Zeta potentials

The zeta potential is the electric potential of a double layer at the slipping point (Fig. 9.8). The slipping point is known to be in front of the colloid s surface at a distance of at least a single hydrated cationic layer (Stern layer) (the exact location of the slipping point is not clear). Based on what was said above with respect to pH dependence and/or ionic strength dependence of the electric double layer, it is also known that as the ionic strength increases, or pH approaches the PZC, the zeta potential decreases (Fig. 9.9). 

Zeta potential can be measured by the use of a zeta meter, which is commonly employed in municipal water-treatment facilities to evaluate the flocculation potential of suspended biosolids. 

Numerous physical and chemical factors can influence the magnitude and sign of the zeta potential. It may depend on the presence or absence of added electrolytes, or on the concentration of the suspension itself. In liquids that contain no surfactant ions the zeta potential falls with increasing concentration. In the presence of surface-active or multivalent ions the sign of the zeta potential may be reversed. The topography of the solid/liquid interface is also significant. 

Choudhary et al investigated the variation of zeta potential of aqueous oxide suspensions in which the pH was controlled by addition of triethylamine, and found that zeta potential increased with pH up to a certain value this value was, however, not constant and probably dependent 

From a fundamental point of view there are therefore a number of difficulties. There is no satisfactory theory that accounts for all observations on electrophoretic deposition. It is desirable to find suitable physical/chemical parameters that characterise a suspension sufficiently in order that its ability to deposit can be predicted. Most investigators use zeta potential or electrophoretic mobility, but these do not uniquely determine the ability of a suspension to deposit. For example, in suspensions of aluminium in alcohol the addition of an electrolyte C2ujses no significant change to the zeta potential, but deposits can only be obtained in the presence of the electrolyte The stability of the suspension is evidently its most significant property, but this is a somewhat empirical property not closely related to fundamental parameters. 

As agglomerated particles are well known in CMP to cause deleterious effects (e.g., scratching and gouging), an understanding of a slurry s zeta potential and the factors that effect it can be important. Various CMP processes may require blending slurries with other chemicals, for example, acids, bases, or hydrogen peroxide to help achieve the desired polishing performance—an initially stable slurry may be made colloidally 

Reproduced from Field Validation of Sub-Micron Defect Correlation with 1 Micron Particle Behavior in Undiluted POU CMP Slurry, http //www.vantagetechcorp.eom/images/pdf/Vantage CMPUG 140709 SubMicron Defect Correlation.pdf (last accessed November 2014). 

16 Qualitative sketch of zeta potential variation with pH. by the author. 

Post-CMP clean chemistries pH may be selected so as to maintain or accentuate the slurry colloidal stability at the post-polish wafer cleaning steps for optimal results. 

Henry s calculations are based on the assumption that the external field can be superimposed on the field due to the particle, and hence it can only be applied for low potentials (f 25 mV). It also does not take into account the distortion of the field induced by the movement of the particle (relaxation effect). Wiersema, Loeb and Overbeek [19] introduced two corrections for the Henry s treatment, namely the relaxation and retardation (movement of the hquid with the double layer ions) effects. A numerical tabulation of the relationship between mobility and zeta-potential has been provided by Ottewill and Shaw [20]. Such tables are useful for converting u to f at aU practical values of kR. 

Two main procedures can be appHed for measuring the zeta potential [15]  

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One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

Calculate the zeta potential for the system represented by the first open square point (for pH 3) in Fig. V-8. 

R. J. Hunter, Zeta Potential in Colloid Seience Principles and Applications, Academic, Orlando, FL, 1981. 

Several effects, due to the existence of the double layer on the surface of most particles suspended in Hquids, can be used to measure the so-called zeta potential. Table 1 gives a simplified summary of the effects. 

Fig. 8. Electrical double layer of a sohd particle and placement of the plane of shear and 2eta potential. = Wall potential, = Stern potential (potential at the plane formed by joining the centers of ions of closest approach to the sohd wall), ] = zeta potential (potential at the shearing surface or plane when the particle and surrounding Hquid move against one another). The particle and surrounding ionic medium satisfy the principle of electroneutrafity.

