Page 189 - Academic Press Encyclopedia of Physical Science and Technology 3rd Polymer

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Encyclopedia of Physical Science and Technology EN012c-598 July 26, 2001 15:59

698 Polymers, Mechanical Behavior

modulus must be specified with respect to the degree these properties are measured and expressed. In addition,
of deformation. some of the molecular origin of the observed behavior is
Shear modulus Initial slope of a shear stress–shear strain considered following basic definitions. Because of space
deformation curve; an indication of the resistance to limitations, only the basics are provided; hence, only the
deformation by shear. terminology and general characteristics of different be-
Storage modulus Parameter that is related to the elas- havioral patterns of polymers in terms of their response
tic behavior of a material when undergoing small to internal (macromolecular) variables, such as molecular
cyclic deformations; generally obtained by dynamic weight, chain topology, cross-linking, and crystallinity,
mechanical spectroscopy. will be considered along with the influence of external
Strain Variable expressing how the dimensions of a ma- parameters, such as temperature, time, and pressure, the
terial change under deformation. former two being of extreme importance.
Tensile strength Engineering stress atthe point of sample Before we address the mechanical parameters and their
failure. In the case of sample tearing, generally the peak definition, a few comments are in order concerning the
value of the engineering stress is quoted as the tensile molecular systems that we will be discussing. In particu-
strength. lar, polymeric or macromolecular systems are composed
Thermal mechanical spectrum Graphic representation of long chains whose backbone is made up either of like
of a specific mechanical property as a function of tem- units (homopolymers) or of varied units (copolymers, ter-
perature in which the data have been obtained under the polymers,etc.),andifonlytwodistinctendsarepresentthe
same loading rate. Generally, either the dynamic stor- system is said to be linear. In many cases macromolecules
age or loss modulus is reported. These values are ob- are not linear but may possess branches, which are short
tained by either dynamic shear or extensional methods. or long, depending on the procedures used to synthesize
True stress Force of deformation obtained in extension these materials. These branches can have a considerable
divided by the cross-sectional area that exists at the effect on mechanical properties since randomly placed
elongation at which the stress is determined. branch points will not fit into a crystal lattice. Therefore,
the percentage of crystallinity is decreased by branching in
those systems that have otherwise suitable chain symme-
THE MECHANICAL BEHAVIOR of a material extends try to pack into a lattice. In addition, these branch points
from its stress–deformation response, in which the mode also influence the general flow properties of the system in
of deformation (uniaxial, biaxial, etc.) is particularly im- melt processing or solution processing particularly if the
portant to define, as are the loading profile and environ- branches are long enough to undergo entanglement with
ment under which a given test is carried out. Often in the neighboring chains. Network structures are also common
application of polymeric materials, the mode of failure due to cross-linking between chains if the reactants have
may be induced by a more complex loading scheme than sufficient functionality to promote network development
is easily applied within a testing laboratory. However, it at high conversion.
is important to develop, where possible, a basic under- Many of the polymers utilized today in the market-
standing of the properties of any new polymeric material place such as polyethylene, polypropylene, polystyrene,
through a well-defined loading profile and to learn how styrene–butadiene rubber, and polymethyl methacrylate
these properties depend on molecular or “system” vari- are viewed as flexible or coil-like chains. This is due to the
ables as well as the nonmolecular or “external” variables ease of bond rotation in these covalently connected repeat
mentioned above. units, which can occur under appropriate conditions and
are in contrast to rigid rod polymers where ease of bond
rotation is highly limited at any reasonable temperature
I. INTRODUCTION at which the system would be used or processed. It is
important to recognize the general “long-chain” nature
The mechanical behavior of polymeric materials is a vast of many of these materials. As an example, consider
subject and one that is particularly important for the prac- a polyethylene molecule of 100,000 molecular weight.
tical application of these materials. Often it is the me- What would be the necessary tube length and tube dia-
chanical properties, in conjunction with economics, that meter to place this molecule into if one were to stretch it
dictate whether a given polymeric material can be utilized out in its fully extended form (see Fig. 1)? For that mo-
for a specific purpose. Other properties, such as optical lecular weight a first-approximation calculation would
transparency and dielectric behavior also play a signifi- show that this number (length/diameter), or aspect ratio
cant role, but this article focuses only on the basics of me- of the molecule, is of the order of 1800. This number far
chanical properties and, in particular, the means by which exceeds the same aspect ratio that would be obtained for