Surface tension, surface energy, and molecules - a basic question

Factual Questions
1

The root cause of surface tension, and thus the tendency for droplets to form with a shape that minimizes their surface area, is stated to hinge upon the fact that “A molecule in contact with a neighbor is in a lower state of energy than if it were alone (not in contact with a neighbor).”

I don’t see why it is self-evident that a molecule’s contact with its neighbours affects its energy that way. For example, identically charged molecules would tend to repel each other and wouldn’t that mean they’d have a higher state of energy when in proximity to their neighbours? (There may or may not be an intermolecular distance that leads to the formation of a stable droplet)

All of which leads me to ask, if a molecule’s energy state is lowered by contact with a neighbour, is the lowering dependent on the sharing of electrons?

2

If all of the molecules in a substance have the same sign of charge, then you won’t have a substance, just a bunch of widely separated molecules. In real life, you’ll almost always have almost complete neutrality: Either all of the molecules are neutral, or you’ll get positive ions to balance the negative ions.

And once you have neutral (or net neutral) substances, you’ll start seeing polarization effects: The positive charges in one molecule will move to be closer to the negative charges in other molecules, and the negative charges will move to be closer to the positive charges. And then, since the opposite charges are closer together than the same charges, there will be, on net, a slight attraction.

3

For further reading on what Chronos is describing, look up Van der Waals forces.

4

What you are trying to take as a root cause and an obvious fact (that doesn’t seem obvious) is just “Another way to view surface tension”, per the Wikipedia article, which is in terms of energy. That is, a liquid is made of molecules that are randomly bouncing around into each other from all directions. Except at a surface, where they are only being bombarded from one side. There is an energy associated with being at the surface that the molecules in the body of the liquid do not possess (something is keeping the molecules at the surface, which are being bombarded from only one side, from being knocked away). As there is a higher energy level (or state) of the molecules at the surface, the lowest energy will be represented by the smallest amount of surface.

5

If you have a couple of these neutral particles, at short distances they will tend to electronically repel each other and be in a higher state of energy, but at longer distances the van der Waals forces will attract each other.

ETA it’s not a covalent bond where they are sharing electrons

6

As always, thank you.

Does a similar reasoning apply in the subatomic realm? Do collections of such particles ever behave like droplets and minimize the surface energy of the ensemble to form a more stable state (and/or a new particle)? Is this what the droplet model is about?

7

Pretty much, yeah. The forces that lead to the effect are even more complicated than van der Waals forces, enough so that we don’t know the details, but the net effect is about the same, allowing for quantum mechanical complications.

8

Excellent. Thanks.

I knew the term ‘droplet model’ (and must have read about it at some time in the past) but I think I now have a better intuition of the motivation for it.

9

Here is the original droplet model. You’ll notice five terms there, the first one being the binding energy of the particles, and the second subtracting off a term proportional to the surface area of the “drop”. As for how accurate it is, you’ll have to compare it to the actual measured values in the periodic table, but the graph doesn’t look too bad as a first approximation.