What is a colloid?

A common definition of a colloid is:

A chemical mixture comprising one or more phases of matter that are dispersed in a continuous phase of matter such a characteristic dimension of the dispersed material is nominally in the range from 1nm to 1μm and that there is little or no appreciable gravitational separation of the dispersed and continuous phases.

Two fundamental phenomena – aggregation and adsorption – play critical roles in the overall behavior of many colloidal products.

Aggregation is the formation of a group of particles by any means. This process may be referred to as coagulation if the aggregates that are formed are compact, or flocculation if the aggregates are loose or open.

In a liquid dispersion, adsorption is the thermodynamically-driven increase in the concentration of a component (e.g., surfactant) at the interface of the dispersed and continuous phases.

After Dobiáš, Qui and von Rybinski, Solid-Liquid Dispersions, Marcel Dekker Inc, 1999

For the purposes of this course, “aggregation” implies either coagulation or flocculation.

Basis for aggregation

Matter attracts matter. For simple molecules, the range of the attractive force decreases rapidly with increasing separation. However, for larger assemblies of molecules (say 10nm diameter and greater), the force is effective over greater distances. The attraction force arises from random fluctuations in electron density in neighboring molecules.

If two particles approach closely enough (within a few tens of nanometers), they will begin to feel the attractive force between them. This force increases as the particles become nearer, hence the two particles will spontaneously approach closer until repulsion occurs due to interaction of the electron clouds of each particle's surface atoms or molecules. At this distance, the attractive force is so strong that it would require a considerable amount of energy to separate the particles. In practical terms, this is unfeasible and the particles are said to be irreversibly aggregated. In order to prevent aggregation occurring, a mechanism is required that can promote sufficient repulsive force to overcome the inherent attractive force. But consider a dispersion consisting of 0.15% by mass of 500nm radius particles (similar to this study). The average particle-particle separation is tens of microns. This is one thousand times greater than the attractive forces extending from the particles into the liquid. So how are the particles able to approach close enough to aggregate? The most important mechanism is described next.

Aggregation due to random diffusion

"Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways... their dancing is an actual indication of underlying movements of matter that are hidden from our sight... It originates with the atoms which move of themselves. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So, the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible."

Lucretius, “On the Nature of Things”, circa 60 BCE

These words, written more than 2000 years ago, describe with remarkable clarity the mechanism by which colloidal particles approach each other closely enough to experience the attractive van der Waals forces. More than eighteen centuries later, in 1827, Scottish botanist and foremost microscopist Robert Brown observed that pollen particles immersed in water moved randomly. However, he literally couldn’t see any reason why the particles should move in such a way and was unable to put forward a mechanism. This motion is now known as Brownian motion. The modern scientific explanation was developed by Albert Einstein in 1905. He theorized that Brownian motion is a result of the particle (e.g., pollen) being moved by individual water molecules. The direction of motion of an individual water molecule is random and the combined interaction of all the particle’s neighboring molecules makes the particle move randomly. Of course, we will never know if Einstein had read Lucretius’ prescient treatise on random particle motion in a fluid…

This random motion is random diffusion and it is easy to demonstrate it in a liquid dispersion. The following video shows how 500nm polystyrene latex particles diffuse when a drop of a concentrated dispersion of them is added to water.

The most common method for quantifying diffusion of colloidal particles in a liquid is dynamic light scattering. Although the primary application of the technique is to estimate particle size, it does so by measuring diffusion. This is performed by analyzing the random fluctuation of the intensity of laser light scattered by the particles due to diffusion. A specific non-commercial implementation of a variant of the technique is able to visualize this random fluctuation in a unique way in real time. The video below shows the random fluctuation of the scattered light for 500nm polystyrene latex particles in water.

Generating repulsive forces to control aggregation

In order to prevent aggregation occurring, a mechanism is required that can promote sufficient repulsive force to overcome the inherent attractive force.

Electrostatic repulsion

The presence of electrostatic charge on the surface of the particles in a suspension can give rise to repulsion between particles as they approach. It is usual to quantify the interfacial charge in terms of the potential difference between the particle/liquid interface and the bulk liquid. The zeta potential, ζ, is commonly used to express the interfacial potential between the particle (including any bound material, such as ions, solvent molecules, surfactants etc.) and the bulk liquid. By measuring the zeta potential, it is possible to predict the magnitude of repulsion that will occur between two approaching particles. This schematic shows a negatively-charged spherical particle dispersed in an electrolyte solution. Cations (red) are attracted to the particle surface whereas anions (blue) are repelled from the surface. The presence of the ions strongly influences the force between approaching particles and, hence, the aggregation behavior. The electrical double layer theory is used to describe this. It is not discussed in this mini course.

