Elastomers and Rubber Elasticity - American Chemical Society

17 Equilibrium Tensile Behavior of Model Silicone Networks of High Junction Functionality KEVIN O. MEYERS

Downloaded by TUFTS UNIV on June 12, 2018 | https://pubs.acs.org Publication Date: July 19, 1982 | doi: 10.1021/bk-1982-0193.ch017

ARCO Oil and Gas Company, Recovery Processes Research, Dallas, TX 75221 EDWARD W. MERRILL Massachusetts Institute of Technology, Department of Chemical Engineering, Cambridge, MA 02139 Elastomeric networks with junction functionalities ranging from 4 to 70 were prepared by endlinking α,ω-divinyl poly(dimethylsiloxane) chains having number average molecular weights ranging from 8,800 to 55,300 with polyfunctional junctions provided by linear and branched poly(methylhydrogensiloxanes). The equilibrium stress-strain isotherms i n elonga tion, and the swelling ratios in benzene, were mea sured at 25°C for these networks. Network chain densities calculated from these measurements ex ceeded the values predicted from stoichiometry. These excesses diminished for those networks with diluent present during network formation or with low extents of the network formation reaction. Molecular theories presuming a contribution from trapped entanglements in small strain gave good agreement with the data and offered reasonable ex planation of the trends observed. The phenomena of rubber e l a s t i c i t y have been under investi gation for over a century. Yet there s t i l l remains much contro versy as to the correct molecular theory to explain elastomeric behavior. These theories relate an elastomer's network structure to i t s equilibrium mechanical properties. Verification of such relationships requires knowledge of the network structure ac quired independently of the theory under review. Therefore, there has been much interest in the synthesis and investigation of "model" elastomeric networks, i.e. networks whose structure is known from and may be controlled through the network synthesis reaction. Such model networks may be prepared by the endlinking reaction of difunctional polymer chains with plurifunctional crosslinking reagents. This endlinking permits control of M (the average molecular weight between chemical crosslinks) and i t s dispersity via the number average molecular weight, M , and c

n

0097-6156/82/0193-0329$06.00/0 © 1982 American Chemical Society

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

330

ELASTOMERS

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ELASTICITY

dispersity of the telechelic polymer. The functionality of the crosslinker, φ , dictates the f i n a l network functionality. U n t i l recently (1.-5) investigations u t i l i z i n g model net works had been limited to f u n c t i o n a l i t i e s of four or less. Net works with higher functionality are predicted by the various theories of rubber e l a s t i c i t y to display unique equilibrium ten s i l e behavior. As such, these multifunctional networks provide insight into the controversy surrounding these theories. The present study addresses the synthesis and equilibrium tensile behavior of endlinked model multifunctional poly(dimethylsiloxane) (PDMS) networks. 0


Theory The results of uniaxial stress-strain experiments are often analyzed i n terms of the reduced stress defined by 2

[f] = f/[A(a - a" )]

(1)

where f i s the e l a s t i c force, A i s the undeformed crosssectional area, and α i s the relative elongation. For moderate values of α the empirical Mooney-Rivlin (6) r e l a t i o n : [f ] = 2C

1

l

+ 2C2CT

(2)

i s found to hold quite s a t i s f a c t o r i l y . 2Cj and 2C£ are con stants independent of strain. Classical molecular theories of rubber e l a s t i c i t y (7»8) lead to an e l a s t i c equation of state which predicts the reduced stress to be constant over the entire range of uniaxial deforma tion. To explain this deviation between the c l a s s i c a l theories and r e a l i t y . Flory (9) and Ronca and Allegra (10) have sepa rately proposed a new model based on the hypothesis that i n a real network, the fluctuations of a junction about i t s mean position may may be s i g n i f i c a n t l y impeded by interactions with chains emanating from s p a t i a l l y , but not topologically, neigh boring junctions. Thus, the junctions i n a real network are more constrained than those i n a phantom network. The e l a s t i c force i s taken to be the sum of two contributions (9):

f - fph + f

O)

c

f i s the additional force a r i s i n g from the aforementioned constraints on junction fluctuations and fp^ i s the force predicted by the phantom network theory (9): c

[ f ] = vkT(V/V ) p H

Q

2/3

(1-2/φ)/ν

(4)

where Τ i s the absolute temperature, k i s the Boltzmann con stant, V i s the volume i n the undeformed state such that the mean-squared end-to-end length < r2> of a chain assumes the 0


17.

