Time to Relax I

The rubber in a pair of boots, retrieved after a long stay in an attic, shows its age in an annoying way. No longer as flexible as it once was, the material (an elastomeric polymer) readily cracks and falls apart. Under the same conditions, many other plastics suffer a similar fate.

One cause of this aging process is chemical. Sunlight or oxygen can initiate chemical reactions that alter the material's properties. But deterioration occurs even when a material is kept in the dark or away from oxygen. The material gradually becomes more dense and brittle, losing its toughness and impact resistance.

The explanation for this behavior lies in the way "defects" within amorphous, or noncrystalline, materials reorganize themselves over long periods of time.

Glass is an example of an amorphous material. PPG Place, Pittsburgh, Pennsylvania.

When expressed in terms of the concept of fractal time, the same mathematical model used to describe polymer aging also applies to the stretching of glass or silk fibers; the recovery, or relaxation, of glassy materials after the removal of a stress; and a wide range of other phenomena in amorphous materials.

In such processes, events occur in self-similar bursts—featuring distinct clusters of activity interspersed with long stretches of inactivity. Some changes in materials occur right away while others take years to show up.

Relaxation is an issue of practical importance. Slow aging processes, both environmental and physical, control the lifetimes of a great many manufactured products, from electronic devices to optical fibers and advanced composite materials. Elucidating of how such processes occur can suggest novel techniques for toughening ceramics and for designing polymers having particular characteristics.

Relaxation processes are common in physical systems. For example, pull on a glass fiber, then let go. The glass first stretches, then shrinks. Apply a strong electric field to a polymer, then turn it off. Areas of positive and negative charge in the polymer line up with the field, then drift out of alignment.

In each case, the material endures a stress, then recovers, or relaxes, when the stress is removed.

Relaxation in a crystalline material typically proceeds at an exponential pace. That type of relaxation follows the same pattern as the decay of a radioactive isotope. Such a process is characterized by a certain time, known in the case of radioactive decay as the half-life.

Normally, you find that relaxation is clustered around a certain time. It might take a second, a day, or a week. But an amorphous solid takes a longer time to relax than would be expected if relaxation simply followed an exponential pattern.

In amorphous systems, some parts relax very quickly. If those parts relax in, say, seconds, other pieces might relax on a time scale of minutes, and still others on a scale of days or weeks. If you were to wait long enough—even years—you would still detect changes taking place. No characteristic time can be defined for such an extended relaxation process.

This type of behavior has come to be known as stretched exponential relaxation. It fits a wide range of relaxation processes in disordered systems, including the way many polymers, glasses, and ceramics respond to stresses caused by changes in pressure and temperature and the imposition of electric and magnetic fields.

Because so many different systems behave in such a strikingly similar fashion, physicists, in their search for an explanation, have concentrated on what these systems have in common. They have found that what's important is not the details of a material's atomic or molecular structure but rather its state of disorder.

Time to Relax II