ABSTRACT
Perfectly elastic deformation and perfectly viscous flow are idealizations that are approximately realized in some limiting conditions. In general the con densed matter has a fading structural memory, and the velocity with which a system that has been perturbed forgets the configuration that it had in the past roughly defines its solid or liquid nature. In ordinary liquids, molecular
reorganization occurs very rapidly and structural memory at the molecular level is very short. The response is essentially viscous unless the frequency of the testing experiment is very high. Consequently the mean relaxation time, roughly defined as the time necessary for the system to forget the configura tion it had previous to the perturbation, is very small. In solids, on the other hand, the relaxation of structure at the molecular level is extremely low. The response is essentially elastic. However, the distinction between solid (or elastic) and liquid (or viscous), is not an absolute distinction between dif ferent classes of materials. It should be pointed out that the distinction between solid and liquid is usually based on a subjective comparison of the relaxation time of the system and the time of observation (1). For example, water behaves as a solid at very high frequencies, and ice behaves as a fluid on a geological time scale. If we can dabble our fingers in a material we can conclude that it is a fluid, though it may return to its initial configuration after one month or one year. In the same way, if we are hit by a hard object we can think that it is a solid even though it can flow on a geological time scale. From a strict point of view, condensed matter exhibits viscoelastic behavior, though the ability to detect elastic or viscous responses depends in many cases on the time scale of the experiment. Usually, the solid or liquid character of a material is expressed by the Deborah number, N D, defined as (2)
where t can provisionally be taken as some order-of-magnitude estimate of the time required for stress relaxation to approach completion and xexp is the time scale of the experiment. For ordinary liquids t 0 and N D ~ 0, while for ordinary solids t —► oo and N D —► oo. For the so-called viscoelastic systems, x and xexp are comparable and the Deborah number of these sub stances is on the order of unity.