MEYERS

A N D MERRILL

Behavior of Model Silicone Networks

331

value for unperturbed, free chains, ν i s the number of chains, V i s the volume of the network, and φ i s the network functionality. The theory (9) predicts that i n simple elongation, the ratio fc/fph decreases with increasing s t r a i n and eventually goes to zero (phantom network). Furthermore, at α =1, the theory holds that f /f c

P h

< 2/(φ-2)

(5)

Therefore, Flory's theory concludes that as the function a l i t y of a network increases, the constraint contribution, f , should decrease and eventually vanish. Furthermore, i n the ex treme l i m i t i n which junction fluctuations are t o t a l l y sup pressed, the Flory theory reduces to the affine network model:


c

2/3

[f] = vkT(V/V ) /V

(6)

Q

The Flory theory considers topological interactions among junctions and chains only i n that they r e s t r i c t junction f l u c tuations, Ferry (11), Langley (12) and Dossin and Graessley (13) have argued that i n the l i m i t of small strain these interactions are also present along the chain contour and contribute d i r e c t l y to the modulus. Their conclusions are based on the rubbery pla teau modulus, G °, which i s observed for high molecular weight linear polymers i n dynamic mechanical testing. This plateau modulus i s believed to be a measure of topological interactions or entanglements between chains. During network formation, a portion of these entanglements are permanently trapped, result ing i n a small-strain modulus greater than that due to chemical crosslinking alone. N

Dossin and Graessley (13) suggest that G = vkT(l - 2hAf>)(V/V ) /V + T G 2/3

0

e

m a x

(7)

e

where G i s the small-strain modulus (a+1), T i s the fraction of the maximum concentration of topological interactions, G , which are permanently trapped by the network, and h i s an em p i r i c a l constant between one and zero, depending on the extent to which the junction fluctuations are impeded i n the network (h « 0 for affine behavior, h = 1 for phantom behavior). Thus equation (7) predicts a small-strain modulus greater than that predicted by the Flory theory due to the T G term. e

m a x

e

m a x

e

e

Experimental Multifunctional poly(dimethylsiloxane) (PDMS) networks were prepared v i a the addition of a silane hydrogen on poly(methylhydrogensiloxanes) (PMHS) to v i n y l terminated linear PDMS


332

ELASTOMERS AND RUBBER ELASTICITY

polymers i n the presence of cis-dichlorobis(diethyl sulfide) platinum ( I I ) catalyst: CH

CH

3

H

3

I

i l φ /2 CH =CH-Si[0-Si]CH=CH 9

I CH

I CH

3

9

+ (CHo)oSi[OSi]OSi(CHo)o

n

>

Iφ CH

3

3


Network Functionality φ

0

Six linear and three branched PMHS ranging i n φ from 6 to 84 were used as junction s i t e s . For tetrafunctional networks, [HSi(CH )20]4Si was the crosslinking agent. Two sets of α,ω-divinyl PDMS were used i n this study. The f i r s t set consisted of commercially available polymers which were supplied by the General E l e c t r i c Corporation and the Dow Corning Corporation. Six different number average molecular weight α,ω-divinyl ΡEMS were provided, with M ranging from 8,800 to 28,600 g-mol" . The second set of α,ω-divinyl PEMS was synthesized by the anionic ring opening polymerization of hexamethylcyclotrisiloxane by the difunctional i n i t i a t o r , d i l i t h i u m stilbene. This l i v i n g polymer was capped with vinyldimethylchlorosilane [CH =CHSi(CH )2Cl] to give the desired product. α,ω-divinyl PDMS with 14 different values of M ranging from 12,200 to 52,800 were synthesized. The anionic polymerization resulted i n α,ω-divinyl PEMS with r e l a t i v e l y narrow molecular weight distributions (M^/Mn • 1.08 - 1.30). The procedures u t i l i z e d i n the synthesis and characterization of the network precursors are given i n greater d e t a i l elsewhere (1>4.)· Networks were prepared both i n bulk and i n an oligomeric PDMS (no v i n y l groups; M = 1170) which served as a "solvent". The two network precursors and solvent ( i f present) were com bined with 20 ppm catalyst and reacted under argon at 75°C to produce the desired networks. The s o l fractions, w , and equi librium swelling r a t i o i n benzene, V 2 , of these networks were determined according to established procedures (J[,4^). E q u i l i b r i um tensile stress-strain isotherms were obtained at 25°C on dumbbell shaped specimens according to procedures described elsewhere 0,£). The data were well correlated by linear regres sion to the empirical Mooney-Rivlin (J3) relationship. The ten s i l e behavior of the networks formed i n solution was measured both on networks with the solvent present and on networks from which the oligomeric PDMS had been extracted. The interested reader w i l l find detailed tabulations of the experimental data (2Cj,2C2,w ,V2 ) and calculations (e,T ,v /V) for the networks examined i n this study given i n references U ) through (4). 0