Without repulsion, the fastest rate at which the system can aggregate is limited by the diffusion rate of the particles. Many industrial colloidal products that are charge-stabilized may have aggregation rates whose half-lives are of the order of many years. However, aggregation will eventually occur. These kinds of suspensions are kinetically stable.

If the particles are forced close enough together through some mechanism other than diffusion, the energy barrier can be overcome. This can occur when an otherwise kinetically stable suspension undergoes gravitational sedimentation and forms closely packed sediments.

In aqueous media, the minimum magnitude of the zeta potential generally required to promote sufficient stability is often considered to be approximately 25mV. However, there are situations where this generality does not apply.

The main mechanisms that can promote charge-stabilization are:

• Adsorption of potential-determining ions. For example, selective adsorption of Na⁺ ions from aqueous NaCl solution will lead to a positive zeta potential.
• Dissociation of surface ionogenic moieties. For example, the dissociation of surface carboxylate groups will lead to a negative zeta potential.
• The adsorption of larger molecular species such as surfactants or polyelectrolytes.

Surfactant requirements for charge stabilization

Two key requirements for a surfactant to promote charge stabilization are that, firstly, the surfactant adsorbs onto the particle and that, secondly, the surfactant carries a charge. The latter point usually infers that the surfactant is ionic.

Surfactant adsorption

The principles governing the adsorption properties are the same for a range of applications, not just for the promotion of charge stabilization. The principles set out here are relevant to other ideas presented later.

Consider a hydrophobic molecule surrounded by water. The energy of interaction between the water molecules and the hydrophobic molecule will be high (unfavorable). The hydrophobic molecule will be subject to random diffusion by the thermal action of the surrounding water. If the molecule should happen across a hydrophobic surface, it will prefer to interact with the surface rather than water. The energy of interaction will be less. Typically, the result will be an overall negative change in free energy. Thermodynamically, this represents a spontaneous process. Attempts to prepare an aqueous solution of such a hydrophobic molecule will be futile since there will be no thermodynamic driving force to solvate the molecules. However, if one end of the molecule is hydrophilic, then a solution of the molecules may be prepared. The hydrophobic part of the molecule is usually termed the tail and the hydrophilic part the headgroup. At low concentrations, the molecules will exist in solution as discrete molecules. At higher concentrations, the molecules will form associative colloids, such as micelles. The micelles will exist in dynamic equilibrium with the molecularly dispersed material. This is shown schematically below.
In the presence of a hydrophobic surface, the free surfactant molecules will adsorb onto the surface causing the equilibrium shown above to shift to the left:
It is possible to construct an adsorption isotherm which indicates how much surfactant adsorbs onto the particle surface as a function of the concentration of surfactant remaining in solution after the system has reached thermodynamic equilibrium at a given temperature. Typical adsorption isotherms are shown below.

For any system, there will exist an equilibrium between the amount of surfactant adsorbed and the amount of surfactant remaining in solution. Consider a strongly adsorbing surfactant. At low surfactant concentrations, all of the surfactant will adsorb onto the particle surface, leaving no surfactant in solution. As the surfactant concentration increases, more of the particle surface will be covered by surfactant until all of the surface is completely covered by one monolayer of surfactant. Beyond this point, the adsorbed amount of material will remain constant with increasing surfactant concentration. This is typified by isotherm A in the figure above.

Depending on the nature of the surfactant, increasing the concentration of surfactant beyond that needed for monolayer coverage may result in further adsorption, leading to multilayer adsorption (indicated by isotherm B). For a weakly adsorbing surfactant, a different behavior is observed. Whereas for the strong case all surfactant will adsorb until full monolayer coverage is obtained, the amount of surfactant adsorbing in the weak case is dependent on the excess concentration of surfactant in solution. At low surfactant concentrations, only a fraction of the surfactant adsorbs. As the surfactant concentration increases, the adsorbed amount also increases. Full monolayer coverage is only achieved at high surfactant concentrations relative to those for the strongly adsorbing case. Furthermore, the presence of surfactant on the particle surface may promote further adsorption or may make it less favorable for additional surfactant to adsorb. This is reflected in the shape of the isotherm in the sub-monolayer region. Isotherm C represents a system where the presence of surfactant at the surface makes it easier for subsequent surfactant to adsorb (indicated by the convex shape of the isotherm relative to the concentration axis).

