Colloidal Stability

Because slip casting of metals is a wet process, some understanding of the interaction between the material and water must be established. Most materials when immersed in a polar solvent become charged. The different mechanisms by which the surface acquires such charge depend greatly on the type of material used. These mechanisms include ion dissolution and ion adsorption (Ref 4, 7). Ionic materials acquire their surface charge through preferential dissolution. A very well known example is Agl, where the solubility product gives the amount of soluble species Ag+ and I- When an excess of I- ions is present, the colloid is negatively charged, and vice versa. These ions are called potential-determining ions (PDI). For the case of metal oxides, hydronium and hydroxyl ions become PDIs. This process is illustrated by the next reaction:

A material can also gain surface charge by unequal adsorption of ions in the surrounding solution. If a larger quantity of positive ions is adsorbed on a particle surface, then a positive surface charge will result, and vice versa.

Electrical Double Layer. It is necessary to understand the behavior of the potential and charge distribution around the vicinity of colloidal particles. For this reason, it is very important to understand the source of the charge distribution. The electrical double layer is thought to be composed of two parts, the inner portion of the double layer and the diffuse double layer.

Helmholtz was the first to relate the electrical double layer to a metal surface (Ref 7). He assumed that the charge on the particle surface was balanced by an equal and opposite charge located near the particle surface in the surrounding solution. This theory was then modified by French and British scientists and the model was called the Gouy-Chapman model. This model is the simplest quantitative treatment for the diffuse part of the double layer. The assumptions are (Ref

• The particle surface is assumed to be planar with a uniform surface charge.

• Ions of the diffuse portion of the double layer are distributed according to the Boltzmann distribution.

• The solvent is assumed to influence the double layer only by its dielectric constant.

• A symmetrical one-to-one electrolyte is assumed.

A schematic of this model for a particle medium interface is shown in Fig. 4. This model gives the mathematical function that describes the potential distribution at a distance from the particle surface:

where the potential at a distance x from the particle surface, is the surface potential, and ftis the Debye parameter, or the inverse double layer thickness. For low surface potential, the potential can be related to the surface charge through:

where i70 is the surface charge and cis the medium dielectric constant. The surface potential depends on both the surface charge density and the Debye parameter, which is in turn affected by the ionic strength of the medium. As a result, when the double layer is compressed, ^increases and both the surface charge and the surface potential are affected. Surface charge must increase and surface potential must decrease, respectively, or both can occur.

Fig. 4 Electrostatic potential distribution in parallel planes near a metal surface. Source: Ref 7

In the Gouy-Chapman treatment, the ions on the diffuse layer are considered point charges. Stern modified the double-layer theory to account for specific adsorption of ions as well as for the fact that ions have a finite size. This theory proposed a division of the double layer into two parts by a plane called the Stern plane. Ions with centers located within an ionic radius of the particle surface are in the inner part of the double layer. The ions located beyond the Stern plane are in the diffuse portion of the double layer, where the Gouy-Chapman treatment is considered to be applicable. The potential changes from to 4V Figure 5 shows schematic of Stern's representation of the electrical double layer.

Fig. 5 Representation of Stern's electrical double layer. Source: Ref 4

In the presence of specific adsorption, either co-ion or counter-ion adsorption can occur. The Stern potential is either reduced or reversed with respect to the surface potential, as shown in Fig. 6. The Stern potential can be determined by electrokinetic measurements. Electrokinetic behavior depends on the potential at the surface of shear between the charged surface and the electrolyte solution (Ref 4). This potential is called the zeta potential |C |. The exact location of the shear surface is unknown, but it is accepted that it is located very close to the Stern plane. Therefore, it is usual to assume identity between and C. The zeta potential is a property that can be readily measured, while the Stern potential cannot. For this reason, zeta potential values are used in determining material surface properties.

Fig. 6 (a) Reversal of charge due to adsorption of surface-active counter-ions. (b) Adsorption of surface-active co-ions. Source: Ref 4

DVLO Theory. The stability of colloidal-sized particles depends essentially on the balance of attractive and repulsive forces surrounding the suspended particle. A quantitative theory enabling determination of stability was developed independently by Deryagin and Landau and Verwey and Overbeek and is called the DVLO theory. According to this theory, the total interaction between particles is the sum of two contributions, VR, the repulsive part due to the overlapping of double layers, and VA, the attractive portion resulting from Van der Waals attraction (Ref 4, 7, 8):

Figure 7 shows total interaction energy curves. The repulsive forces are an exponential function that is effective on the range of the double layer. It is positive for all values of distances between the two particles. The attractive forces, on the other hand, decrease as the inverse power of the distance between the particles. At very small distances, the attractive potential becomes very negative, forming the potential energy well described as the primary minimum. When particles lie at this distance, they typically form very strong aggregates that cannot be broken up under normal shear conditions. As the distance between these particles increases, the repulsive forces start taking over and a maximum energy barrier results. The magnitude of this barrier depends on the concentration of electrolyte present. A secondary minimum develops at large separation distances between particles. The attractive forces dominate at this distance, leading to a potential well. In order for flocculation of particles to occur, the energy barrier between particles should be either very small or very big. One way in which an energy barrier may be reduced is the presence of a significant amount of electrolyte that will cause a compression of the electrostatic double layer between particles and allow for Van der Waals forces to dominate between particles. A more detailed review of this theory can be found in Ref 4 and 7.

Fig. 7 Total interaction energy curves, V(1) and V(2), obtained by the summation of an attractive curve, VA, with different repulsion curves, VR(1) and VR(2). Source: Ref 4

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