Particle agglomeration refers to the formation of assemblages in a suspension and represents a mechanism leading to the functional destabilization of colloidal systems. During this process, particles dispersed in the liquid phase stick to each other, and spontaneously form irregular particle assemblages, flocs, or agglomerates. This phenomenon is also referred to as coagulation or flocculation and such a suspension is also called unstable. Particle agglomeration can be induced by adding salts or other chemicals referred to as coagulant or flocculant.[1]
Scheme of particle agglomeration. Particles are dispersed individually in a functionally stable suspension, while they agglomerate in a functionally unstable suspension. As agglomeration proceed from early to later states, the agglomerates grow in size, and may eventually gel.
Particle agglomeration can be a reversible or irreversible process. Particle agglomerates defined as "hard agglomerates" are more difficult to redisperse to the initial single particles. In the course of agglomeration, the agglomerates will grow in size, and as a consequence they may settle to the bottom of the container, which is referred to as sedimentation. Alternatively, a colloidal gel may form in concentrated suspensions which changes its rheological properties. The reverse process whereby particle agglomerates are re-dispersed as individual particles, referred to as peptization, hardly occurs spontaneously, but may occur under stirring or shear.
Colloidal particles may also remain dispersed in liquids for long periods of time (days to years). This phenomenon is referred to as colloidal stability and such a suspension is said to be functionally stable. Stable suspensions are often obtained at low salt concentrations or by addition of chemicals referred to as stabilizers or stabilizing agents. The stability of particles, colloidal or otherwise, is most commonly evaluated in terms of zeta potential. This parameter provides a readily quantifiable measure of interparticle repulsion, which is the key inhibitor of particle aggregation.
Similar agglomeration processes occur in other dispersed systems too. In emulsions, they may also be coupled to droplet coalescence, and not only lead to sedimentation but also to creaming. In aerosols, airborne particles may equally aggregate and form larger clusters (e.g., soot).
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, particle doublets A2 will form from singlets A1 according to the scheme[2]
In the early stage of the aggregation process, the suspension mainly contains individual particles. The rate of this phenomenon 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, defined as
where kfast 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.
Schematic stability plot of a colloidal suspension versus the salt concentration.
Often, colloidal particles are suspended in water. In this case, they accumulate a surface charge and an electrical double layer forms around each particle.[3] 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 the critical coagulation concentration (CCC) ranges for different net charge of the counter ion.[4] The charge is expressed in units of elementary charge. This dependence reflects the Schulze–Hardy rule,[5][6] 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.
Charge
CCC ( × 10−3 mol/L)
1
50-300
2
2-30
3
0.03-0.5
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.[2] 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 at it is the case with polycarboxylate ether (PCE), the last generation of chemically tailored superplasticizer specifically designed to increase the workability of concrete while reducing its water content to improve its properties and durability. 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.
Later stages
Structure of larger aggregates formed can be different. In the fast aggregation regime or DLCA regime, the aggregates are more ramified, while in the slow aggregation regime or RLCA regime, the aggregates are more compact.
As the aggregation process continues, larger clusters form. The growth occurs mainly through encounters between different clusters, and therefore one refers to cluster-cluster aggregation process. The resulting clusters are irregular, but statistically self-similar. They are examples of mass fractals, whereby their mass M grows with their typical size characterized by the radius of gyrationRg as a power-law[2]
where d is the mass fractal dimension. Depending whether the aggregation is fast or slow, one refers to diffusion limited cluster aggregation (DLCA) or reaction limited cluster aggregation (RLCA). The clusters have different characteristics in each regime. DLCA clusters are loose and ramified (d ≈ 1.8), while the RLCA clusters are more compact (d ≈ 2.1).[7] The cluster size distribution is also different in these two regimes. DLCA clusters are relatively monodisperse, while the size distribution of RLCA clusters is very broad.
The larger the cluster size, the faster their settling velocity. Therefore, aggregating particles sediment and this mechanism provides a way for separating them from suspension. At higher particle concentrations, the growing clusters may interlink, and form a particle gel. Such a gel is an elastic solid body, but differs from ordinary solids by having a very low elastic modulus.
