Elastomers and Rubber Elasticity - American Chemical Society


new rubber elasticity theory (J-5) in describing some of the depar tures from the simple ... elastic effects of chain entangling and chemical cross-li...
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Recent Two-Network Results on the Effect of Chain Entangling in Cross-linked Elastomers W. BATSBERG Riso National Laboratory, Chemistry Department, DK-4000 Roskilde, Denmark O. KRAMER University of Copenhagen, Department of Chemistry, Universitetsparken 5, DK-2100 Copenhagen, Denmark Chain entangling i s found to dominate the elastic properties of highly cross-linked 1,2-polybutadiene at elastic equilibrium. Cross-linking of the linear polymer with 125 kGy of 10 MeV electrons in the strained state v i r t u a l l y separates the effects of chain entangling and chemical cross-links: G = 0.75 MPa and G = 0.25 MPa for the corresponding moduli, independent of type of strain during cross-linking. The two-network method and the re­ quired assumptions are examined in d e t a i l . A new stress­ -relaxation two-network method, requiring fewer assump­ tions, i s also discussed. The latter method shows direct­ ly, without the need of a theory, that the equilibrium contribution of chain entangling i s equal to the nonequilibrium stress-relaxation modulus prior to cross­ -linking in the strained state. The new method also direct­ ly confirms six of the eight assumptions required for the original two-network method. N

x

The role of chain entangling in cross-linked elastomers i s an old issue which has not yet been settled. The success of Flory s new rubber e l a s t i c i t y theory (J-5) in describing some of the depar­ tures from the simple Gaussian theory has acted as a strong catalyst for new work i n this area. Since the excellent work of Moore and Watson ((3), who crosslinked natural rubber with t-butylperoxide, most workers have as­ sumed that 'physical cross-links contribute to the equilibrium elastic properties of cross-linked elastomers. This idea seems to be f u l l y confirmed in work by Graessley and co-workers who used the Langley method on radiation cross-linked polybutadiene (7.) and ethylene-propylene copolymer (60 to study trapped entanglements. Two-network results on 1,2-polybutadiene (9.,J0) also indicate that the equilibrium elastic contribution from chain entangling at high degrees of cross-linking i s quantitatively equal to the pseudoequilibriian rubber plateau modulus (11) of the uncross-linked poly­ mer. 1

1

0097-6156/82/0193-0439$06.00/0 © 1982 American Chemical Society

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

440

ELASTOMERS AND

RUBBER ELASTICITY

Ronca and Allegra (2) and Flory (J»2) assume e x p l i c i t l y i n their new rubber e l a s t i c i t y theory that trapped entanglements make no contribution to the equilibrium e l a s t i c modulus. It i s proposed that chain entangling merely serves to suppress junction f l u c tuations at small deformations, thereby making the network deform a f f i n e l y at small deformations. This means that the l i m i t i n g value of the front factor i s one for complete suppression of junction fluctuations. Experimental values of 4 - 6 for the apparent front factor ( 7 ) have been reported for networks produced by radiation cross-linking of long linear chains. Analyzing the data according to the Langley method, Graessley and co-workers (J 8) found very large contributions from trapped entanglements and front factors of one for the contribution from chemical cross-links. It seems to be c l e a r l y demonstrated that chain entangling plays a major role i n elastomers such as polybutadiene, styrene-butadiene rubber, and ethylenepropylene copolymer which have high rubber plateau moduli ( 1 1 ) . Networks with t r i - and tetra-functional cross-links produced end-linking of short strands give moduli which are more i n accord with the new theory if quantitative reaction can be assumed G » J 3 ) . However, the data on polydimethylsiloxane networks, may equally well be analyzed in terms of modulus contributions from chemical cross-links and chain entangling, both, if imperfect reaction i s taken into account ( 1 J O . Absence of a modulus contribution from chain entangling has therefore not been demonstrated by endlinked networks. The two-network method (Jj5) offers an alternative method for studying the effect of chain entangling in cross-linked elastomers. It i s the only method which allows a v i r t u a l separation of the e l a s t i c effects of chain entangling and chemical cross-links: An uncross-linked elastomer i s strained at a temperature of about Tg+8K i n order to be in the rubber plateau region. Then the sample i s quenched to below T and heavily cross-linked with high energy electrons. After heating and release, the sample retracts to a stress-free equilibrium state i n which the e l a s t i c effects of chain entangling and chemical cross-links are equal and opposite i n direct i o n . It was found by Ferry and coworkers ( 1 6 ) that the modulus contribution from chemical cross-links i s much smaller than the equilibrium contribution from chain entangling. And furthermore, the equilibrium contribution from chain entangling in a highly cross-linked network was found to be approximately equal to the non-equilibrium rubber plateau modulus ( 9 » 1 7 ) . In spite of these important r e s u l t s , the two-network method has had l i t t l e impact on the discussion of the role of chain entangling in cross-linked elastomers. It was therefore decided to make a more detailed examination of the method and to t r y to develop a simpler method which would require fewer assumptions. The present paper i s a discussion of recently published and unpublished work. The paper i s divided into three parts. The f i r s t part presents

