Charge-density profile

Solving the one-dimensional Poisson equation with the charge density profile pc z), the electrostatic potential drop near the interface can be calculated according to... 

In Fig. 8 density profiles are presented for several values of charge density a on the wall and for the wall potential h = — and h= Fig. 9 contains the corresponding ionic charge density profiles. For the adsorptive wall potential h < 0) the profiles q z) in Fig. 9(a) and j (z) in Fig. 8(a) are monotonic, as in the Gouy-Chapman theory. For a wall which is neutral relative to the adsorption A = 0 the density profiles are monotonic with a maximum at the wall position. This maximum also appears on the charge... 

Figure 9 shows the electrical potential and the space charge density profiles for concentrations c" = 1000 mM and c = 20 mM and Galvani potential difference f =... 

FIG. 9 Simulated electrical potential and space charge density profiles at the water-1,2-DCE interface polarized at/= 5 in the absence (a) and in the presence (b) of zwitterionic phospholipids. The supporting electrolyte concentrations are c° = 20 mM and c = 1000 mM. The molecular area of the phospholipids is 150 A, and the corresponding surface charge density is a = 10.7 xC/cm. The distance between the planes of charge associated with the headgroups is d = 3 A. 

Previously derived results for the charge-density profile and polarization profile in this model solution, valid only for small fields, were used. Although these did not consider the penetration of the electrons into the solution, the change in the field is small. A Harrison-type pseudopotential84 was used to represent the effect of core electrons of the solution species on the metal electrons. 

FIGURE 5.6 (See color insert following page 302.) Momentum and coordinate space charge density profiles for the reaction path from HNC to HCN. 

Figure 2. (a) Density of water oxygens and hydrogens, (b) The water dipole density profile and the associated potential drop, (c) The total charge density profile and the potential drop, as a function of the distance between two parallel slabs of the Pt( 100) surface at T = 300 K. 

Figure 3.38. Principle of the photorefractive effect By photoexcitation, charges are generated that have different mobilities, (a) The holographic irradiation intensity profile. Due to the different diffusion and migration velocity of negative and positive charge carriers, a space-charge modulation is formed, (b) The charge density profile. The space-charge modulation creates an electric Held that is phase shifted by re/2. (c) The electric field profile. The refractive index modulation follows the electric field by electrooptic response, (d) The refractive index profile.

Figure 1. Two types of photoinduced charge separation (upper diagrams). The interfacial proton transfer (IPT) mechanism applies both to cytoplasmic proton binding and extracellular proton release at the membrane surface (only proton binding is shown). The oriented dipole (OD) mechanism applies to charge separation inside the membrane (or rather, inside bacteriorhodopsin). The thick curve across the membrane shows the space charge density profile, which, together with the potential profile across the membrane (not shown), allows us to deduce the two microscopic equivalent circuits shown in the lower diagrams. The two slightly different microscopic equivalent circuits are equivalent to the same irreducible equivalent circuit. (Reproduced with permission from reference...

Liu, M., McNeal, C.J., and Macfarlane,R.D. Charge density profiling ofcirculating human low-density lipoprotein particles by capillary zone electrophoresis. Electrophoresis, 25, 2985, 2004. 

The charge density profile and the dipole density profile can be calculated from the atomic density profiles and the orientational distributions. Figures 19b and 19c show the dipole and charge density, respectively, for water near the mercury surface. 

In Fig. 17 we plot density profiles for a 1 1 electrolyte with size asymmetry confined by uncharged walls. The conditions are the same as in Fig. 15. The DFT here is less accurate, although the charge density profile quite well agrees with simulation. The disparity can be traced to the lack of correlations in the mean field treatment of electrostatics, which become important for an uncharged wall system. The presence of correlations is best seen in the contact density, related to the pressure via the contact value theorem, which is lower in the simulation results, and which indicates negative correlational contributions due to formation of Bjemim pairs [50]. 

Figure 6.10 The velocity profile, U, and the negative Debye layer charge density profile, in an ideal electroosmotic (EO) flow inside a channel. The EO flow is induced by the external potential difference A0 = Ay, resulting in the homogeneous electric field E. The velocity profile reaches the constant value at a distance of a few times the Debye length from the walls...

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