Debye’s length

Table 1 Debye s lengths for the adhesion (A ) and detachment (A " and of the suspending medium. ) of the particles as a function of the corresponding ionic strengths...

Then for Debye s length the following relationship is valid ... 

Debye s length /, the correlation length Ljt) arc determined as in the case of a one-component system (see subsection 2.3.5). 

Debye s technique is not always applicable and fails completely for complex, branched structures ( trees ). In such cases, a slightly different technique can be used. One special unit, say the j-th unit, can be selected as a reference point, and all pairs of units of the same path length can be grouped together, and the result may be summed over all path length occurring. We shall call the reference unit the root of the tree . To get the total double sum, each unit has to be selected as a root and the result of the summation over the different trees has to be added. This leads to the final result... 

In another study, the nonlinear PB equation with added salt has been approximately solved for a cylindrical polyion of radius a, by matching the near- and far-field solutions in an asymptotic expansion in terms of a small parameter, s= l/ln(l/Ka), and where k 1 is the Debye screening length [60],... 

FIGURE 4.2 Schematic illustration of the behavior of the electric potential function in the two models. The thin line is a sketch of < >(x) for the approximation thick line is a plot of an exponentially decaying function, for which d = 0.135s. The potential dimensionless surface potential 4>s and the Debye screening length 1/k, respectively. The dashed line at x = 2/k designates the midplane. 

Radic N, Marcelja S. Solvent contribution to the Debye screening length. Chem. Phys. Lett. 1978 55 377-379. 

Several comments are in order. First, s) is one for A < < U2, where A is the Debye screening length. Second, along the central portion of the polyion the condensation fraction of counterions has the Manning value 1 — 1/ o. Third, when the distance from the end is of the order of the Debye length, the condensed fraction of counterions starts to decrease substantially from the Manning value. 

Equation (6) is obtained by using Debye s theory (14,IS). Here a (A) is called the correlation length and is a measure of the size of the heterogeneous structure inside the polymer. The symbol denotes the mean-square average of the fluctuation of all dielectric constants, n is the refractive index of medium, and A is the wavelength of light in a medium. 

The correlation length ( was measured with the aid of Ornstein-Zernike-Debye s plots (cf. Equation 89) ... 

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