Surface charge density, equation defining

The surface charge density is given as a = eKif/, where e is the permittivity and K is not conductivity but a special variable defined in equation 19 thus, ij/ depends on surface charge density and the solution ionic composition (through k). The variable 1/k is called the double-layer thickness, and for water at 25 °C it is given by... 

The radial potential distribution inside the capillary, (r), is then obtained by solving the Poisson-Boltzmann equation for cylindrical symmetry (30). The resulting potential depends on a single adjustable constant which is fixed by the boundary condition on the potential which relates the p gential gradient at r=l/2Dp to the surface charge density, J c. Then we define... 

Grahame equation and also as the contact theorem [6]. This, fundamentally, is a relationship between the surface charge density, (Tq (which is defined as o-q = — Jpedy, with a SI unit of C/m ), and the limiting value of the ionic density profile at the substrate-fluid interface. For a single fiat surface with an infinite extent of the adjacent liquid, an expression for co can be obtained from the Poisson-Boltzmann equation as... 

These equations clearly show that the the slope of the electrocapillary curve of nonpolarized interface does not give the surface charge density but the relative surface excess of ionic components, as defined by Eq. (18) for case Ilb. In other words, the electrocapillary maximum potential does not correspond to the potential of zero charge . An approach to investigate the surface charge density and the double layer structure may be predicted as follows. When the values of the second terms of the right-hand sides of Eq. (18) (that is, the and Tnb values), are known or estimated on reasonable argument, Fd and F(so that by Eq. (19)) can be found from the slope... 

Here A and B are constants defined by boundary conditions, which are either constant surficial electric potential (Dirichlet boxmdary conditions) or constant density of the surface charge (Neumann boundary conditions). If we assume q>(x = 0) equal and (x -> o°) equal 0, then A = q>, and B = 0, and equation (2.124) is simplified ... 

Provided that the KMC simulation counts electrons lost during ionization events, the dissolution charge density for the simulation can be obtained from Equation (4.10). Some caution should be used in defining the value of the area because, as the dissolution reaction proceeds—especially in the case of selective dissolution in which the noble alloy components remain behind—the exposed surface area will change as the dissolution reaction interface proceeds into the alloy. However, provided that the explicit path of the electrons is not needed, the electrons lost by the oxidized metal components... 

The potential at the boundary between the Stern layer and the diffuse part of the double layer is called the zeta potential ( ) and has values ranging from 0-100 mV. Because the charge density drops off with distance from the surface, so does the zeta potential the distance from the immobile Stern layer to a point in the bulk liquid at which the potential is 0.37 times the potential at the interface between the Stern layer and the diffuse layer, is defined as the double layer thickness and is denoted 8 (Figure 3.26). The equation describing 8 (Knox 1987) is ... 

Another useful model that has been employed in recent years is the soft-layer model of Ohshima and Furusawa for an ion-penetrable surface charge layer (4). In this model, the soft layer is defined as a region having fixed viscosity, frictional property and charge, with the charge distribution of mobile ions in the soft layer being considered separately in the Navier-Stokes equation. Such a model can yield layer thickness and charge density of adsorbed polyelectrolytes, or effective thicknesses of adsorbed neutral polymers. 

While the energy flux method requires the calculation of a flux through a surface, other equations can be derived that make reference only to quantities defined for the molecule and the nanoparticle. In fact, Prad can be considered as the power emitted by the oscillating molecular dipole and by the oscillating charge density induced in the nanoparticle by the field emitted by the molecule. If the latter is approximated by the dipole term only (fimet.on), Prad is just the power of the light emitted by a total dipole /ton + Pmet.on, i-e. ... 

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