Elastomers and Rubber Elasticity - American Chemical Society


The University of Akron, Institute of Polymer Science, Akron, OH 44325. The tear .... calculated from the Mooney-Rivlin elasticity coefficient C, dete...
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Threshold Tear Strength of Some Molecular Networks A. N. GENT and R. H. TOBIAS The University of Akron, Institute of Polymer Science, Akron, OH 44325

The tear strength of polydimethylsiloxane (PDMS) networks was found to be only one-third as large as that of polybutadiene (PB) or polyisoprene (PI) net­ works of similar M when the tear strength was measured under threshold conditions, i.e., at high temperatures, low rates of tearing, and with swollen samples. This striking difference i n strength i s attributed to the smaller length and extensibility of PDMS molecules i n comparison with PB or PI mole­ cules of the same molecular weight. Networks formed by trifunctional or tetrafunctional endlinking reac­ tions with difunctional PDMS polymers were found to be only slightly stronger under threshold conditions, by up to 30 per cent, than PDMS networks formed by random crosslinking to the same M . Endlinked PB networks were found to have substantially the same threshold strength as randomly-linked PB networks of the same M . Thus, the threshold tear strength does not appear to depend strongly upon the uniformity of network strand lengths. c

c

c

When dissipative processes are minimized, the tear strength of elastomeric materials i s found to reach a lower l i m i t , termed here the threshold strength (1 2). Experimentally, the thres­ hold strength i s reached at high temperatures, at low rates of tearing and when the material i s highly swollen with a lowviscosity liquid. Its magnitude has been predicted theoretically from the length of the molecular strands comprising the network and the dissociation energy of the chemical bonds comprising the strand (3). Expressed as the energy T required to tear through a unit area of the material, the theoretical result takes the form 9

Q

T where M

c

0

= KM

% c

(1)

i s the mean molecular weight of the network strands and Κ 0097-6156/82/0193-0367$06.00/0 © 1982 American Chemical Society

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

368

ELASTOMERS

AND RUBBER

ELASTICITY

i s a constant involving the mass, length and effective f l e x i ­ b i l i t y of a monomeric unit, the density of the polymer and the dissociation energy of the relevant bonds. For C-C molecular strands Κ i s predicted to be about O.3 J/m /(molecular weight u n i t ) . Experimental values of T for randomly-crosslinked net­ works of polybutadiene were found to be consistent with equation 1, when Κ was given a somewhat higher value, about 1.0 J/m / (molecular weight u n i t ) . Thus, apart from t h i s numerical d i s ­ crepancy, the threshold strength of polybutadiene networks i s reasonably well accounted for. We now address two further aspects of threshold strength. Does the tear strength of other elasto­ mers, of different chemical type, conform to equation 1? And are randomly-crosslinked materials weaker than more regular networks, prepared, for example, by linking strands of uniform molecular weight into a network by endgroup coupling reactions? A higher tensile strength has been reported for endlinked networks of polyisoprene i n comparison with randomly-crosslinked networks of similar average strand length (4). However, those measurements were not made under threshold conditions and did not examine a wide range of strand lengths, so that direct comparison with molecular theory i s not possible. Measurements have now been carried out on endlinked and randomly-linked samples of polybutadiene, polydimethylsiloxane, and randomly-linked samples of cis-polyisoprene. The results are presented here. 2

Q

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2

Experimental Details Endlinked PDMS. Linear polydimethylsiloxanes with v i n y l endgroups were supplied by Dow Corning Corporation. Three d i f ­ ferent molecular weight ranges were employed. Membrane osmometry yielded values for \ of 16,000, 24,000, and 37,000 g/g-mole. Endgroup analysis using mercuric acetate (5) gave v i n y l contents of O.47 ±O.03,O.24± O.02, and O.15 ± O.02 per cent, corres­ ponding to values for M of 11,500, 22,500 and 36,000 g/g-mole. GPC data gave P / l ratios of approximately 2.0, as reported by Valles and Macosko (6, 7) for their similar polymers. Trifunctional and tetrafunctional silane l i n k i n g agents were supplied to us by Prof. Macosko. They consisted of trikis-dimethylsiloxyphenylsilane and tetrakis-dimethylsiloxysilane and are denoted here A3 and A4, respectively. Gas chromatography, carried out by Prof. Macosko, revealed that they were approximate­ ly 95 and 89 per cent pure. Si-Η group analysis (5) gave average f u n c t i o n a l i t i e s of 3.15 and 3.50, somewhat different from the ex­ pected values of 3 and 4, indicating that other constituents are present. The linking agent, A3 or A4, was mixed i n various concentra­ tions with the divinyl-PDMS, together with 5 ppm of a Pt catalyst (8). The mixture was then degassed and cast as a thin sheet on a Teflon surface. Complete reaction was found to occur on heating n

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

19.

