Why too much dispersant causes problems.
Zeta potential in aqueous suspensions is a function of two variables: charge at the shear plane and free salt ion concentration. [Free here means not attached to the particle surface.] If a dispersant is added to increase the surface charge density (increase stability) and it’s too concentrated, the contribution it makes to the free salt ion concentration is counterproductive (promotes instability).
Colloidal suspensions are stabilized in one of two ways. Surface charge, naturally occurring or added, enhances electrostatic stability. Adsorption of non-polar surfactants or polymers enhances stability through static stabilization. Electrostatic stabilization gives rise to a mobile, charged, colloidal particle whose electrophoretic mobility can be measured. Zeta potential is calculated from mobility.
The square of the zeta potential is proportional to the force of electrostatic repulsion between charged particles. Zeta potentials are, therefore, measures of stability. Increasing the absolute zeta potentials increases electrostatic stabilization. As the zeta potential approaches zero, electrostatic repulsions becomes small compared to the ever-present Van der Waals attraction. Eventually, instability increases, that can result in aggregation followed by sedimentation and phase separation.
Electrostatic Potential Differences: Surface Potential Defined
Imagine that you had two, infinitesimally small metal probes attached to a voltmeter. Now imagine one probe is attached to the surface of a colloidal particle and the other one is in the liquid in which the particle is suspended. The reading on the meter is the electrostatic potential difference between these two points. It is called the surface potential Ψo. See Figure 1 where Ψo = +80 mV.
The y-axis in this figure also represents the solid-liquid boundary. The x-axis, in nanometers, is the distance from the surface out into the liquid, it being assumed there is no other particle close by. There are two idealizations in a figure like this one. First, real solid particles are not smooth at the atomic level. They are more like low lying, rough hills on the atomic level. Second, the charge density on the surface is not typically uniform, but often patchy. The surface has lots of hydrophobic spaces characterized by no charge and lots of hydrophilic spaces characterized by charge.
Therefore, if we could attach a tiny voltmeter probe at specific surface locations, the surface potential would vary from place to place. But we can neither freeze the particle motion in a liquid nor are there probes small enough. Thus, a cartoon like this one arises when we average spatially (vertically) over the rough surface to define an imaginary plane to call the surface.
In addition, we are averaging temporally over the rotational diffusion time of the particle that is much faster than the time to make an electrostatic measurement. Still, these idealizations work well and have been the basis for using zeta potential determinations to describe colloidal stability for more than 50 years.
Before describing the zeta potential, it is wroth nothing a few special features of the curves in Figure 1. If nothing is specifically adsorbed onto the surface, the corresponding anions (the suspensions much be neutral overall), or the anions from added salts (or surfactants) preferentially gather near the positive surface. Thermally-driven diffusion increases the randomization of all ions as the distance from the surface increases. The electrostatic potential difference thus decreases. Far enough away from the surface, if the voltmeter probes are placed in the liquid; the electrostatic potential difference is zero since the average charge density is constant.
Depending on the sophistication of the theory to describe what takes place close to the surface, a variety of imaginary, but theoretically useful planes or layers are defined. Here, the simplest is shown. It is called the Stern plane. The electrostatic potential difference is called ?d. It represents the average position of the counter-ions that move with the surface.
Zeta Potential Defined
Any molecule covalently bonded to the surface move with the particle when it diffuses or is induced to move electrophoretically in an applied electric field. When wetting, dispersing or stabilizing agents are strongly adsorbed onto the surface, they too move with the particle. Counter-ions very near the surface, perhaps within the first nanometer or two also move with the particle. Finally, solvent molecules are sometimes also strongly bound to the surface.
However, at some short distance from the surface, the less tightly bound species are more diffuse and do not move with the particle. So another imaginary yet useful theoretical layer is defined: the shear plane. Everything inside the shear plane is considered to move with the particle; everything outside of the shear plane does not. In other words, as the particle moves it shears the liquid at this plane.
The zeta potential is defined to be the electrostatic potential difference between an average point on the shear plane and one out in the liquid away from any particles.
