Rheologica Acta

, Volume 27, Issue 2, pp 179–185 | Cite as

Composite viscoelasticity in glassy, transitional and molten states

I. Steady melt flow
  • Shu-de Rong
  • C. E. Chaffey
Original Contributions
Received:

Abstract

As part of a study of viscous and elastic behaviors, over a range of temperatures from below the glass transition up to the hot melt, we here report steady-shear viscosities at 0.007 to 13 s−1 and at 160 to 220 °C of polystyrene containing 0 to 60% by mass of 0.18-micron diameter titanium dioxide particles. The materials were shearthinning without a yield stress, with a constant activation energy at constant stress, but having a shear-dependent activation energy at constant shear rate — proportional to the volume fraction of the polymer matrix. Superposition of the flow curves at different temperatures for the unfilled and filled systems was possible. All the data were represented by one equation with four parameters: 1) a shear stress coefficient (units Pa · s2); 2) a characteristic stress level for non-Newtonian behavior, independent of temperature and composition; 3) an activation energy at constant stress; and 4) an Einstein coefficient (or intrinsic viscosity of the filler). Other equations also fitted the data, but the others diverged widely when extrapolated.

Key words

Activation energy composite materials filler volume fraction shearthinningviscosity polystyrenemelt 
a

shift factor for superposition

B

Einstein coefficient

c1,c2

parameters in WLF equation

E

activation energy

f

function ofλ\(\dot \gamma\), eqs. (2, 8–10)

g

function ofT, eqs. (3, 11, 12)

h

function of ø, eqs. (3, 13–15)

I

interaction coefficient, eq. (3)

m

fraction in eq. (10)

n, n′

slopes of logarithmic flow curves

p

close-packed volume fraction

R

gas constant = 8.314 J · K−1 · mol−1

s2

estimate of variance

T

absolute temperature

v

specific volume

α

volume expansion coefficient

\(\dot \gamma\)

shear rate

η

non-Newtonian viscosity

λ

characteristic time

µ

Newtonian viscosity

σ

shear stress

τ

characteristic stress

ø

volume fraction of filler

ψ

stress coefficient (unit: Pa · s2)

0

reference conditions (180°C,ø = 0)

f, m

\(E_{\dot \gamma }\) of filler, polymer matrix

i

i'th term in summation

\(\dot \gamma\),σ, ø

at constant\(\dot \gamma\),σ, ø

µ, λ, τ, ψ

identify coefficients in equations like eq. (3)

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References

  1. 1.
    Chaffey CE (1983) Ann Rev Mater Sci 13:43Google Scholar
  2. 2.
    Vinogradov GV, Malkin AY (1980) Rheology of polymers, Mir Publisher, MoscowGoogle Scholar
  3. 3.
    Han CD (1976) Rheology in polymer processing, Academic, New YorkGoogle Scholar
  4. 4.
    Porter RS, Johnson JF (1961) J Appl Phys 32:2326Google Scholar
  5. 5.
    Porter RS, Johnson JF (1966) J Polym Sci C 15:365Google Scholar
  6. 6.
    Dunlop A (1972) PhD Thesis Univ TorontoGoogle Scholar
  7. 7.
    Lakdawala K, Salovey R (1985) Polym Eng Sci 25:797Google Scholar
  8. 8.
    Tang HHY (1985) MASc Thesis, Univ TorontoGoogle Scholar
  9. 9.
    Vinogradov GV, Malkin AY, Plotnikova EP, Sabsai OY, Nikolayeva NE (1972) Inter J Polym Mater 2:1Google Scholar
  10. 10.
    Mendelson RA (1968) Polym Eng Sci 8:235Google Scholar
  11. 11.
    Mendleson RA (1976) Polym Eng Sci 16:690Google Scholar
  12. 12.
    Santamaria A, Guzman GM (1982) Polym Eng Sci 22:365Google Scholar
  13. 13.
    Teh JW, Rudin A, Schreiber HP (1984) Plast Rubber Proc Appl 4:149Google Scholar
  14. 14.
    Faitel'son LA, Yakobson EE (1977) Poly Mech (USSR) 13:898Google Scholar
  15. 15.
    Czarnecki L, White JL (1980) J Appl Polym Sci 25:1217Google Scholar
  16. 16.
    Kataoka T, Kitano T, Sasahara M, Nishijima K (1978) Rheol Acta 17:149Google Scholar
  17. 17.
    Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric fluids, Vol 1, 2nd ed, John Wiley, New YorkGoogle Scholar
  18. 18.
    Jeffrey DJ, Acrivos A (1976) AIChE J 22:417Google Scholar
  19. 19.
    Eu BC, Ohr YG (1984) J Chem Phys 81:2756Google Scholar
  20. 20.
    De Kee D, Turcotte G (1980) Chem Eng Commun 6:273Google Scholar
  21. 21.
    Ferry JD (1970) Viscoelastic properties of polymers, 2nd ed, John Wiley, New YorkGoogle Scholar
  22. 22.
    Quemada D (1977) Rheol Acta 16:82Google Scholar
  23. 23.
    Samsonov GV (1973) The Oxide Handbook, IFI/Plenum, New YorkGoogle Scholar
  24. 24.
    Watson RJ, Chaffey CE (1986) Polym Comp 7:442Google Scholar
  25. 25.
    Draper NR, Smith H Jr (1981) Applied Regression Analysis, 2nd ed, John Wiley, New YorkGoogle Scholar
  26. 26.
    Rong SD, Chaffey CE (1988) Rheol Acta 27:186Google Scholar

Copyright information

© Steinkopff 1988

Authors and Affiliations

  • Shu-de Rong
    • 1
  • C. E. Chaffey
    • 2
  1. 1.Génie chimiqueÉcole PolytechniqueMontréalCanada
  2. 2.Department of Chemical Engineering and Applied ChemistryUniversity of TorontoTorontoCanada

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