GENT

A N D TOBIAS

369

Tear Strength of Molecular Networks

for about 3 days at 70°C, as judged by equilibrium swelling mea­ surements i n benzene; thereafter, a period of 4 days at 70°C was used to ensure complete reaction. As shown i n Figure 1, values of M calculated from e q u i l i ­ brium swelling ratios i n benzene (9), were found to depend strongly upon the concentration of endgroups i n the l i n k i n g agent r e l a t i v e to those i n the polymer. The highest effective degree of crosslinking, i . e . , the lowest degree of swelling and the low­ est value for M , was obtained at a characteristic endgroup r a t i o lying between about 1.1 and 1.6 instead of the expected r a t i o of 1.O. Thus, even when allowance i s made for the true functional­ i t y of the l i n k i n g agent, i t i s s t i l l necessary to employ a greater amount than expected to produce a minimum value for M . Presumably, a significant fraction of polymer endgroups do not become linked into the network u n t i l an excess of l i n k i n g agent i s present. This implies that the junction points are not ex­ clusively t r i f u n c t i o n a l or tetrafunctional i n nature. Networks were prepared i n a l l cases using the amount of endl i n k i n g agent necessary to give a minimum M . Values of M were calculated from the Mooney-Rivlin e l a s t i c i t y coefficient C , determined from tensile stress-strain measurements (10), c

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c

c

c

c

M = pRT/2C,

(2)

c

where ρ i s the density, O.97 g/ml, R i s the gas constant and Τ i s absolute temperature, for comparison with e a r l i e r work (2). Ex­ perimentally-determined values of the e l a s t i c coefficients C and Q»2 * values of M calculated from C- are given i n Table I. anc

c

Randomly - Crosslinked PDMS. The polydimethylsiloxane (PDMS) used to make random networks was obtained from General E l e c t r i c . Membrane osmometry showed M to be 430,000 g/g-mole. The polymer was mixed with various amounts of a free-radical crosslinking agent, dicumylperoxide (Di-Cup R, Hercules Chemical Co.). Samples were then pressed into sheets and crosslinking was effected by heating for 2 h at 150°C i n a heated press. M values were calculated using equation 2, and are included i n Table I. n

c

Endlinked PB. Endlinked polybutadiene samples were pro­ vided by Prof. F. N. Kelley and Mr. Long-Ji Su of these labora­ tories. They were made by reacting toluene -2,4- diisocyanate with the hydroxy endgroups of hydroxy- terminated polybutadiene (Arco R45-HT, M = 2,800 g/g-mole) and then employing trimethylolpropane as a t r i f u n c t i o n a l l i n k i n g agent. The prepolymer was also chain-extended with 1,4 - butanediol to give a higher M value on subsequent endlinking. M values, calculated by means of equation 2, were 3,100 g/g-mole for the sample made with the i n i t i a l polymer and 7,100 g/g-mole when the chain-extended material was used. n

c

c

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

ELASTOMERS

AND

RUBBER

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370

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

ELASTICITY

19.

GENT

371

Tear Strength of Molecular Networks

A N D TOBIAS

Table I. Threshold Tear Strength T of Randomly-linked and Endlinked Elastomers of Varying M Q

c

C (kPa)

q

MnXlO (g/g-mole)

±

C (kPa) 2

4

M xlO (g/g-mole)

T (J/m ) Q

2

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PDMS endlinked with A3 3.6 2.25 1.15

54 65 110

45 43 48

1.23 1.10 O.75

39 ± 2 33 ± 2 27 ± 2

1.32 1.11 O.84

48 ± 2 42 ± 2 35 ± 2

O.71 O.31

62 ± 4 47 ± 3

PDMS endlinked with A4 3.6 2.25 1.15

46 61 97

45 47 46 Endlinked PB

ca ça

O.84 O.28

Dicumyl peroxide (%)