Homoaggregation versus heteroaggregation
When aggregation occurs in a suspension composed of similar monodisperse colloidal particles, the process is called homoaggregation (or homocoagulation). When aggregation occurs in a suspension composed of dissimilar colloidal particles, one refers to heteroaggregation (or heterocoagulation). The simplest heteroaggregation process occurs when two types of monodisperse colloidal particles are mixed. In the early stages, three types of doublets may form:[8]
While the first two processes correspond to homoaggregation in pure suspensions containing particles A or B, the last reaction represents the actual heteroaggregation process. Each of these reactions is characterized by the respective aggregation coefficients kAA, kBB, and kAB. For example, when particles A and B bear positive and negative charge, respectively, the homoaggregation rates may be slow, while the heteroaggregation rate is fast. In contrast to homoaggregation, the heteroaggregation rate accelerates with decreasing salt concentration. Clusters formed at later stages of such heteroaggregation processes are even more ramified that those obtained during DLCA (d ≈ 1.4).[9]
An important special case of a heteroaggregation process is the deposition of particles on a substrate.[1] Early stages of the process correspond to the attachment of individual particles to the substrate, which can be pictures as another, much larger particle. Later stages may reflect blocking of the substrate through repulsive interactions between the particles, while attractive interactions may lead to multilayer growth, and is also referred to as ripening. These phenomena are relevant in membrane or filter fouling.
Experimental techniques
Numerous experimental techniques have been developed to study particle aggregation. Most frequently used are time-resolved optical techniques that are based on transmittance or scattering of light.[10]
Light transmission. The variation of transmitted light through an aggregating suspension can be studied with a regular spectrophotometer in the visible region. As aggregation proceeds, the medium becomes more turbid, and its absorbance increases. The increase of the absorbance can be related to the aggregation rate constant k and the stability ratio can be estimated from such measurements. The advantage of this technique is its simplicity.
Light scattering. These techniques are based on probing the scattered light from an aggregating suspension in a time-resolved fashion. Static light scattering yields the change in the scattering intensity, while dynamic light scattering the variation in the apparent hydrodynamic radius. At early-stages of aggregation, the variation of each of these quantities is directly proportional to the aggregation rate constant k.[11] At later stages, one can obtain information on the clusters formed (e.g., fractal dimension).[7] Light scattering works well for a wide range of particle sizes. Multiple scattering effects may have to be considered, since scattering becomes increasingly important for larger particles or larger aggregates. Such effects can be neglected in weakly turbid suspensions. Aggregation processes in strongly scattering systems have been studied with transmittance, backscattering techniques or diffusing-wave spectroscopy.
Single particle counting. This technique offers excellent resolution, whereby clusters made out of tenths of particles can be resolved individually.[11] The aggregating suspension is forced through a narrow capillary particle counter and the size of each aggregate is being analyzed by light scattering. From the scattering intensity, one can deduce the size of each aggregate, and construct a detailed aggregate size distribution. If the suspensions contain high amounts of salt, one could equally use a Coulter counter. As time proceeds, the size distribution shifts towards larger aggregates, and from this variation aggregation and breakup rates involving different clusters can be deduced. The disadvantage of the technique is that the aggregates are forced through a narrow capillary under high shear, and the aggregates may disrupt under these conditions.
Indirect techniques. As many properties of colloidal suspensions depend on the state of aggregation of the suspended particles, various indirect techniques have been used to monitor particle aggregation too. While it can be difficult to obtain quantitative information on aggregation rates or cluster properties from such experiments, they can be most valuable for practical applications. Among these techniques settling tests are most relevant. When one inspects a series of test tubes with suspensions prepared at different concentration of the flocculant, stable suspensions often remain dispersed, while the unstable ones settle. Automated instruments based on light scattering/transmittance to monitor suspension settling have been developed, and they can be used to probe particle aggregation. One must realize, however, that these techniques may not always reflect the actual aggregation state of a suspension correctly. For example, larger primary particles may settle even in the absence of aggregation, or aggregates that have formed a colloidal gel will remain in suspension. Other indirect techniques capable to monitor the state of aggregation include, for example, filtration, rheology, absorption of ultrasonic waves, or dielectric properties.[10]
Relevance
Particle aggregation is a widespread phenomenon, which spontaneously occurs in nature but is also widely explored in manufacturing. Some examples include.
