Electrostatic energy-distance curves

In Fig. 6.15 the interaction free energy distance curves are shown for several layer thicknesses adsorbed polymer in a good solvent. The weak minimum due to the van der Waals force decreases with increasing layer thickness. In Fig. 6.16, a typical interaction free energy curve is shown in the presence of van der Waals attraction, electrostatic repulsion and steric repulsion due to adsorbed polymer. Note the absence of a primary minimum. 

An illustration of some of the various states that may be produced is provided in Figure 9.10. These states may be described in terms of three different energy-distance curves as (i) electrostatic, produced for example by the presence of ionogenic groups on the surface of the particles, or the adsorption of ionic surfactants (ii) steric, produced for example by the adsorption of nonionic surfactants or polymers and (iii) electrostatic -I- steric (electrosteric), as for example produced by polyelectrolytes. 

Figure 11.3 Energy-distance curves for three stabilisation mechanisms (a) electrostatic (b) steric and (c) electrosteric.

Figure 8.3. Electrostatic stabilization of colloidal particles (a) schematic representation of the electrostatic interaction energy-distance curve for two approaching particles (not to scale) (b) calculated electrostatic interaction curves according to equations (8.20a-8.20c)...

Such a repulsive energy can be produced by charge separation and the creation of electrical double layers, as discussed in detail in Chapters 6 and 7. Combination of the van der Waals attraction and double layer repulsion at various separation distances between the particles produce an energy-distance curve, which will have an energy barrier at intermediate separations [10] and this is the origin of electrostatic stabilisation. The energy-distance curve is controlled by the following parameters. 

Another method of curbing sedimentation is controlled flocculation. For systems where the stabilizing mechanism is electrostatic in nature, for example those stabilized by surfactants or polyelectrolytes, the energy-distance curve shows a secondary minimum at larger particle separations. This minimum can be quite deep (few tens of kT units), particularly for large (> 1 pm) and asymmetric particles. The... 

For particles dispersed in an aqueous phase at 25 °C, ko = 5.5 x 10 k is usually related to ko by the stability ratio W, i.e. W = ko/k. The higher W is the more stable the dispersion. Thus, by plotting W versus system parameters such as surfactant and/or electrolyte concentration, one can obtain a quantitative assessment of the stability of the suspension under various conditions. Notably, the stability ratio W is related to the energy maximum in the energy-distance curve for electrostatically stabilized suspensions. The higher this energy maximum is, the higher the value of W. 

Fig. 1.3 Energy-distance curves for electrostatic (a), steric (b) and electrosteric (c).

The third class of dispersing agents which is commonly used in SC formulations is that of polyelectrolytes. Of these, sulfonated naphthalene-formaldehyde condensates and lignosulfonates are the most commonly used is agrochemical formulations. These systems show a combined electrostatic and steric repulsion and the energy-distance curve is schematically illustrated in Fig. 3.40 (c). It shows a shallow minimum and maximum at intermediate distances (characteristic of electrostatic repulsion) as well as strong repulsion at relatively short distances (characteristic of steric repulsion). The stabilization mechanism of polyelectrolytes is sometimes referred to as electrosteric. These polyelectrolytes offer some versatility in SC formulations. Since the interaction... 

As discussed above, the total energy-distance of separation curve for electrostatically stabilised shows a shallow minimum (secondary minimum) at a relatively long distance of separation between the droplets. However, by adding small amounts of electrolyte, such minima can be made sufficiently deep for weak flocculation to occur. The same applies to stericaUy stabihsed emulsions, which show only one minimum, but whose depth can be controlled by reducing the thickness of the adsorbed layer. This can be achieved by reducing the molecular weight of the stabiliser and/or the addition of a nonsolvent for the chains (e.g., an electrolyte). 

Fig. 1 Dimensionless interparticle interaction energies Va, Fi, Fb and their superposition F-distance curves for electrostatically stabilized 10 nm spherical magnetite particles. Hammaker constant of the magnetite = 2.3 10 and of the carrier = 3.5 IQ- J, an 1 1-electrolyte concentration of0.003 mol/1, and a zetapoten-tial of 35 mV...

Fig. 2 Dimensioidess interparticle interaction energies Fei, F, Fb, F and their superposition F-distance curves of electrostatically stabilized magnetite particles in an external magnetic field same constants as in Fig. 1...

If a piece of metal, such as silver, is dipping into a solvent, and a positive atomic core is taken from the surface into the solvent, the ion is again surrounded by its electrostatic field but free energy has been lost by the dielectric, and a relatively small amount of work has had to be done. The corresponding potential-energy curve (Fig. 96) is therefore much less steep and has a much shallower minimum than that of Fig. 9a. For large distances d from a plane metal surface this curve is a plot of — c2/4td where t is the dielectric constant of the medium at the temperature considered The curve represents the work done in an isothermal removal of the positive core. 

Forces Superimposed on the Coulomb Forces. The discussion has been based on the idea that, superimposed on the electrostatic forces between a pair of ions, there are rather short-range forces of other origin, which may be attractive or repulsive. Consider now what the situation will be if these forces cause the mutual potential energy to fall at short distances, below the value — e2/er that is assumed in the Debye-Hlickel theory. In Fig. 74 let the broken curve be a plot of — e2/er, while the full curve gives the actual potential energy between a certain pair of... 

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