In a colloid dispersion, the colloidal particles are randomly colliding together resulting in the particles following an irregular route which is called Brownian motion. If the particles are no longer randomly move in the dispersed phase and start to aggregate, the colloid system is no longer stable therefore emulsion, flocculation or sedimentation of particles may have occurred.
Colloids particles are classified into 2 classes; lyophilic colloid and lyophobic colloid. The reasons why the lyophilic colloid particles maintain a good stabilisation in dispersed phase are they were stabilised by electrical double layer interaction and solvation. Electrical double layer is formed in a charged colloidal particle. Figure.1 A self-drawn diagram to show a general idea of a double layer when the charged particles interact with an aqueous solution.
For a typical implant, positively or negatively charged materials are often in contact with an aqueous solution, which contains both positive and negative ions. These surface charges will affect the distribution of ions in the aqueous solution: Ions of opposite charge to the surface called counter-ions, to be attracted to the surface by electrostatic force, and ions of the same charged to the surface called co-ions to be repelled away from the implant surface. Alongside this attraction and repulsion effect, thermal agitation can also distribute ions in the system, where ions are redispersed in the solution because of the extra energy. These two principle forms the basic electrical double layer, which is made up of a charged surface layer and a neutralizing layer between counter-ions and co-ions which is based on diffusion in the aqueous solution.
Figure 2 [1] (A) Shows the stern plane, shear of layer. (B) Shows the change in potential with the change of distance.
The double layer suggested by its name are consist of two parts, the inner part- which contains absorbed ions (stern layer) and the diffuse part where ions are influenced by electrical force and random thermal movement (Gouy-Chapman layer). An overview of the double layer is shown in figure 2. The stern plane indicates the point of separation between the layers, which is at about a hydrated ion radius from the surface of the material. This gives the stern potential, which is dependent on the particle chemistry and surface charge or the presence of adsorbed materials such as surfactants or polymer (which we are going to mention later on). Inside the distance from the surface of material to its stern plane, the potential changes linearly, where else it will decay exponentially from the stern plane to zero inside the diffuse double layer. This effect is shown by the equation when DLVO is explained. Alongside the ions in the stern layer, some solvent are bounded to the ions and the charged surface, forming the solvating layer. The outer part of this layer is called the plane of shear, which can be used to define the boundary of relative movement between the material surface and the liquid. However, as the actual thickness of this layer is hard to define, so the potential at the plane of shear which is called the zeta potential indicates the potential at an unknown distance from the material surface. The zeta potential will govern electrokinetic behaviour of particles such as electrophoresis, sedimentation [2,3]. Due to the uncertainly of the actual thickness, the value of zeta potential used in calculation is often slightly less than the stern potential. This means that the zeta potential is dependent on the stern potential and the ionic strength of medium.
As we have mentioned before, due to Brownian movement the particles will collide into each other. Three results were proposed when this happens: Coagulation is where particles are permanently contacted together, forming large aggregates. Flocculation is where these particles come together temporarily and finally, Stable colloidal system is where particles remain freely dispersed. For lyophobic colloids (water loving, charged particles) both repulsion and attraction force between particles are seen. In order to produce a stable lyophobic colloidal system, electrical repulsion force (VR) and van der Waals force (VA) play important role in this stabilisation. Considering the distance of two colloidal particles, the repulsive force and the attractive force varies when the distance changes between two particles. DLVO theory is therefore established to analysis the interaction between particles and stability of colloid system. This theory can be applied to all types of colloidal particles, including emulsions, suspension and nanomaterials.
There are four main types of forces which affects the system, Van der Waals (attractive), electrostatic (repulsive) and solvation force (repulsive) as mentioned earlier on, there are also steric forces (repulsive) which we will look in further detail later on.
The energy of the attraction (VA) comes from Van der waals forces of attraction. This force is addictive, allowing a long ranged attraction force appear between colloidal particles. The force of attraction can be calculated by using the equation [4]:
a is the radius of the spherical particle, A is the Hamaker constant for the particular material from Van der Waals force and H is the distance between particles. This equation is used to describe the energy of attraction between pairs of atoms or molecules of neighbouring particles. Based on this equation, a simpler form can be derived:
The energy of attraction varies with the distance H between the pairs of atoms or molecules or neighbouring particles with the inverse of the 6th power. The equation simply means that the shorter the distance between atoms, the higher the attraction force between them.
