Debye screening model

The asymptotic ion densities satisfy the electrical neutrality condition JT riiZi(oo) = n(oo). The model developed by Stewart and Pyatt [58] was very general and limiting cases of the Debye screening model, and also that due to strongly coupled plasma, follow as special cases. 

In the second group of models, the pc surface consists only of very small crystallites with a linear parameter y, whose sizes are comparable with the electrical double-layer parameters, i.e., with the effective Debye screening length in the bulk of the diffuse layer near the face j.262,263 In the case of such electrodes, inner layers at different monocrystalline areas are considered to be independent, but the diffuse layer is common for the entire surface of a pc electrode and depends on the average charge density <7pc = R ZjOjOj [Fig. 10(b)]. The capacitance Cj al is obtained by the equation... 

K = Debye screening length 4 = model parameter n = osmotic pressure p = density T = tortuosity factor <1> = swelling ratios... 

In the model, Xp is determined by a temperature dependent electrophoretic mobility factor [123] which contains the viscosity of the solvent as well as its relative permittivity, Xc °, the radius of the polymer chain and the Debye screening length 1D. The following equation holds for the case that electrolyte and polyelectrolyte are in the same concentration range ... 

Fig. 3.13. (Top) An electron micrograph of an artificial chromatin model composed of T4 DNA and cationic nanoparticles of diameter 15nm. (Bottom) Typical snapshots of a model DNA (semiflexible polyelectrolyte) complexed with cationic nanoparticles. At low salt concentration (Debye screening length m/a = 1), a beads-on-a-string nucleosome-like structure is observed (left), while locally segregated clusters are formed at higher salt concentrations (rn/a = 0.3) (right) (See [46] for more details)...

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. 

In spite of the partial success in theoretical description, we believe that more realistic models are needed for the theory to have a predicting power. For example, measurements usually take place in the presence of a large excess of simple electrolyte. The electrolyte present is often a buffer, a rather complicated mixture (difficult to model perse) with several ionic species present in the system. Note that many effects in protein solutions are salt specific. Yet, most of the theories subsume all the effect of the electrolyte present into a single parameter, the Debye screening parameter n. In the case of the Donnan equilibrium we measure the subtle difference between the osmotic pressures across a membrane permeable to small ions and water but not to proteins. We believe that an accurate theoretical description of protein solutions can only be built based on the models which take into account hydration effects. 

This is exactly the form expected for gyir) on the basis of the Debye-Hiickel model if 2F replaces k as the screening parameter. 

Equation (32) of this model implies that the surface roughness is realized by the spatial configuration whose scale is well above the thickness of the EDL, in particular the Debye screening length of the solution, Ld (18), to allow the interfacial structure to follow the curved surface without its especial distortion. Sometimes in earlier studies, (see [34] for review) the treatment of the capacitance data for solid metals was based on a different relation ... 

The main assumption in all these approaches is that the characteristic sizes of the single-phase regions are much larger than the Debye screening length (26). Provided that the dielectric permittivity and electric conductivity of the individual phases are known, the MW models enable us to calculate the total frequency-dependent permittivity of the system. 

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