Fig. 9. Correlation of contact angle, flotation recovery, surface coverage by collector, and 2eta potential. Solid, quart2, collector reagent, 4 x 10 Af dodecylammonium acetate. = recovery, % A = zeta potential, mV Q — contact angle, degrees and = surface coverage, % of one monolayer. Ref.

Hydrolysis. The surfaces of metal oxides and hydroxides can take up or release or OH ions and become charged. Potentials as high as 100 mV may be sustained ia aqueous solutions. For aqueous solutions this is a function of the pH the zeta potential for the particle is positive if the solution pH is below the particle s isoelectric pH (pH ), and negative if the pH is above pH Isoelectric poiats for metal oxides are presented ia several pubheations (22,23). Reactions of hydroxyl groups at a surface, Q, with acid and base may be written as follows ... 

Fig. 7. Dependence of zeta potential on pH for a typical metal hydroxide particle ia water. The isoelectric pH (pH ) is at low pH for acidic hydroxides and...

Response to Electric and Acoustic Fields. If the stabilization of a suspension is primarily due to electrostatic repulsion, measurement of the zeta potential, can detect whether there is adequate electrostatic repulsion to overcome polarizabiUty attraction. A common guideline is that the dispersion should be stable if > 30 mV. In electrophoresis the appHed electric field is held constant and particle velocity is monitored using a microscope and video camera. In the electrosonic ampHtude technique the electric field is pulsed, and the sudden motion of the charged particles relative to their counterion atmospheres generates an acoustic pulse which can be related to the charge on the particles and the concentration of ions in solution (18). 

The well-known DLVO theory of coUoid stabiUty (10) attributes the state of flocculation to the balance between the van der Waals attractive forces and the repulsive electric double-layer forces at the Hquid—soHd interface. The potential at the double layer, called the zeta potential, is measured indirectly by electrophoretic mobiUty or streaming potential. The bridging flocculation by which polymer molecules are adsorbed on more than one particle results from charge effects, van der Waals forces, or hydrogen bonding (see Colloids). 

Electroultrafiltration (EUF) combines forced-flow electrophoresis (see Electroseparations,electrophoresis) with ultrafiltration to control or eliminate the gel-polarization layer (45—47). Suspended colloidal particles have electrophoretic mobilities measured by a zeta potential (see Colloids Elotation). Most naturally occurring suspensoids (eg, clay, PVC latex, and biological systems), emulsions, and protein solutes are negatively charged. Placing an electric field across an ultrafiltration membrane faciUtates transport of retained species away from the membrane surface. Thus, the retention of partially rejected solutes can be dramatically improved (see Electrodialysis). 

R = factor for electrical relaxation D = dielectric constant of medium F = factor for size of spheres and = zeta potential. 

This equation is a reasonable model of electrokinetic behavior, although for theoretical studies many possible corrections must be considered. Correction must always be made for electrokinetic effects at the wall of the cell, since this wall also carries a double layer. There are corrections for the motion of solvated ions through the medium, surface and bulk conductivity of the particles, nonspherical shape of the particles, etc. The parameter zeta, determined by measuring the particle velocity and substituting in the above equation, is a measure of the potential at the so-called surface of shear, ie, the surface dividing the moving particle and its adherent layer of solution from the stationary bulk of the solution. This surface of shear ties at an indeterrninate distance from the tme particle surface. Thus, the measured zeta potential can be related only semiquantitatively to the curves of Figure 3. 

The electrostatic repulsive forces are a function of particle kinetic energy (/ T), ionic strength, zeta potential, and separation distance. The van der Waals attractive forces are a function of the Hamaker constant and separation distance. 

Zeta Potential. When a textile is immersed in water a negative charge is developed on its surface. This is caked the 2eta potential. This happens even with ionic fibers in neutral dyebaths. Negatively charged dyes therefore are coulombicaUy repeUed. 

Not all of the ions in the diffuse layer are necessarily mobile. Sometimes the distinction is made between the location of the tme interface, an intermediate interface called the Stem layer (5) where there are immobilized diffuse layer ions, and a surface of shear where the bulk fluid begins to move freely. The potential at the surface of shear is called the zeta potential. The only methods available to measure the zeta potential involve moving the surface relative to the bulk. Because the zeta potential is defined as the potential at the surface where the bulk fluid may move under shear, this is by definition the potential that is measured by these techniques (3). 

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