Formation of river delta. When river water carrying suspended sediment particles reaches salty water, particle aggregation may be one of the factors responsible for river delta formation. Charged particles are stable in river's fresh water containing low levels of salt, but they become unstable in sea water containing high levels of salt. In the latter medium, the particles aggregate, the larger aggregates sediment, and thus create the river delta.
Papermaking. Retention aids are added to the pulp to accelerate paper formation. These aids are coagulating aids, which accelerate the aggregation between the cellulose fibers and filler particles. Frequently, cationic polyelectrolytes are being used for that purpose.
Water treatment. Treatment of municipal waste water normally includes a phase where fine solid particles are removed. This separation is achieved by addition of a flocculating or coagulating agent, which induce the aggregation of the suspended solids. The aggregates are normally separated by sedimentation, leading to sewage sludge. Commonly used flocculating agents in water treatment include multivalent metal ions (e.g., Fe3+ or Al3+), polyelectrolytes, or both.
Cheese making. The key step in cheese production is the separation of the milk into solid curds and liquid whey. This separation is achieved by inducing the aggregation processes between casein micelles by acidifying the milk or adding rennet. The acidification neutralizes the carboxylate groups on the micelles and induces the aggregation.
A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend the definition to include substances like aerosols and gels. The term colloidal suspension refers unambiguously to the overall mixture. A colloid has a dispersed phase and a continuous phase. The dispersed phase particles have a diameter of approximately 1 nanometre to 1 micrometre.
In polymer chemistry, emulsion polymerization is a type of radical polymerization that usually starts with an emulsion incorporating water, monomers, and surfactants. The most common type of emulsion polymerization is an oil-in-water emulsion, in which droplets of monomer are emulsified in a continuous phase of water. Water-soluble polymers, such as certain polyvinyl alcohols or hydroxyethyl celluloses, can also be used to act as emulsifiers/stabilizers. The name "emulsion polymerization" is a misnomer that arises from a historical misconception. Rather than occurring in emulsion droplets, polymerization takes place in the latex/colloid particles that form spontaneously in the first few minutes of the process. These latex particles are typically 100 nm in size, and are made of many individual polymer chains. The particles are prevented from coagulating with each other because each particle is surrounded by the surfactant ('soap'); the charge on the surfactant repels other particles electrostatically. When water-soluble polymers are used as stabilizers instead of soap, the repulsion between particles arises because these water-soluble polymers form a 'hairy layer' around a particle that repels other particles, because pushing particles together would involve compressing these chains.
In chemistry, a suspension is a heterogeneous mixture of a fluid that contains solid particles sufficiently large for sedimentation. The particles may be visible to the naked eye, usually must be larger than one micrometer, and will eventually settle, although the mixture is only classified as a suspension when and while the particles have not settled out.
A dilatant material is one in which viscosity increases with the rate of shear strain. Such a shear thickening fluid, also known by the initialism STF, is an example of a non-Newtonian fluid. This behaviour is usually not observed in pure materials, but can occur in suspensions.
A sol is a colloidal suspension made out of tiny solid particles in a continuous liquid medium. Sols are stable and exhibit the Tyndall effect, which is the scattering of light by the particles in the colloid. Examples include amongst others blood, pigmented ink, cell fluids, paint, antacids and mud.
The DLVO theory explains the aggregation and kinetic stability of aqueous dispersions quantitatively and describes the force between charged surfaces interacting through a liquid medium. It combines the effects of the van der Waals attraction and the electrostatic repulsion due to the so-called double layer of counterions. The electrostatic part of the DLVO interaction is computed in the mean field approximation in the limit of low surface potentials - that is when the potential energy of an elementary charge on the surface is much smaller than the thermal energy scale, . For two spheres of radius each having a charge separated by a center-to-center distance in a fluid of dielectric constant containing a concentration of monovalent ions, the electrostatic potential takes the form of a screened-Coulomb or Yukawa potential,
A nanoparticle or ultrafine particle is usually defined as a particle of matter that is between 1 and 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 100 nm in only two directions. At the lowest range, metal particles smaller than 1 nm are usually called atom clusters instead.
