Electrostatic potential Debye length

One of the main assumptions of the Donnan partition model is that two well-defined phases (polymer and solution) exist and the electrostatic potential presents a sharp transition between them. This approximation is fulfilled when the typical decay length of the electrostatic potential (Debye length) is much shorter than the film thickness. The other limiting situation is that where all the redox sites are located in a plane and thus the Debye length is larger than the film thickness. This situation can be described by the surface potential model ... 

In such systems the requirement of the electrostatic contribution to colloidal stability is quite different than when no steric barrier is present. In the latter case an energy barrier of about 30 kT is desirable, with a Debye length 1/k of not more than 1000 X. This is attainable in non-aqueous systems (5), but not by most dispersants. However when the steric barrier is present, the only requirement for the electrostatic repulsion is to eliminate the secondary minimum and this is easily achieved with zeta-potentials far below those required to operate entirely by the electrostatic mechanism. 

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... 

The disjoining pressure vs. thickness isotherms of thin liquid films (TFB) were measured between hexadecane droplets stabilized by 0.1 wt% of -casein. The profiles obey classical electrostatic behavior. Figure 2.20a shows the experimentally obtained rt(/i) isotherm (dots) and the best fit using electrostatic standard equations. The Debye length was calculated from the electrolyte concentration using Eq. (2.11). The only free parameter was the surface potential, which was found to be —30 mV. It agrees fairly well with the surface potential deduced from electrophoretic measurements for jS-casein-covered particles (—30 to —36 mV). 

PLASMA (Particle). 1 An assembly of ions, electrons, neutral atoms and molecules in which the motion of the particles is dominated by electromagnetic interactions. This condition occurs when the macroscopic electrostatic shielding distance (Debye length) is small compared to the dimensions of the plasma. Because of the large electrostatic potentials... 

We begin consideration of electrostatic interactions between a particle and a wall with the simplest of the various cases that where the particle-to-wall separation is large compared to the Debye length, and hence the interaction is weak. This situation is shown in Fig. 1, where a spherical particle with radius a is shown at a distance H from a charged wall, where H /k. In the superposition approximation, one finds the potential of interaction between two bodies by using the sum of the potentials that would exist around the same bodies in isolation. In this case, we use the sum of the potential near an isolated, charged wall and an isolated, charged sphere. 

As in the case of two interacting soft plates, when the thicknesses of the surface charge layers on soft spheres 1 and 2 are very large compared with the Debye length 1/k, the potential deep inside the surface charge layer is practically equal to the Donnan potential (Eqs. (15.51) and (15.52)), independent of the particle separation H. In contrast to the usual electrostatic interaction models assuming constant surface potential or constant surface... 

Electrostatic interactions in solutions containing charged particles and ions can be described using the Poisson-Boltzmann equation. A charged surface attracts counterions into a double layer of thickness defined by the Debye length, which depends on counterion concentration and solvent dielectric constant. From simplified theories, expressions can be derived for the attractive interaction potential between charged spheres. 

There are several main mechanisms to accumulate the ions or molecules near the surface [5] dispersion or van der Waals interaction with the potential d>(y) = where A is the Hamaker constant Coulomb electrostatic interaction in electrolytes with the potential h(y) = -ql exp(-y/A), where q is the electric charge of the surfactant ion, f is the particle electroki-netic potential, and A is the Debye length [2] and the adsorption and structure forces due to structural changes in the surface layer, which have no analytical dependence of the surface potential on the distance but have the parameters eq and h derived from the experimental data (see Table 1). 

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