Charged Surface with Dissociable Groups

Since the number of adsorbed ions on the particle surface is A max N, the electrochemical potential n of the ions on the surface is 

Since the change in the Helmholtz free energy of the surrounding electrolyte solution caused by desorption of N ions from the particle surface is Npi, the total change F, in the Helmholtz free energy of the particle and the surrounding solution is thus given by 

The free energy of the electrical double layer F=F, — F° is thus given by 

If the dissociation of ionizable groups on the particle surface can be regarded as complete, then N = and Sc can be dropped so that the surface free energy increase Ft is just equal to the electrical part of the double-layer free energy F (Eq. (5.4)), namely. 

Note that Eqs. (5.17) and (5.18) hold among Fj, F, and y, that is, F = F = yA and that in this case the electrical double-layer free energy F is equal to the electric work Fei, namely, 

---

Another possible mechanism is the ionization or dissociation of a surface group (e.g., dissociation of a proton from a carboxylic group, namely, —COOH - —COO- + H +, which leaves the surface with a negative charge). 

To calculate the surface potential we consider the simplest example of a surface with one dissociable group. Dissociation leads to a negatively charged group according to... 

Capillary electrophoresis separations are dependent on the relative mobilities of analytes under the influence of an electric field and do not depend on mobile phase/stationary phase interactions. A fused silica capillary is filled with a buffer and both ends submerged into two reservoirs of the buffer. A platinum electrode is immersed in each reservoir and a potential difference (5-30 kV) is applied across the electrode. An aliquot of sample of a few nanoliters is injected onto the capillary by either hydrostatic or electrokinetic injection, and the components migrate to the negative electrode. Separations of analytes arise from differences in the electrophoretic mobilities, which are dependent on the mass-to-charge ratio of the components, physical size of the analyte, and buffer/analyte interactions. An electro-osmotic flow (EOF) of the buffer occurs in the capillary and arises as a result of interactions of the buffer with dissociated functional groups on the surface of the capillary. Positive ions from the buffer solution are attracted to negative ions... 

Colloidal metal-oxide particles, with hydroxyl groups at their surface, may undergo proton association or dissociation depending on the pH of the solution. At low pH, a metal-oxide particle will be charged positively and at high pH negatively. The pH at which the net charge is zero, is the iso-electric point. 

Consider a cylindrical soft particle, that is, an infinitely long cylindrical hard particle of core radius a covered with an ion-penetrable layer of polyelectrolytes of thickness d in a symmetrical electrolyte solution of valence z and bulk concentration (number density) n. The polymer-coated particle has thus an inner radius a and an outer radius b = a + d. The origin of the cylindrical coordinate system (r, z, cp) is held fixed on the cylinder axis. We consider the case where dissociated groups of valence Z are distributed with a uniform density N in the polyelectrolyte layer so that the density of the fixed charges in the surface layer is given by pgx = ZeN. We assume that the potential i/ (r) satisfies the following cylindrical Poisson-Boltz-mann equations ... 

Consider two parallel identical plates coated with a charged polymer brush layer of intact thickness at separation h immersed in a symmetrical electrolyte solution of valence z and bulk concentration n as shown in Fig. 17. la [2]. We assume that dissociated groups of valence Z are uniformly distributed in the intact brush layer at a number density of No- We first obtain the potential distribution in the system when the two brushes are not in contact h > 2d. We take an x-axis perpendicular to the brushes with its origin 0 at the core surface of the left plate so that the region... 

Figure 42.2 shows a hypothetical polymeric NF membrane with carboxylic groups attached to the surface of the membrane, which is brought in contact with an aqueous solution of electrolytes. The presence of dissociated carboxylic groups on the membrane surface causes the occurrence of membrane charge. 

From the data collected in Fig. 1 we may conclude that the Intensity of excitonic emission increases with an increased surface charge due to dissociation of TGA and MUA carboxyl groups at basic conditions. The dissociation of MPS sulfate groups is not influenced by the pH level. Also, this demonstrates that the presence of OH-groups themselves in the solution of QDs does not affect their PL emission. 

Consider an adsorbing variable-charge mineral with a concentration of reactive surface hydroxyl groups, (St), defined earlier in this chapter (section 4.1c). As before, at any particular pH these groups can be protonated, uncharged, or deprotonated, so that equation 4.15 applies. The association and dissociation reactions of the groups are defined as before (reactions 4.7 and 4.8) using the equilibrium constants, and Ki. The assumptions and weaknesses inherent to this approach are described in section 4.1c. 

Adsorbed humate of arei close to 0.5 produces complex layers of zero potential in all situations. This reveals surface charge annihilation where Al3+ (main component), Al(OH)2+, and Al(OH)2 paired with acid groups exactly compensate for the remaining dissociated acid groups R-COCT. 

---