Modulus Semicrystalline polymer

Bigg, D.M. Smith, E.G. Epstein, M.M. Fiorentino, R.J. High modulus semicrystalline polymers by solid state rolling. Polym. Eng. Sci. 

These differences on the stress-strain behavior of P7MB and PDTMB show the marked influence of the mesomorphic state on the mechanical properties of a polymer. When increasing the drawing temperatures and simultaneously decreasing the strain rate, PDTMB exhibits a behavior nearly elastomeric with relatively low modulus and high draw ratios. On the contrary, P7MB displays the mechanical behavior typical of a semicrystalline polymer. 

Regiodefects are less readily incorporated into crystallites than defect-free chain sequences. In semicrystalline polymers, increasing levels of misinsertion result in reduced crystallinity. This can affect numerous physical properties, resulting in reduced modulus, lower heat distortion temperature, and decreased tensile strength. 

Fig. 3.14. The data is for a very broad range of times and temperatures. The superposition principle is based on the observation that time (rate of change of strain, or strain rate) is inversely proportional to the temperature effect in most polymers. That is, an equivalent viscoelastic response occurs at a high temperature and normal measurement times and at a lower temperature and longer times. The individual responses can be shifted using the WLF equation to produce a modulus-time master curve at a specified temperature, as shown in Fig. 3.15. The WLF equation is as shown by Eq. 3.31 for shifting the viscosity. The method works for semicrystalline polymers. It works for amorphous polymers at temperatures (T) greater than Tg + 100 °C. Shifting the stress relaxation modulus using the shift factor a, works in a similar manner.

Fig. 23.4 Typical transition behavior in mechanical storage modulus for a semicrystalline polymer. The subscripts a and c refer to the amorphous and crystalline phases, of the polymer, with aa as the main 7g process.

Higher values can be reached for semi-crystalline polymers below Tg the crystalline phase is stiffer than the glassy amorphous phase (e.g. PEEK, E 4 GPa). Semicrystalline polymers above Tg have, however, a much lower E-value, such as PE (0.15 to 1.4 GPa) and PP 1.3 GPa) E is, in these cases, strongly dependent on the degree of crystallinity and on the distance to Tg. Sometimes a low modulus is also found for semi-crystalline polymers below Tg, due to the effect of one or more secondary transitions a strong example is PTFE (E = 0.6 GPa ). 

Figure 7. Storage modulus vs. temperature curves for (A) linear amorphous polymer (B) crosslinked polymer (C) semicrystalline polymer (D) PTMA/MDI/BD-segmented copolymer (32% MDl by wt) (E) PTMA/MDI/BD-segmented copolymer...

A number of theories of the contribution of interdomain polymeric material to the stress-strain, modulus, and swelling behavior of block copolymers and semicrystalline polymers are examined. The conceptual foundation and the mathematical details of each theory are summarized. A critique is then made of each theory in terms of the validity of the theoretical model, the mathematical development of the theory, and the ability of the theory to explain experimental findings. 

Modulus. Jackson et al. (1) calculate the contribution of amorphous material to the shear modulus of a semicrystalline polymer by assuming that only tie chains (chains whose ends are attached to different crystallites) contribute to the modulus and that these chains follow Gaussian statistics. They assume that the chains deform affinely. The predicted modulus values are lower than the observed values. The... 

The viscoelastic properties of the crystalline zones are significantly different from those of the amorphous phase, and consequently semicrystalline polymers may be considered to be made up of two phases each with its own viscoelastic properties. The best known model to study the viscoelastic behavior of polymers was developed for copolymers as ABS (acrylonitrile-butadiene-styrene triblock copolymer). In this system, spheres of rubber are immersed in a glassy matrix. Two cases can be considered. If the stress is uniform in a polyphase, the contribution of the phases to the complex tensile compliance should be additive. However, if the strain is uniform, then the contribution of the polyphases to the complex modulus is additive. The... 

The interest in multicomponent materials, in the past, has led to many attempts to relate their mechanical behaviour to that of the constituent phases (Hull, 1981). Several theoretical developments have concentrated on the study of the elastic moduli of two-component systems (Arridge, 1975 Peterlin, 1973). Specifically, the application of composite theories to relationships between elastic modulus and microstructure applies for semicrystalline polymers exhibiting distinct crystalline and amorphous phases (Andrews, 1974). Furthermore, as discussed in Chapter 4, the elastic modulus has been shown to be correlated to microhardness for lamellar PE. In addition, H has been shown to be a property that describes a semicrystalline polymer as a composite material consisting of stiff (crystals) and soft, compliant elements. Application of this concept to lamellar PE involves, however, certain difficulties. This material has a microstructure that requires specific methods of analysis involving the calculation of the volume fraction of crystallized material, crystal shape and dimensions, etc. (Balta Calleja et al, 1981). 

The Chow equations [5] and the Halpin-Tsai equations [8,9] are also useful in modeling the effects of the crystalline fraction and of the lamellar shape (see Bicerano [23] for an example) on the moduli of semicrystalline polymers. Grubb [24] has provided a broad overview of the elastic properties of semicrystalline polymers, including both their experimental determination and their modeling. Janzen s work in modeling the Young s modulus [25-27] and yielding [27] of polyethylene is also quite instructive. 

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