Universal, polymer melts

The Arrhenius equation holds for many solutions and for polymer melts well above their glass-transition temperatures. For polymers closer to their T and for concentrated polymer and oligomer solutions, the WiUiams-Landel-Ferry (WLF) equation (24) works better (25,26). With a proper choice of reference temperature T, the ratio of the viscosity to the viscosity at the reference temperature can be expressed as a single universal equation (eq. 8) ... 

D. Y. Yoon, M. Vacatello, G. D. Smith. Simulation studies of polymer melts at interfaces. In K. Binder, ed. Monte Carlo and Molecular Dynamics Simulations in Polymer Science. New York Oxford University Press, 1995, pp. 422-A15. 

Klein, 1., The Melting Factor in Extruder Performance, SPEL, 28, 47 (1972) Altinkaynak, A., Three-Dimensional Finite Element Simulation of Polymer Melting and Flow in a Single-Screw Extruder Optimization of Screw Channel Geometry, Ph. D. Thesis, Michigan Technological University, Houghton, MI (2010)... 

J. L. S. Wales, The Application of Flow Birefringence to Rheological Studies of Polymer Melts, Delft University Press, Rotterdam (1976). 

J. P. W. Baaijens, Evaluation of Constitutive Equations for Polymer Melts and Solutions in Complex Flows, Eindhoven University of Technology, Department of Mechanical Engineering, Eindhoven, The Netherlands (1994). 

H. Zamodits and J. R. A. Pearson, Flow of Polymer Melts in Extruders. Part I. The Effect of Transverse Flow and of Superposed Steady Temperature Profile, Trans. Soc. Rheol, 13, 357-385 (1969) see also B. Martin, J. R. A. Pearson, and B. Yates, On Screw Extrusion. Part I. Steady Flow Calculations, University of Cambridge, Department of Chemical Engineering, Polymer Processing Research Center, Report No. 5, 1969. 

Fig. 13.30 Four stages of coinjection molding, (a) Short shot of skin polymer melt (shown in dark shade) is injected into the mold, (b) Injection of core polymer melt until cavity is nearly filled, as shown in (c). (d) Skin polymer is injected again, to purge the core polymer away from the sprue. [Reprinted by permission from Design Center, School of Engineering, Santa Clara University, Santa Clara, CA.]...

This effect may be responsible for the popular belief that the extensional viscosity of polymer melts increases with increasing rate of deformation. Obviously, this statement is too simplistic, as one more parameter is needed to describe the relationship between extensional viscosity and rate of deformation. The situation is even more complicated. It is certain that the correlation of Fig. 15.22 has no universal validity, but depends on the nature of the polymer. Therefore, at this moment it is not possible to predict the extensional viscosity behaviour of an arbitrary polymer. 

Having considered some fundamental aspects of polymer structure, we now wish to consider some basic questions—what is the effect of chain defects (co-monomers, branches etc.), molecular weight, the presence of solvent An even more fundamental, question, and the one we will address first, is why do polymers have the melting points they have Is it a matter of divine imposition that the melting point of polyethylene is about 135°C while that of Kevlar is about 370°C (Figure 10-43). (Note we can only say things like about 135°Q, and use the symbol - to represent this, because, as we have seen, in practice polymers melt over a range of temperatures.) We re with Einstein on that one, who (in another context) said God does not play dice with the universe. . 

Miinstedt H (1979) New universal extensional rheometer for polymer melts. Measurements on a polystyrene sample. J Rheol 23 421-36. 

The enthalpy change for this polymerization is AWp = —6.5 Real mor. The polymerization reaction in this problem is finished at a fixed steam pressure (1 atm). The equilibrium concentration of H2O in the polymer melt varies with temperature and steam pressure in this case. Tlte enthalpy of vaporization of H2O is about 8 Real mol . Compare the limiting values of number average molecular weight of the polyamide produced at 280 and 250°C final polymerization temperatures. Hint Recall that the variation of an equilibrium constant K with temperature is given by r/(ln K)/d /T) = —AH/R, where AH is the enthalpy change of the particular process and R is the universal gas constant. Calculate Ki and the equilibrium concentration of H2O in the melt at 250°C and use Eq.(10-8).]... 

M.H.Wagner, J.Schaeffer, Rubbers and polymer melts Universal aspects of nonlinear stress-strain relations, J. Rheol. 31 (1993), 643-661. 

Studies of Polymer Melts", Delft University Press (1976)... 

Israelachvili JN(1992). Intermolecular and Surface Forces, 2nd ed, Academic Press, New York. Janeschitz-Krieg] H (1983). Polymer Melt Rheology and Flow Birefringence, Delft University Press. 

Stevenson, J. F. Elongational flow of polymer melts. Ph. D. Thesis, University of Wisconsin (1970). 

FIGURE 13.27 Frequency dependences of G (co) and G"(co) for a typical polymer melt. (From Graessley, W.W., Viscoelasticity and flow in polymer melts and concentrated solutions in Physical Properties of Polymers, 3rd ed., Cambridge University Press, 2004, Chap. 3. With permission.)... 

These values are considered as the universal WLF constants, giving the widest range of agreement over many prominent amorphous polymers. From these choices one calculates that the free-volume fraction /g at the glass-transition temperature is 0.025 and the dilatational thermal coefficient of expansion of a sub-cooled polymer melt at the glass-transition temperature is a = 2.8 x 10 ... 

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