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

23.

BATSBERG

Chain Entangling in Elastomers

A N D KRAMER

441

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some of the results of the two-network theory which forms the basis of the two-network method. The second part describes the two-network method and the necessary assumptions. Results for three different types of strain are presented. The third part i s a discussion of a new stress-relaxation two-network method which requires fewer as­ sumptions. I t shows d i r e c t l y , without the need of a theory, that the equilibrium contribution from chain entangling i s equal to the non-equilibrium stress-relaxation modulus immediately prior to cross-linking. Part 1. Two-Network Theory The two-network theory for a composite network of Gaussian chains was o r i g i n a l l y developed by Berry, Scanlan, and Watson (18) and then further developed by Flory (19). The composite network i s made by introducing chemical cross-links i n the isotropic and sub­ sequently i n a strained state. The Helmholtz e l a s t i c free energy of a composite network of Gaussian chains with affine motion of the junction points i s given by the following expression: ΔΑ

=

Θ 1

2

τα λ λ -3) 2

2

χ+

γ+

ζ

+

2

RTU

2

+

A

2

y

;

2

+

Af

;

2

-3)

(

1

)

v

where oth networks, the theory shows that the effects of the two networks are conveniently separated, mathematically. A l l el a s t i c properties may be calculated from eq. 1. After introduction of cross-links i n the strained state, the composite network r e t r a c t s , upon release, to a stress-free stateof-ease ( J 9 ) . The amount of retraction i s determined by the degree of strain during cross-linking and by the r a t i o v - j A . The e l a s t i c properties r e l a t i v e to the state-of-ease are isotropic for a Gaus­ sian composite network (18,19»20). Flory (j9) has treated the interesting case of subsequent removal of the f i r s t stage cross-links without chain scission. Even after complete removal, i.e. v-j =0, there i s still a certain memory of the structure of the f i r s t network since the composite network strands were physically part of both networks. According to F l o r y s theory, the resulting network may be treated as if a certain fraction, Φ , of the strands of the second network were e f f e c t i v e l y converted into strands of the f i r s t network, v .

(λ ,λ ,λ )

2

ζ

1

1

ν,

le

= Φν 2

ν

ο

= (ΐ-Φ)ν

ze

e

(2)

0

0

λ

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

(3)

442

ELASTOMERS

AND RUBBER

ELASTICITY

1

Φ i s given i n Flory s paper as a function of φ 2 where φ

(4)

£

Ψ

2

V +V 1

K

J

2

The result i s important for the discussion i n Part 3 . Multiplication of the ν-values by RT gives the corresponding moduli. The e f f e c t i v e modulus of the f i r s t network after removal of f i r s t network cross­ l i n k s , G i , has been calculated for a f i r s t network modulus, G of O.75 MPa. In Figure 1 , G i s plotted against the modulus of the second network before removal of the f i r s t network cross-links, G2. It can be seen that the memory effect increases with increasing modulus or degree of cross-linking of the second network. G and 2,max the experiment to be discussed i n Part 3 . e