168 389 Ci (kPa)

165 165 C (kPa) 2

4

M xl0(g/g-mole) c

T (J/m ) Q

2

PDMS randomly linked with dicumyl peroxide 1.0 1.2 1.5 1.75 2.0 2.5 2.75 3.0 4.0

9 14 19 21 26 31 32 36 45

20 23 29 30 31 31 35 33 25

13.6 9.0 6.3 5.9 4.6 3.9 3.7 3.4 2.6

78 ± 6 74 ± 3 62 ± 3 56 ± 3 48 ± 3 46 ± 2 44 ± 3 42 ± 3 39 ± 2

PI randomly linked with dicumyl peroxide 1.0 2.0 4.0

a

121 197 387

71 78 48

1.01 O.62 O.31

Molecular weight of polymer before endlinking. Calculated from C- by means of equation 2.

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

108 ± 9 63 ± 4 51 ± 5

372

ELASTOMERS

A N D RUBBER

ELASTICITY

Randomly - Crosslinked PB and PI. Polybutadiene (Diene 35 NFA, Firestone Tire and Rubber Co.) and cis-polyisoprene (Natsyn 2200, Goodyear Tire and Rubber Co.) were crosslinked with dicumylperoxide, as for PDMS. M values were also calculated by means of equation 2. They are given for PI i n Table I and are l i s t e d for PB i n reference 2.

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c

Measurements of Threshold Tear Strength. Rectangular s t r i p s , about 50 mm long, 10 mm wide and 1.4 mm thick were scored along a central l i n e to a depth of about O.7 mm, leaving about one-half of the o r i g i n a l thickness to be torn through. The tear energy Τ was calculated from the measured tear force F, Τ = 2 F/t,

(3)

where t i s the width of the tear path (Figure 2). Tearing was found to take place at an angle of approximately 45° to the sheet thickness (11). Measurements were carried out on both swollen and unswollen samples, using m-xylene or s i l i c o n e o i l as swelling liquids with PDMS networks and m-xylene or paraffin o i l with PB and PI net­ works. Samples were torn at temperatures between 70°C and 140°C. Values of the tear energy Τ for swollen samples were multiplied by λ , where X i s the linear swelling r a t i o , to take into account the reduced number of network strands crossing the tear path (1-3). Typical results for samples of endlinked PDMS, both unswollen and swollen with m-xylene, are given i n Table I I . Close agreement was obtained with the results obtained for unswollen samples at the high temperatures and low rates of tearing (about 4ym/s) used i n the present experiments, when the values for swollen samples were multiplied by X . The mean values have therefore been taken as measures of the threshold tear strength T i n a l l cases. They are given i n Table I. 2

3

s

2

s

Q

Experimental Results and Discussion Experimentally-determined values of T for PDMS networks are plotted i n Figure 3 against values of M calculated from the e l a s t i c coefficient C by means of equation 2. T was found to be accurately proportional to M , i n accordance with equation 1, with the coefficient of proportionally: y Κ being aboutO.30,O.25, and O.23 J/m /(molecular weight unit) for the A4, A3, and random­ ly-linked materials, respectively. These differences are small, barely s i g n i f i c a n t , but i n the expected direction. Values of T are also shown i n Figure 3 forjthe other materials examined. Again, a proportionality to M was found, i n accordance with theory. Moreover, the present values for endlinked PB and randomly-linked PI are i n good agreement with previously-reported data on randomly-linked PB, with Κ =O.85J/m . This i s much larger than for the PDMS materials, however. Thus, at the same Q

c

0

c

2

Q

c

2

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

GENT

A N D TOBIAS

Tear Strength of Molecular Networks

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19.