In summary, the adsorption isotherm provides the following information:

• How much surfactant is required to achieve full monolayer coverage
• What concentration of surfactant is required to achieve full monolayer coverage
• Whether the adsorption is strong or weak

The experimental determination of an adsorption isotherm usually involves the preparation of a series of samples of the particles, surfactant and liquid medium. The concentration of particles (with respect to the liquid) is kept constant and the concentration of surfactant is varied from zero up to a level above that estimated to achieve full monolayer coverage of the particles. It is necessary to know the specific surface area of the particles. This can be determined experimentally (e.g., by nitrogen adsorption) or estimated geometrically from the particle size distribution. In general, most surfactants adsorb to particles to yield monolayer coverages of the order 1-2 mg m^-2.

Once equilibrium is reached (typically by gentle agitation overnight), the concentration of surfactant remaining in solution is measured. The concentration of surfactant in the bulk liquid is the equilibrium concentration required for construction of the isotherm. The difference between the initial concentration of surfactant and the equilibrium concentration allows the adsorbed amount of surfactant to be calculated. Expressed as mass per unit area of particle surface, this provides the remaining data needed to complete the isotherm.

Charge generation by surfactants

Surfactants used to promote charge stabilization are ionic. The polar headgroup is usually the ionic part of the molecule. The choice of polar headgroup determines the sign and magnitude of the interfacial charge developed. For example, sodium dodecyl sulfate (SDS) is a surfactant which dissociates in water to yield an anionic material that adsorbs onto the surface and a simple cation in solution:

By changing the headgroup to a quaternary ammonium salt, a cationic surfactant is obtained such as dodecyl trimethyl ammonium bromide (DTAB):

Applicability of charge stabilization

For charge stabilization to work, there are two main requirements:

• The magnitude of the surface charge is suitably high
• The electrostatic potential can be sensed sufficiently far away from the particle surface

The first requirement usually means that the dispersion medium (liquid) be semi-polar or polar.

The second requirement concerns the concentration of dissolved electrolytes. The presence of electrolytes in solution screens the charge on the particle surface such that particles can approach each other closer than they could in the absence of electrolyte. The electrostatic potential decays away from the particle surface over a length scale dictated by the ionic strength (salt concentration) of the medium. In aqueous systems, the maximum ionic strength that can be tolerated before aggregation occurs is usually of the order of 10^-2 mol dm^-3. This has implications for formulation suspensions that need to be isotonic. Physiological saline has an ionic strength of approx. 0.15 mol dm^-3 in order to match the body’s tonicity. If formulations are developed that rely on charge stabilization, the presence of saline at such levels will result in rapid, irreversible aggregation.

Commercial light scattering instruments have been shown to significantly underestimate or even fail to measure ζ at isotonic electrolyte concentrations and higher.

Enlighten Scientific has developed the Next Generation Electrophoretic Light Scattering system (NG-ELS) that over comes these and other significant short-comings of commercial equipment.

Steric repulsion

The adsorption of surface-active materials at the particle/liquid interface can give rise to another repulsion mechanism which does not suffer the same limitations as electrostatic repulsion and provides a greater degree of control of the colloidal dynamics of the system (aggregation rates, ease of redispersibility etc.)

Consider two like particles that have a surfactant adsorbed onto the particle surface such that the thickness of the adsorbed layer is δ (below).

When the particles are separated by more than 2δ, the attractive force will be the same as for identical particles without the adsorbed material. As the particles continue to approach, there will come a point at a separation of 2δ where the adsorbed molecules start to interact resulting in steric hinderance that will prevent the particles from approaching closer. As long as the attractive force at this point is small then the energy associated with diffusion will be enough to overcome the attractive force.

Electrosteric repulsion

From the arguments set out above for both charge and steric stabilization, the use of some ionic surfactants will result in a system where both repulsion mechanisms can exist. Such systems are said to be “electrosterically” stabilized. Steric repulsion arising from small surfactants is often insufficient to overcome the attraction. Electrosteric stabilization helps redress this but requires that δ is suitably large.