1e

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x

a r e

r e l a t e d

t o

Part 2 . Two-Network Method. Different Types of S t r a i n . Uncross-linked linear polymers of high molecular weight ex­ h i b i t a pronounced rubber plateau for a certain range of time and temperature ( 1 1 ) . In t h i s region, the material behaves s i m i l a r l y to a cross-linked elastomer: The shear modulus i s t y p i c a l l y of the order of 1 MPa, the e x t e n s i b i l i t y i s several hundred percent with nearly complete recovery, and the isochronal stress-strain curve follows Mooney-Rivlin behavior ( 2 1 ) . These properties are a l l nonequilibrium properties; given enough time the chains w i l l disentan­ gle, the modulus drops towards zero, and the recovery w i l l be incomplete. However, the properties described above indicate that the highly entangled chains form a temporary network structure with rubberlike properties. The question i s whether the introduc­ tion of chemical cross-links w i l l trap the entangled structure i n such a way that i t gives a large modulus contribution at e l a s t i c equilibrium or whether the effect relaxes to zero. It was proposed by J.D. Ferry ( 1 5 , 2 2 ) that the temporary network of highly entangled chains could replace the f i r s t network of the two-network theory. The experiment i s performed i n the following manner : An uncross-linked amorphous polymer i s strained at about Tg+8K. The central portion of the rubber plateau should be reached after a few minutes and the sample i s quenched to a temperature well below Tg and irradiated with high energy electrons to a high degree of cross-linking. After heating and release, the sample retracts to the stress-free state-of-ease, see Figure 2 . Expressed in terms of moduli, the Helmholtz e l a s t i c free energy relation i s given by eq. 5 . M

el

=ν χ λ



3

Κ" >

+

G

a

x x 2 ;

+ A

y 2

where G i s the equilibrium modulus of the f i r s t network of entan­ gled chains, and G i s the equilibrium modulus of the second network due to chemical cross-links. From eq. 5 , the stress-strain relations for different types of strain can be derived ( J 0 ) . Measurements of the stress-strain properties and the three lengths shown i n Figure 2 allow calculation of G and G . N

x

N

x

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

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23.

BATSBERG

AND

443

Chain Entangling in Elastomers

KRAMER

Figure 1. Effective first network modulus, G , after complete removal of first network cross-links plotted against second network modulus, G . Calculated from the composite network theory of Flory (19) for G =O.75MPa. le

2

t

TWO-NETWORK METHOD Chain entangling : >*f

Crosslinking :

G +

G

N

X

State-of-ease after release Figure 2. The principle of the two-network method for cross-linking in a state of simple extension. First network with modulus G is entirely due to chain entangling. Second network with modulus G is formed by cross-linking in the strained state. Both G and G can be calculated from the two-network theory. N

