A View from the Back of the Envelope top

Atomic bonding
Good description
Deep understanding
Simple models

I wanted to know why atoms stick together. I couldn't find a good description, so I pieced together this one.

Atomic bonding is a balance between
attraction (electrostatic)
and repulsion (electron-cloud compression).

"Whenever you feel in your daily life the hardness of solids, be they metals, rocks, ceramics, or wood, remember that it is the Schrödinger pressure which causes it, the resistance of electrons being forced to assume smaller wavelengths." [Weisskopf,AmJPhys v53n2,p110]

Warning: I'm still not sure what the right answer is. I now collect seemingly contradictory explanations from graduate-level physics texts. :( Perhaps my next step is to corner a bond-dynamicist...

[2003-Feb: Which I did last year (or in 2001?). The attraction is both electrostatic and electron clouds preferring to be less compressed. (And possibly a small third component, which was a topic of research at the time.) The relative importance of the two depends on the type of bond. I plan to update and finish this page at some point...]

Stuff is made of small hard atomic nuclei surrounded by clouds of electrons. (Picture marbles in fuzzballs.) The nuclei are tiny and far apart.
So two questions... Why do the nuclei stay together?
Why do the nuclei stay apart?

Atomic nuclei are pulled together by the electrostatic attraction between negatively-charged electron clouds and positively-charged nuclei.

Atomic nuclei are kept apart by Schrödinger pressure. When the nuclei get too close, their electron clouds get crowded, and as they don't like to overlap, they push the nuclei back.

Atomic nuclei vibrate back and forth, stuck between this attraction and shorter-range repulsion.

The attraction and repulsion pressures are very high. (10~10 Pa. Say 105 atmospheres.) The nuclei fluff out until the pressures are balanced, holding each other in check. When you push or pull [caveat] on stuff, you get involved in this tug of war, and there is a lot of pressure there to resist you.

"The [electron-pair] chemical bond is often described as an "exchange effect". I believe that such a formulation is misleading. It refers to mathematical terms appearing in the detailed calculation, in which two wave functions appear, differing by an exchange of coordinates. These terms are a consequence of the Pauli principle requiring antisymmetric wave functions. They have no direct physical significance. Electrons are "exchanged" only in the sense that in the merged molecular quantum state it is no longer possible to assign an electron to one or the other nucleus." [Weisskopf,AmJPhys v53n5, p399-400]

Atomic material is simply a suspension of nuclei (to a first approximation).

Electrostatics is what makes your hair stand up when you rub it with a balloon.

Temperature is the speed the atomic vibration. [well...]

The back of my envelope...

This is an early and raw draft. It has drawn little comment. And I have never gotten back to it.

Metal / solids / liquid / gas distinctions currently muddled.

A warning: In assembling this page, I am operating outside of my domain of expertise. Having not found references which approached things from quite this angle, I am left to filter and glue together pieces of reliable information with my fallible understanding. Caveat.

This page is mostly based on Weisskopf's "Search for Simplicity" column, with help from [Tabor].

I have said simply that the attraction is electrostatic. This abstracts away a lot of richness, in the shape and location of the electron clouds, and in the variety of flavors of electrostatic attraction.

It seems to be common for introductions skip from the simple "atoms stick", directly into obscuringly organized taxonomies of the flavors of electrostatic attraction. Categories of covalent, ionic, metallic, dipole, van der Waals, etc etc. Without explicitly mentioning or exploring their fundamentally electrostatic nature. I suspect a clearer presentation might be built on explicit exploration of electrostatic variety (mono- and di-pole, localized and distributed, stable, transient and induced, etc). Perhaps I will get to it.

Beyond the basic question of why matter has extent, one can move on to why it has the properties it does. Tabor suggests bulk properties can be derived simply. And one might build from the fundamental quantum `having of shape' of electron states, up through all the spatial order of molecular matter and life which results. And going in the opposite direction, from familiar matter, to the origins of its components and its context in the universe. I would also be nice to have a basic introduction to atoms which is more quantitative / descriptive / context-full / usable than is usual. I have various pieces, and perhaps with time they will assemble into pages.

Perhaps "electron-cloud compression" rather than "electron compression"? Latter requires Weisskopf quote to clarify ("electrons being forced to assume smaller wavelengths").

I've replaced the misleading phrase "When the nuclei get too close, their electron clouds get crowded and scrunched, and push them back." Scrunched suggests reduction in size. Their quantum unhappiness about overlapping forces them towards higher energy levels, which I'm guessing tends more towards expanding than shrinking. I unfortunately don't have a good feel for electron clouds in their relaxed state, let alone stressed.

A View from the Back of the Envelope
Comments encouraged. - Mitchell N Charity <mcharity@lcs.mit.edu>

 2003-Feb-04   Added correction.
 1999.Mar.24   Added stronger Caveat.
 1997.Oct.30   Patched the misleading
                 "When the nuclei get too close, their electron clouds
                  get crowded and scrunched ...".
  long ago     First draft.