3

n

1

2

3

n

n

s

m

s

m

e


s

17.

MEYERS

A N D MERRILL

333

Behavior of Model Silicone Networks

Results and Discussion


To compare the predictions of the various molecular theories of rubber e l a s t i c i t y , three sets of high functionality networks were prepared and tested i n this investigation. The f i r s t set of networks tested were formed i n bulk and attained a high extent of the endlinking reaction, i . e . , εΧ)·9 where ε i s the extent of reaction of the terminal v i n y l groups. The second set of networks studied were formed i n the presence of diluent and also achieved a high extent of reaction (ε>0.9). The f i n a l group of experiments were performed on networks formed i n bulk at low extents of reaction (0.4 1) had been used i n forming the networks to ensure complete reaction of the v i n y l groups (φ~φ Μ). A l l the networks represented i n Figure 1 were made with the M = 21,600 α,ω-divinyl PDMS. 2C± and 20^ + 2C2 are found to increase with increasing network functionality i n the low-functionality region (4-10); however, further increases i n functionality be yond 20 result i n l i t t l e change i n these moduli. A prediction of the Flory theory i s that i n the l i m i t of large s t r a i n (α~*-»·0), the network w i l l exhibit phantom behavior. Thus, the i n f i n i t e s t r a i n modulus would increase as l-2/φ with functionality from 0.5vkT/V at φ - 4 to 0.9 vkT/V at φ - 20. Increasing φ to I n f i n i t y would result i n only a 10% further increase i n the phan tom modulus. 20γ being an extrapolation from f i n i t e to i n f i n i t e strain, overestimates the phantom modulus but the trend should remain the same. Therefore, the increase i n 2C\ q u a l i t a t i v e l y follows the Flory predictions. The ratio 2 0 / 2 0 ι i s observed i n Figure 1 to decrease as ymptotically with increasing Φο/R. Once again the majority of the decrease occurs between four and ten. 2C2, being a measure of the magnitude of the transition from phantom to affine behav ior, i s predicted by the Flory theory to decrease asymptotical ly with increasing functionality as i s 2C2/2C^. However, the theoretical asymptote for both i s zero [see equation (5)]. The experimentally determined l i m i t for 2C was found to be 0.11 MPa for the M » 21,600 networks. For 2C /2Ci, an asymptote of 0.56 was observed. Both of these values are s i g n i f i c a n t l y greater than the zero prediction. Further disagreement with the Flory theory i s found i n the magnitude of 2C^ and 2Cj + 2C2 i n Figure 1. These results are quantified i n terms of the structure factors A\ and Α2· A| and A2 relate the small and large-strain moduli to the number of 2

0

0

0

n

2

2

n

2


ELASTOMERS

334

AND

RUBBER

ELASTICITY

Ο OJ CsJ


00 Ο ~T~

CD

Ο

C\J

•s:

