Electrostatic potential profile

Figure 7. The total electrostatic potential profile across the DPPC bilayer as given by Tieleman and Berendson [49], Redrawn by permission of the American Institute of Physics...

The electrostatic potential profile is rather complex. In the hydrophobic region, the features are similar to those discussed above for the pure DPPC layer cf. Figure 15. The electrostatic potential profile in the PE layer is parabolic, and outside the PE layer the potential is very low, but decays according to the classical Gouy-Chapmann theory, i.e. exponential decay towards zero. 

As an entry into O-functionalized disaccharides, the cathodic deprotonation of hydroxy groups and the subsequent trapping of the alkoxide with suitable reagents were evaluated. The regioselectivity was correlated hy way of computer simulations to electrostatic potential profiles of the relevant conformers of sucrose [133]. 

Figi 1-4. Electrostatic potential profile near a charged metal sphere X = distance from metal surface ... 

Fig. 6-53. Interfadal charges, electron levels and electrostatic potential profile across an electric double layer with contact adsorption of dehydrated ions on semiconductor electrodes ogc = space charge o = charge of surface states = ionic charge due to contact adsorption dsc = thickness of space charge layer da = thickness of compact la3rer.

Fig. 6-4 Electromotive force Em, electron level a., and electrostatic potential profile for an electrochemical cell = inner potential.

We shall now consider what happens when the film thickness is of the order of the Debye length. In such a situation, no analytical expressions can be derived and numerical calculations should be used [125]. The real situation could be even more complicated, since an ill-defined film thickness can exist, like the example in Figure 2.6. We can use the molecular theory to obtain a self-consistently determined electrostatic potential profile across the interface as was shown in Figure 2.7 (see... 

Figure 5. A schematic diagram illustrating the electrostatic potential profile as a function of position across die normal axis of the unit cell. The system shown here contains two symmetric Cu(l 1 1)/H20 slab faces contained within the periodic simulation cell/ Reprinted from Physical Review B, 61C. D. Taylor, S. A. Wasileski, J.-S. Filhol, M. Neurock, Phys. Rev. B 73 (2006) 165402. Copyright (2006), with permission from American Physical Society.

The influence of a cut-off relative to the full treatment of electrostatic interactions by Ewald summation on various water parameters has been investigated by Feller et al. [33], These authors performed simulations of pure water and water-DPPC bilayers and also compared the effect of different truncation methods. In the simulations with Ewald summation, the water polarization profiles were in excellent agreement with experimental values from determinations of the hydration force, while they were significantly higher when a cut-off was employed. In addition, the calculated electrostatic potential profile across the bilayer was in much better agreement with experimental values in case of infinite cut-off. However, the values of surface tension and diffusion coefficient of pure water deviated from experiment in the simulations with Ewald summation, pointing out the necessity to reparameterize the water model for use with Ewald summation. 

Once the electrostatic potential profile ( ) between two parallel plates is known for 0 < x < l, the repulsive force p per unit area of surface can be evaluated from... 

Figure 2. Schematic presentation of the electrostatic potential profile in the interfacial region according to the double layer model (DLM) and triple layer model (TLM).

Figure 1. Dreiding and CPK representation (standard geometries) and electrostatic potential profiles of N-methyl acetamide, trans-2-butene and 2-fluoro-2(Z)-butene...

In this paper, recombination processes of nonequilibrium charge carriers in the doped GaAs superlattices are examined. Self-consistent calculations of the electrostatic potential profile in the superlattices are presented. Transformation of electron energy levels and wave functions as well as variation of the overlap of... 

Appendix A.3.1 outlines the calculations for the electrostatic potential profile, as well as the values of the three voltages described here, relating to the case of a conducting surface-charged sphere that Is In equilibrium. In vacuum. 

The importance of the electrostatic potential profile on the molecular bridge in determining the conduction properties of a metal-molecule-metal junction was recently discussed by Tian et al [72] in conjunction with the current-voltage characteristics of a junction comprised of an STM tip, a gold substrate and a molecule with two bonding sites (e.g. a, a xylyl dithiol) connecting the two. 

The relationship between the electrostatic potential profile and the space charge distribution is given by the Poisson equation (Nnssbaum 1965 Feynman, Leighton, and Sands 1970 PurceU 1984) ... 

FIGURE 3.6 The electrostatic potential profile inside a cylindrical pore of radius a and infinite length for different a values and at different ionic strengths. 

The distribution of the A ions in the electrolyte double layer and the electrostatic potential profile between the limits and can be in principle calculated,for instance according... 

The mobile ions play a dominant part in determining the electrostatic potential profiles within the material. In fact, they cons-... 

Regarding carbon corrosion. Reiser et al. have proposed a one-dimensional static (steady-state) model devoted to the calculation of the PEMFC electrode/ electrolyte electrostatic potential profiles when the anode is partially exposed to air, in order to define the conditions that could be favourable for the cathode... 

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