Mechanical Properties of Polymers J. J. Aklonis University of Southern California. Los Angeles. CA 90007 The term mechanical properties is commonly used to denote stress-strain ~ e l a t i o h s hfor ~ ~polymer s syshms. Unlike many more familiar materials where these relationships depend essentially only on temperature, in polymeric systems time dependence is also of importance. This time dependence necessitates verv careful definitions of narameters such as moduli and compliances which result from experiments involving discontinuous stress or strain levels. In addition, the time dependence may be explored using oscillatory perturbations as is done when investigating dynamic mechanical properties or dielectric relaxation in polymers. An experimental "master curve" d e ~ i c tthe s behavior of a polymeric system at any temperature over a broad spectrum of time. On the other hand, mechanical behavior may he presented isochronally as a function of temperature; one usually observes four distinct regions of viscoelastic behavior in such a curve for a linear amorphous polymer and each of these regions may he related to specific types of molecular motion. Voigt and Maxwell elements are frequently used in the treatment of mechanical properties. It is well known that elements such as these do hotpossess sufficient flexibility to mimic experimentally observed behavior with high fidelity, but combinations of these elements are found to do a much better job. In this paper, an overview of the study of mechanical properties of polymers will bepresented. No attempt will be made a t rieor or comnleteness. Ultimate nronerties and non-linear gehavior wiil not he covered. he ideas will he presented in an intuitive fashion from the viewpoint of a chemist or physicist. Careful study of works such as those included in the biblioma~hv - . .will he necessarvfor acomnlete understanding of this area. Modulus-Temperature Behavior 01 Polymers Although we recognize that time plays a very imprtant role in the determination of merhanical properties of polymers, for the moment, let U. ignore this fact. In this section, we will
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Journal of Chemical Education
TEMPERATURE IT.) Figure 1. Schematic Modulus-temperature curves faa rubber (polyisobdylene) and lor a plastic (polystyrene).
concentrate on the influence of temperature in determining mechanical properties of polymers. Let us start by considering a simple tensile experiment carried out on a strip of polyisohutvlcne (PIRJ.For the sake of nmcrewness, assume that the strip is 2 cm long and has a cross sectional area of 0.3 cm2. At this level of aonroximation. .. . a tensile experiment simply consists of hanging a weight on this strip of PIB and observine the chanee in samole leneth (AI). udder these conditions, the tensilekodulus;~defined as Here, E is the tensile modulus; a, the tensile stress defined as the force applied to the system divided by the cross sectional area, A; and r, the tensile strain which is equal to the change in sample length divided by the original sample length 1. Alternatively, one might define the tensile compliance:
TEMPERATURE Figure 2. Schematic modulu~-temperaturecurve showing the four regions of
ViSCOeiaRiC behavior.
Let us imagine an experiment in which the strip of PIB is cooled. ~ e r h a nin s liauid nitroeen. to a rather low temnerature: the st& is sihjecteh to a force and the resultant sample ex: tension is observed. At this low temperature, the resistance to elongation of a marerial like PIB is substantial and the calculated mtxlttlus. shown in Fimre I . is correspondingly high with a value in the range of 3 lo9 ~ e w t o ~ s l m e(t e 3~ ~ ~ 10'0Dvne/cm2). Such high modulus values are characteristic of glassy or plastic mntrrials. The sample is next warmed several degrees and an identical exoeriment carried out: similar results are observed until. in the neighborhood of -70% for PIB, a dramatic decreasd in modulus by approximately a factor of one thousand is observed. Now the modulus has a value in the range of lo6 N/m2 which is characteristic of rubhew materials. Thus. near -70°C, the properties of polyisohu~ylenechange froi those of a elass to those of a rubber and, i t is said that polvisobutyleie has undergone its "glass tradition" near this temperature. Upon further heating, the modulus remains reasonably constant until considerably higher temperatures are reached. At these higher temperatures, another drastic decrease in modulus is observed for linear amorphous materials. In this ranee. u , the samnle actuallv becomes liauid-like and does not support any stress, not even the stress generated by its own weieht. The overall modulus versus temDerature hehavior for ~ l g i schematically d depicted in viguri 1. I
