalized to include the presence of mixed electrolytes, (3) the apparent surface charge density for curved surfaces for which the Debye-Hiickel potential asymptotically matches the Poisson-Boltzmann profile, and (4) a unified treatment of two interacting charged surfaces. 

Discussion of the Gouy-Chapman (GC) Solution In Figure 4 the GC potential profile of Eq. [26] is compared to the Debye-Hiickel (Eq. [32]) and apparent Debye-Hiickel (Eq. [93], discussed later) potentials for two monovalent salt concentrations (0.01 and 0.1 M) for a surface with charge density a = 0.01 eolA. (The value for the surface... 

For a sphere with charge Qa o, the apparent charge for which the Debye-Hiickel potential asymptotically fits the Poisson-Boltzmann profile is simply... 

The apparent Gouy-Chapman length for which the Debye-Hiickel potential asymptotically matches the PB profile, subject to the accuracy of Eq. [152], as shown for a sphere in Figure 18, is... 

Figure 38 The ratio OADH/cta of Eqs. [322] and [323] for the Debye-Hiickel potential of Eq. [315] that asymptotically matches the PB profile given hy Eq. [152] as a function of the ratio aa/ao, where is the surface charge density and ctq is defined by Eq. [322] values of KdQ for each curve are given at right with the planar surface indicated hy the dotted line. Reliability bounds according to Eqs. [325] and [327] are indicated by arrows. To get a feel for the variable ranges, a mixed 1 1-2 1 electrolyte with concentration 0.1-0.02 M has kd = 0.132 A and ctq = 0.0017 eo/A for this case, the ordinate ranges from = 0 to 0.017 eolk and the curvature radii at the right correspond to spheres of radius a — 8,15,38 and 123 A (or cylinders of diameter a).

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