806:
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,
306:
68:
439:
344:. This dependence reflects the SchulzeāHardy 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.
772:. At later stages, one can obtain information on the clusters formed (e.g., fractal dimension). 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
704:. 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 (
799:. 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.
672:
1282:
Holthoff, Helmut; Schmitt, Artur; FernĆ”ndez-Barbero, Antonio; Borkovec, Michal; CabrerıĢzo-VıĢlchez, Miguel Ć”ngel; Schurtenberger, Peter; Hidalgo-Ć”lvarez, Roque (1997). "Measurement of
Absolute Coagulation Rate Constants for Colloidal Particles: Comparison of Single and Multiparticle Light Scattering
873:
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
859:
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
805:
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
839:
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
526:
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
715:
on a substrate. 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
447:
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
558:
514:
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
155:
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
76:
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
398:. 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 SchulzeāHardy rule can be derived from DLVO theory as well.
71:
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
794:
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
401:
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
676:
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
849:
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.
414:
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.
442:
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
240:
process, the units of this coefficients are ms since particle concentrations are expressed as particle number per unit volume (m). Since absolute aggregation rates are difficult to measure, one often refers to the
1074:"The generalization that the critical coagulation concentration for a typical lyophobic sol is extremely sensitive to the valence of the counter-ions (high valence gives a low critical coagulation concentration)"
563:
391:) 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.
1076:. Source: PAC, 1972, 31, 577 (Manual of Symbols and Terminology for Physicochemical Quantities and Units, Appendix II: Definitions, Terminology and Symbols in Colloid and Surface Chemistry) on page 610.
667:{\displaystyle {\begin{aligned}\mathrm {A+A} &\longrightarrow \mathrm {A} _{2}\\\mathrm {B+B} &\longrightarrow \mathrm {B} _{2}\\\mathrm {A+B} &\longrightarrow \mathrm {AB} \end{aligned}}}
302:
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.
287:
790:
This technique offers excellent resolution, whereby clusters made out of tenths of particles can be resolved individually. The aggregating suspension is forced through a narrow capillary
768:
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
228:
523:ā 2.1). 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.
232:
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
505:
1037:
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".
1186:
Kim, Anthony Y; Hauch, Kip D; Berg, John C; Martin, James E; Anderson, Robert A (2003). "Linear chains and chain-like fractals from electrostatic heteroaggregation".
555:). The simplest heteroaggregation process occurs when two types of monodisperse colloidal particles are mixed. In the early stages, three types of doublets may form:
403:
728:
Numerous experimental techniques have been developed to study particle aggregation. Most frequently used are time-resolved optical techniques that are based on
830:
Particle aggregation is a widespread phenomenon, which spontaneously occurs in nature but is also widely explored in manufacturing. Some examples include.
325:
potential, which leads to particle stabilization. When salt is added to the suspension, the electrical double layer repulsion is screened, and
124:. This parameter provides a readily quantifiable measure of interparticle repulsion, which is the key inhibitor of particle aggregation.
104:
Colloidal particles may also remain dispersed in liquids for long periods of time (days to years). This phenomenon is referred to as
716:
interactions may lead to multilayer growth, and is also referred to as ripening. These phenomena are relevant in membrane or filter
252:
840:
levels of salt. In the latter medium, the particles aggregate, the larger aggregates sediment, and thus create the river delta.
169:
329:
become dominant and induce fast aggregation. The figure on the right shows the typical dependence of the stability ratio
38:, and spontaneously form irregular particle assemblages, flocs, or agglomerates. This phenomenon is also referred to as
336:
The table below summarizes the critical coagulation concentration (CCC) ranges for different net charge of the counter
321:
forms around each particle. The overlap between the diffuse layers of two approaching particles results in a repulsive
955:
860:
sewage sludge. Commonly used flocculating agents in water treatment include multivalent metal ions (e.g., Fe or Al),
760:
These techniques are based on probing the scattered light from an aggregating suspension in a time-resolved fashion.
754:
and the stability ratio can be estimated from such measurements. The advantage of this technique is its simplicity.
539:
When aggregation occurs in a suspension composed of similar monodisperse colloidal particles, the process is called
112:. Stable suspensions are often obtained at low salt concentrations or by addition of chemicals referred to as
1151:
James, Robert O.; Homola, Andrew; Healy, Thomas W. (1977). "Heterocoagulation of amphoteric latex colloids".
93:. The reverse process whereby particle agglomerates are re-dispersed as individual particles, referred to as
55:
39:
1102:
1361:
781:
1087:
Gold Book IUPAC (1997). SchulzeāHardy rule. IUPAC Compendium of
Chemical Terminology 2nd Edition (1997).
472:
1356:
333:
versus the electrolyte concentration, whereby the regimes of slow and fast aggregation are indicated.
547:). When aggregation occurs in a suspension composed of dissimilar colloidal particles, one refers to
765:
742:
The variation of transmitted light through an aggregating suspension can be studied with a regular
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132:
1153:
Journal of the
Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases
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23:
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120:. The stability of particles, colloidal or otherwise, is most commonly evaluated in terms of
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35:
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increases. The increase of the absorbance can be related to the aggregation rate constant
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in the visible region. As aggregation proceeds, the medium becomes more turbid, and its
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Adsorption of oppositely charged species (e.g., protons, specifically adsorbing ions,
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Quantitative interpretation of colloidal stability was first formulated within the
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Often, colloidal particles are suspended in water. In this case, they accumulate a
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309:
Schematic stability plot of a colloidal suspension versus the salt concentration.
