Page 520 - Carrahers_Polymer_Chemistry,_Eighth_Edition

14 Rheology and Physical Tests

Rheology is the science of deformation and flow. Throughout this chapter, please remember that the

main reasons for studying rheology (stress–strain relationships) are (1) to determine the suitability

of materials to serve specific applications; and (2) to relate the results to polymer structure and form.
Understanding structure–property relationships allow a better understanding of the observed results
on a molecular level, resulting in a more knowledgeable approach to the design of materials. Look
for these ideas as you study this chapter.
Polymers are viscoelastic materials meaning they can act as liquids, the “visco” portion, and as
solids, the “elastic” portion. Descriptions of the viscoelastic properties of materials generally falls
within the area called rheology. Determination of the viscoelastic behavior of materials generally
occurs through stress–strain and related measurements. Whether a material behaves as a “viscous”
or “elastic” material depends on temperature, the particular polymer and its prior treatment, poly-
mer structure, and the particular measurement or conditions applied to the material. The particular
property demonstrated by a material under given conditions allows polymers to act as solid or vis-

cous liquids, as plastics, elastomers, or fibers, and so on. This chapter deals with the viscoelastic
properties of polymers.

14.1 RHEOLOGY

The branch of science related to the study of deformation and flow of materials was given the name
rheology by Bingham, whom some have called the father of modern rheology. The prefi x rheo is

derived from the Greek term rheos, meaning current or flow. The study of rheology includes two
vastly different branches of mechanics called fl uid and solid mechanics. The polymer scientist is
usually concerned with viscoelastic materials that act as both solids and liquids.
The elastic component is dominant in solids, hence their mechanical properties may be described
by Hooke’s law (Equation 14.1), which states that the applied stress (s) is proportional to the resul-
tant strain ( γ ) but is independent of the rate of this strain (dγ /dt).

s = Eγ (14.1)

Stress is equal to the force per unit area, and strain or elongation is the extension per unit length.
For an isotopic solid, that is, one having the same properties regardless of direction, the strain is
defi ned by Poisson’s ratio, V = γ /γ , where γ is the change in length and γ is the change in thick-
w
1
l
w
ness or lateral contraction.
When there is no volume change, as when an elastomer is stretched, Poisson’s ratio is 0.5. This
value decreases as the T of the polymer increases and approaches 0.3 for rigid solids such as
g
poly(vinyl chloride) (PVC) and ebonite. For simplicity, the polymers dealt with here will be consid-
ered to be isotropic viscoelastic solids with a Poisson’s ratio of 0.5, and only deformations in tension
and shear will be considered. Thus, a shear modulus (G) will usually be used in place of Young’s
modulus of elasticity (E; Equation 14.2) where E is about 2.6G at temperatures below T . For com-
g
parison, the moduli (G) for steel, HDPE, and hevea rubber (NR) are 86, 0.087, and 0.0006 dynem ,
2
respectively.
ds = G dγ and s = Gγ (14.2)

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