The electrical repulsion force (VR) in the system arises from the osmotic effect, which is produced by the increase in the number of charged species on overlap of the diffuse parts of the electrical double layer. VR can be given by the equation:
In this equation εis the permittivity of the polar liquid, a is the radius of the spherical particle of surface potential, k is the Debye-Huckel reciprocal length parameter, H is the distance between particles. This equation describes the repulsive forces (VR) from the interaction of the electrical double layers surrounding pairs of particles. From this equation we can say that the repulsion energy is an exponential function of the distance between particles. It is also found that repulsive forces will decay more rapidly than attractive forces. []
The sum of the repulsion forces (VR) and the attractive forces (VA) acting on a pair of particles are equal to the total potential energy of interaction (VT). An equation is given to describe the relationship:
Using this equation, a force-distance graph can be plotted to further explain this relationship. This is shown by figure.3. From the total potential energy of interaction (VT) versus distance between particles (H) graph, we can see that the forces of attraction are at its greatest at small distance, this is indicated by the very deep primary minimum. At this point, particles don't have enough kinetic energy to escape (kT<VT). If the primary minimum is low, the particles in the system will be able to be forced together, leading to aggregation of the droplets. A high/deep primary minimum means that the particles cannot get any closer together than the distance at which the separation occurs; this will lead to a stable dispersion.
Figure 3[1] Shows a typical DLVO curve, Total potential energy of interaction (VT) versus distance of separation (H).
A secondary minimum can be seen at larger interdistances because as mentioned above, repulsive energy decays more rapidly with distance than attractive energy with distance. There is an overall attractive force, but not as strong as in the primary minimum. At this point, forces of attraction are usually weak and will not lead to a permanent coalescence of the droplets. The particle behaviour will be depended on kinectic energy. If the secondary minimum smaller than the thermal energy kT, the particles will not be able to aggregate and always repel each other. If the secondary minimum is much larger than the thermal energy kT, a loose assemblage of particles will be formed, which means that the aggregated particles could be re-dispersed upon shaking, where flocculation is seen.
As particles come closer together at in intermediate distance, double layer repulsion will predominate and the particles will start to experience some repulsion which will peak at the primary maximum. If the maximum point (Vcrit) is very large compared to the thermal energy kT of the particles, the colloid system will be stable where the particles will stay dispersed. If the maximum point (Vcrit) is equal or less than the thermal energy kT, the interacting particles will reach goes down to the point of primary minimum, where irreversible aggregation such as coagulation will occur, which is unstable. Therefore the height- intensity of this repulsion force is important. The height of the primary maximum energy is depended on the size of the repulsion force (VR), which is depended on the zeta potential. Altering the electrolyte concentration via k (Debye-Huckel reciprocal length parameter) can affect the height. The addition of electrolyte such as sodium chloride (NaCl) can reduce potential on particles by compressing the double layer, of which only the diffuse layer is affected. By the addition of electrolyte, the number of ions in the solution will be increased, making 1/k smaller, where making the diffuse layer thinner and hence reducing the zeta potential. This will lower the primary maximum and deepen the secondary minimum, particles will then start to aggregate, making the colloid system less stable. Additionally, the primary maximum and secondary minimum can be further lowered by the addition of ionic surface-active agents. This will lower the zeta potential, hence limiting the level of compression of the double layer.
As we can see the DLVO theory are able to predict the movement of the particles, but this only applies to ionic surfactants. This theory fails to predict the stabilities of the extremes (either very hydrophilic or very hydrophobic particle suspensions)[]. It doesn't take into account some facts such as ion correlations due to the discrete nature of charge distribution at small separation, depletion interaction, the stern layer where there are hydrated ions of finite size (the addition of additives and electrolytes) and steric effects where polymer absorption in non-ionic surfactants.
As mentioned earlier on, the stern plane is at about a hydrated ion radius from the particle surface, of which that the hydrated ions are attracted to the particle surface by electrostatic forces. In some cases, specific adsorption can occur, where ions or molecules are more strongly attached or adsorbed at the surface than just by simple attraction of the electrostatic force [6, 7, 8]. In other cases, the specific adsorbed ions or molecules maybe uncharged in cases of non-ionic surface active agents. This can make a huge change on the stern potential, where the surface potential and stern potential have opposite sign, or for stern potential to have the same sign as surface potential but having a larger magnitude. This effect can be shown by figure 4. As we have briefly talked about earlier, additives have an effect on the particle behaviour. The stern layer can also be affected by the addition of adsorbing layer to the medium such as surfactant (anionic, cationic or non-ionic).
