Viscoelastic properties of macromolecules

Abstract

An acoustic wave traveling through a material deforms the material, thereby probing its mechanical properties. The classical theory of elasticity deals with the mechanical properties of elastic solids. In accordance with Hooks law, for small deformations stress is always directly proportional to strain. Furthermore, stress is independent of the rate of strain. The classical theory of hydrodynamics deals with properties of viscous liquids. In accordance with Newtons law, stress is always directly proportional to rate of strain but independent of the value of strain itself. Purely elastic solids and purely viscous liquids are idealizations as well as the two boundaries of system behavior, which combines liquid-like and solid-like characteristics. Those material properties have been called viscoelastic. A viscoelastic material does not maintain a constant deformation under constant stress. It continues to deform slowly with time. On the other hand, when the stress is removed, a viscoelastic material recovers part of its deformation. When a viscoelastic material is constrained at constant deformation, the stress required to hold it, diminishes with time. When a viscoelastic material is subjected to sinusoidally oscillating stress, the strain is neither in phase with stress as valid for purely elastic solids nor 90° out of phase as valid for purely viscous liquids. Stress and strain are some amount out of phase, which depends on the viscoelastic properties of the body. If both strain and rate of strain are infinitesimal, and if the time-dependent stress-strain relations can be described by linear differential equations with constant coefficients, the system shows linear viscoelastic behavior and the ratio of stress to strain is a function of time or frequency, not a function of stress magnitude [1, 2]. Viscoelastic properties of material should not be mixed up with deviations from purely elastic or viscous behavior due to finite strain(non-Hookean deformation) or finite strain rates (non-Newtonian flow). The necessity to distinguish between infinitesimal and finite depends on the level of precision of measurement and properties of the material under consideration. Viscoelastic anomalies are negligible or at least of minor significance for many classical engineering materials. By contrast, the mechanical behavior is dominated by viscoelastic phenomena in macromolecular materials. Due to the extreme importance of those materials for chemical and biochemical sensors, the consequences of viscoelasticity for acoustic sensors will be analyzed in some more detail. A comprehensive analysis of viscoelastic properties of polymers can be found in Ferrys fundamental book [1]. The following text summarizes those statements about the phenomenon of viscoelasticity [1-3] which are important to understand specific features of acoustic-wave based sensors. © Springer-Verlag Berlin Heidelberg 2008.