x

N

x

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

444

ELASTOMERS

AND

RUBBER

ELASTICITY

The r e s u l t s are shown i n Figure 3 f o r 1 2 - p o l y b u t a d i e n e c r o s s l i n k e d i n s t a t e s o f e i t h e r simple e x t e n s i o n , e q u i b i a x i a l e x t e n s i o n , or pure shear. The samples were allowed to r e l a x f o r 3 0 s at T + 8 K before quenching and i r r a d i a t i o n with 10 MeV e l e c t r o n s at T g - 2 7 K . I t can be seen t h a t the magnitude o f the e q u i l i b r i u m modulus cont r i b u t i o n from chain e n t a n g l i n g i s independent o f type o f s t r a i n . When e x t r a p o l a t e d to zero s t r a i n , G/G = 3 , which means t h a t chain e n t a n g l i n g c o n t r i b u t e s about 7 5 % of the t o t a l modulus f o r these samples which are h i g h l y c r o s s - l i n k e d ( 1 0 ) . Furthermore, the e q u i l i b r i u m modulus c o n t r i b u t i o n o f chain e n t a n g l i n g i s found to be approximately equal to the pseudo-equilibrium p l a t e a u modulus, Gjf, o f a polybutadiene with a s i m i l a r m i c r o s t r u c t u r e ( 1 1 ) . F i g u r e 3 shows t h a t G decreases and G i n c r e a s e s with i n c r e a s i n g s t r a i n for simple e x t e n s i o n . The s t r e s s - s t r a i n p r o p e r t i e s o f the composite networks are c l e a r l y non-Gaussian f o r simple e x t e n s i o n . For e q u i b i a x i a l extension and pure shear, the s t r e s s - s t r a i n p r o p e r t i e s are more n e a r l y Gaussian ( 1 0 ) . The two-network method has s e v e r a l advantages, e s p e c i a l l y when the f r e e energy i s expressed i n terms o f moduli as shown i n eq. 5 . The f o l l o w i n g i n f o r m a t i o n need not be known: 1. I n i t i a l molecular weight and molecular weight d i s t r i b u t i o n as long as the molecular weight i s very h i g h . 2 . F u n c t i o n a l i t y o f the c r o s s - l i n k s . 3. Value o f the f r o n t f a c t o r . 4. Degree o f c r o s s - l i n k i n g . 5 . The r e l a t i o n s h i p between degree o f c r o s s - l i n k i n g and t r a p p i n g of the entangled s t r u c t u r e (the t r a p p i n g i s n e a r l y complete i n the present work). Please note t h a t the f r e q u e n t l y used terms 'entanglements and 'entanglement t r a p p i n g (7.»8.,J1) i n the present work are replaced by the l e s s s p e c i f i c terms 'chain e n t a n g l i n g ' and 'trapping o f the entangled s t r u c t u r e ' . U n f o r t u n a t e l y , the method i s based on a f a i r l y l a r g e number o f assumptions. I f we want to r e l a t e G t o the pseudo-equilibrium rubber plateau modulus, G§, and to the e f f e c t o f chain e n t a n g l i n g i n o r d i n a r y networks produced by c r o s s - l i n k i n g i n the unstrained s t a t e , the f o l l o w i n g assumptions are r e q u i r e d : A 1 . C r y s t a l l i n i t y i s n e g l i g i b l e (23,24,25). A2. C r o s s - l i n k s introduced at a c e r t a i n s t r a i n c o n t r i b u t e nothing to the s t r e s s at t h a t p a r t i c u l a r s t r a i n . A3. The end-to-end d i s t a n c e o f the f r e e strands i s p r a c t i c a l l y unchanged by the c r o s s - l i n k i n g process, i . e . , the,extent o f chemical m o d i f i c a t i o n o f the polymer chains produced by h i g h energy r a d i a t i o n should be s m a l l . A4. Chain s c i s s i o n i s n e g l i g i b l e . A5. Chain d i s e n t a n g l i n g p r i o r to and a f t e r i n t r o d u c t i o n o f chemic a l c r o s s - l i n k s i n the s t r a i n e d s t a t e i s n e g l i g i b l e . A6. The f i r s t network i s p r a c t i c a l l y at e l a s t i c e q u i l i b r i u m when the second network i s being formed. A7. The c r o s s - l i n k i n g process i s f a i r l y random ( 2 6 ) . t

g

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x

N

x

1

1

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

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BATSBERG

445

Chain Entangling in Elastomers

A N DKRAMER

Figure 3. Modulus contributions from chemical cross-links (G ,filledtriangles) and from chain entangling (G , unfilled symbols) plotted against the extension ratio during cross-linking, λ , for 1,2-polybutadiene. Key: O, G , equibiaxial extension; • , G , pure shear; A, G , simple extension; G °, pseudo-equilibrium rubber plateau modulus for a polybutadiene with a similar microstructure. See Ref. 10. x

