Electrostatic forces Debye length/thickness

On the basis of this description, a relationship between the two lengths 8 and K can be established. Different 5 values are obtained by gradually increasing the amount of micelles and fitting the force profiles. The evolution of 5 as a function of the calculated Debye length is plotted in Fig. 2.8. The thickness 5 increases linearly with The inherent coupling between depletion and doublelayer forces is reflected by this empirical linear relationship which is a consequence of the electrostatic repulsion between droplets and micelles. The thickness 5 may be conceptually defined as a distance of closer approach between droplets and micelles and thus may be empirically obtained by writing ... 

Pincus [212] has studied polyelectrolyte chains the monomers of which are in 0 solvent conditions, i.e., the excluded volume is zero. This assumption is justified by the fact that most polyelectrolytes are rather hydrophobic and their solubility in water is only due the presence of charges along the chains. The author shows that electroneutrality is locally achieved within the brush, providing that the fraction of charged monomers p and the densities of adsorption points l/d2 are not too low. Actually, the high concentrations of charged monomers and counterions lead to a Debye length much lower than the brush thickness. Consequently, the only relevant electrostatic contribution to the forces within the brush is the osmotic pressure of the counterions, which behave as a constraint ideal gas with a pressure equal to pckT, in the absence of added salt. Hence the equilibrium thickness of the brush results from the balance between the elastic force and the counterions ... 

The dependence of the double-layer thickness on both the electrolyte concentration and type is shown in Figure 10.17. The electrostatic force is expected to be very weak after about 2-3 Debye lengths. This underlines the importance of having a high Debye thickness to achieve good stability. 

That electrostatic double-layer forces play a dominant role in the stabilization of soap films can be demonstrated by measuring the change in film thickness with a variation of the salt concentration. With increasing ionic strength, the Debye length decreases and we expect the film to shrink in thickness. Such experiments were... 

A typical disjoining pressure variation with film thickness is shown in Figure 7a. At small thicknesses, a repulsive force is observed which can be fitted with an exponential form exp-(jch), as expected for screened electrostatic repulsion k is close to the calculated inverse Debye Huckel length in the solution ... 

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