Polymeric surfactants

Although simple surfactants such as SDS and DTAB can be used to promote steric stabilization under certain conditions, it is more common to use polymeric materials due to their higher molecular weight. Three general classes of polymer can be used:

• Homopolymers - where all of the monomer units in the polymer are the same. An example is poly(vinyl pyrrolidone) (PVP). The polymer needs to be soluble in the continuous phase (dispersion liquid) and have some affinity for the particle surface (so that adsorption occurs).
• Random copolymers - where the polymer consists of a random mixture of two (or more) monomer types. One monomeric moiety is soluble in the continuous phase; the other is insoluble and will preferentially adsorb onto the particle surface. Poly(vinyl alcohol) (PVA) is such a polymer, consisting of typically 80-90% vinyl alcohol moieties and 10-20% vinyl acetate moieties. (The nomenclature is confusing since "PVA" implies a homopolymer but invariably refers to the copolymer with poly(vinyl acetate)). Such polymers are more effective on a weight-for-weight basis than homopolymers.
• Block copolymers - where the polymer consists of blocks of one monomer type joined to one or more blocks of another type (below). As for random copolymers, soluble and insoluble moieties are used. Usually, the polymer will consist of 60-80% of the soluble block (A) and 20-40% of the insoluble block (B). The insoluble block acts as an anchor, attaching itself to the particle; the soluble block becomes a free tail. Block copolymers are usually the most effective stabilizers on a weight-for-weight basis. The most common type of block copolymer is an AB block copolymer. If the soluble block contains ionogenic moieties such as -COOH, -NH₂ and -OH, then charge generation may occur and promote electrosteric stabilization.

Gravity

In a colloidal dispersion, the particles are subject to the force of gravity and the thermal agitation of the surrounding liquid (random diffusion).

For particles whose radii are less than 500nm, random diffusion is usually enough to overcome the effects of gravity (unless the density difference between the particles is unusually high). Larger particles, however, do not diffuse so fast and so gravity can have an effect.

The degree of dispersion (or aggregation) strongly dictates how the suspension will settle which, in turn, has an important impact on the ease of redispersibility of the formulation.

Two limiting behaviors exist: that of highly dispersed systems and that of highly aggregated systems.

Sedimentation of highly dispersed systems

The following figure shows the basic stages that occur when a highly dispersed system sediments due to the influence of gravity (it is assumed that the particles are denser than the dispersion medium):

Stage A represents the fully-dispersed state (i.e., no aggregates). Once the suspension is left standing, gravity will act upon the system. Particles from the lower part of the suspension will begin to arrive at the bottom (B). Since these particles are stabilized against aggregation through either of the mechanisms described earlier, they can get very close to each other without aggregating. Hence, the particles can slowly orient themselves into a highly close-packed array. By time all the particles have settled (C), a sediment is formed whose volume is almost wholly comprised of particles. In order to redisperse the particles back into a state resembling A, significant energy needs to be imparted into the system to remove particles from the sediment. Particles will resist being removed from the sediment since pulling a particle away from the sediment creates a temporary partial vacuum before liquid can fill the void. These types of systems lead to the undesirable caking so often encountered with pharmaceutical suspensions.

Sterically stabilized particles are more likely to be redispersed after sedimenting than charge stabilized ones, since, in the latter case, the close proximity of the particles in the sediment may lead to aggregates. An ionic surfactant stabilized system may require in excess of 100 manual shakes to remove the sediment. A polymer stabilized system may require less than five manual shakes to yield highly dispersed, unaggregated suspensions. Invocation of electrosteric stabilization can reduce the effort required further.

Sedimentation of highly aggregated systems

The difference in sedimentation behavior of highly dispersed and highly aggregated systems is very marked. The following figure shows a schematic representation of the sedimentation of an aggregated system:

The aggregates will settle at a much faster rate than the non-aggregated case and, once they have reached the bottom, they will not be able to rearrange themselves into close-packed sediments. Instead, a porous, loose sediment is formed that occupies a significant volume of the total system. The more aggregated the system, the greater the sediment volume (or height). As a result of the open, loose structure, it is possible to agitate the sediment very readily (often just one inversion of the vessel is sufficient). However, the system is still aggregated.

A word of caution. In developing formulations, it is very easy to assume that just because a sedimented system is readily agitated, it must be dispersed, too. This misconception is based upon the visual observations made of such systems. As soon as a formulation is shaken, the turbulence and velocity of particles in the system will make the suspension look uniform at first glance. Often, closer inspection (such as by holding the suspension at an angle to an overhead light source) will reveal the true aggregated nature.