Derive the van der Waal interaction between 2 spheres.

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Discussion Overview

The discussion revolves around deriving the van der Waals interaction potential between two spheres using the Hamaker approach. Participants explore the theoretical underpinnings, mathematical derivations, and references related to this topic.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant requests assistance in deriving the van der Waals interaction potential between two spheres of different radii, specifying the use of the Hamaker approach and the distance between their centers.
  • Another participant shares a link to a paper and asks for clarification on whether the van der Waals interaction is a starting point or a consequence, and inquires about a quick derivation for a specific formula.
  • A third participant explains that the Hamaker approach involves pairwise addition and begins with a double volume integration of densities, mentioning the dependence on the separation distance and a constant.
  • Further, a participant provides a link to the original Hamaker paper, noting its length and suggesting that it primarily focuses on calculating an integral related to the derivation.
  • One participant expresses gratitude for the references and mentions that Mathematica is helpful for the calculations.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants express varying levels of understanding and seek clarification on different aspects of the derivation and theoretical background.

Contextual Notes

Participants reference various papers and resources, indicating a reliance on external materials for deeper understanding. There is mention of specific formulas and integrals that may require further exploration.

Who May Find This Useful

This discussion may be useful for students or researchers interested in van der Waals forces, particularly in the context of theoretical physics and engineering applications involving intermolecular interactions.

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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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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.
 
Last edited by a moderator:
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!
 
Last edited by a moderator:
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.
 
Last edited by a moderator:
Thank you for your help. Mathematica does help.
 

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