The chemorheological models used for the description of thermoset polyurethanes are too often specific to a given formulation. This paper discusses the application of a more generic modeling approach which describes the evolutive rheological behavior of a polyurethane reactive mixture from a set of fitted monomer characteristic parameters and its calculated molecular weight distribution (MWD) at a given conversion level. The MWD is evaluated numerically from stochastic simulations. Once the adjusted parameters are obtained, the model becomes applicable at any starting formulation using a liquid prepolymer built from the same monomer. The linear viscoelastic properties were obtained from MWDs using the double reptation mixing rule. The mixing rule was adapted to include a contribution of Rouse’s relaxation times to account for short chains species, as those encountered in the beginning of the polymerization reaction. This procedure was successfully applied to two different difunctional thermoset polymeric systems that included either hydroxy-terminated polybutadiene or polypropylene glycol.
REFERENCES
1.
Baumgaertel
, M.
, A.
Schausberger
, and H. H.
Winter
, “The relaxation of polymers with linear flexible chains of uniform length
,” Rheol. Acta
29
, 400
–408
(1990
). 2.
Blake
, J. W.
, W. P. G.
Yang
, R. D.
Anderson
, and C. W.
Macosko
, “Adiabatic reactive viscometry for polyurethane reaction injection molding
,” Polym. Eng. Sci.
27
, 1236
–1242
(1987
). 3.
Colby
, R. H.
, L. J.
Fetters
, and W. W.
Graessley
, “Melt viscosity-molecular weight relationship for linear polymers
,” Macromolecules
20
, 2226
–2237
(1987
). 4.
Cox
, W. P.
and E. H.
Merz
, “Correlation of dynamic and steady flow viscosities
,” J. Polym. Sci.
28
, 619
–622
(1958
). 5.
de Gennes
, P. G.
, “Reptation of a polymer chain in the presence of fixed obstacles
,” J. Chem. Phys.
55
, 572
–579
(1971
). 6.
Des Cloizeaux
, J.
, “Double reptation vs simple reptation in polymer melts
,” Europhys. Lett.
5
, 437
–442
(1988
). 7.
Des Cloizeaux
, J.
, “Relaxation and viscosity anomaly of melts made of long entangled polymers. time-dependent reptation
,” Macromolecules
23
, 4678
–4687
(1990
). 8.
Des Cloizeaux
, J.
, “Relaxation of entangled and partially entangled polymers in melts: time-dependent reptation
,” Macromolecules
25
, 835
–841
(1992
). 9.
Doi
, M.
, “A basic principle in the viscoelasticity of polymeric liquids
,” J. Non-Newtonian Fluid Mech.
23
, 151
–162
(1987
). 10.
Doi, M. and S. F. Edwards, The theory of polymer dynamics (Oxford University Press, New York, 1986).
11.
Dombrow, A. B., Polyurethanes (Reinhold Publishing Corporation, New York, 1957).
12.
Dubois, C., “Use of Monte-Carlo Simulations in Polyurethane Polymerization Processes,” Canadian Dept. of National Defence report DREV-TM-9509 UNCLASSIFIED (1995a).
13.
Dubois
, C.
, S.
Désilets
, A.
Aı̈t-Kadi
, and P. A.
Tanguy
, “Bulk polymerisation of hydroxyl terminated polybutadiene (HTPB) with tolylene diisocyanate (TDI) : A kinetics study using NMR spectroscopy
,” J. Appl. Polym. Sci.
58
, 827
–834
(1995b
). 14.
Ferry, J. D., Viscoelastic properties of polymers, 3rd ed. (Wiley, New York, 1980).
15.
Gillespie
, D. T.
, “Exact stochastic simulation of coupled chemical reactions
,” J. Phys. C
81
, 2340
–2361
(1977
). 16.
Govindan
, G.
and S. K.
Athikan
, “Studies on curing of polyurethane propellant binder system
,” Propellants, Explosives, Pyrotechnics
19
, 240
-244
(1994
). 17.
Graessley
, W. W.
and M. J.
Stuglinski
, “Effects of polydispersity on the linear viscoelastic properties of entangled polymers. 2. comparison of viscosity and recoverable compliance with tube model predictions
,” Macromolecules
19
, 1754
–1776
(1986
). 18.
