External charge density

The Poisson-Boltzman (PB) equation relates the electric displacement to the charge density (see Equation (4.28)). The total charge distribution includes the solute charge inside the solute cavity (pint) and that generated by the ion atmosphere outside the cavity (Pext) The external charge density can be represented as shown in Equation (4.30), which leads to the expanded form of the PB equation (Equation (4.31)), which can be simplified for low (Equation (4.32)) and zero (Equation (4.33)) ionic strengths. 

External charge density Conductivity Electric potential... 

From equation (12) div D is equal to p, the true, free, or external charge density. In view of equation (17), divP may be replaced by — /op the polarization or boimd charge density. 

To obtain the second equality we have integrated by parts using Eq. (1.30). According to (1.224) the electrostatic potential field is seen to arise from two charge densities the regular p(r) and an additional contribution associated with the dipole density pp(r ) = —Vr P(r). We will refer to p(r) as the external charge density. This reflects a picture of a dielectric solvent with added ionic charges. 

The action of the environment on the cluster can be treated as an external potential due to the external charge density p (r). This external potential consists of three parts... 

The Maxwell s equations link the four macroscopic Helds D, E, H and B with the external charge density pe and the external current density Jg. The term (9/9t)D is called displacement current and it is added to the external current density term in Eq. (1.4) to satisfy the charge conservation, i.e. the continuity equation ... 

In DFT, the electronic density rather than the wavefiinction is tire basic variable. Flohenberg and Kohn showed [24] that all the observable ground-state properties of a system of interacting electrons moving in an external potential are uniquely dependent on the charge density p(r) that minimizes the system s total... 

Vehicle Fa.ctors. Because knock is a chemical reaction, it is sensitive to temperature and reaction time. Temperature can in turn be affected either by external factors such as the wall temperature or by the amount of heat released in the combustion process itself, which is directiy related to the density of the fuel—air mixture. A vehicle factor which increases charge density, combustion chamber temperatures, or available reaction time promotes the tendency to knock. Engine operating and design factors which affect the tendency to produce knocking are... 

Carbon atoms in free space have spherical symmetry, but a carbon atom in a molecule is a quite different entity because its charge density may well distort from spherical symmetry. To take account of the finer points of this distortion, we very often need to include d, f,. .. atomic orbitals in the basis set. Such atomic orbitals are referred to as polarization functions because their inclusion would allow a free atom to take account of the polarization induced by an external electric field or by molecule formation. 1 mentioned polarization functions briefly in Section 9.3.1. 

FIG. 10 Nomalized unbalanced surface charge in a cylindrical pore with R = 5din the presence of an external potential The results, from left to right, are for original surface charge densities of —0.001, —0.005, —0.01, —0.02, —0.04, —0.05, —0.07123 C/m respectively. The x-intercepts are values of the corresponding equilibrium Donnan potentials. 

More generally, one considers an external test-charge density n0(r, t) acting on a plasma (here, the electron density) in the presence of a uniform charge density of opposite sign which is fixed. The polarization of the plasma is described by a change in the electron density 8n r, t) which is assumed to be related linearly to the potential V0 of the density n0. The most general linear relation is... 

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