# Where does the spring force come from?

## Main Question or Discussion Point

We know that atoms are held together by atomic bonds and when one atom is moved away from the one it's bonded to, there is a restorative force that 'pulls' it back. But how can we explain the nature of this force in terms of the electrostatic/electromagnetic forces between charged atomic particles (proton & electron)? In a covalent bond an electron is shared between two atoms (i.e. its wavefunction is spread over a wider area), but how does that explain the restorative force? If I move one atom away from another, I'm moving the positively charged nucleus away from this shared electron, so the electrostatic force between the nucleus and the electron should only get smaller, not larger (as hooke's law predicts).

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I always thought it was a property of the structure of the material that it absorbs energy(kinetic) of a force directed at it and depending on the material it will release that energy back in an effort to return to its original structure.

Brian99 said:
If I move one atom away from another, I'm moving the positively charged nucleus away from this shared electron, so the electrostatic force between the nucleus and the electron should only get smaller, not larger (as hooke's law predicts).
Initially em and qm forces are ballanced. When we stretch a material in a certain direction the distances between -ve and + ions become slightly bigger than the equilibrium case. This extra distance (space) will become filled with a static field. (Perhaps also a magnetic one which for simplicity i'll ignore).
(E- field)^2 X space is energy. We will have to supply this energy.
There's a limit to this process when on bigger distances (say a couple of Angstroms) fields from different ions from the same direction are starting to merge. At that point we are starting to form 2 new surfaces.

Where's the spell checker?

I realise i’ve overlooked your main argument.

When we separate the 2 plates of a (charged disconnected) capacitor, initially the attractive force is not getting smaller. It only starts to decrease when fringe effects need to be taken in account.

In my view, one of the reasons that the total restorative force is getting bigger is that at first upon stretching not all +ve and –ve ions in one cross section will be effected. The number of restoring force dipoles will go up when stretching increases.

Ich
No, it´s more like in your first post: Initially, the forces are counterbalanced. When you one atom away, the counterbalancing qm force necessarily decreases faster than the em force. As long as you don´t pull too much, this gives a linearily increasing net force. When you pull too much, the decrease in em force becomes significant an the spring breaks.

OK Ich good point.
What about the above mentioned wavefunction? When we store more energy in this system will the PE and KE of the restoring electrons increase and therefore will the spread become more localised?

Ich
http://www.mse.uiuc.edu/info/mse182/t79.html" [Broken] explains the variation of bond lenght with energy (=Thermal Expansion Coefficient).

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vanesch
Staff Emeritus
Gold Member
Brian99 said:
But how can we explain the nature of this force in terms of the electrostatic/electromagnetic forces between charged atomic particles (proton & electron)? In a covalent bond an electron is shared between two atoms (i.e. its wavefunction is spread over a wider area), but how does that explain the restorative force?
This is a purely quantum-mechanical effect, which cannot be understood in classical terms. What you have to do, is to solve the quantum-mechanical problem of the electron eigenfunctions for a given separation of the nucleae, say, distance R. That means, for a given R, you place two nucleae at this distance, and you calculate the possible wavefunctions of the (relevant) electron system (in other words, the binding electrons). There will be a "lowest energy" state (the ground state), with energy E0, and there will be excited states, with energy E1, E2... (the eigenstates of the Hamiltonian for this system). But remember that we placed the nucleae at distance R ; if we had chosen a distance R', we'd have found different values E0', E1', E2'... for the energy eigenvalues. So in general, the energy eigenvalue is a function of R: E0(R), E1(R), E2(R)...

Now, you can plot these values as a function of R (the typical potential well curves), and if E0(R) shows a minimum for a certain value R = R0, then this will be the bond length. The step from E0(R0) to E(R-> infinity) is the bond strength (well, almost! I'm putting something under the carpet here). The pit of the potential curve around E0(R0) looks like a parabola in this case (it is a smooth minimum), hence this looks a lot like the potential curve of a spring.
The other curves E1(R), E2(R) ... do not need to show a minimum: they are called non-binding states ; but they could: we then have an excited binding orbital. If E0(R) also doesn't show a minimum, then there is no possibility for a chemical bond.

cheers,
Patrick.

I can just about follow that. So qm includes both the attractive em force and the repulsive force due to wave mechanics? You see i’m still trying to hang on to some kind of visual picture.

Patrick cheers to you too, especially on friday.

vanesch
Staff Emeritus