In colloidal chemistry, flocculation is a process by which colloidal particles come out of suspension to sediment in the form of floc or flake, either spontaneously or due to the addition of a clarifying agent. The action differs from precipitation in that, prior to flocculation, colloids are merely suspended, under the form of a stable dispersion and are not truly dissolved in solution.
In materials science, the sol–gel process is a method for producing solid materials from small molecules. The method is used for the fabrication of metal oxides, especially the oxides of silicon (Si) and titanium (Ti). The process involves conversion of monomers into a colloidal solution (sol) that acts as the precursor for an integrated network of either discrete particles or network polymers. Typical precursors are metal alkoxides. Sol–gel process is used to produce ceramic nanoparticles.
Electrocoagulation (EC) is a technique used for wastewater treatment, wash water treatment, industrially processed water, and medical treatment. Electrocoagulation has become a rapidly growing area of wastewater treatment due to its ability to remove contaminants that are generally more difficult to remove by filtration or chemical treatment systems, such as emulsified oil, total petroleum hydrocarbons, refractory organics, suspended solids, and heavy metals. There are many brands of electrocoagulation devices available and they can range in complexity from a simple anode and cathode to much more complex devices with control over electrode potentials, passivation, anode consumption, cell REDOX potentials as well as the introduction of ultrasonic sound, ultraviolet light and a range of gases and reactants to achieve so-called Advanced Oxidation Processes for refractory or recalcitrant organic substances.
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using the intensity or photon auto-correlation function. In the time domain analysis, the autocorrelation function (ACF) usually decays starting from zero delay time, and faster dynamics due to smaller particles lead to faster decorrelation of scattered intensity trace. It has been shown that the intensity ACF is the Fourier transform of the power spectrum, and therefore the DLS measurements can be equally well performed in the spectral domain. DLS can also be used to probe the behavior of complex fluids such as concentrated polymer solutions.
The peptization of a liquid mixture is the process of converting the mixture into a colloid by shaking it with a suitable electrolyte called a peptizing agent. That is, the insoluble solid particles which have settled out of the mixture are reformed into microscopic particles suspended in the mixture. Peptization is the reverse of flocculation, the aggregation of colloidal particles into precipitate; as such, it is also known as deflocculation.
A colloidal crystal is an ordered array of colloidal particles and fine grained materials analogous to a standard crystal whose repeating subunits are atoms or molecules. A natural example of this phenomenon can be found in the gem opal, where spheres of silica assume a close-packed locally periodic structure under moderate compression. Bulk properties of a colloidal crystal depend on composition, particle size, packing arrangement, and degree of regularity. Applications include photonics, materials processing, and the study of self-assembly and phase transitions.
Colloidal silicas are suspensions of fine amorphous, nonporous, and typically spherical silica particles in a liquid phase. It may be produced by Stöber process from Tetraethyl orthosilicate (TEOS).
Adsorption of polyelectrolytes on solid substrates is a surface phenomenon where long-chained polymer molecules with charged groups bind to a surface that is charged in the opposite polarity. On the molecular level, the polymers do not actually bond to the surface, but tend to "stick" to the surface via intermolecular forces and the charges created by the dissociation of various side groups of the polymer. Because the polymer molecules are so long, they have a large amount of surface area with which to contact the surface and thus do not desorb as small molecules are likely to do. This means that adsorbed layers of polyelectrolytes form a very durable coating. Due to this important characteristic of polyelectrolyte layers they are used extensively in industry as flocculants, for solubilization, as supersorbers, antistatic agents, as oil recovery aids, as gelling aids in nutrition, additives in concrete, or for blood compatibility enhancement to name a few.
