GRANT THAT THE UNIVERSE is filled with atomic-size billiard balls. Then, with a few insightful definitions and some mathematical gymnastics, physicists can provide you with a near-perfect explanation of our everyday world. The theory is called statistical mechanics. Many people know that it limits the amount of work a machine can deliver. But it actually goes much further. Statistical mechanics describes the engines that drive the earth's weather. It governs the temperatures and pressures inside stars and constrains the evolution of the cosmos. It even sheds light on the arrow of time--why we remember the past and not the future. Indeed, Albert Einstein and Richard Feynman saw the theory as the highest achievement of classical physics.

Sadly, many amateurs have avoided this important subject because, in this case, the highest plateau is also the hardest to reach. One cubic centimeter of air at atmospheric pressure contains more than 10 billion billion atoms of various sizes, all smashing into one another at different speeds. No computer can project the exact trajectories of all these particles, and even if one could, no human mind could make sense of it. Therefore, physicists have devised clever but devilishly difficult mathematical methods to extract comprehension from the chaos.

But the subject is not as abstruse as it seems. The trick is to find models that let you visualize how these random collisions average out to yield the familiar properties of matter, such as temperature, pressure and entropy. The right mental pictures can elucidate the behavior of materials and in turn can help advance amateur projects involving chemistry, sound, heat transfer, crystals and vacuum techniques. That's why I'm pleased to let you know about Molecular Dynamics, an innovative piece of educational software. It doesn't cover every topic within classical statistical mechanics, and it ignores quantum-mechanical effects completely. But it is still the most accessible modeling software I've seen. What is more, the authors of the program at Stark Design in Morristown, N.J., have made it available to Scientific American readers for free until October 2000.

This kind of simulation is nothing new. Many amateur scientists fondly remember writing such programs back in the days of hobbyist computing [see Computer Recreations, by A. K. Dewdney; Scientific American, March 1988], and several limited versions are available on the World Wide Web (such as a Maxwell's demon game).

But Molecular Dynamics takes this all to a new level. It allows you to conduct an impressive array of virtual experiments to see how different atoms interact under all kinds of conditions. The program consists of numerous modules that demonstrate diffusion, osmotic pressure, the relation between temperature and pressure, the distribution of molecular speeds in a gas and many other topics. And you can use the software to discover things that even the most mathematically gifted physicist would be hard-pressed to wrestle from the basic theory.

The simulation runs so fast that when I first saw it at a conference I was certain it was a trick. The presenter put about 50 each of four different kinds of electrically neutral atoms inside a three-dimensional volume. The particle positions updated so quickly that I thought it had to be a computer movie, not a real-time simulation. So I decided to challenge the fellow.

In nature even neutral atoms can bond together. The mutual repulsion of the orbital electrons polarizes the atoms, and it turns out there is a range of distances over which these polarized atoms are attracted. So I asked the presenter to add these electrostatic interactions and then slowly decrease the temperature. He did. The heavier atoms began clumping together while the lighter ones kept speeding about, just as they should. He then rapidly brought the temperature to zero. The free atoms settled into small isolated clumps, again just as they should. That made me a believer.

Geologists see this clumping effect because a volcanic rock that cools slowly possesses larger mineral grains than one that cools quickly. Molecular Dynamics makes it possible to study the underlying principles of this process (called annealing) by varying the number and kind of atoms as well as the rate of cooling. By pausing the simulation at each temperature and rotating the virtual container, one can count the clumps and see how many atoms of which type are in each. That suggests an interesting study. Try repeating the experiment a few times and plotting the average size of the clumps versus the cooling rate. You may discover some fundamental facts about annealing that are quite difficult to derive mathematically.

One delightful demo starts with a cubic crystal of 63 krypton atoms. A few added helium atoms quickly bond to the surface. Tweaking the temperature upward causes the helium atoms to walk randomly on the crystal's face. At a little higher temperature the heliums leave the crystal, and if you raise the temperature still further, the crystal will fly apart. These kinds of effects are observed in real crystals. You can do other experiments here as well. Try lowering the temperature and see whether you can get the crystal to re-form. Then plot the time required for the krypton crystal to form versus the number of hydrogen atoms bouncing about. Does the hydrogen interfere with the crystal formation and, if so, why?

You can also explore gas behavior, such as how a gas adjusts to changes in temperature, volume, or number and types of its atoms. The simulation can approximately reproduce the proportionalities that are combined into the well-known ideal gas law. But only approximately. That is because the ideal gas law itself is just an approximation. It holds only if the gas atoms occupy a negligible fraction of the container's volume and if the atoms' kinetic energies are much larger than the interatomic potential energies that tend to make them clump together. As a result, any real gas departs from the ideal gas law at high densities or low temperatures. Molecular Dynamics includes these effects automatically.

My favorite module, "Maxwell-Boltzmann Speed Distribution," lets you discover how few atoms you need before the physicists' mathematical tricks start working. One of the early triumphs of statistical mechanics in the 19th century was its ability to predict the fraction of atoms moving with a particular range of speeds within a gas at a given temperature. The curve of the fraction versus speed has a sharp rise--meaning there are fewer atoms at lower speeds--and a long tail, indicating that some atoms have speeds that are much higher than the average. I placed 100 atoms of helium and argon into the box and watched the distribution of speeds in real time. After just a few collisions, the two curves took on the expected shape. The heavier atoms peaked at a slower speed, as the theory predicts. You might enjoy removing atoms and observing how the distributions deteriorate.

Unfortunately, the software does have some glaring omissions. For instance, it does not allow treatment of heat flow, work or entropy. You cannot, for example, simulate a piston. Also, the support materials were clearly developed by educators with different views of the target audience; some sections are aimed at beginners, whereas others are perhaps more appropriate for graduate students. The software designer has set up a special Web page for Scientific American readers to submit suggestions for a future version. Despite its limitations, Molecular Dynamics is a wonderful aid for understanding how atoms build up our universe. And for free, how can you possibly go wrong?

To download your free copy of Molecular Dynamics, link to Stark Design's site. For more information about this and other projects, check out the Society for Amateur Scientists's Web site. You may write to the society at 4735 Clairemont Square, PMB 179, San Diego, CA 92117, or call 1-401-823-7800.

Image: George Musser; Daniels & Daniels; Source: Molecular Modeling

The Society for Amateur Scientists (SAS) is a nonprofit research and educational organization dedicated to helping people enrich their lives by following their passion to take part in scientific adventures of all kinds.