Local electric charge density

In order to understand the diffuse layer in detail, we need to go back to the fnndamental eqnations of electrostatics due to J.C. Maxwell. The equation of interest relates the local electric field E(r) at the position vector r to the net local electric charge density p(r) ... 

The local electric charge density of the present theory can have either sign. In the photon model, however, the boundary conditions on the electric field cause... 

Here, pe is the local electric charge density in C/m3. With the Poisson equation, the potential distribution can be calculated once the exact charge distribution is known. The complication in our case is that the ions in solution are free to move. Before we can apply the Poisson equation we need to know more about their spacial distribution. This information is provided by Boltzmann5 statistics. According to the Boltzmann equation the local ion density is given by... 

Apart from the electroactive and electroinactive species in solution (A, B, M and X), we also need to include the description of the electric potential in the simulation. The Poisson equation relates the potential 4> with the local electric charge density, p (C cm ) ... 

The electrical state of the system is so sensitive to small changes in composition [9] that the gradient Vtp in Eq. (7) cannot be assumed, in general, to be a simple constant [12], and an additional equation is required to determine it. Given the slowness of particle motion in solution, it is justified to use the Poisson equation from electrostatics to relate the changes in electric potential to the local electric charge density pe... 

The existence of the strong form of chemisorption on the surface, that is, of the form in which a lattice electron or hole is localized near the chemisorbed particle, leads, among other things, to the appearance of a charge on the semiconductor surface. Denoting by surface electric charge density due to chemisorption we obtain, according to (7) and (9),... 

The first term Tji]zfiQ gives the charge on the electrolytic solution as a whole. This is zero because the solution as a whole must be electrically neutral. The local excess charge densities near ions cancel out because the excess positive charge density near a negative ion is compensated for by an excess negative charge density near a positive ion. Hence,... 

The ion and electrical potential distributions in the electrical double layer can be determined by solving the Poisson-Boltzmann equation [2,3]. According to the theory of electrostatics, the relationship between the eleetrieal potential ij/ and the local net charge density per unit volume at any point in the solution is deseribed by the Poisson equation ... 

Solving the Poisson-Boltzmann equation with proper boundary conditions will determine the local electrical double layer potential field y/ and hence, via Eq.(3), the local net charge density distribution. 

It is assumed that the electric charge density is not affected by the external electric fields due to the thin EDLs and small fluid velocity therefore, the charge convection can be ignored, and the electric field equation and the fluid flow equation are decoupled. Based on the assumption of local thermodynamic equihbrium, for small zeta potential, the electric potential due to the charged wall is described by the linear Poisson-Boltzmann equation which can be written in terms of dimensionless variables as... 

Within the diffuse layer of the EDL, the local net charge density, p, is not zero. If an electric field is applied such that it is tangential to the EDL, an electrical body force is exerted on the ions in the diffuse layer of the EDL. The ions will move under the influence of the applied electrical field to form a conduction current, pulling the liquid with them and resulting in an electroosmotic flow. The liquid movement is carried through to the rest (beyond the EDL region) of the liquid in... 

When an electric field is applied perpendicular to the decay of the EDL (or equivalently parallel with the surface), the surplus of either positive or negative ions results in a net body force on the fluid proportional to the local net charge density. The resulting velocity profile consist of a region... 

Electric field measurement at the boundary of a metal container filled with charged material. Examples include pipelines and storage vessels. The electric field can be used to calculate charge density (3-5.1). Eield meters can also be lowered into containers such as silos to determine the local fields and polarities. Quantitative interpretation of the reading requires correction for field intensification and is sometimes accomplished using computer simulations. 

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