Self-Assembly of Synthetic and Biological Polymeric Systems of ...

2.9.1.- Viscoelasticity
Many materials can be classified as solid or fluids, displaying elastic and viscous behaviour
respectively. Viscoelastic materials such as polymers combine the characteristics of both
elastic and viscous materials depending on the experimental time scale. Application of a stress
of relatively long duration may cause some flow and irrecoverable deformation, while a rapid
shearing would induce an elastic response in some polymeric fluids. Then, a classification of
these materials should include a consideration of the timescale of the measurement relative to
the characteristic time of the material. This ratio is given by the Deborah number (De): when De
is 1 the material will display both viscous and elastic behaviour and is described as viscoelastic,
whilst, for De » 1 and De « 1 the material has solid-like and viscous-like behaviour, respectively
(49)(50).
Pure elastic solid behaviour may be exemplified by a Hookean spring, and pure viscous flow
can be exemplified by the behaviour of a dashpot, which is essentially a piston moving in a
cylinder of Newtonian fluid. Nevertheless, the viscoelasticity cannot be described accurately by
neither spring nor dashpot alone, but a combination of both. In this way, several mechanical
models have been developed to describe the viscoelastic response of a given material. All of
these mechanical models are, then, supported on the combination of these two simple
elements (spring and dashpot), which represented the elastic behaviour of a solid body, and
the viscous flow for a liquid, respectively. Among all models, Maxwell’s and Kelvin-Voigt’s
models are the most frequently used (Figure 2.21) (50).
a) b)
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Figure 2.21. a) Maxwell’s and b) Voigt’s models.
The use of mechanical models such as the spring and dashpot as analogues of the behaviour of
real materials enables us to describe very complex experimental behaviours using a simple
combination of models. The uses of models to represent a wide range of deformation are not
restricted to the application of shear stress; however, in this section, we will focus on the shear
properties of the material (1).
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