Elastic Modulus, Network Structure, and Ultimate Tensile Properties of

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22 Elastic Modulus, Network Structure, and Ultimate Tensile Properties of Single-Phase Polyurethane Elastomers THOR L . SMITH IBM Research Laboratory, San Jose, California 95193

The equilibrium shear modulus of two similar polyurethane elastomers is shown to depend on both the concentration of elastically active chains, v , and topological interactions between such chains (trapped entanglements). The elastomers were carefully prepared in different ways from the same amounts of toluene-2,4-diisocyanate, a poly(propylene oxide) (PPO) triol, a dihydroxy-terminated PPO, and a monohydroxy PPO in small amount. Provided the network junctions do not fluctuate significantly, the modulus of both elastomers can be expressed as v (1 + v /v )RT, the average value of v /v being 0 . 6 1 . The quantity v equals T G /RT, where TG is the contribution of the topological interactions to the modulus. Both v and T were calculated from the sol fraction and the initial formulation. Discussed briefly is the dependence of the ultimate tensile properties on extension rate. c

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Studies have been made of the elastic (time-independent) properties of single-phase polyurethane elastomers, including those prepared from a diisocyanate, a triol, and a diol, such as dihydroxy-terminated poly(propylene oxide) 0,2), and also from dihydroxy-terminated polymers and a triisocyanate (3,4,5). In this paper, equilibrium stress-strain data for three polyurethane elastomers, carefully prepared and studied some years ago (6), are presented along with their shear moduli. For two of these elastomers, primarily, consideration is given to the contributions to the modulus of elastically active chains and topological interactions between such chains. Toward this end, the concentration of active chains, v , is calculated from the sol fraction and the initial formulation which consisted of a diisocyanate, a triol, a dihydroxy-terminated polyether, and a small amount of monohydroxy polyether. As all active junctions are afunctional, their concentration always c

0097-6156/82/0193-0419$06.00/0 © 1982 American Chemical Society

Mark and Lal; Elastomers and Rubber Elasticity ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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equals (2/3)v and depends on the extend of the curing reaction and on the amount of the monohydroxy polyether. Data are also presented that show the dependence of the tensile strength and ultimate elongation on extension rate and temperature. In the discussion, emphasis is placed on the behavior when the stress is sensibly in equilibrium with the strain prior to fracture.


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Materials and Experimental Methods Hydroxy-Terminated Poly(propylene oxide) (PPO). This material was nonacidified PPG-2025 (ONE grade) supplied by Union Carbide Chemicals Company, hereafter designated PPG. Although this material is largely dihydroxy-terminated PPO, it does contain some carbon-carbon double bonds. (The concentration of such bonds increases rapidly with the molecular weight of the PPG (7,8).) The double bonds are terminal groups, both allyl ether and cis-propenyl (9), and hence those molecules containing such groups are monohydroxy, or monofunctional when reacted with a diisocyanate. After prolonged degassing of a large batch of PPG, analyses showed that its hydroxyl, unsaturation, and water contents were O.97 meq/g, O.033 meq/g, and O.0035%, respectively. The hydroxyl content was determined by an acetylation method, carried out with acetic anhydride (10). The amounts of unsaturation and water were determined by the mecuric acetate and Karl Fischer methods (10), respectively. The obtained analytical results indicate that the number-average molecular weight of the dihydroxy material is 2062, provided its molecular weight is arbitrarily assumed to be twice that of the monohydroxy material, and that the mole fraction of the monohydroxy poly(propylene oxide) is O.066. This value corresponds to a number-average functionality of 1.93 for the PPG. Triols. One triol used was the propylene oxide adduct of 1,2,6-hexanetriol, designated LHT-240 and supplied by Union Carbide Chemicals Company. After degassing, its hydroxyl, unsaturation, and water contents were 4.31 meq/g, RT and G ™ for the LHT-240 elastomer become O.13 MPa and O.48 MPa, respectively. Such results because, to obtain the observed sol fraction (O.041), the extent of reaction must be O.9728 instead of O.9859 (Table III). Similarly, if the true values of the sol fraction are somewhat larger than those found, calculations then show that ? RT is less and Gj? is larger than those reported in Table ΙΠ. c

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Single-Phase Polyurethane Elastomers 4

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The finding that v is O.814 χ 10" mole/cm for the LHT-240 elastomer indicates that M / p = 1.23 χ 10 where M is here the molecular weight of the linear portion of the active chains and p is the concentration (g/cm ) of such chains. The concentration of the linear portion of the active chains is clearly less than the density of the elastomer because both sol and inactive chains are present. The obtained values of ? RT differ from 2C by only 10% or less, whereas other investigators (]3,lj8,34) have found that topological interactions contribute significantly to 2Cj. To account for this different finding, additional data on polyurethane elastomers would be required. Data are presented which illustrate that the tensile strength and elongation-at-break depend significantly on the extension rate even when the stress remains in equilibrium with the strain prior to fracture. A crude estimate was made of the threshold (lowest possible) values of the true stress-at-break and the elongation-at-break for the TIPA elastomer. The estimated quantities are about 26% less than those found at an extension rate of about O.01 m i n at 30°C. c

