We have some sort of particle or emulsion or colloid that we hope will remain stable in its liquid environment. All particles have a self-attraction we can do almost nothing about. So to keep the system stable we have to find some repellent forces, which in practice mean charges, in aqueous systems, or steric forces. DLVO theory lets us calculate this balance. Unfortunately it features lots of parameters and relatively complex equations. Fortunately, with the app the equations are handled for you, and, to get a good feel for the key ideas, you need to play only with:
- The radius, r, of your particle
- φ, the Zeta potential (the charge on the particle) and the molar concentration of ions in the solution
- the length, δ, of your stabilizer and the Flory-Huggins χ parameter of the stabilizer in the solvent.
Play with those key values, looking at Vt which is the total (hopefully) repulsive (positive) energy keeping your system stable.
DLVO (Derjaguin and Landau, Verwey and Overbeek) theory is obligatory for everyone wanting some insights into stability of nanoparticles, emulsions and colloids. The fact that it often requires input values (and there are lots of them!) that are unknown to the users, and the fact that other factors can completely overwhelm DLVO effects is an unfortunate truth. But all the same, any formulation team should share the common language of DLVO and should make at least some attempt to place their formulations within the context. The model here takes the minimum number of relevant inputs and plots the three key effects plus the resulting balance. Any standard text on DLVO (even Wikipedia) will provide much more detail. The model used here is based on one created by Dr Robert Lee of Particle Sciences and his assistance is warmly acknowledged. A companion model explores the meaning of Zeta potential
This is all very fine for theoreticians, but how does one get hold of all those input values when you just know that you have some particles you want to disperse? The first advice is "Don't Panic". Now think things through one at a time.
- You know the radius of your particle, you know T, you know the Density of your liquid (1 is good enough for most purposes) and its Molar Volume is simply MWt/Density (so MWt is close enough).
- You can look up Dielectric Constants (and Molar Volumes) here .
- The A12 Hamaker constants don't vary all that much, so 1 is good enough, but you can look up some values here .
- We're almost there. Your particle is either neutral (Zeta=0) or strongly charged (Zeta=+50 or -50) or has a modest charge somewhere in between.
- Your dispersant is either a small molecule (δ=0.5nm), an oligomer (δ=1nm) or a polymer (δ=10nm). It is either absorbed to a small (Γ=0.5) or large amount (Γ=2).
- And finally your dispersant is either highly compatible with the solvent (Χ=<0.1) or highly incompatible with the solvent (Χ>0.5).
Once you get used to making rough estimates of the parameters using such thinking, you can quickly work out for your specific system which (if any) parameters need to be defined more carefully. You might also work out that other effects (solubility via HSP thinking, bridging or depletion flocculation, Smoluchowski exceptions) are more important, making DLVO largely irrelevant.
A specific application of DLVO is discussed in the Polymers section of Practical Surfactants. To stabilise an emulsion a polymeric surfactant can be very effective provided:
- It can reach the surface fast enough during creation of the emulsion
- The polymer is a di-block with strong attachment of the hydrophobic part to the oil
- The other part of the di-block is highly water soluble so Χ is low
- The length of the water soluble chain is high - so δ=5-10nm
- The coverage (Γ) is high