Particle Aggregation - Early Stages

Early Stages

A well dispersed colloidal suspension consists of individual, separated particles and is stabilized by repulsive inter-particle forces. When the repulsive forces weaken or become attractive through the addition of a coagulant, particles start to aggregate. Initially, only particle doublets will form according to the scheme

A + A → A₂

In the early stage of the aggregation process, the suspension mainly contains particle monomers and some dimers. The rate of this reaction is characterized by the aggregation rate coefficient k. Since doublet formation is a second order rate process, the units of this coefficients are m3s−1 since particle concentrations are expressed as particle number per unit volume (m−3). Since absolute aggregation rates are difficult to measure, one often refers to the dimensionless stability ratio W = k_fast/k where k_fast is the aggregation rate coefficient in the fast regime, and k the coefficient at the conditions of interest. The stability ratio is close to unity in the fast regime, increases in the slow regime, and becomes very large when the suspension is stable.

When the interaction potential between the particles is purely attractive, the aggregation process is solely limited by mutual diffusion (or Brownian motion) of the particles, one refers to fast, rapid or diffusion limited aggregation (DLA). When the interaction potential shows an intermediate barrier, the aggregation is slowed down by the fact that numerous attempts will be necessary to overcome this barrier, and one refers to slow or reaction limited aggregation (RLA). The aggregation can be tuned from fast to slow by varying the concentration of salt, pH, or an other additive. Since the transition from fast to slow aggregation occurs in a narrow concentration range, and one refers to this range as the critical coagulation concentration (CCC).

Often, colloidal particles are suspended in water. In this case, they accumulate a surface charge and an electrical double layer forms around each particle. The overlap between the diffuse layers of two approaching particles results in a repulsive double layer interaction potential, which leads to particle stabilization. When salt is added to the suspension, the electrical double layer repulsion is screened, and van der Waals attraction become dominant and induce fast aggregation. The figure on the right shows the typical dependence of the stability ratio W versus the electrolyte concentration, whereby the regimes of slow and fast aggregation are indicated.

The table below summarizes CCC ranges for different net charge of the counter ion. The charge is expressed in units of elementary charge. This dependence reflects the Schulze-Hardy rule, which states that the CCC varies as the inverse sixth power of the counter ion charge. The CCC also depends on the type of ion somewhat, even if they carry the same charge. This dependence may reflect different particle properties or different ion affinities to the particle surface. Since particles are frequently negatively charged, multivalent metal cations thus represent highly effective coagulants.

Adsorption of oppositely charged species (e.g., protons, specifically adsorbing ions, surfactants, or polyelectrolytes) may destabilize a particle suspension by charge neutralization or stabilize it by buildup of charge, leading to a fast aggregation near the charge neutralization point, and slow aggregation away from it.

Quantitative interpretation of colloidal stability was first formulated within the DLVO theory. This theory confirms the existence slow and fast aggregation regimes, even though in the slow regime the dependence on the salt concentration is often predicted to be much stronger than observed experimentally. The Schulze-Hardy rule can be derived from DLVO theory as well.

Other mechanisms of colloid stabilization are equally possible, particularly, involving polymers. Adsorbed or grafted polymers may form a protective layer around the particles, induce steric repulsive forces, and lead to steric stabilization. When polymers chains adsorb to particles loosely, a polymer chain may bridge two particles, and induce bridging forces. This situation is referred to as bridging flocculation.

When particle aggregation is solely driven by diffusion, one refers to perikinetic aggregation. Aggregation can be enhanced through shear stress (e.g., stirring). The latter case is called orthokinetic aggregation.