Counterions cloud

Unlike charges attract and like charges repel each other, so there is a high concentration of counterions attracted to the particle surface whilst co-ions (those with the same sign charge as that of the surface) are repelled. Thermal motion, i.e. diffusion, opposes this local concentration gradient so that the counterions are in a diffuse cloud around the particle. Of course particles which have a like charge will also repel each other but the interaction of the particle surfaces will be screened by the counterion clouds between the particles. The interaction potential is a function of the surface potential, i]/o, and the permittivity of the fluid phase, e = r80, where r is the relative permittivity.12,27... 

Therefore, the coupling of polymer segments to the counterion cloud, which is directly responsible for the term N in the above equation, dominates the collective diffusion coefficient. Since Rg N for salt-free solutions, Df is independent of N. 

Although the coupling of counterion dynamics and polyelectrolyte dynamics has been accounted for at the mean field level, the relaxation of counterion cloud needs to be included in comparing with experimental data. 

Fig. 10 Schematic PE brush structure. In a we show the weakly charged limit where the counterion cloud has a thickness d larger than the thickness of the brush layer, h. In b we show the opposite case of the strongly charged limit, where all counterions are contained inside the brush and a single length scale d h exists...

Some interesting results have recently become available for the effects of a range of n-alkyl triethyl ammonium bromides upon the mechanical stability of natural rubber latex. The number of carbon atoms in the alkyl group varied from 6 to 18. Figure 6 summarises the results. It is usually believed that the addition of cationic surfactants to an anionic latex such as natural rubber latex invariably leads to a reduction in colloid stability, the effect being attributed to adsorption of the cations with consequent partial neutralisation of the particle charge and reduction of the counterion cloud surrounding the particles. 

Electrophoresis is the motion of charged particles relative to the electrolyte in response to an applied DC-electric field the field causes a shift in the particle counterion cloud, the counterion-diminished end of the particle attracts other counterions from the bulk fluid, counterions from the displaced cloud diffuse out into the bulk fluid, and the particle migrates. The particle velocity is predicted by the Smoluchowski equation. 

However, as a practical matter, once the counterion cloud contributions have been worked out as discussed above then AG values for specific Mg2 1 binding can be deduced as parameters defining their contributions to thermodynamic models of measured folding curves for the transition between different conformational states of the RNA. 

Figure 19.3 Interpretation of form factor products in Eq. (19.3). This figure illustrates the meaning of the cross-terms of Eq. (19.3), using an atomic representation of B-DNA, along with condensed counterions (blue circles). The FDNAFDNA term, discussed in the text, is related to the set of all vectors that begin and end in the DNA, for example, the yellow arrow. The Fdna-Fions term is related to the set of all vectors with one end in the DNA and the other end in the counterion cloud, for example, the red arrow. Finally, the / ions-Fions term is related to the set of all vectors connecting ions, represented by the cyan arrow in the figure.

Figure 15. Orientational presentation of liberation of solid-phase information content into self-replicating biomesogenic information patterns, neglecting complex intermediate states of highly condensed information channel designs (left top to bottom) solid-phase space-partitioners Ca3[Al2Si 20 2J, Li 4MgSi4, TagCl 5 [32c] (right) replicative DNA, including water cover and counterion clouds [33 a, c, p, q].

Figure 21. Biomesogen regulations between structure and phase (left to right and top to bottom) visualization of biomesogen polyelectrolyte regulations exemplified by DNA/water-shell/(hydrated) counterion-cloud pattern statics and dynamics arbitrary DNA/ counterion-cloud/water-domain arrangements symbolizing operative biomesogen nucleations between structure and phase [7a, 29, 33 a, c, f, p, q].

As shown in Figure 10.24, the conductance exceeds this maximum value considerably when the field exceeds about 5 kV/cm. An early explanation involved some kind of Wien effect. The first Wien effect is due to the liberation of ions from the counterion cloud around charged particles such as proteins, whereas the second one describes the creation of new charge carriers by field dissociation of week electroljrtes. Both of these effects together can explain a conductivity increase by several percent but not by 40% as seen in Figure 9.24. Moreover, this dramatic conductivity increase is only found in solution containing aggregated amphiphiles like lipids. 

However, the application of eqn [1] to the SPEB is less straightforward than anticipated. In principle, the counterion cloud of the polyelectrolyte brushes will be disturbed by the motion of the maaoions leading to electroviscous effects. However, the number of counterions that may leave the brash is small compared to the total number of counterions. When this assumption is valid, this effect can be dismissed and Rh can be determined directly by use of eqn [1]. ° This is also justified when considering Rh which has been determined by dilute solution viscometry. 

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