Dipole-dipole interaction

In summary, the conversation is about providing proof for equation 2.4 in the lecture notes on van der Waals forces. The equation involves the scalar potential from an electric dipole and the electric field. There is some discussion about the use of spherical coordinates, but it is determined that there should not be a problem with the transformation between spherical and other coordinates.
  • #1
secret2
37
0
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 [Broken]

Many thanks
 
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  • #2
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)!
 
  • #3
I don't think I get the 3 in the numerator, nor the p dot p term.
 
  • #4
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?
 
  • #5
Oh...I was working with spherical coordinates.
 
  • #6
There should not be a problem whether it is a sphere coordinate or not. Every two coordinates can transform into each other.
 
  • #7
It's been 4-1/2 years since he asked the question, I'm afraid,
 

1. What is a dipole-dipole interaction?

A dipole-dipole interaction is a type of intermolecular force that occurs between two molecules with permanent dipoles, meaning they have a separation of positive and negative charges. This force is caused by the attraction between the oppositely charged ends of the dipoles.

2. How does a dipole-dipole interaction differ from other intermolecular forces?

A dipole-dipole interaction is different from other intermolecular forces, such as London dispersion forces and hydrogen bonding, because it specifically involves the attraction between permanent dipoles. Other forces may involve temporary dipoles or other types of molecular interactions.

3. What factors affect the strength of a dipole-dipole interaction?

The strength of a dipole-dipole interaction is affected by the magnitude of the individual dipoles, the distance between the molecules, and the orientation of the dipoles with respect to each other. The closer and more aligned the dipoles are, the stronger the interaction will be.

4. How does temperature impact dipole-dipole interactions?

Increasing temperature can weaken dipole-dipole interactions because it causes molecules to vibrate more vigorously, making it more difficult for them to remain aligned and attracted to each other. However, at very low temperatures, dipole-dipole interactions can become stronger due to a decrease in thermal energy.

5. In what types of substances are dipole-dipole interactions most significant?

Dipole-dipole interactions are most significant in polar substances, such as water, where the molecules have a permanent dipole. They are also important in substances with molecules that have large differences in electronegativity, resulting in a larger dipole moment. Ionic compounds, which have strong electrostatic interactions between ions, do not exhibit dipole-dipole interactions.

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