Chapter 10
Ductile Polycarbonates Containing Bisaryl Units: Theory and Modeling 1
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John T. Bendler and David A. Boyles Downloaded by STANFORD UNIV on February 18, 2015 | http://pubs.acs.org Publication Date: March 8, 2005 | doi: 10.1021/bk-2005-0898.ch010
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Physics Department, U.S. Naval Academy, Annapolis, MD 21402 Department of Chemistry and Chemical Engineering, South Dakota School of Mines and Technology, Rapid City, SD 57701
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Abstract Theoretical arguments suggest that polymer segment geometries and, in particular, molecular aspect ratios play an important role in controlling bulk polymer ductility. Under tensile loading, competition between crazing and shear flow determines the ultimate failure mechanism of a glassy polymer. Shear yielding stresses are less variable from polymer to polymer than are craze initiation stresses and craze strengths. Craze strengths are strongly influenced by the entanglement densities and overall polymer molecular weight. A quantitative relationship has been proposed by Fetters et al. relating the entanglement molecular weight, M , to the monomer shape or packing length, p. This correlation indicates that incorporation of tetraaryl units into a polycarbonate chain can lead to a higher entanglement density and craze strength, and hence improved bulk toughness, as well as enhanced heat and solvent resistance. A novel synthetic route to these new polymers has been found and ductility measurements are planned. e
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© 2005 American Chemical Society In Advances in Polycarbonates; Brunelle, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2005.
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Downloaded by STANFORD UNIV on February 18, 2015 | http://pubs.acs.org Publication Date: March 8, 2005 | doi: 10.1021/bk-2005-0898.ch010
Introduction Amongst the useful properties of bisphenol A polycarbonate (BPA-PC), of particular interest is its notable impact toughness and ductility which can persist to -40°C for high molecular weights. Numerous analogues of B P A - P C have been synthesized which display higher heat or improved solvent resistance, but to date all new variants of B P A - P C exhibit poorer ductility. Unraveling the secret of B P A - P C s glass state ductility could, in principle, result in a new generation of engineering polymers with useful properties well-suited to electronic, automotive, medical and military applications. In recent years, both theory and molecular simulations have broadened and deepened our knowledge of mechanical behavior of polymers, so that now, perhaps, the first steps towards "arm-chair" design of new polymers may soon become practical. In this article we review several theoretical ideas and computational results which suggest that overall monomer geometries play a significant role in controlling glassy state fracture strengths, entanglement densities and ultimately bulk polymer toughness. These ideas have been applied to the example of biaryl units incorporated into a polycarbonate backbone, with the implication that incorporation of such units can improve craze strength and bulk toughness. Recently a successful synthetic route has been found to make these polymers, so that soon the predictions can be directly tested in the laboratory.
Monomer Geometries and Polymer Toughness Polymers exhibit two principal modes of mechanical failure, shear yielding and brittle fracture. A l l glassy thermoplastics are ductile in compression, when the hydrostatic component of the stress is negative. A l l glassy polymers fail by craze formation and subsequent brittle fracture if the cavitational component of the stress is positive and sufficiently large relative to the octahedral shear stress. Brittle failure is the less desirable mode since the energy absorbed is much smaller than that found for shear yielding. This difference in energy absorption is chiefly due to the relatively small fraction of the total polymer volume that participates in brittle (i.e., craze) failure compared with the large fraction of the polymer sample involved in shear yielding. Vincent was one of the first to characterize the ductile-brittle transition (in tension) for polymers in terms of the ratio of the tensile brittle strength to the tensile yield stress.(2,5) He noted that the shear yield mechanism in a polymer glass involves substantial long range reorganization and molecular motion of the polymer chains which causes yielding to be quite sensitive to temperature. Brittle fracture, on the other hand, is initiated locally (often by dirt or imperfections), and though brittle strength is
In Advances in Polycarbonates; Brunelle, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2005.
124 influenced directly by molecular weight and molecular orientation, it is relatively sensitive to temperature. Vincent defined the ductile-brittle transition, T B> as the temperature at which the yield stress becomes equal to the brittle strength.(ij Since it becomes increasingly difficult to rearrange the chains as thermal energy is reduced, the yield stress continues to rise with falling temperature, and so at temperatures below T the polymer fails in a brittle mode, since now the brittle strength has become smaller than the yield stress. Vincent noted that polymers with bulky side groups, such as polystyrene and polycyclohexyl methacrylate, generally have lower brittle strengths than chains without side groups, and he finally concluded that brittle strengths were correlated with the average molecular cross-sectional area (MCSA) of a polymer chain measured perpendicular to the chain ax\s.(2,3) He defined the average M C S A (per mole) of a chain as; D
Downloaded by STANFORD UNIV on February 18, 2015 | http://pubs.acs.org Publication Date: March 8, 2005 | doi: 10.1021/bk-2005-0898.ch010
D B
MCSA — Mass of the repeat unit densityxlengthof the repeat unit
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Vincent considered a number of polymers for which he had measured both yield stresses and brittle strengths, and found a convincing correlation between M C S A and brittle strength. He interpreted this result as meaning that the chain backbone acts as a reinforcement for the polymer. When tensile stress is applied to the solid polymer, those chain backbones crossing each unit area parallel to the stress (see Figure 1) help support the load and therefore increase the brittle strength. The smaller is the polymer's M C S A , the more chain backbones will cross each unit area, and the stronger will be the polymer:
Brittle strength number of bonds per unit area
