Counter-ion layer

Fig. 6 Average brush height (filled symbols) and height of the counter-ion layer (open symbols) of completely charged brushes versus grafting density. lB=0.7 b (diamonds) and ZB=0.1 b (triangles). The lines give power laws (ze) pa ...

Figure 1 2-3 The electrical double layer of a colloid consists of a layer of charge adsorbed on the surface of the particle (the primary adsorption layer) and a layer of opposite charge (the counter-ion layer) in the solution surrounding the particle. Increasing the electrolyte concentration has the effect of decreasing the volume of the counter-ion layer, thereby increasing the chances for coagulation.

An even more effective way to coagulate a colloid is to increase the electrolyte concentration of the solution. If we add a suitable ionic compound to a colloidal suspension, the concentration of counter-ions increases in the vicinity of each particle. As a result, the volume of solution that contains sufficient counter-ions to balance the charge of the primary adsorption layer decreases. The net effect of adding an electrolyte is thus a shrinkage of the counter-ion layer, as shown in Figure 12-2b. The particles can then approach one another more closely and agglomerate. 

In adsorption, a normally soluble compound is carried out of solution on the surface of a coagulated colloid. This compound consists of the primarily adsorbed ion and an ion of opposite charge from the counter-ion layer. 

When a crystal is growing rapidly during precipitate formation, foreign ions in the counter-ion layer may become trapped, or occluded, within the growing crystal. Because supersaturation and thus growth rate decrease as precipitation progresses, the amount of occluded material is greatest in that part of a crystal that forms first. 

Coulometric titration A type of coulometric analysis that involves measurement of the time needed for a constant current to produce enough reagent to react completely with an analyte. Counter electrode The electrode that with the working electrode forms the electrolysis circuit in a three-electrode cell. Counter-ion layer A region of solution surrounding a colloidal particle within which there exists a quantity of ions sufficient to balance the charge on the surface of the particle. 

Electric double layer Refers to the charge on the surface of a colloidal particle and the counter-ion layer that balances this charge also, the charged layer on the surface of the working electrode in voltammetry. 

A) In 2A, the ion-double layer is shown (top), and the resultant Hat profile that results from the electroosmotic flow (EOF) which results from the movement of the counter-ion layer in the presence of an applied field B) In 2B, the result on band-width for the flat flow profile (CE) versus Laminar flow profile (LC) is shown. 

Fig. 14.3 Voltage-driven movement of the cations at the channel wall (left-hand side) produces a flat EOF velocity profile across the channel except within the nm thick diffuse counter-ion layer (right-hand side).

Both 1,2,3,5- and 1,3,2,4-dithiadiazolylium salts are susceptible to hydrolysis, although the ease of hydrolysis is affected by the solid-state structure and hence the counter-ion. Layered structures (Types B-D) with strong secondary interactions are remarkably resistant to hydrolysis [90JCS(D)2793], with some samples retaining their luster even after standing in water for 20 minutes. Class A salts tend to be more susceptible to hydrolysis, eventually yielding the amidine (IR spectrum), sulfur, and S02. 

It is important for one to remember that if the surface potential is high, at short separation distances eq. (III. 17) should be replaced by the more accurate eq. (III. 18), which takes into account the structure of the dense portion of counter-ion layer, as well as the individual size of the counter-ions. It can be verified that the asymptotic eq. (III. 15) can be readily obtained by... 

One can expect (see fine print further) that the greater diffusivity of the counter-ion layer as compared to that established in Helmholtz model, would only affect the velocity distribution profile of the displacement of individual fluid layers in the direct vicinity of the solid surface. The experimentally observed velocity of the mutual motion of the phases with respect to each other, v0, determined, as in Helmholtz model, by the potential change significantly (curve 2 approaches the same limiting value as curve 7 ). This is also confirmed by the fact that the distance between the capacitor plates, 8, which is the only parameter defining the geometry of the system in the Helmholtz model, is not present in the final expression.4 The thickness of the ionic atmosphere, k 1, may be used as the parameter closest to the distance 8, i.e. 8=1/k. 

This model is pertinent for polyelectrolytes which have a counter ion layer surrounding the molecules. However, the mathematical difficulties are considerable for the ellipsoidal shape with a shell. Fricke 5) derived an equation for an ellipsoid with a nonconducting shell. Since polyelectrolytes are surrounded by a conducting counter ion atmosphere, his treatment may not be relevant to the present case. 

In the above calculation, the volume fraction is estimated without the counter ion layer. If we include the counter ion layer (with the Debye-Hiickel radius approximately 200 A. at the ionic strength used for measurements), the volume fraction will be larger than that used above by a factor of 15 to 20. Therefore, the volume fraction of the solution used for the measurement is 6.0 instead of 0.375%. Thus the observed specific dielectric increment would be 2.5 X 104, which is still considerably larger than the theoretical value. As we have seen, there are great uncertainties concerning the estimation of the volume fraction of polyelectrolytes. Under these conditions, it may be better to discuss the problem on a qualitative basis and not take the numerical agreement as conclusive. 

According to Equation 71, the dielectric increment is proportional to a2/b. Since we can safely assume that b is practically constant, Ae is actually proportional to a2. This relation agrees with the experimental observation (see Experimental). Moreover, if we insert appropriate values into Equation 71, a = 10-4 cm., b = 400 X 10-8 cm. (including the counter ion layer assuming the Debye-Hiickel radius to be 200 X 10-8 cm.), P = 0.06, o- = 2.5 X 1012 cm.-2, and e = 4.8 X 10-10 e.s.u., the value for the dielectric increment is approximately 5050, which is about three times larger than the observed value of 1500. However, the above treatment is carried out with an assumption that DNA molecules are aligned completely in the direction of the electric field. Actually the DNA molecules are almost randomly distributed. Therefore, Equation 70 must be rewritten as... 

The activity coefficient exponent, v- 1 -i- Ioiy, for the solute ion, Y y, influences the solute activity coefficient through the solution properties, kay, and the ion valence, Vy. These effects are the familiar Debye-Huckel behavior resulting from screening of the electrostatic potential of a solute ion by the diffuse counter ion layer. Since Z < 1.0, will vary inversely with the activity coefficient due to solute ion screening by neighboring solute ions. To understand this behavior better it is instructive to examine electrostatic potential screening of solute ions. 

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