Electrical Double Layer Forces

When particles are immersed in a liquid they may develop a surface charge by any one of a number of mechanisms. Here, consider the case of oxide particles immersed in aqueous solutions. The surface of a particle is comprised of atoms that have unsatisfied bonds. In vacuum, these unfulfilled bonds result in an equal number of positively charged metal ions and negatively charged oxygen ions as shown in Figure 5.5(a). When exposed to ambient air (which usually has at least 15 % relative humidity) or immersed in water, the surface reacts with water to produce surface hydroxyl groups (denoted M-OH) as shown in Figure 5.5(b).

The surface hydroxyl groups react with acid and base at low and high pH, respectively, via surface ionization reactions as follows (Hunter, 2001):

M-OHþ H^þ!^Ka M-OH^þ₂ ð5:9aÞ

-(a) vacuum (b) water (at IEP)

(c) low pH (d) high pH

-Figure 5.5 Schematic representation of the surface of metal oxides (a) in vacuum.

Unsatisfied bonds lead to positive and negative sites associated with metal and oxygen atoms, respectively. (b) The surface sites react with water or water vapour in the environment to form surface hydroxyl groups (M-OH). At the isoelectric point (IEP) the neutral sites dominate, and the few positive and negative sites present exist in equal numbers. (c) At low pH the surface hydroxyl groups react with H^þin solution to create a positively charged surface composed mainly of ðM-OH^þ₂Þ species. (d) At high pH the surface hydroxyl groups react with OH^in solution to create a negatively charged surface composed mainly of (M-O^) species

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resulting in either a positively charged surfaceðM-OH^þ₂Þ as in Figure 5.5(c), or a negatively charged surfaceðM  O^Þ as in Figure 5.5(d). The value of the surface ionization reaction constants (K_a and K_b) depend upon the particular type of material (for example SiO2, Al2O3and TiO2). For each type of material, there is a pH known as the isoelectric point (IEP), where the majority of surface sites are neutral (M-OH) and the net charge on the surface is zero. At a pH below or above the IEP, the particle’s surfaces become positivelyðM-OH^þ₂Þ or negatively (M-O^) charged due to the addition of either acid (H^þ) or base (OH^), respectively.

Figure 5.6 shows how the concentration of surface sites changes with pH.

Table 5.2 contains a listing of the IEPs of some common materials.

For each charged surface site there is a counterion of opposite charge in solution. For example, the counterion for a positive surface site is a Cl^ anion in the case when HCl is used to reduce the pH and the counterion for a negative surface site is a Na^þcation if NaOH is used to increase the pH. The entire system is electrically neutral. The separation of charge between the surface and the bulk solution results in a potential difference known as the surface potentialð0Þ.

M-OH₂⁺

M-OH

M-O^–

IEP pH

Number of sites per unit area

Figure 5.6 Number density per unit area of neutral (M-OH), positiveðM  OH^þ₂Þ and negative (M-O^) surface sites as a function of pH

Table 5.2 Isoelectric points of some common materials

Material pH of IEP

Silica 2–3

Alumina 8.5–9.5

Titania 5–7

Zirconia 7–8

Hematite 7–9

Calcite 8

Oil 3–4

Air 3–4

The counterions form a diffuse cloud that shrouds each particle in order to maintain electrical neutrality of the system. When two particles are forced together their counterion clouds begin to overlap and increase the concentration of counterions in the gap between the particles. If both particles have the same charge, this gives rise to a repulsive potential due to the osmotic pressure of the counterions which is known as the electrical double layer (EDL) repulsion. If the particles are of opposite charge an EDL attraction will result. It is important to realize that EDL interactions are not simply determined by the Columbic interaction between the two charged spheres, but are due to the osmotic pressure (concentration) effects of the counterions in the gap between the particles.

A measure of the thickness of the counterion cloud (and thus the range of the repulsion) is the Debye lengthðk^1Þ where the Debye screening parameter ðkÞ, for monovalent salts is (Israelachvili,1992):

k ¼ 3:29 ffiffiffiffiffi p½c

ðnm^1Þ ð5:10Þ

where [c] is the molar concentration of monovalent electrolyte. When the Debye length is large (small counterion concentration) the particles are repulsive at large separation distances so that the van der Waals attraction is overwhelmed as in Figure 5.2(c) and (d). The electrical double layer is compressed (Debye length is reduced) by adding a salt, which increases the concentration of the counterions around the particle. When sufficient salt is added, the range of the EDL repulsion is decreased sufficiently to allow the van der Waals attraction to dominate at large separation distances. At this point, an attractive potential energy well as shown in Figure 5.2(a) and (b) results.

An approximate expression for the EDL potential energy (VEDL) versus the surface to surface separation distance (D) between two spherical particles of diameter (x) with the same surface charge is (Israelachvili,1992):

VEDL¼ peeox²₀e^kD ð5:11Þ where 0 is the surface potential (created by the surface charge), e the relative permittivity of water, not voidage as frequently used in other parts of the book, e0

the permittivity of free space which is 8:854
10^12C²=J=m, and k the inverse Debye length. This expression is valid when the surface potential is constant and below about 25 mV and the separation distance between the particles is small relative to their size (Israelachvili, 1992).

Because a layer of immobile ions and water molecules exists at the surface of the particle it is not easy to directly measure the surface potential of particles.

Instead, a closely related potential known as the zeta potential is usually measured. The zeta potential can be determined by measuring the particle’s velocity in an electric field. The zeta potential is the potential at the plane of shear between the immobilized surface layer and the bulk solution. This plane is typically located only a few Angstroms from the surface so that there is little difference between the zeta potential and the surface potential. In practice, the zeta potential can be used in place of the surface potential in Equation (5.11) to predict the interparticle forces as a function of separation distance with little

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error. Addition of salt to a suspension reduces the magnitude of the zeta potential as well as compressing the range of the double layer (reducing Debye length) as described above. Figure 5.7 is an example of how pH and salt concentration influence the zeta potential of alumina particles.