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

373

374

ELASTOMERS

AND

RUBBER

ELASTICITY

Table I I . Effect of Swelling with m-Xylene on the Threshold Tear Strength of PDMS 4

MnxlO" (g/g-mole)

T (Swollen) (J/m )

T (Unswollen) (J/m )

0

0

2

2

X

S

2 T

O

(Swollen)

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PDMS endlinked with A3 38 ± 3 32 ± 3 26 ± 3

3.6 2.25 1.15

15 ± 1.5 13 ± 2 13 ± 1.5

1.62 1.57 1.48

39 ± 3 33 ± 4 28 ± 3

PDMS endlinked with A4 3.6 2.25 1.15

17 ± 1.5 18.5± 1.5 15 ± 1

1.65 1.57 1.52

49 ± 1 41 ± 5 35 ± 2

47 ± 4 46 ± 4 35 ± 2

T

L o g !0 o 2

(J/m )

Log

l o

M

c

(g/g-mole)

Figure 3. Threshold tear energy T . Key: Ο, Δ , •> PDMS networks; . , A , PB networks; Θ, PI networks; versus molecular weight M between cross-links calcu­ lated from C i . Ο, Θ, . , random cross-linking; Δ , L, trifunctional end-linking; • , tetrafunctional end-linking. 0

c

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

19.

G E N T AND

TOBIAS

Tear Strength of Molecular Networks

375

value of M , elastomeric networks based on C-C molecular chains have a threshold strength about three times that of Si-0 networks. Values of M calculated from the small-strain tensile modulus, i . e . , using C- + C i n equation 2 i n place of C , were, of course, smaller than those obtained from C\ values. However, the general form of the dependence of threshold tear strength upon M and the r e l a t i v e values obtained for different polymers at the same M were not s i g n i f i c a n t l y affected by this alternate procedure for calculating the mean molecular weight of network strands. Although the bond dissociation energies for C-C and Si-0 bonds are quite similar, 89 and 80 kcal/g-mole respectively, the molecular weight per main-chain atom i s considerably higher for PDMS (37 molecular weight units) than for PI (17) and PB (13.5). The extended length of a network strand i s therefore much smaller for PDMS at the same value of M . There are also s t e r i c r e s t r i c tions on straightening the Si-0 chain due to unequal main-chain bond angles. Thus, the threshold strength of PDMS networks would be expected to be less than one-half as large as for C-C networks, in accordance with observation. c

c

2

c

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c

Q

Conclusions The threshold tear strength of elastomeric molecular networks does not appear to depend strongly, if at a l l , upon the uniformity of network strand lengths. It i s found to be proportional to M where M i s the mean molecular weight of the strands, i n accordance with the theory of Lake and Thomas Ç3). However, i t i s considerably smaller for Si-0 networks than for C-C networks at equal M values. This i s attributed to differences i n strand length and e x t e n s i b i l i t y . c

c

c

Acknowledgements This work was supported by research grants from the Office of Naval Research (Contract ONR N00014-76-C-0408) and Lord Kinematics Division of Lord Corporation. Professor F. N. Kelley and Mr. L.-J. Su of these laboratories supplied the samples of endlinked polybutadiene. The authors are also indebted to Professor C. W. Macosko of the University of Minnesota for supplying the endlinking reagents, A3 and A4, and helpful advice on their use, and to Dow Corning Corp. for samples of polydimethylsiloxane poly­ mers having reactive endgroups. Literature Cited 1. 2. 3.

Mueller, H. K.; Knauss, W. G. Trans. Soc. Rheol. 1971, 15, 217. Ahagon, Α.; Gent, A. N. J. Polym. Sci: Polym. Phys. Ed. 1975, 13, 1903. Lake, G. J.; Thomas, A. G. Proc. Royal Soc. (London) 1967, A300, 108.

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

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4. Morton, M.; Rubio, D. C. Plastics and Rubber: Mat. Appl. 1978, 3, 139. 5. Smith, R. C.; Angelotti, N. C.; Hanson, C. L. "Analysis of Silicones", Smith, A. L. ed., John Wiley & Sons, New York, 1974, p. 150. 6. Valles, Ε. M.; Macosko, C. W. Rubber Chem. Technol. 1976, 49, 1232. 7. Valles, Ε. M.; Macosko, C. W. Macromolecules 1979, 13, 521. 8. Kauffman, C. B.; Cowan, D. O. "Inorganic Synthesis", Vol. 6, Rochow, E. G., ed., McGraw-Hill, New York, 1969, p. 214. 9. Shih, H.; Flory, P. J . Macromolecules 1972, 5, 759. 10. Treloar, L. R. G. "Physics of Rubber E l a s t i c i t y " , 2nd Ed., Clarendon Press, Oxford, 1958. 11. Ahagon, Α.; Gent, A. N.; Kim, H. J.; Kumagai, Y. Rubber Chem. Technol. 1975, 48, 896. RECEIVED December 4,

1981.

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