Double-layer thickness

Fawcett et a/.317-319 have studied the Hg/EtOH interface in the presence of various anions (BIv, CIO , Cl", Br , I-). The surface activity of the anions has been found to increase in the above order. The double-layer data for Hg/EtOH have been found to be similar to those for MeOH,127,293 with some difference attributable to the bigger size of EtOH molecules. The double-layer thickness has been found to differ from that expected from the real cross section of the solvent molecules. 

Previously, we have proposed that SFG intensity due to interfacial water at quartz/ water interfaces reflects the number of oriented water molecules within the electric double layer and, in turn, the double layer thickness based on the p H dependence of the SFG intensity [10] and a linear relation between the SFG intensity and (ionic strength) [12]. In the case of the Pt/electrolyte solution interface the drop in the potential profile in the vicinity ofelectrode become precipitous as the electrode becomes more highly charged. Thus, the ordered water layer in the vicinity of the electrode surface becomes thiimer as the electrode is more highly charged. Since the number of ordered water molecules becomes smaller, the SFG intensity should become weaker at potentials away from the pzc. This is contrary to the experimental result. 

The dme in the analyte solution acts as a spherical condenser with a periodically renewed growing surface kr = 9 = 0.8515 m2/V/6 (cf., p. 116) and a double-layer thickness <5dl, which is negligibly small compared with hence the capacity of the condenser is... 

Another problem is an uncertainty involved in the estimation of the double-layer thickness. This thickness is often calculated from the size of the solvent molecule, using macroscopic data (e.g., the molar volume) under a doubtful assumption about the shape of the molecule, which is often taken as spherical. There are some indications, also provided by modern experimental techniques (X-ray spectroscopy, quartz crystal microbalance, QCM), that the density of water near the interface can change drastically (see later discussion). 

Due to the extremely small size of the double layer (thickness ranges from 3 to 300 nm), the EOF originates close to or almost at the wall of the capillary. As a result, the EOF has a flat plug-like flow profile, compared to the parabolic profile of hydrodynamic flows (Figure 8). Flat profiles in capillaries are expected when the radius of the capillary is greater than seven times the double layer thickness and are favorable to avoid peak dispersion. Therefore, the flat profile of the EOF has a major contribution to the high separation efficiency of CE. 

One possible, although speculative explanation of the effect of the addition of sulfamic acid or sodium sulfate may be based on Eq. (4.9). According to this equation, the variation in the concentration c of a nonreacting electrolyte changes the thickness of the metal-solution interphase, the double-layer thickness It appears that as the thickness of the double layer, decreases, the coercivity of the Co(P) deposited decreases as well. 

Fig. 12. Evolution of the double-layer thickness with the ionic strength of the solution for a 1 1 electrolyte.

The zeta potential is also modified by the ionic strength. When ionic strength increases, the absolute value of Zeta potential reduces. This observed phenomenon can be explained by both the presence of more counterions in the shear layer due to the decreasing double-layer thickness and to the increasing counterion adsorption into the stern layer. 

Fig. 16. Influence of the ionic strength in the prevention of readhesion phenomenon in the case of a positive particle on a negative substrate (alumina slurries on silicon oxide layer) a high-ionic-strength limit the double layer thickness. Particle and substrate are therefore electrically masked at a closer particle-substrate distance. (The double layer of the substrate is not represented here.)...

Equation 6.3 is identical to the equation that relates the charge density, voltage difference, and distance of separation of a parallel-plate capacitor. This result indicates that a diffuse double layer at low potentials behaves like a parallel capacitor in which the separation distance between the plates is given by k. This explains why k is called the double layer thickness. 

The radial voltage at the particle is g /capacity per unit area = q, where B is the double layer thickness and q the charge... 

An illustration of the effect of micelle/nanoparticle volume fraction on contact line motion is found in [57]. They used 0.1 M NaCl solution to reduce the electrical double layer thickness surrounding the NaDS micelle. At a given number concentration of micelles, decreasing the size of each micelle decreases the volume fraction greatly, since the volume of each spherical micelle varies as the third power of the radius. Thus, the addition of electrolyte effectively reduced the micellar volume fraction in the aqueous medium. The authors found that the oil droplet that would otherwise become completely detached from the solid surface, came back to reattach itself to the solid when electrolyte was present. They rationalized this finding as being caused by the inability of the weakened structural disjoining forces to counteract the attraction of the oil drop to the solid surface. 

Calculate the capacity of the Helmholtz layer per unit area for an interface of mercury in contact with a 0.0 XM NaF electrolyte. Model the value of the double layer thickness assuming a two-state water model, a positive charge on the electrode, and a local dielectric constant of six. (Bockris)... 

This thickness is about the same magnitude as the prediction based on the capacitor model (Equation (16)). The diffuse model is clearly superior, however, since it shows how the double layer thickness depends on the concentration and valence of the ions in the solution. 

The curves in Figure 11.5 are marked at the x value that corresponds to k-1. Note that the potential has dropped to the value ( p0/e) at this point. Calling k the double layer thickness is clearly a misnomer. We see presently, however, that there is some logic underlying this terminology. 

Rewriting Equation (47) in terms of k , the double-layer thickness, yields... 

FIG. 12.1 Streamlines (which also represent the electric field) around spherical particles of radius Rs. The dashed lines are displaced from the surface of the spheres by the double-layer thickness k. In (a) kRs is small in (b) kRs is large. 

Distances within the double layer are considered large or small, depending on their magnitude relative to k-1. Thus in dilute electrolyte solutions, in which k is large, the surface of shear —which is close to the particle surface even in absolute units —may be safely regarded as coinciding with the surface in units relative to the double-layer thickness. Therefore, in the case for which k is large (or k small), Equation (21) becomes... 

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