Derive the van der Waal interaction between 2 spheres.

In summary, the van der Waal interaction potential between two spheres of radius R_1 and R_2 can be derived using the Hamaker approach, which involves a double volume integration of density_1 and density_2 over the separation distance between the spheres. This approach is based on the assumption of pairwise addition and results in a formula (1) that can be calculated using Mathematica. Further explanation and references can be found in the provided links.
  • #1
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Hi guys, I need some help on this question:

Derive the van der Waal interaction potential between 2 spheres of radius R_1 and R_2 using the Hamaker approach. Take the distance between the center of each sphere to be D.

Thank you very much for your help!
 
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  • #2
Read this:

http://dept.lamar.edu/chemicalengineering/www/tadmor/papers/vanderwaalsforces/vdw1.pdf

Could you explain me a little bit more about that?
Or some reference?
I know nothing about it.

Is the van der Waal interaction a starting point, or is it a consequence?
Is there a short (fast) derivation for formula (1) somewhere available?

Interresting because of the geeko.
 
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  • #3
The Hamaker approach assume a pairwise addition, so the derivation start with a double volume integration of density_1 and density_2 and c over r^6, where r is the separation between the small volume in the integration, and c is a constant. Not sure if I make myself clear here.

Maybe this pdf will help, please refer to page 2, equation (1) for the mathematical description of what I had describe above. Thanks! Here is the link: http://chemeng.queensu.ca/courses/CHEE460/lectures/documents/CHEE4602010Lecture4.pdf

And yes the gecko is a master of VDW forces!
 
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  • #4
I don't know if it is helpfull, but here is a link to the original paper by Hamaker:

http://www.utwente.nl/tnw/pcf/education/jmbc_course_on_capillarity_driv/Articles/anton_darhuber/surface_tension_etc/Hamaker_Physica1937_vdW_attract_spherical_particles.pdf

It is a little bit lengthy and even boring.
It looks like it is only about calculating the integral of formula (1) in the paper.
Probably a piece of cake if you have 1 hour free and Mathematica.

Thanks for the reference: it is very clear and readable.
 
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  • #5
Thank you for your help. Mathematica does help.
 

1. What is the van der Waals interaction between two spheres?

The van der Waals interaction, also known as London dispersion forces, is a type of intermolecular force that occurs between two molecules or particles. It is caused by temporary fluctuations in the electron distribution of the particles, leading to a temporary induced dipole moment. This results in an attractive force between the particles.

2. How is the van der Waals interaction between two spheres calculated?

The van der Waals interaction between two spheres can be calculated using the van der Waals equation, which takes into account the size and distance between the two spheres, as well as the strength of the attractive force. This equation is based on the work of Johannes Diderik van der Waals, a Dutch scientist who studied the behavior of gases.

3. What factors affect the strength of the van der Waals interaction between two spheres?

The strength of the van der Waals interaction between two spheres is affected by the size and distance between the spheres, as well as the polarizability of the particles. Larger particles and shorter distances result in stronger interactions, while particles with higher polarizability have stronger interactions due to their ability to induce larger temporary dipoles.

4. How does the van der Waals interaction between two spheres differ from other intermolecular forces?

The van der Waals interaction is a weaker force compared to other intermolecular forces, such as hydrogen bonding and dipole-dipole interactions. It is also a non-specific force, meaning it can occur between any two particles regardless of their chemical composition. In contrast, other intermolecular forces are more specific and occur between particles with certain chemical properties.

5. Can the van der Waals interaction between two spheres be observed in real-life systems?

Yes, the van der Waals interaction plays a significant role in many natural phenomena, such as the cohesion of water molecules in plant cells and the adhesion of gecko feet to surfaces. It is also important in industrial processes, such as the adsorption of gases on solid surfaces. However, the van der Waals interaction is often overshadowed by stronger forces in everyday situations.

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