# DLVO interaction: Choice of Hamaker constants

• LucidWaker
In summary, the project involves describing the interaction energy between two particles suspended in water with ions. The double layer effect has been figured out, but there is difficulty with the Van der Waals contribution and determining the total combined Hamaker constant. The two particles are of different sizes and have protein coatings, with one containing magnetite particles. There are various factors to consider, such as the Hamaker constants of the materials, the outer layer of the particles, and the potential influence of the magnetite and protein coatings. Further research and references by Mahanty and Ninham, Parsegian, and Israelachvili may provide more insights for dealing with these complex particles.
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.

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.

## 1. What is DLVO interaction?

DLVO interaction refers to the forces of attraction and repulsion between colloidal particles in a liquid medium, which are caused by the combined effects of electric double layer repulsion and van der Waals attraction.

## 2. What are Hamaker constants?

Hamaker constants are a set of parameters that quantify the strength of van der Waals interactions between different materials. They are used to determine the magnitude of attractive forces between colloidal particles in a liquid medium.

## 3. Why is the choice of Hamaker constants important in DLVO theory?

The choice of Hamaker constants is important in DLVO theory because they determine the strength of van der Waals forces between colloidal particles. This directly affects the stability and behavior of colloidal systems, which has implications in various scientific and industrial fields.

## 4. How are Hamaker constants determined?

Hamaker constants are typically determined experimentally by measuring the interaction forces between two materials using techniques such as atomic force microscopy or surface forces apparatus. They can also be estimated theoretically using empirical models or quantum mechanical calculations.

## 5. Can the choice of Hamaker constants be optimized?

Yes, the choice of Hamaker constants can be optimized by adjusting the materials and experimental conditions used to determine them. Additionally, theoretical models can be refined and improved to provide more accurate values. However, it is important to note that Hamaker constants are specific to a particular system and cannot be universally optimized.

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