Diffusion force from thermal motion

Electrical neutrality is established near the surfaces of the particles and a charge with the opposite sign, equivalent to the surface charge, gathers like a cloud in the form of ions around the particle surface (refer to Figure 54). In this structure, the layer attached to the particle surface is called the Stem layer, and outside that, the layer that is present as a result of equilibrium distribution through the balance between electrostatic attraction and diffusion force from thermal motion, is called the diffuse electric double layer. If an external electric field is applied to this kind of dispersion system, the particle and diffuse electric double layer are drawn electrically to an electrode of the opposite sign, and relative motion occurs at the boundary of a certain slide plane . The potential of this slide plane is called the zeta potential, and it is used as the scale of surface potential [6, 7, 8]. 

The outer layer (beyond the compact layer), referred to as the diffuse layer (or Gouy layer), is a three-dimensional region of scattered ions, which extends from the OHP into the bulk solution. Such an ionic distribution reflects the counterbalance between ordering forces of the electrical field and the disorder caused by a random thermal motion. Based on the equilibrium between these two opposing effects, the concentration of ionic species at a given distance from the surface, C(x), decays exponentially with the ratio between the electro static energy (zF) and the thermal energy (R 7). in accordance with the Boltzmann equation ... 

Thermal motion of the ions in the EDL was included in the theories developed independently by Georges Gouy in Erance (1910) and David L. Chapman in England (1913). The combined elfects of the electrostatic forces and of the thermal motion in the solution near the electrode surface give rise to a diffuse distribution of the excess ions, and a diffuse EDL part or diffuse ionic layer with a space charge Qy x) (depending on the distance x from the electrode s surface) is formed. The total excess charge in the solution per unit surface area is determined by the expression... 

Atoms taking part in diffusive transport perform more or less random thermal motions superposed on a drift resulting from field forces (V//,-, Vrj VT, etc.). Since these forces are small on the atomic length scale, kinetic parameters established under equilibrium conditions (i.e., vanishing forces) can be used to describe the atomic drift and transport, The movements of atomic particles under equilibrium conditions are Brownian motions. We can measure them by mean square displacements of tagged atoms (often radioactive isotopes) which are chemically identical but different in mass. If this difference is relatively small, the kinetic behavior is... 

For particles of any other shape, the value of r derived from Stokes Law has no exact geometrical interpretation but is known as the equivalent spherical radius and is used as a convenient measure of the size of the particle. Stokes s Law is only true for particles greater than about l(x in diameter, however for smaller particles their natural thermal motion (called the Brownian Movement) becomes increasingly important. This movement causes small particles to diffuse upwards against the sedimenting force, and if they are sufficiently small they can prevent complete sedimentation. Such a suspension is said to be colloidal, and exhibits... 

Since similar approach vas used in [37] for Brownian diffusions, it should be noted the principal difference of turbulent diffusion from Brownian one. In the process of Brownian diffusion, the particles perform random thermal motion due to collisions with molecules of ambient liquid. In [37] the appropriate force acting on the considered particle, is taken into account as quasi-elastic force proportional to the particle s displacement Fcontr = —c(x. As a result, the form of the equation (11.60) changes, there appears a term proportional to x, and from the condition of thermodynamic equUibrium of the system it follows that... 

Nonspecifically adsorbed ions are those ions which retain their primary solvation shells and which are concentrated adjacent to the electrode surface due to electrostatic forces only. However, because of thermal motion, the nonspecifically adsorbed ions are actually distributed in a layer extending some distance from the electrode surface. This layer is called the diffuse layer, and... 

The effect of these electric forces is counteracred by the thermal motion of the ions, which gives the liquid charge layer its spatial extension ( diffuse layer). In order to take this thermal equilibrium into account the theory makes the implicit assumption that the average concentration of these ions at a given point can be calculated from the average value of the electric potential at the same point with the aid of Boltzmann s theorem ... 

The structure of the EDL is neither simple nor universal it depends to a great extent on the physico-chemical properties of particles and dispersion medium. In general, it is assumed that some ions from the solvent adhere on the particle surface and partially neutralise the surface charge. This layer of immobile ions is called Stem layer. The other ions spread in the solvent by thermal motion yet are subject to the electric field generated from the charged surface. With growing surface distance the concentrations of the ionic species tend to their equilibrium values of the free solvent. The region adjacent to the Stem layer with excess of counter-ions is called the diffuse layer. In this part of the EDL, the ion distribution results from the balance of electrostatic and osmotic forces. 

Consider the structure of an interface layer between a metal electrode and an electrolyte solution kept under a potential difference electrostatic adsorption) and the dipolar molecules are oriented along the lines of the electric force. They can also be physically or chemically adsorbed specifically adsorbed) on the electrode. In the case of electrostatic adsorption alone, ions can approach the electrode to a distance given by their primary solvation shells. The plane parallel to the electrode surface through the centers of elecfrostatically adsorbed ions at their maximum approach to the electrode is called the outer Helmholtz plane (OFIP) and the solution region between the OHP and the electrode surface is called the Helmholtz or compact layer. Due to thermal motion the ions are not confined within the compact layer, but are distributed over the so-called diffuse layer. The plane through the centers of specifically adsorbed ions is referred to as the inner Helmholtz plane (IHP) (Fig. 2.21). 

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