N

0

N

N

N

N

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

446

ELASTOMERS

A N D RUBBER

ELASTICITY

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A8. The Helmholtz e l a s t i c free energy relation of the composite network contains a separate term for each of the two networks as i n eq. 5. However, the precise mathematical form of the strain dependence i s not c r i t i c a l at small deformations. Although a l l the assumptions seem to be reasonably f u l f i l l e d , a simpler method, which would require fewer assumptions, would ob­ viously be desirable. A simpler method can be used if we just want to compare the equilibrium contribution from chain engangling i n the cross-linked polymer to the stress-relaxation modulus of the uncross-linked polymer. The new method i s described in Part 3. Part 3. Stress-Relaxation Two-Network Method The method (27) can best be explained with reference to Figure 2. After stretching to 1 , the force f i s measured as a function of time. The strain i s kept constant throughout the entire experiment. At a certain time, the sample i s quenched to a temperature well below the glass-transition temperature, T , and cross-linked. Then the temperature i s raised to the relaxation temperature, and the equilibrium force i s determined. A direct comparison of the equi­ librium force to the non-equilibrium stress-relaxation force can then be made. The experimental set-up i s shown i n Figure 4. The results for a sample of 1,2-polybutadiene with a T of 263K (27) are shown i n Figure 5. The upper curve shows the tem­ perature, and the lower curve shows the logarithm of the stretching force plotted against the logarithm of time reduced ( J J ) to the stress-relaxation temperature, T +8K. The sample i s quenched to T -27K after 1000s, and chemical cross-links are introduced in the glassy state at a dose of 150kGy of 10 MeV electrons (the dose was erroneously given as 200 kGy i n references 27 and 28). The spike observed on the force curve i s due to thermal contraction of the sample and the connecting rods by cooling below T . As the rate of relaxation i s p r a c t i c a l l y zero i n the glassy state, log t / a remains unchanged during the cross-linking process. After cross-linking, the rate of relaxation i s observed to be extremely slow at T +8K. When the temperature i s increased to T +68K, the rate of relaxation i s increased approximately by a factor of 1 0 . Ten minutes at T +68K means that log t/a-j- i s increased to about 9. The equilibrium force, f q , at T +8K i s f i n a l l y obtained by lowering the temperature to T +8K. The equilibrium force i s found to be only 7% less than the non-equilibrium stress-relaxation force immediately prior to cross - l i n k i n g . This difference i s the mean of two experiments. A d i f ­ ference of only 4% has been observed in an experiment i n which the stress-relaxation prior to cross-linking was extended to log t / a equal to 4.5. Subsequent measurements of the strain (λ = 1.152) and the modulus (G = 1.29 MPa at 323K) in the state-of-ease together with the strain during cross-linking (λ = 1.49) allow calculation of G =O.75MPa and G = O.49 MPa from the two-network theory (10). The new method (27) has a number of advantages i n comparison to the o r i g i n a l two-network method (10). Sample dimensions and the 0

g

g

g

g

g

T

g

g

g

e

g

g

T

s

s

N

x

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

23.

BATSBERG

AND KRAMER

Chain Entangling in Elastomers

447

C

Β

IZZZZ3

Έ

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G

Figure 4. Experimental setup for stress-relaxation and cross-linking at constant simple extension. Key: A, electron accelerator; B, beam aperture; C, force trans­ ducer; D, thermostated box; E, sample; F, stretching device; G, connecting rods.

log

t/a

T

(s)

Figure 5. Logarithm of the retractive force at 49% strain (lower curve) and sam­ ple temperature (upper curve) plotted against logarithm of time reduced to 263 K. Cross-links are introduced at log t/a is 3 in the glassy state where the spike on the force curve is due to thermal contraction upon cooling below the glass transition temperature. Equilibrium force at 263 Κ after cross-linking is f . (Reproduced, with permission, from Ref. 27. Copyright 1981, Journal of Chemical Physics.) T

eq

American Chemical Society Library

1155 18th St., N.W. Mark and Lal;Washington, Elastomers D.C. and 20036 Rubber Elasticity ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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448