Zeta potential is important because, for most real systems, one cannot measure the surface potential. One cannot measure the zeta potential directly either; however, one can measure the electrostatic mobility of the particles and calculate zeta potential. Though strictly incorrect, it is common to hear the zeta potential spoken of as a substitute for the surface potential. The surface potential is a function of the surface charge density. The zeta potential is a function of the charge density at the shear plane. The magnitude of the zeta potential is almost always much smaller than the surface potential. Even the sign of the zeta potential can be different.
Figure 1 also shows the case of specific adsorption of an anionic dispersing agent onto the positively charged surface. This may occur if the hydrophobic, patchy surfaces that are uncharged can firmly anchor the non-polar tail of a sufficiently long, anionic surfactant. The shear plane is shifted further out (for simplicity, not shown here) and is now negative. The zeta potential is now negative; whereas, the original zeta potential is positive.
Whether or not the sign of the zeta potential is the same as that of the surface potential, it is clear that the zeta potential is a measure of the charge density ultimately arising from the surface or species attached to it. There is another contribution to zeta potential that is too often ignored when trying to properly interpret colloidal stability.
Effect of Salt on Zeta Potential
Theories describing how the charge density around a particle varies with distance always use the concept of the diffuse double layer. In the simplest theory, the electrostatic potential decays exponentially with distance away from the shear plane. The inverse of the decay constant is a distance called the Debye double layer thickness. It is a function of free salt ion concentration (as embodied in the value of the ionic strength): the higher the concentration, the faster the decay, the smaller the double layer thickness. At high enough salt, the double layer collapses to the extent that the ever-present attractive van der Waals forces overcome the charge repulsion. This is one example of the so-called “salting out” effect. Electrostatically stabilized colloidal suspensions will become unstable with the addition of enough salt.
See Figure 2. The zeta potential decreases when the concentration of free salt ions increases. In the figure, c is the free salt ion concentration. Since c2 > c1 it follows that ?2< ?1. (For simplicity, the shift in the position of the shear plane was not shown.)
Too Much Dispersant
Oxide surfaces often have an affinity for phosphates. Phosphate ions can increase surface charge density, resulting in higher absolute zeta potential. An example is shown in Figure 3. Colloidal silica, SiO2, catalog no. 421552, obtained from the Sigma-Aldrich Company is 30% v/v aqueous suspension as received. It was diluted about 100:1 for these measurements. All measurements were made with a Brookhaven NanoBrook ZetaPALS zeta potential analyzer. The zeta potential is approximately -30 mV diluted in just DI water.
When tetrasodium pyrophosphate, TSPP, is added to water, it hydrolyzes completely to form phosphate. The hydrogen phosphate hydrolyzes a little bit to form dihydrogen phosphate plus hydroxide ion. For this reason, solutions of TSPP are basic with pH around 10, depending on the initial concentration of TSPP.
With the initial addition of TSPP, the zeta potential decreases. This suggests that the hydrogen phosphate, the phosphate species in highest concentration, adsorbs at the silica surface. The negative surface charge density is increased, and the zeta potential decreases to approximately -70 mV, a substantial change towards greater electrostatic stability.
However, TSPP is a 4:1 electrolyte and for every mole of TSPP added, the ionic strength increases by a factor of 10. A lot of free ions are created that begin to decrease the double layer.
Initially, the decrease in the double layer thickness that would result in a higher zeta potential is insignificant compared to the effect of the hydrogen phosphate adsorbing at the surface. Yet, there is a competition and the two effects strike a balance from 0.01 to 0.1% wt/vol. Beyond 0.1% the particle surface is saturated and additional TSPP now works against stability by collapsing the double layer resulting in a significant decrease in the zeta potential.
Clearly, for this particular distribution of SiO2 surface areas, somewhere between 0.01 and 0.1% wt/vol is optimum for stability. Adding more is counterproductive. Since the concentration of SiO2 in this case was 0.6% w/vol, the optimum TSPP concentration varies from 1.7% to 17% of the solids concentration. A rule of thumb is 10% of the solids concentration for the dispersant. Clearly, that rule depends on the particle size distribution as that determines surface area and coverage requirements. Yet, here, it held up reasonably well.
Ionic dispersants can help stabilize oxide surfaces by adding surface charge density. Zeta potential is a measure of the success of the addition. However, too much dispersant can be counterproductive when the surface is saturated and the ionic strength rises too much.