The Stöber process is a chemical process used to prepare silica particles of controllable and uniform size for applications in materials science. It was pioneering when it was reported by Werner Stöber and his team in 1968, and remains today the most widely used wet chemistry synthetic approach to silica nanoparticles. It is an example of a sol-gel process wherein a molecular precursor is first reacted with water in an alcoholic solution, the resulting molecules then joining together to build larger structures. The reaction produces silica particles with diameters ranging from 50 to 2000 nm, depending on conditions. The process has been actively researched since its discovery, including efforts to understand its kinetics and mechanism – a particle aggregation model was found to be a better fit for the experimental data than the initially hypothesized LaMer model. The newly acquired understanding has enabled researchers to exert a high degree of control over particle size and distribution and to fine-tune the physical properties of the resulting material in order to suit intended applications.
Particle deposition is the spontaneous attachment of particles to surfaces. The particles in question are normally colloidal particles, while the surfaces involved may be planar, curved, or may represent particles much larger in size than the depositing ones. Deposition processes may be triggered by appropriate hydrodynamic flow conditions and favorable particle-surface interactions. Depositing particles may just form a monolayer which further inhibits additional particle deposition, and thereby one refers to surface blocking. Initially attached particles may also serve as seeds for further particle deposition, which leads to the formation of thicker particle deposits, and this process is termed as surface ripening or fouling. While deposition processes are normally irreversible, initially deposited particles may also detach. The latter process is known as particle release and is often triggered by the addition of appropriate chemicals or a modification in flow conditions.
Double layer forces occur between charged objects across liquids, typically water. This force acts over distances that are comparable to the Debye length, which is on the order of one to a few tenths of nanometers. The strength of these forces increases with the magnitude of the surface charge density. For two similarly charged objects, this force is repulsive and decays exponentially at larger distances, see figure. For unequally charged objects and eventually at shorted distances, these forces may also be attractive. The theory due to Derjaguin, Landau, Verwey, and Overbeek (DLVO) combines such double layer forces together with Van der Waals forces in order to estimate the actual interaction potential between colloidal particles.
A depletion force is an effective attractive force that arises between large colloidal particles that are suspended in a dilute solution of depletants, which are smaller solutes that are preferentially excluded from the vicinity of the large particles. One of the earliest reports of depletion forces that lead to particle coagulation is that of Bondy, who observed the separation or "creaming" of rubber latex upon addition of polymer depletant molecules to solution. More generally, depletants can include polymers, micelles, osmolytes, ink, mud, or paint dispersed in a continuous phase.
In water treatment, coagulation and flocculation involve the addition of compounds that promote the clumping of fine floc into larger floc so that they can be more easily separated from the water. Coagulation is a chemical process that involves neutralization of charge whereas flocculation is a physical process and does not involve neutralization of charge. The coagulation-flocculation process can be used as a preliminary or intermediary step between other water or wastewater treatment processes like filtration and sedimentation. Iron and aluminium salts are the most widely used coagulants but salts of other metals such as titanium and zirconium have been found to be highly effective as well.
References
1 2 M. Elimelech, J. Gregory, X. Jia, R. Williams, Particle Deposition and Aggregation: Measurement, Modelling and Simulation, Butterworth-Heinemann, 1998.
1 2 3 W. B. Russel, D. A. Saville, W. R. Schowalter,Colloidal Dispersions,Cambridge University Press, 1989.
↑ D. F. Evans, H. Wennerstrom, The Colloidal Domain, John Wiley, 1999.
↑ Tezak, B.; Matijevic, E.; Schuiz, K. F. (1955). "Coagulation of Hydrophobic Sols in Statu Nascendi. III. The Influence of the Ionic Size and Valency of the Counterion". The Journal of Physical Chemistry. 59 (8): 769–773. doi:10.1021/j150530a018. ISSN0022-3654.
↑ James, Robert O.; Homola, Andrew; Healy, Thomas W. (1977). "Heterocoagulation of amphoteric latex colloids". Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases. 73: 1436. doi:10.1039/f19777301436. ISSN0300-9599.
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