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Acknowledgements The experimental work was carried out at Stanford Research Institute in 1966-67 under USAF Contract No. AF33(615)-3248. The author acknowledges the contributions of R. A. Dickie, F. J. Martinelli, and R. L . Moore. Appendix Miller and Macosko (24) have derived equations that enable ρ and in eq 4 to be calculated from the sol fraction. In the derivation, they assumed that all functional groups of a given type are equally reactive, that the groups react independent of one another, and that no small loops form. Although certain systems having groups of unequal reactivities have been considered (35), the effect of unequal reactivities gradually disappears as the reaction approaches completion, as shown by the treatment. Thus, unequal reactivities need not be considered here, even though the meta and para isocyanate groups in TDI have substantially different reactivities and some primary hydroxyl groups exist in LHT-240 and PPG, though the hydroxyls are largely secondary. In the terminology of Miller and Macosko (24), the present formulations can be denoted by A + A + A j + B where the A's are the tri-, di-, and monohydroxy materials and B is TDI. The following equations are applicable only when the concentration of hydroxyl and isocyanate groups are equal, which is assumed to be true, as discussed in the text. 3

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2

[(2a + a ) p - l ] / a p


3

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where aj = fjAj/SfjAj in which Aj is the initial moles of component A | (i = 1,2,3) whose functionality is f| and ρ is the extent of reaction for the cured elastomer. The probability that a randomly selected chain is elastically active can be equated, in the Miller-Macosko terminology, to either [1 - P ( F f ) ] [ l - P ( F | ) ] or [1 - P ( F ) ] [ l - P ( F ) ] . By use of eq A l and their eqs 17, 18, and 20, both of these expressions can be shown to equal ( P / p ) . Thus, the probability, T , that two interacting chains are active is (P j/p)The sol fraction is given by ut

u t

2

e

4

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where Q = (1 - P ) and the Wj's are the weight fractions of the A s in the entire formulation, and similarly w is the weight fraction of TDI. The above expression is eq 39 in ref. 24 except that the factor (1 — Ρχΐ/ρ) is there denoted by P(Fg ). These quantities can be shown to be equivalent. xi

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11. 12. 13. 14. 15.

Smith, T. L.; Magnusson, A. B. J. Polym. Sci. 1960, 42, 391. Allen, G.; Egerton, P. L.; Walsh, D. L . Polymer 1976, 17, 65. Morton, M.; Rubio, D. C. Plastics and Rubber: Mat. Appl. 1978, 3, 139. Sung, P.-H.; Mark, J. E . J. Polym. Sci., Polym. Phys. Ed. 1981, 19, 507. Nelb, G. W.; Pedersen, S.; Taylor, C. R.; Ferry, J. D. J. Polym. Sci., Polym. Phys. Ed. 1980, 18, 645. Dickie, R. Α.; Smith, T. L . Technical Report AFML-TR-68-112, May 1968, prepared for the Air Force Materials Laboratory. Simons, D. M.; Verbanc, J. J. J. Polym. Sci. 1960, 44, 303. Havlik, A. J.; Moacanin, J.; Otterness, I. J. Polym. Sci. Part A, 1963, 1, 2213. Dege, G. J.; Harris, R. L.; MacKenzie, J. S. J. Am. Chem. Soc. 1959, 81, 3374. David, D. J.; Staley, Η. B. "Analytical Chemistry of the Polyurethanes" (High Polymers, Vol. 16, Pt. III); Wiley-Interscience: New York, 1969; Chapt. V. Smith, T. L . J. Appl. Phys. 1964, 35, 27. Smith, T. L . J. Polym. Sci. Part C, 1967, 16, 841. Pearson, D. S.; Graessley, W. W. Macromolecules 1980, 13, 1001. Langley, N. R.; Polmanteer, N. R. J. Polymer Sci.; Polym. Phys. Ed. 1974, 12, 1023. Erman, B.; Flory, P. J. J. Polym. Sci., Polym. Phys. Ed. 1978, 16, 1115.


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16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.

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Flory, P. J. Proc. Roy. Soc. (London) Ser. A 1976, 351, 351. Flory, P. J. J. Chem. Phys. 1977, 66, 5720. Dossin, L. M.; Graessley, W. W. Macromolecules 1979, 12, 123. Gottlieb, M.; Macosko, C. W.; Benjamin, G. S.; Meyers, K. O.; Merrill, E . W. Macromolecules 1981, 14, 1039. Llorente, Μ. Α.; Mark, J. E. Macromolecules 1980, 13, 681. Erman, B.; Wagner, W.; Flory, P. J. Macromolecules 1980, 13, 1554. Mark, J. E. Rubber Chem. Technol. 1981, 54, 809. Smith, T. L.; Magnusson, A. B., J. Appl. Polym. Sci. 1961, 5, 218. Miller, D. R.; Macosko, C. W. Macromolecules 1976, 9, 206. Havlik, A. J.; Moacanin, J. Research Summary No. 36-10, Vol. 1, p. 92, Jet Propulsion Laboratory, Pasadena, CA. Fox, T. G.; Allen, V. R. J. Chem. Phys. 1964, 41, 344. Dusek, K.;Ilavsky,M . Polym. Preprints 1981, 22(2), 167. Smith, T. L . Polym. Eng. Sci. 1977, 17, 129. Smith, T. L . in "Rheology", Eirich, F. R., Ed., Academic Press, 1969; Vol. 5, Chapter 4. Gent, A. N. in "Science and Technol. of Rubber", Eirich, F. R., Ed., Academic Press, 1978; Chapter 10. Ahagon, Α.; Gent, A. N. J. Polym. Sci., Polym. Phys. Ed. 1975, 13, 1903. Gent, A. N.; Tobias, R. H . Polym. Preprints 1981, 22(2), 163. Lake, G. J.; Lindley, P. B. J. Appl. Polym. Sci. 1964, 8, 707. Meyers, K. O.; Bye, M. L.; Merrill, E . W. Macromolecules 1980, 13, 1045. Miller, D. R.; Macosko, C. W. Macromolecules 1978, 11, 656.

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Elastic Modulus, Network Structure, and Ultimate Tensile Properties of

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