Lipshitz
, S. D.
and C. W.
Macosko
, “Rheological changes during a urethane network polymerization
,” Polym. Eng. Sci.
16
, 803
–810
(1976
). 19.
Lipshitz
, S. D.
, F. G.
Mussati
, and C. W.
Macosko
, “Kinetic and viscosity relations for urethane network polymerizations
,” Soc. Plastics Eng. Antec. Tech. Papers
21
, 239
-241
(1975
). 20.
Macosko
, C. W.
and D. R.
Miller
, “A New derivation of average molecular weights on nonlinear polymers
,” Macromolecules
9
, 199
–205
(1976
). 21.
Manjari
, R.
, V. C.
Joseph
, L. P.
Pandureng
, and T.
Sriram
, “Structure-property relationship of HTPB-based propellants I. Effect of hydroxyl value of HTPB resin
,” J. Appl. Polym. Sci.
48
, 271
–289
(1993
). 22.
Mead
, D. W.
, “Numerical interconversion of linear viscoelastic material functions
,” J. Rheol.
38
, 1769
–1795
(1994
a). 23.
Mead
, D. W.
, “Determinations of molecular weight distributions of linear flexible polymers from linear viscoelastic material functions
,” J. Rheol.
38
, 1796
–1827
(1994
b). 24.
Metzner
, A. B.
, “Rheology of suspensions in polymeric liquids
,” J. Rheol.
29
, 739
–775
(1985
). 25.
Milner
, S. T.
, “Relating the shear-thinning curve to the molecular weight distribution in linear polymer melts
,” J. Rheol.
40
, 303
–313
(1996
). 26.
Montfort
, J. P.
, G.
Marin
, J.
Armin
, and Ph.
Monge
, “Viscoelastic properties of molecular weight polymers in the molten state II. Influence of the molecular weight distribution on linear viscolesatic properties
,” Rheol. Acta
18
, 623
–628
(1979
). 27.
Pandit
, S. S.
, V. A.
Juvekar
, and M. K.
Trivedi
, “Stochastic simulation of polymer reactions
,” Chem. Eng. Sci.
7
, 1237
–1250
(1993
). 28.
Perry
, S. J.
, J. M.
Castro
, and C. W.
Macosko
, “A viscometer for fast polymerizing systems
,” J. Rheol.
29
, 19
–36
(1985
). 29.
Richter
, E. B.
and C. W.
Macosko
, 1978, “Kinetics of fast (RIM) urethane polymerization
,” Polym. Eng. Sci.
18
, 1012
–1018
(1978
). 30.
Stockmayer
, W. H.
, “Molecular distribution in condensation polymers
,” J. Polym. Sci.
9
, 69
–71
(1953
). 31.
Struglinski
, M. J.
and W. W.
Graessley
, “Effects of polydispersity on the linear viscoelastic properties of entangled polymers. 1. experimental observations for binary mixtures of linear polybutadiene
,” Macromolecules
18
, 2630
–2643
(1985
). 32.
Tsenoglou
, C.
, “Molecular weight polydispersity effects on the viscoelasticity of entangled linear polymers
,” Macromolecules
24
, 1762
–1767
(1991
). 33.
Tuminello
, W. H.
and N.
Cudre-Mauroux
, “Determining molecular weight distributions from viscosity versus shear rate flow curves
,” Polym. Eng. Sci.
31
, 1496
–1507
(1991
). 34.
Wasserman
, S. H.
, “Calculating the molecular weight distribution from linear viscoelastic response of polymer melts
,” J. Rheol.
39
, 601
–625
(1995
). 35.
Wissbrun
, K. F.
, “Numerical comparison of empirical rules for prediction of nonlinear rheology from linear viscoelasticity
,” J. Rheol.
30
, 1143
–1164
(1986
). 36.
Ziegel
, K. D.
, A. W.
Fogiel
, R.
Pariser
, “Prediction of molecular weights for condensation polymerization of polyfunctional monomers
,” Macromolecules
5
, 95
–99
(1972
).
This content is only available via PDF.
© 1998 Society of Rheology.
1998
Society of Rheology
You do not currently have access to this content.
