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              Polymers, Mechanical Behavior                                                               717

              shows the strain at break (ultimate property) as a func-  goal to discuss the morphological textures of semicrys-
              tion of molecular weight at a given temperature. There  talline polymers, but it is important to point out that by
              is a decrease in the strain at break for this polycarbon-  varying the methods of crystallization (quench rates, etc.)
              ate system as rate is increased in this range of  ˙ε as ex-  one  can  change  the  morphological  textures  in  a  given
              pected. A particularly important point is that, at a fixed  polymer, thereby affecting the mechanical behavior even
              ˙ ε, there is a major change in behavior above a critical  though the level of crystallinity may not greatly vary. It is
              molecular weight, which is of the order of 10,000 g/mol  therefore important to be aware of the crystallization pro-
              for this material. This critical molecular weight occurs  cedures in conjunction with the level of crystallinity if one
              where  the  length  of  these  macromolecules  is  sufficient  hopes to predict the mechanical behavior of a semicrys-
              to promote molecular entanglements, which in turn lead  talline system.
              to a pseudo network—a more useful material for struc-
              tural applications. This critical molecular weight varies
              for different macromolecular chain chemistry depending  VIII.  EFFECT OF COVALENT
              on the relative chain stiffness and the mass of the repeat  CROSS-LINKING
              unit.
                                                                Placing covalent cross-links into a system influences the
                                                                mechanical properties in a fairly predictable manner. Be-
              VII.  EFFECT OF CRYSTALLINITY                     low the glass transition temperature, cross-links increase
                  ON PROPERTIES                                 the modulus, but the effect is somewhat like that of crys-
                                                                tallinity in that the increase is not a large one. As the level
              Because many of today’s polymers are semicrystalline,  of cross-linking increases and places restrictions on the
              we shall discuss briefly how crystallinity influences me-  thermal Brownian motion of a chain segment, the glass
              chanical properties, as well as other important properties  transition temperature is generally shifted upward. Often
              such as optical transparency. Let us first consider the ef-  this transition is broadened and produces behavior simi-
              fect of crystallinity on stiffness or modulus behavior. If  lar to that of crystallinity (Fig. 24). It is clear, however,
              the system is unoriented (oriented systems will be dis-  that (as pointed out earlier) when sufficient cross-linking
              cussed in Section X) and if one is below the glass transi-  exists to promote an infinite network (i.e., the gel point
              tion temperature of the amorphous phase, increasing the  is reached), the viscous flow region is no longer avail-
              crystallinity  of  a  material  has  relatively  little  effect  on  able to the thermal mechanical spectrum. As expected,
                                                        9
              modulus; that is, modulus will be of the order of 10 to  the degree of cross-linking is directly correlated with the
              10 10   Pa, regardless of the level of crystallinity. On the  modulus behavior in the rubbery region. In fact, if the level
              other hand, if one is above the glass transition temper-  of cross-linking becomes considerable, rubbery behavior
                                                                                  6
                                                                            5
              ature of the remaining amorphous component, the pres-  (modulus of 10 to 10 Pa) is not likely to be found, but
              ence of crystallinity will strongly influence modulus and  rather the material will be stiffer and have the properties of
              cause it to increase accordingly, as long as one is below  a leather-like system. In fact, with excessive cross-linking,
              the melting point of the crystals. A general sketch of this  the glass transition temperature may never be observed
              behavior is illustrated in Fig. 24, where the general ther-  before thermal degradation! Of course, cross-linking can
              mal mechanical behavior is shown with respect to level of  be placed into polymeric materials by different means,
              crystallinity.                                    such as sulfur vulcanization, peroxide cross-linking, or
                If stress–strain measurements were being made above  radiation, but the details of these methods will not be
              the glass transition temperature of the amorphous phase,  discussed.
              the modulus would be enhanced in these measurements as
              well, but so would other properties such as strain to break
              and stress at break. In the presence of crystallinity, a dis-  IX. EFFECT OF FILLERS ON
              tinct yield point is often displayed (see Fig. 5). Generally,  MECHANICAL BEHAVIOR
              the presence of crystallinity may also strongly influence
              the nature of cold drawing or ductile flow, although the  Often polymers are modified by the placement of soft par-
              crystallinity does not have to exist for this phenomenon  ticulates within them (e.g., rubber particles within a hard
              to occur. It certainly must, however, if a yield or ductile  glassy matrix). The reverse approach is also undertaken.
              character is to be observed above the glass transition for a  An example of the latter is the placement of hard particles
              nonfilled homopolymeric material. Crystallites also serve  in a softer matrix such as calcium carbonate or glass parti-
              basically as “physical cross-links” and therefore strongly  clesplacedinarubberymatrix.Alsointhegrowingfieldof
              dominate the mechanical properties above T g . It is not our  composites, polymeric components serve typically as the
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