Surface charge density parameter space

Figure 23 The radial Manning parameter (r) (top frame, cell model only Eq. [244]) and potential c )(r) (bottom frame Eq. [245]) in the PB cell and bulk models for a charged cylinder of radius <3 = 10 A and surface charge density = —0.094 e(jk (corresponding to an average charge spacing of h = 1.69 A as in B-DNA). A site concentration (corresponding to a phosphate concentration in DNA) of 0.1 M has been chosen, giving a Manning radius of Rm = 29.6 A and a cell radius of R = 56 A. The PB cell model potential profile (solid lines) is compared to the bulk PB (dotted-dashed line Eq. [389]), DH cell model (dashed lines Eq. [256]), DH bulk model (dotted line Eq. [259]), and no-ion (circles Eq. [362]) values.

Equation (1.24) is the much-used Mott-Schottky equation, which relates the space charge capacity to the surface barrier potential Vs. Two important parameters can be determined by plotting versus Vapp the flatband potential Vn, at = 0 (where Vs = 0) and the density of charge in the space charge layer, that is, the doping concentration N. ... 

FIGURE 2.6 Parameter space spanned by the surface density of electric charge on the particle (o, in units of e/rmd-) and the contact line radius (Tq = R sin 9y, in i,m) of a system of spherical particles at an air/water interface, assuming the Debye-Hiickel theory for water with a screening length of 1 pm. The solid line is the locus of values of Ep such that above that line the capillary attraction given by Equation 2.32 dominates over the electric repulsion. The dashed line is the locus Ep = 1 (the small-deformation approach corresponds formally to Ep < 1). (Reproduced from Dominguez, A. et al. /. Chem. Phys. 127, 204706, 2007. With permission.)... 

The potential distribution and width of space charge depend on the amount of charges transferred to the surface and the density of shallow donors in the material, Nx). Quantitative expressions for these relationships are indispensible in PEC research, and to understand where they come from, we derive them below. The geometry of the problem and the relevant parameters are schematically illustrated in Fig. 2.12. The starting point for the derivation is Poisson s law, which relates the potential to the net amount of charge ... 

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