Particles equally charged

Concentration gradients can cause particles to flow, whether the particles are neutral or charged. In addition, charged particles flow if they are subject to gradients of electrostatic potential. According to Equation (20.12), the force on a charged particle equals (charge ze) x (electrostatic field E),... 

VVTien two objects/particles separate after being in contact (equal charges), one par dele loses electrons and becomes positively charged while the other gains electrons and becomes negatively charged. 

The DLVO theory, a quantitative theory of colloid fastness based on electrostatic forces, was developed simultaneously by Deryaguin and Landau [75] and Verwey and Overbeek [76], These authors view the adsorptive layer as a charge carrier, caused by adsorption of ions, which establishes the same charge on all particles. The resulting Coulombic repulsion between these equally charged particles thus stabilizes the dispersion. This theory lends itself somewhat less to non-aqueous systems. 

As shown in Fig. 7.7d polymers can destabilize colloids even if they are of equal charge as the colloids. In polymer adsorption (cf. Fig. 4.16) chemical adsorption interaction may outweigh electrostatic repulsion. Coagulation is then achieved by bridging of the polymers attached to the particles. LaMer and coworkers have developed a chemical bridging theory which proposes that the extended segments attached to one of the particles can interact with vacant sites on another colloidal particle. 

The movement of the charged analyte in the electric field can be described in the simplest way by balancing two forces fhaf influence fhe ion movement. Ions are accelerated by the force of the electric field equal to F = zE, where 2 is the charge of the analyte and E is the electric field sfrengfh. This acceleration is balanced by the frictional resistance Fj of fhe environment for which a spherical particle equals Ff = 6nqrv, where tj is the viscosity of fhe medium, r is fhe radius of the analyte and v is the velocity of fhe analyte. If fhe two forces are equal, the analyte moves at the constant electrophoretic velocity proportional to the strength of fhe elecfric field as follows ... 

The argument is so general that its particularization for the metal/electrolyte interface was only for convenience. One could have carried out the discussion with equal validity for the gas/electrolyte or the glass (container)/electrolyte boundary of the electrolyte. Of course, one would have had to note the difference between the particles that constitute gases and glass and those that compose a metal. In all these systems, the conclusion would be reached that forces are direction dependent at the phase boundary and therefore new and compromise arrangements are assumed by the particles (of the two phases) in the phase boundary. If the particles are charged or are dipoles, not only is there a redistribution of particles but also an electrification of the interface and the development of a potential difference across it... 

Dispersion (lat. dispersere, distribute) are distribution of two different phases within each other. They are called colloids (gr. gluelike) if the particles are between 10 s and 10"7 m small. Such a mixture in liquids scatters the light (Tyndall effect), is thus not clear. But due to electrostatic repulsion (equally charged particles), colloids do not tend to coagulate and precipitate. 

The Poisson-Boltzman (P-B) equation commonly serves as the basis from which electrostatic interactions between suspended clay particles in solution are described ([23], see Sec.II. A. 2). In aqueous environments, both inner and outer-sphere complexes may form, and these complexes along with the intrinsic surface charge density are included in the net particle surface charge density (crp, 4). When clay mineral particles are suspended in water, a diffuse double layer (DDL) of ion charge is structured with an associated volumetric charge density (p ) if av 0. Given that the entire system must remain electrically neutral, ap then must equal — f p dx. In its simplest form, the DDL may be described, with the help of the P-B equation, by the traditional Gouy-Chapman [23-27] model, which describes the inner potential variation as a function of distance from the particle surface [23]. 

The electrostatic repulsion between the colloids can also be strengthened by adsorption of polyelectrolytes with the same net charge as the colloids. Such adsorption has been observed experimentally by several groups [55,56]. Another example is adsorption of polyelectrolytes on clay particles and in Fig. 13 it is shown that more salt must be added to coagulate the clay particles when the polyelectrolyte concentration has been increased (except for very low concentrations of polyelectrolytes, which has been described above). The polyelectrolytes only adsorb on equally charged clay particles in the presence of salt [51]. There are many explanations to this phenomenon and one theory is that the adsorption preferentially takes place at edges of the clay particles and it has been found that the probability for adsorption is higher for short polymers [56]. 

Colloidal dispersions owe their stability to a surface charge and the resultant electrical repulsion of charged particles. This charge is acquired by adsorption of cations or anions on the surface. For example, an ionic precipitate placed in pure water will reach solubility equilibrium as determined by its solubility product, but the solid may not have the same attraction for both its ions. Solid silver iodide has greater attraction for iodide than for silver ions, so that the zero point of charge (the isoelectric point) corresponds to a silver ion concentration much greater than iodide, rather than to equal concentrations of the two ions. The isoelectric points of the three silver halides are ° silver chloride, pAg = 4, pCl = 5.7 silver bromide, pAg = 5.4, pBr = 6.9 silver iodide, pAg = 5.5, pi = 10.6. For barium sulfate the isoelectric point seems to be dependent on the source of the product and its de ee of perfection. ... 

Equations (1) and (2) enable the interpretation of the changes in y>Ka values in the different organic solvents, compared to water. One must take into account not only the stabilization of the proton (this is given by the mutual basicity of the solvents) but also the different ability to stabilize the other individual particles. Besides the neutral particles HA and B, oppositely charged ions H+ and A take part in the equilibrium in case of the neutral adds, and equally charged HB+ and B ions in case of the cation acid. This occurrence leads to a different change of the values for these two different types of weak electrolytes, depending on the ability of the solvent to stabilize anions or cations. 

This effect has been known for quite some time [76-81] and used to influence the reaction rate between the charged particles. Examples include some hydrolysis reactions [80] where a small addition of polyelectrolyte causes a dramatic acceleration of the chemical reaction between equally charged divalent counterions in solution. The effect of a polyelectrolyte on ion-ion collision frequencies has also been used to probe the distribution of ions around the polyion. For example, Meares and coworkers [82] probed the electrosta-... 

The theoretical description of electrophoretic migration2 begins with a consideration of a particle of charge q suspended in an insulating medium, and exposed to an electric field E. Fundamental laws of physics state that the electric force exerted on the particle will be equal to its viscous drag, as shown in Eq. 9.2 ... 

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