Dipole-Induced Dipole Interaction

In summary, the induced dipole moment of a polarizable atom at position r2 in the presence of a permanent dipole at the origin pointing along r1 can be calculated using the equation pHe=a1Epar+a2Eperp, where a1 and a2 are the coefficients of polarizability in the parallel and perpendicular directions to the electric field, respectively. The induced dipole will point in the direction of the electric field due to the permanent dipole. To find the electric field, the negative gradient of the dipole potential can be taken, or a Taylor expansion can be used for small separations between the positive and negative charges.
  • #1
djeikyb
42
0

Homework Statement


Given a permanent dipole, call it pNO, at the origin pointing along r1 (general vector, not along any particular axis). A polarizable atom as at position r2. What is the induced dipole moment, call it pHe, of this atom in terms of pNO and r2?


Homework Equations


pNO=a1Epar+a2Eperp
a1 is the coefficient of polarizability in the direction parallel to the electric field, a2 is the perpendicular one.
The second part of this expression should be zero, as the induced dipole should point in the direction of the electric field.

The Attempt at a Solution


I know/understand that whatever this induced dipole is, it will point in the direction of the electric field due to the permanent dipole. Really, it's not the answer I'm after- rather, I need help with the method. Would I just say that for the permanent dipole, there is essentially a negative charge at the origin and a positive charge at p1 and superimpose the electric fields? It seems like this should work, but it's messy/tedious/not giving me the right answer, so I am probably making a wrong assumption with this method.
I suppose the real problem I have is not solving for the dipole, but rather the electric field due to a general permanent dipole. I would vastly prefer a point in the direction of deriving it rather than someone just giving a formula.
 
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  • #2
Addendum- If I can just find the electric field, it would be simple to solve for the projection of it along r2.
 
  • #3
Do you know what the dipole potential looks like? If so, take its negative gradient and you have the dipole electric field.
 
  • #4
Also, if this affects anybody's willingness to help, this is not a graded homework assignment. It's an assignment in that I am working under an AMO professor, and this is one of the many calculations he wants me to do- not that this is going to help him in any way, but I need to have the ability/understanding of this to understand one of the terms we will be adding to our Hamiltonian.
 
  • #5
kuruman said:
Do you know what the dipole potential looks like? If so, take its negative gradient and you have the dipole electric field.

That... was a lot easier than I was making it out to be. Kudos to you, sir. Shame on me.
 
  • #6
Out of curiosity, should the more complicated still yield the correct answer?
 
  • #7
It should, but at some point you will have to do a Taylor expansion for d <<r where d is the separation between the positive and negative charges and keep the leading term. Finding the approximate field along the direction of the dipole (the easiest case) is a standard problem in introductory physics.
 

FAQ: Dipole-Induced Dipole Interaction

What is a dipole-induced dipole interaction?

A dipole-induced dipole interaction is a type of intermolecular force that occurs between a polar molecule (one with a positive and negative end) and a nonpolar molecule. The polar molecule induces a temporary dipole in the nonpolar molecule, leading to an attractive force between the two molecules.

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

Dipole-induced dipole interactions are weaker than other intermolecular forces such as hydrogen bonding or London dispersion forces. They also only occur between a polar and nonpolar molecule, whereas other forces can occur between polar-polar or nonpolar-nonpolar molecules.

What determines the strength of a dipole-induced dipole interaction?

The strength of a dipole-induced dipole interaction depends on the magnitude of the dipole moment in the polar molecule and the polarizability of the nonpolar molecule. The larger the dipole moment and polarizability, the stronger the interaction will be.

How does temperature affect dipole-induced dipole interactions?

As temperature increases, the kinetic energy of molecules also increases, making them more likely to overcome intermolecular forces and move away from each other. This can weaken dipole-induced dipole interactions and make them less significant at higher temperatures.

What are some real-life examples of dipole-induced dipole interactions?

Dipole-induced dipole interactions play a role in many everyday processes, such as dissolving salt in water, the interaction between water molecules and oil, and the formation of micelles in soap solutions. They also contribute to the surface tension of water and the properties of liquid crystals.

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