ELASTOMERS

AND RUBBER

ELASTICITY

degree of strain need not be known. Assumption 1 from Part 2 i s not required if we just want to make a comparison of the equilibrium and non-equilibrium forces. It i s still required if we want to find the magnitude of the modulus contribution from chain entangling by i t s e l f . This point w i l l be discussed i n d e t a i l below. The other assumptions can quickly be disposed o f . The experimental fact, that the equilibrium and non-equilibrium forces are p r a c t i c a l l y equal, s i m p l i f i e s the analysis, and i t shows d i r e c t l y that assumptions 2-6 of Part 2 are f u l f i l l e d , subject to the comments given below. Assumptions 7 and 8 are unnecessary i n the stress-relaxation method since the sample i s kept at constant length during the entire experiment. The cross-links merely serve the purpose of trapping the entangled structure. Re A3. High energy radiation causes some cyclization of the pendant v i n y l groups (29). This should cause a s t i f f e n i n g of the chain and thus an increase i n of the free network strands. The modulus should then be decreased by the r a t i o / (30). However, the effect i s apparently too small to cause a significant decrease i n the modulus. Re A5. The experiment shows that no chain disentangling takes place after introduction of chemical cross-links i n the strained state. Chain disentangling may take place prior to cross-linking if the relaxation period i s long enough. Re A6. I t may seem surprising that the entangled network should be at v i r t u a l equilibrium when the second network i s being formed. I t probably means that there i s short range equilibrium during most of the process of disentangling of linear chains, namely the reptation process (3}). I t i s the l a t t e r process which i s prevented by trapping of the entangled structure. The stress-relaxation two-network experiment would have been d i f f i c u l t to analyze if the equilibrium force were much smaller than the non-equilibrium force immediately prior to cross-linking. It would then have been necessary to make a detailed discussion of the p o s s i b i l i t y of complete disappearance of the f i r s t stage network ( 19). The memory effect discussed i n Part 1 could give r i s e to an appreciable equilibrium force. However, Figure 1 shows that the memory e f f e c t , expressed as the modulus G , could never exceed about 50% of f o r the degree of cross-linking produced i n the present experiment. The curve i n Figure 1 i s calculated for G = GJJ = O.75 MPa. Since the composite network modulus G >, G-j + G2, i t follows that the maximum possible modulus of the second network 2 max 9 MPa. This case i s included for comparison only. G i s the modulus contribution from the second network calculated from the two-network theory without taking disappearance of the f i r s t network into consideration. I t i s concluded from Figure 1 that the memory effect cannot explain the experimentally observed near equality of the non-equilibrium and equilibrium moduli shown in Figure 5. The only question remaining, i s the following: Is i t possible 2

1 E

G

G

=

1 , 2

X

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

23.