Ο

ο

Τ -r-

ο

CM \

Ο ο

CM

ο

CM

Ο

+

Γ-

ο

ο

CM

CM I

ο

Ο CM

•2

ο

CM

Ο

10) to a single l i n e offers further v e r i f i c a t i o n of the theory. Furthermore, both networks prepared with the linear and the branched PMHS were well f i t by the same line. Networks Formed i n the Presence of Diluent, ε>0.9. A series of s i x networks were prepared both i n bulk and i n the presence of oligomeric PEMS (M • 1170, no v i n y l groups) using as junc tions a φο = 43.9 linear PMHS and as chains α,ω-divinyl PDMS ranging i n M from 9,320 to 28,600 g-mol" . The volume fraction of solvent present during network formation, νχ , was 0.30 for a l l s i x networks and was calculated assuming simple a d d i t i v i t y of volumes. The tensile behavior of the networks formed i n bulk was measured i n bulk, v « Vf/V » 1. The ten s i l e behavior of the networks formed i n solution was measured both on networks with solvent present ( v =1) and on networks from which the oligomeric PDMS had been extracted ( v = 1.47). In Figure 5, the values of Αχ for the three sets of tensile experiments are plotted against Vg/V^ (V 10. 0

Key: · , A, • , commercial α,ω-divinyl PDMS networks; Ο, Δ , • , narrow molecular weight distribution α,ω-divinyl PDMS networks. Functionality ( ): •, 10.58; 21.5 L; · , 23.8 B; 33.0 L; T , 38.1 B; A, 43.9 L; φ , 58.4 L; -ψ-, 83.6 L; R is gas constant, ε > 0.9 (I). 0

g

4.0 h

3.0 h

V

4.0 6.0 8.0 s/Vcj (gmol /cm3 1 0 ) 5

x

Figure 5. Dependence of A on v /V for networks formed and tested in bulk. Conditions: · , formed and tested in solution; | , formed in solution but tested in extracted deswollen state; Α , Φο = 43.9L. t

8

d


ELASTOMERS

340

AND RUBBER

ELASTICITY

m a x

calculated from G for the networks formed i n solvent by as suming a linear dependence on v (= Vf/V - 1.47). Furthermore, e

t

5

the intercept i s almost i d e n t i c a l to (0.119) ( 1 . 4 7 ) /

6

- 0.164

MPa obtained assuming a 5/6 power dependence on v . The behavior of the small-strain data i n the three sets of experiments suggests a more universal format for the smallstrain theory of Langley (12) and Graessley (13,16); t

2/3

G = v kT(V/V ) /V + T v s

Q

e

2 2 f

v

5 / 6 t

(G

m a x e

(12)

)°

wherein a 5/6 power dependence on v has been assumed and ( G ) ° i s the absolute maximum entanglement contribution to the small-strain modulus. This maximum would be obtained for a network formed and tested i n bulk and i n which a l l entanglements had been trapped ( v f = v • T = 1). Equation (12) considers the effects of solvent present during network formation and testing, as well as, the effect the removal of this solvent has on the small-strain modulus. In Figure 7, the small-strain data plotted i n Figure 6 are replotted as suggested by equation (12): (2C + 2C ) ( V / V ) ( V / V ) / T vs v k T ( V / V ) ( V / V f ) / T V . The data for the three series of tensile experiments displays an excellent f i t to a single l i n e . The slope of this l i n e was determined by l i n e a r regression to be 1.05 and the intercept, ( G ) ° , was determined t

max


e

2

t

e

2

l

5/6

2

f

d

1/2

f

e

s

f

d

e

d

max

e

to be 0.272 MPa.

The large-strain structure factor A i s plotted for these networks vs Vg/V^ i n Figure 8. The values of A for the three series of tensile experiments a l l display a dependency on v /V^ and are well i n excess of unity. The presence of solvent during network formation s i g n i f i c a n t l y decreases the value of A . Deswelling of these networks results i n a further decrease i n A . The values of A i n Figure 8 are considerably less than the cor responding values of Αχ i n Figure 5. If the magnitudes of these structure factors i n excess of unity are attributed to trapped entanglements, then i t would appear that the entanglement con tribution to the stress i s strain-dependent and decreases with increasing elongation. 2

2

s

2

2

2

Networks Formed i n Bulk, 0.4

Elastomers and Rubber Elasticity - American Chemical Society

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