Several decades ago, John T. Bendler and his colleagues applied the notion of fractal time and defect mobility to understanding the properties of Lexan, a tough polycarbonate resin used for making bullet-resistant windows for automobiles. Defect diffusion turned out to be a good model for how the material responds to stresses and how it ages.
A chunk of Lexan consists of an irregular, three-dimensional network of long polymer molecules, with a precisely defined, repeating pattern of atoms. Experiments indicate that cooling the polycarbonate results in the freezing in of a small population of high-energy kinks in the molecular chains.
Molecular model of a polycarbonate molecule showing the carbonate linkages that act as kinks. The fractal-time motion of such kinks leads to stress relaxation.
The movement of these kinks in a fractal-time process along the molecular chains leads to relaxation. Kink movements reorganize the molecular backbone and effectively absorb mechanical energy, such as the impact of a bullet or sledgehammer.
They are also responsible for aging. As energy-absorbing kinks reach chain ends, the material gradually becomes more brittle and weak. With this insight, researchers looked into the possibility of slowing down aging by modifying chain ends.
The fractal-time, or defect-diffusion, model also helps to explain the stretching of silk and glass threads.
In 1835, physicist Wilhelm Weber noticed that attaching a weight to a long silk thread causes it to stretch to a certain length immediately. But that instantaneous elongation is unexpectedly followed by a gradual further lengthening that depends on how long the weight is applied.
The reason for such behavior lies in the fractal-time movement of defects within the materials.
Silk is a complicated natural polymer and has a variety of amorphous and crystalline forms. Under an applied load, the material tries to rearrange itself to redistribute and minimize stresses. Under these conditions, silk molecules relax by unwinding and changing the hydrogen bonding along their backbones.
In a glass fiber, the mobile defects correspond to imperfections in the distorted, tetrahedral network of oxygen and silicon atoms. Under a load, materials such as silk and glass mechanically reorganize themselves.
Although ceramicists, engineers, and artisans such as glassblowers have long been aware of the peculiar behavior of glasses, polymers, and ceramics and have taken these properties into account when working with the materials, little progress in understanding relaxation phenomena occurred for a long time because the mathematics initially used to describe such processes seemed complicated and difficult.
The concepts of mobile defects and fractal-time motion appear to offer a more tractable, self-consistent picture of the relaxation behavior of supercooled liquids and glassy solids.
One of the chief merits of the defect-diffusion theory is that it's mathematically simple. Researchers can use fractal-time mathematics—the mathematics of intermittent pausing—to model the kind of behavior displayed by almost all amorphous materials.
The theory also suggests ways of modifying in a useful manner the properties of industrially important materials.
No comments:
Post a Comment