BATSBERG

A N D KRAMER

Chain Entangling in Elastomers

449

that the s t r e s s - r e l a x a t i o n modulus and the e q u i l i b r i u m modulus observed i n Figure 5 could be p a r t l y due t o c r y s t a l l i n i t y ? The a t a c t i c 1,2-polybutadiene sample used i n the experiment has a dens i t y o f 885 kg m"3 j shows no s i g n o f c r y s t a l l i n i t y by d i f f e r e n t i a l scanning c a l o r i m e t r y w i t h a scanning r a t e o f 40K per minute. I t has been suggested by F l o r y (23) and by Mark and co-workers (24,25) that m i c r o c r y s t a l l i t e s may still p l a y a b i g r o l e f o r the e l a s t i c p r o p e r t i e s . The s t r e s s - r e l a x a t i o n two-network experiment o f f e r s an i d e a l method f o r t e s t i n g t h i s h y p o t h e s i s . R e f e r r i n g t o Figure 2, o n l y chain e n t a n g l i n g and p o s s i b l y c r y s t a l l i n i t y cont r i b u t e t o the r e t r a c t i v e f o r c e a t the l e n g t h 1 . The e q u i l i b r i u m force should t h e r e f o r e be measured as a f u n c t i o n o f tempeature f o r constant extension r a t i o , X c o r r e c t e d f o r thermal expansion. Any m e l t i n g o f c r y s t a l l i t e s should g i v e r i s e t o an abrupt change i n the force-temperature curve or i n the slope o f the curve. The r e s u l t s are shown i n Figure 6. In the temperature range 263 t o 373K t h e behavior i s completely r e v e r s i b l e , i . e . , no m e l t i n g has taken p l a c e . When the temperature i s increased t o 393K and s l i g h t l y above, d i s c o l o r a t i o n and degradation take p l a c e . The experiment i s performed i n a n i t r o g e n atmosphere but consumption o f t h e ant i o x i d a n t i n the c r o s s - l i n k i n g process has decreased the s t a b i l i t y o f the polymer. I t i s obyious from Figure 6 t h a t no m e l t i n g o f c r y s t a l l i t e s takes place up t o a t l e a s t 383K. According t o Obata and co-workers ( 2 ) any m e l t i n g i n a t a c t i c or n e a r l y a t a c t i c 1,2-polybutadiene should take place below 340K. I t i s concluded that m i c r o c r y s t a l l i n i t y plays no r o l e i n the present work. a n c

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Q

Q f

Conclusions The two-network method has been c a r e f u l l y examined. A l l the previous two-network r e s u l t s were obtained i n simple extension f o r which the Gaussian composite network theory was found t o be inadequate. Results obtained on composite networks o f 1,2-polybutadiene for three d i f f e r e n t types o f s t r a i n , namely e q u i b i a x i a l e x t e n s i o n , pure shear, and simple e x t e n s i o n , a r e discussed i n the present paper. The Gaussian composite network e l a s t i c f r e e energy r e l a t i o n i s found t o be adequate i n e q u i b i a x i a l extension and p o s s i b l y pure shear. E x t r a p o l a t i o n t o zero s t r a i n g i v e s the same r e s u l t f o r a l l three types o f s t r a i n : The c o n t r i b u t i o n from chain e n t a n g l i n g at e l a s t i c e q u i l i b r i u m i s found t o be approximately equal t o the pseudo-equilibrium rubber plateau modulus and about three times l a r g e r than the c o n t r i b u t i o n from chemical c r o s s - l i n k s . A new s t r e s s - r e l a x a t i o n two-network method i s used f o r a more d i r e c t measurement o f the e q u i l i b r i u m e l a s t i c c o n t r i b u t i o n o f chain e n t a n g l i n g i n h i g h l y c r o s s - l i n k e d 1,2-polybutadiene. The new method shows c l e a r l y , without the need o f any t h e o r y , t h a t the e q u i l i b r i u m c o n t r i b u t i o n i s equal t o the n o n - e q u i l i b r i u m s t r e s s - r e l a x a t i o n modulus o f the u n c r o s s - l i n k e d polymer immediately p r i o r t o c r o s s l i n k i n g . The new method a l s o d i r e c t l y confirms s i x o f t h e e i g h t assumptions r e q u i r e d f o r the o r i g i n a l two-network method.

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

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AND

RUBBER

ELASTICITY

Figure 6. Retractive force at constant strain, λ corrected for thermal expansion, plotted against temperature. Behavior is completely reversible in range of 263 to 373 K. Serious degradation takes place above 393 K. 0

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

23.

BATSBERG AND KRAMER

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I t i s c l e a r l y shown t h a t c h a i n e n t a n g l i n g p l a y s a m a j o r r o l e i n networks o f 1 2 - p o l y b u t a d i e n e produced b yc r o s s - l i n k i n g o f long l i n e a r c h a i n s . The t w o - n e t w o r k method s h o u l d p r o v i d e c r i t i c a l t e s t s f o r new m o l e c u l a r t h e o r i e s o f r u b b e r e l a s t i c i t y w h i c h t a k e c h a i n entangling into account. f

Acknowledgements This

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the

Danish

work

was

supported

i n part

b y Grant

N o . 511-15425

from

Research C o u n c i l .

