Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 41

regarded as having both elastic (solid) and viscous (liquid) properties. For that reason the
majority of measurements are made using conventional commercial small-strain oscil-
latory instruments. However, it is very important to point out here that such small-
deformation experiments may have little to do with applications, which often involve
large-deformation fracture or rupture.

2.5.1 Small-deformation measurements

There is no absolute measure of ' small ' and ' large ' ; the (static) elastic modulus of any

solid is de ned as the ratio of stress to strain. In some experimental set-ups it is the stress

that is varied, and in others the strain, but there is a clear implication in the above
de

nition that stress and strain are proportional. This is always true in the limit of small
enough stresses and strains, but the absolute value of this linear viscoelastic strain limit
can be as high as 25% or as low as 0.01%, depending upon the nature of the gel system.
This does not mean that measurements outside these limits are pointless, just that they
have a different purpose. They are concerned, say, with the absolute stress or strain ' to

failure and the area measured under the stress/strain curve under

various conditions (for example, rate of deformation or temperature). Traditional meth-
ods of gel characterization include those based on falling or oscillating microspheres, and
gels oscillating in a U-tube manometer (Ross-Murphy, 1994 ). Although cheap to con-
struct, they are now mainly of historic interest, but some recent gel work still employs
falling-ball and tilting-tube methods ( Chapters 8 and 9 ).

'- fracture or rupture -

2.5.1.1 Small-deformation oscillatory shear methods

Nowadays the vast majority of physical measurements on gels are made using oscill-
atory shear rheometry (Ferry, 1980 ; Kavanagh and Ross-Murphy, 1998 ). The essential
feature of a typical rheometer for studying gels is a vertically mounted motor
(which can either drive steadily in one direction or oscillate). In a controlled-stress
machine, this is usually attached to the upper

fixture. A stress is produced, for example
by applying a computer-generated voltage to a DC motor, and the strain induced in
the sample is measured using an optical encoder or radial position transducers attached
to the driven member. In a controlled-strain instrument, a position-controlled motor,
which can be driven from above or below, is attached to one fixture, and opposed to this is

a transducer housing with torque, and in some cases normal force, transducers.
Figure 2.15 represents a typical controlled-stress instrument. The sample geometry can
be changed from, for example, Couette to cone/plate or disc/plate, and the sample
temperature controlled.
In a typical experiment, a sinusoidal oscillation of maximum strain γ M and oscillatory

frequency is applied to the sample. If the material is perfectly elastic, then the resultant

stress wave is exactly in phase with the strain wave, and does not depend upon the
oscillatory frequency, so we can de

ω

ne the (Hookean) equilibrium elastic modulus G as
the ratio of stress to strain. If the material is a purely viscous

fluid, since the rate of change
of the sinusoidal oscillation is a maximum when the strain is zero, the resultant stress
wave will be exactly 90° out of phase with the imposed deformation.