Volume 7, No. 1, Spring 2003
Volume 7, No. 1, Spring 2003 |
Contents5 | Seeing Math | Video Case | PDF Version |
By Robert Tinker
Atoms and their properties determine our world. The way atoms and molecules bounce, stick, stretch, bend, combine, fall apart, and interact determines what you feel, touch and see, how every living thing grows and dies, and why we use certain materials in our environment. Most of the important modern technologies - molecular biology, chemistry, nanotechnology, electronics, cryogenics, lasers, and composites - can be understood only by considering atoms and their interactions. The common thread of atomic-scale interactions could integrate the sciences and technology around a few core ideas that run through the entire curriculum.
Figure 1. An ionic crystal dissolving in water. The ions are labeled with plus and minus signs. All the ions are surrounded by uncharged water molecules represented here by unlabeled balls. When this model is run, the ions tend to clump, but if there is sufficient water, they become completely surrounded with water "snowballs," one of which can be seen on the right. |
One of the reasons that the connections between macroscopic and microscopic properties are not well addressed in the typical curriculum is that the order of subjects is wrong. The basic ideas of atomic-scale energy conservation, temperature, heat, pressure, electrostatic forces, and electrons belong in physics. But physics is usually taught after chemistry and biology, which need to build on these ideas. Worse, physics courses usually fail to apply mechanics and electrostatics to atoms and molecules. Physics or physical science at the ninth grade should address atoms and molecules to support subsequent chemistry and biology courses, but they rarely do.
Enter computers. Now it is a simple matter to model lots of atoms that collide according to Newton's Second Law applied to the kinds of forces that actually exist between atoms. This is called a molecular dynamics (MD) model. Students can understand the forces that apply to each atom in such a model and experiment with ensembles of lots of them. The gas laws are an experimental result of such a system. Students can even observe non-ideal behavior in a very dense gas of attracting atoms or molecules.
This is an example of the many macroscopic properties that "emerge" from simple laws governing the microscopic world. It is not at all obvious that the gas laws will emerge from classical mechanics applied to interacting atoms, but a molecular dynamics model can convincingly demonstrate that this is so.
Molecular dynamic models can help students discover:
Energy conservation. Put any number of atoms in a "box" and start them each off at any velocity. The total energy of the system will stay constant.
Temperature. Each atom in a mix of atoms in a box - whether small, large or part of a molecule - will have the same average kinetic energy, defined as temperature.
Thermal conduction. Put a hot gas of fast atoms in contact with a cold gas of slow atoms. The hot gas will cool and the cold one will warm until the two are the same temperature.
Entropy. Start a model with atoms arranged in some distinct pattern; the atoms always end up looking essentially the same, bouncing around at random.
Phase change. At high temperatures, a collection of atoms resembles a gas. Remove energy and it will condense into a disordered, dense swarm - a liquid. Continue removing heat and the atoms become ordered - a solid.
These examples are only the beginning. The ideal and non-ideal gas laws, vapor pressure, diffusion, dissolving (see Figure 1), osmosis, filtering (see Figure 2), breaking, and many other basic phenomena can be understood by exploring MD models.
Figure 2. A solid, liquid, and gas encounter a sieve. Here a sieve or filter is modeled by two barriers shown as brick rectangles. When the model is run at a low temperature (top), the balls form a rigid crystal that is trapped on the right side of the sieve. When the temperature rises (middle), a liquid forms, but it still cannot squeeze through, because the atoms attract one another. This illustrates surface tension. Further heating (bottom) creates a gas that can get through. (To appreciate fully these images requires seeing the models evolve dynamically and interacting with them.) |
Molecular dynamics provides another way to understand relationships such as the gas laws. "Laws" such as these are no longer seen as the mysterious result of an abstract mathematical derivation, but can now be understood in the light of something new: simple, quick computer experiments. Because these experiments are more accessible to young learners, it should be possible to use them to make new connections between subjects and to give students a far better understanding of large segments of science. New three-dimensional, interactive models make it possible to visualize cause and effect, turning abstract, theoretical ideas into concrete phenomena.
Indeed, our initial classroom experiences indicate that middle and high school students can learn through experimentation with molecular dynamics models; they can understand atomic-scale models, relate them to macroscopic phenomena, and transfer their learning to new situations. Encouraged by our initial findings, we are in the process of extending our models to encompass new content: chemical reactions and protein conformation.
The molecular dynamics work at the Concord Consortium is laying the foundation for major reform in introductory science teaching that focuses on atoms, molecules, their interactions, and how these determine macroscopic properties. We encourage you to use and modify the software and curriculum materials. Please see "CC Resource Center Offers Free Software and Curriculum" on page 9 for additional information.
Robert Tinker (bob@concord.org10) is President of the Concord Consortium.
The projects described in this newsletter are supported by grants from the National Science Foundation, the U.S. Department of Education, the Noyce Foundation and others. All opinions, findings, and recommendations expressed herein are those of the authors and do not necessarily reflect the views of the funding agencies. Mention of trade names, commercial products or organizations does not imply endorsement.
All Contents Copyright © 2002 The Concord Consortium11. All rights reserved.
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