Literature Cited 1. Flory, P.J. Proc.R.Soc.London, Ser. A. 1976, 351, 351-378. 2. Flory, P.J. J.Chem.Phys. 1977, 66, 5720-5729. 3. Flory, P.J. Polymer 1979, 20, 1317-1320. 4. Flory, P.J. Macromolecules 1979, 12, 119-122. 5. Flory, P.J., paper in this book. 6. Moore, C.G.; Watson, W.F. J.Polym.Sci. 1956, 19, 237-254. 7. Dossin, L . M . ; Graessley, W.W. Macromolecules 1979, 12, 123-130. 8. Pearson, D.S.; Graessley, W.W. Macromolecules 1980, 13, 10011009. 9. Carpenter, R . L . ; Kramer, O.; Ferry, J.D. Macromolecules 1977, 10, 117-119. 10. Hvidt, S.; Kramer, O.; Batsberg, W.; Ferry, J.D. Macromolecules 1980, 23, 933-939. 11. Ferry, J.D. "Viscoelastic Properties of Polymers", 3rd ed.; Wiley: New York, N.Y., 1980. 12. Ronca, G . ; Allegra, G. J.Chem.Phys. 1975, 63, 4990-4997. 13. Mark, J.E. Makromol.Chem.Suppl. 1979, 2, 87-97. 14. Gottlieb, M . ; Macosko, C.W.; Benjamin, G . S . ; Meyers, K . O . ; M e r r i l l , E.W. Macromolecules 1981, 14, 1039-1046. 15. Kramer, O.; Carpenter, R.L.; Ty, V.; Ferry, J.D. Macromolecules 1974, 7, 79-84. 16. Carpenter, R . L . ; Kramer, O.; Ferry, J.D. J.Appl.Polym.Sci. 1978, 22, 335-342. 17. Kan, H . - C . ; Ferry, J.D. Macromolecules 1979, 12, 494-498. 18. Berry, J.P.; Scanlan, J.; Watson, W.F. Trans.Faraday Soc. 1956, 52, 1137-1151. 19. Flory, P.J. Trans.Faraday Soc. 1960, 56, 722-743. 20. Lodge, A.S. Rheology Research Center Report, 61,University of Wisconsin, Madison, 1980. 21. Noordermeer, J.W.; Ferry, J.D. J.Polym.Sci., Polym.Phys.Ed. 1976, 14, 509-520. 22. Ferry, J.D. Prelim.Rept., ARPA Mater. Summer Conf. 1971, 1, 327. 23. Erman, B . ; Wagner, W.; Flory, P.J. Macromolecules 1980, 13, 1554-1558. 24. Mark, J.E.; Llorente, M.A. Polymer J. 1981, 13, 543-553.

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25. Llorente, M.A.; Mark, J.E. J.Polym.Sci., Polym.Phys.Ed. 1981, 19, 1107-1120. 26. Falender, J.R.; Yeh, G.S.Y.; Mark, J.E. J.Chem.Phys. 1979, 70, 5324-5325. 27. Batsberg, W.; Kramer, O. J.Chem.Phys. 1981, 74, 6507-6508. 28. Batsberg, W.; Kramer, O. Polymer Preprints 1981, 22(2),171-172. 29. von Raven, Α.; Heusinger, H. J.Polym.Sci., Polym.Chem.Ed. 1974, 22, 2255-2271. 30. Graessley, W.W. Adv.Polym.Sci. 1974, 16, 1-179. 31. de Gennes,P.G.J.Chem.Phys.1971, 55, 572-579. 32. Obata, Y.; Tosaki, C.; Ikeyama, M. Polymer J. 1975, 7, 207-216. RECEIVED

February 5, 1982.

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