higher, than those obtained for Newtonian liquids. This implies that it is
difficult to reach a high elongation rate during flow of a non-Newtonian
liquid with strongly elastic behavior.
Elasticity often stems from the resistance of the bonds in a material to
extension or bending. Deformation will thus increase bond energy (see
Figure 3.1). Another cause is that the conformational entropy of a material
will decrease upon deformation: this occurs especially in polymeric systems
and it is further discussed in Chapter 6. In either case, the material will
return to its original state upon release of stress—i.e., behave in a purely
elastic manner—provided that no bonds have been broken. In a viscoelastic
material, part of the bonds break upon deformation. (A purely viscous
material has no permanent bonds between the structural elements.)
Dynamic Measurements. Viscoelastic materials thus show an
elastic and a viscous response upon application of a stress or a strain. To
separate these effects, so-called dynamic measurements are often performed:
the sample is put, for instance, between coaxial cylinders, and one of the
cylinders is made to oscillate at a frequencyo. Stress and strain then also
oscillate at the same frequency. In Figure 5.9, a shear strainðgÞis applied,
and it is seen to vary in a sinusoidal manner. If the material is purely elastic,
the resulting shear stressðsÞis always proportional to the strain, and the
ratio sel=g is called the elastic or storage shear modulus G^0 (‘‘storage’’
because the mechanical energy applied is stored). If the material is a
Newtonian liquid,sis proportional to the strain rate dg=dt. Hence the stress
is out of phase with the strain by an amountp=2. The ratiosvis;max=gmaxis
called the viscous orloss modulus G^00 (‘‘loss’’ because the mechanical energy
applied is lost, i.e., dissipated into heat). The subscripts max denote the
highest values of these parameters during a cycle, and these have to be taken
because stress and strain are out of phase. The relation with the apparent
viscosity is thatZa¼G^00 =o.
For viscoelastic materials, the response is as in Figure 5.9d. Here
sve¼selþsvis.Acomplex shear modulus GG~ can be derived, and the
following relations hold:
GG~¼G^0 iG^00 ð 5 :12aÞjGG~j¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðG^0 Þ^2 þðG^00 Þ^2q
ð 5 :12bÞtand¼G^00
G^0
ð 5 :12cÞwherei¼Hð 1 Þ,jGG~jis the absolute value ofGG~, anddis the loss angle (see
Figure 5.9). The absolute value of the modulus measures total stress over