How Do Dipole-Dipole Interactions Influence Molecular Behavior?

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Discussion Overview

The discussion revolves around the proof of a specific equation (2.4) related to dipole-dipole interactions as presented in a document on van der Waals forces. The scope includes mathematical reasoning and technical explanation regarding the scalar potential and electric field generated by a dipole.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant requests assistance in proving equation (2.4) from a referenced document.
  • Another participant provides a formula for the scalar potential of an electric dipole and claims it leads to the desired equation.
  • A different participant expresses confusion regarding specific terms in the equation, particularly the numerator and the dot product of dipole moments.
  • Further clarification is sought on the differentiation of a term related to the potential, with a participant attempting to confirm the correctness of a mathematical expression.
  • One participant mentions working in spherical coordinates, suggesting a potential source of confusion.
  • Another participant asserts that the choice of coordinate system should not affect the outcome, as transformations between coordinate systems are possible.
  • A final comment reflects on the time elapsed since the original question was posed, indicating a sense of ongoing uncertainty or unresolved discussion.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding the proof and the mathematical details involved. There is no consensus on the correctness of the interpretations or the proof itself, indicating that multiple competing views remain.

Contextual Notes

Limitations include potential misunderstandings related to coordinate systems and the specific mathematical steps required to derive the equation in question. The discussion does not resolve these issues.

secret2
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Could anyone please provide (or start off) the proof of (2.4) of the following document?

http://www-its.chem.uva.nl/research/complex_fluids/Teaching/LectureNotes%202004%20vdWaals%202.pdf

Many thanks
 
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The scalar potential from a electric dipole is given by
[tex]\phi=\frac{\vec{p}\cdot \vec{r}}{4\pi \epsilon_0 r^3}[/tex]
Then
[tex]\vec{E}=-\bigtriangledown \phi[/tex]
and with
[tex]U=-\vec{p}\cdot \vec{E}[/tex]

you'll get exactly Eq. (2.4)!
 
I don't think I get the 3 in the numerator, nor the p dot p term.
 
You don't think you get it OR you didn't get it?

[tex]\partial_x (x^2+y^2+z^2)^{-3/2}=-\frac{3}{(x^2+y^2+z^2)^{5/2}}[/tex]

Right?
 
Oh...I was working with spherical coordinates.
 
There should not be a problem whether it is a sphere coordinate or not. Every two coordinates can transform into each other.
 
It's been 4-1/2 years since he asked the question, I'm afraid,
 

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