Figure 4[1] (A) the surface potential and stern potential have opposite sign due to adsorption of counter ion. (B) Increase in magnitude of stern potential due to adsorption of co-ions.
When a non-ionic surfactant stabilised an emulsion, there are no electrostatic charge present to stabilise the droplet, resulting a neutral charge on droplet. Emulsions are stabilised by hydrophilic polymer chains by either osmotic (solvation) forces or entropic (steric) effects. Osmotic (solvation) forces are seen when two droplets come into close contact, allowing each of the polymer chains to overlap, leading to a concentrated polymer solution. This will create an osmotic gradient in solution where dilute solution will remain in the bulk solution and concentrated polymer solution will be in the overlap region. Because of osmosis, water will attempt to enter the concentrated region to dilute the solution, in doing so the polymer chains will be forced apart. Entropic (steric) effects are seen when two droplets come into close contact, where overlapping occurs as well. This leads to a loss into the freedom of motion of the polymer chains, restricting their movement and randomness, lowering the entropy. This will force the particles apart as this restriction is thermodynamically unfavourable.
Figure 5[1] shows chains overlapping, following up by the release of water molecules.
A modified equation can be used to describe the effect with non-ionic surfactants:
The effect of osmotic (solvation) force s and entropic (steric) effects can be substitute as VS. It is proven that electrostatic forces (VA) are more efficient at stabilising emulsion droplets than steric forces [5] Based on these osmotic (solvation) force and entropic (steric) effects, the particles will not approach each other closer than around twice the thickness of the adsorbed layer, so the system won't fall into primary minimum. This is shown on the diagram 5. Sometimes there will be the presence of both electrostatic and steric (solvation) force, where we can just combine VS with the normal DVLO equation:
This equation sums up the attractive (VA), steric (solvation) (VS) and electrostatic (VR) forces, allowing steric stabilisation. This is shown on the figure 6. By adding VS into the equation, we can see that repulsion is now seen all shorter distances provided that the adsorbed polymeric materials are not moving from the particle surface. As mentioned briefly earlier on, steric repulsion is based on thermodynamics, which can be used to explain the free energy changes that take place when two polymer-covered particles interact. The free energy equation is given as:
ΔG is the change of free energy, ΔH is the change of enthalpy, ΔS is the change of entropy. A positive value of the free energy is needed for the dispersion to be stable; where else a negative value means that the particles inside the dispersion have aggregated. Entropic effects lower the change if entropy, making the change of free energy to be small explained earlier on. Another way to make the change of free energy to be positive is to have both the change of enthalpy and entropy be positive, and ΔH has to be much bigger than ΔS. This is termed enthalpic stabilization where enthalpy will help the dispersion to stabilise. It is common seen with stabilising polymer which has polyoxyethylene chains in aqueous dispersions. Due to hydrogen bonding between water molecules and the oxygen molecule in the ethylene group, those chains will be hydrated. This shows a similar effect of what we have discussed before. Steric stabilisation is an ideal solution in constructing non-fouling surfaces because by having a high chance of repulsion in almost all the distant between particles will deny the chance of protein or bacteria aggregation on the implant. In recent studies, poly(ethylene glycol) were grafted [9, 10, 11] on to the material, this is similar to PEO grafting. This pushes the shear plane to be further away from the surface of the material. This can be used to minimise the chance of foreign body reaction or infection inside the body. Altering the surface can make a difference in bioadsorption: taking bacteria as an example: bacteria contains heterogeneously charged surface, which means that the magnitude of the repulsion force will be reduced. The bacteria particle can then re-position by rotation, when it approaches to heterogeneous surface. This can be prevented if the biomaterial surfaces have a uniform negative charge or a high zeta potential.
Figure 6[1] (A) Shows the total potential energy if interaction in the absence of electrostatic repulsion. (B) Shows the total potential energy if interaction in the presence of electrostatic repulsion.
