DLVO interaction: Choice of Hamaker constants

[LucidWaker]

For a project, I'm trying to describe the interaction energy between two particles suspended in water which contains ions. I seem to have the double layer effect worked out pretty well, but I'm having trouble with the Van der Waals contribution, or more specifically, with the choice of Hamaker constants to determine the total combined Hamaker constant of the system.

The two particles are of different sizes (micrometer range), the smaller ones are polystyrene orbs coated in protein, the bigger ones (approx. 10 times bigger) are protein coated polystyrene orbs containing magnetite particles. The two protein kinds are different, and compatible to engage in a bond.

What Hamaker constants of what material should I choose? Should I use a total combined Hamaker constant of two polystyrene particles in water, or should I consider the outer layer of the particles, the protein layer? Or maybe, the Hamaker constant of magnetite in one of the particles plays a role?

Thanks in advance for the help.

 

[Andy Resnick]

The Hamaker constant, as presented in my book, is:

A = \frac{3\hbar}{2}\alpha_{1}(0)\alpha_{2}(0) \frac{\omega_{1}\omega_{2}}{\omega_{1}+\omega_{2}}

Where \alpha(0) is the static polarizability and \omega the frequency of principal absorption (?).

The references claimed to have complete formulaies for different shapes and spacings are books by Mahanty and Ninham, Parsegian, and Israelachvili.

Since you have rather complex particles, it's hard to say exactly what to use- if the magnetite changes the absorption and polarizability (which it likely does), then you need to deal with that. The protein coatings may only have a minor effect.