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              Polymer Processing                                                                          621

              temperature,  T g . At T g  there  is  an  increase  in  the  free  associated with the change from the crystalline phase to
              volume allowing molecules more freedom of movement.  the completely amorphous state is obtained by integrating
              Above T g , the polymer chains become more mobile and  the area under the curve of C p  versus temperature. The
              more easily deformed. It is observed that above T g  there is  energy associated with this phase transition is called the
              very little change in the thermal properties. For example,  heat of fusion,  H f . Note also that the melting point is not
              C p  changes from 0.46 kcal/g K at 435 K to 0.5 kcal/g K  really distinct, but covers a broad temperature range. The
              at 480 K (K is degrees Kelvin). The thermal conductivity  cooling of a semicrystalline polymer from a temperature
              changes even less. The density changes less than 5% over  above T m  to some lower temperature leads to crystalliza-
              the whole temperature range shown. On the other hand,  tion. The energy associated with crystallization, called the
              the  changes  in  thermal  properties  for  a  semicrystalline  heat of crystallization ( H c ), is affected by the tempera-
              polymer are more distinct as shown in Fig. 15. Here it is  ture at which crystallization takes place and depends on
              observed that C p  increases rapidly with temperature pass-  M w . Furthermore, the values of  H c  are somewhat lower
              ing through a maximum and then decreasing with temper-  than those of  H f .
              ature. The temperature at the peak value is taken as the  The ratio, k /ρC p , is called the thermal diffusivity, α, and
                                                                           2
              melting point, T m . The area under the curve is associated  has units of m /sec. It represents the rate at which heat can
              with the melting of the crystalline phase and is referred to  penetrate a polymeric material and change its temperature.
              as the heat of fusion,  H f . Above T m  the thermal proper-  For most polymers in the melt state, α is about the same
                                                                                           2
              ties are observed not to change significantly with temper-  with a value of about 1.0 × 10 −7  m /sec. The low value is
              ature. The density changes markedly for polypropylene  primarily due to the low value of k, as most polymers are
                                                        3
                                     3
              varying from about 0.5 g/cm at 300 C to 0.9 g/cm at  insulators. In other words, it takes a long time to raise and
                                            ◦
              50 C. This large change in density leads to large changes  lower the temperature of a polymer, which represents the
                ◦
              in  the  dimensions  of  parts  on  cooling  down  from  the  limiting step in their processing.
              melt and can lead to warpage of large injection molded
              panels.
                For semicrystalline polymers it is observed that melt-
                                                                IV.  EXTRUDERS
              ing occurs leading to the absorption of energy. The energy
                                                                A.  Single-Screw Extruders
                                                                The most frequently used extruder is a plasticating ex-
                                                                truder,  which  is  shown  in  Fig.  16.  Polymer  pellets  are
                                                                fed to the extruder by means of a hopper (sometimes the
                                                                pellets are metered in). The gravitational flow of solids in
                                                                the hopper is rather complex and will not be covered here.
                                                                The pellets are compressed in the channel of the screw
                                                                and then dragged forward by friction between the pellets
                                                                and the barrel. Heat generated by sliding friction at the bar-
                                                                rel surface and transferred from the heated barrel causes
                                                                the pellets to melt. The melt film is scraped away and col-
                                                                lects at one end of the channel. The solid-bed width de-
                                                                creases as the solid plug advances along the screw channel
                                                                until the solid is completely melted. The melt is pressur-
                                                                ized by means of a drag flow mechanism. The pressure
                                                                generated in the extruder and the performance of the ex-
                                                                truder are significantly affected by the resistance at the end
                                                                of the extruder due to filter packs and shaping channels
                                                                called dies.
                                                                  The single-screw extruder consists of a metallic barrel
                                                                and a rotating screw as shown in Fig. 16. The screw is
                                                                a metallic shaft in which a helical channel has been ma-
                                                                chined. Sometimes parallel channels are machined in the
              FIGURE  15  Thermal  physical  properties  of  a  semicrystalline
              polymer,  polypropylene.  [From  Baird,  D.  G.,  and  Collias,  D.  I.  shaft at the same time leading to what are called mul-
              (1998). “Polymer Processing: Principles and Design,” Wiley, New  tiflighted screws. Typical barrel diameters used in the
              York.]                                            United States are 0.75, 1.0, 1.5, 2.0, 2.5, 3.5, 4.5, 6.0,
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