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M. Y. Lin; H. M. Lindsay; D. A. Weitz; R. C. Ball; R. Klein; P. Meakin (1989).
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143:, airborne particles may equally aggregate and form larger clusters (e.g.,
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Particle
Deposition and Aggregation: Measurement, Modelling and Simulation
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Similar agglomeration processes occur in other dispersed systems too. In
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and represents a mechanism leading to the functional destabilization of
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When particle aggregation is solely driven by diffusion, one refers to
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Gregory, John (2009). "Monitoring particle aggregation processes".
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solid body, but differs from ordinary solids by having a very low
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An important special case of a heteroaggregation process is the
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97:, hardly occurs spontaneously, but may occur under stirring or
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is the aggregation rate coefficient in the fast regime, and
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systems. During this process, particles dispersed in the
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to the bottom of the container, which is referred to as
89:
may form in concentrated suspensions which changes its
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yields the change in the scattering intensity, while
561:
475:
410:
specifically designed to increase the workability of
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172:
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456:grows with their typical size characterized by the
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666:
519:ā 1.8), while the RLCA clusters are more compact (
499:
406:(PCE), the last generation of chemically tailored
281:
222:
50:. Particle agglomeration can be induced by adding
422:aggregation. Aggregation can be enhanced through
135:, and not only lead to sedimentation but also to
108:and such a suspension is said to be functionally
1343:
1150:
992:M. Elimelech, J. Gregory, X. Jia, R. Williams,
1010:W. B. Russel, D. A. Saville, W. R. Schowalter,
282:{\displaystyle W={\frac {k_{\text{fast}}}{k}}}
426:(e.g., stirring). The latter case is called
22:refers to the formation of assemblages in a
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1242:Advances in Colloid and Interface Science
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1285:Journal of Colloid and Interface Science
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1188:Journal of Colloid and Interface Science
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1004:
1002:
535:Homoaggregation versus heteroaggregation
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304:
223:{\displaystyle {\ce {A1 + A1 -> A2}}}
66:
1239:
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983:
340:. The charge is expressed in units of
131:, they may also be coupled to droplet
1103:"Universality in colloid aggregation"
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1094:
1072:Gold Book IUPAC. SchulzeāHardy rule:
999:
46:and such a suspension is also called
1014:, Cambridge University Press, 1989.
16:Clumping of particles in suspension
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500:{\displaystyle M\propto R_{g}^{d}}
54:or other chemicals referred to as
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1039:The Journal of Physical Chemistry
956:Smoluchowski coagulation equation
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236:. Since doublet formation is a
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1017:
996:, Butterworth-Heinemann, 1998.
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1023:D. F. Evans, H. Wennerstrom,
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85:. Alternatively, a colloidal
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7:
877:
782:diffusing-wave spectroscopy
10:
1378:
1250:10.1016/j.cis.2008.09.003
874:induces the aggregation.
788:Single particle counting.
778:backscattering techniques
160:will form from singlets A
835:Formation of river delta
766:dynamic light scattering
327:van der Waals attraction
323:double layer interaction
164:according to the scheme
911:Electrical double layer
907:(stability of colloids)
762:Static light scattering
724:Experimental techniques
713:deposition of particles
319:electrical double layer
1305:10.1006/jcis.1997.5022
971:Suspension (chemistry)
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91:rheological properties
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20:Particle agglomeration
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820:dielectric properties
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452:, whereby their mass
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404:polycarboxylate ether
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1244:. 147ā148: 109ā123.
1165:10.1039/f19777301436
1025:The Colloidal Domain
803:Indirect techniques.
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1362:Colloidal chemistry
1297:1997JCIS..192..463H
1200:2003JCIS..260..149K
1122:1989Natur.339..360L
1051:10.1021/j150530a018
1027:, John Wiley, 1999.
936:Particle deposition
900:Double layer forces
740:Light transmission.
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931:Nanoparticle
921:Flocculation
867:
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424:shear stress
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151:Early stages
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941:Peptization
905:DLVO theory
864:, or both.
845:Papermaking
420:perikinetic
396:DLVO theory
385:surfactants
133:coalescence
114:stabilizers
95:peptization
40:coagulation
1346:Categories
978:References
808:filtration
748:absorbance
736:of light.
734:scattering
61:flocculant
24:suspension
1352:Chemistry
1313:0021-9797
1258:0001-8686
1216:0021-9797
1173:0300-9599
1059:0022-3654
826:Relevance
650:⟶
616:⟶
582:⟶
480:∝
377:0.03-0.5
204:⟶
129:emulsions
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1266:18930173
1224:12742045
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951:Settling
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878:See also
812:rheology
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450:fractals
443:compact.
412:concrete
141:aerosols
137:creaming
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1321:9367570
1293:Bibcode
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1118:Bibcode
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289:where
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1106:(PDF)
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1301:doi
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234:k
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188:+
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156:A
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