Urethane Chemistry and Applications - ACS Publications - American

24 Characterization of Polyurethane Networks

Downloaded by UNIV ILLINOIS URBANA-CHAMPAIGN on November 10, 2016 | http://pubs.acs.org Publication Date: November 30, 1981 | doi: 10.1021/bk-1981-0172.ch024

B. ERSHAGHI, A. J. CHOMPFF, and R. SALOVEY Department of Chemical Engineering, University of Southern California,

Los Angeles, CA 90007

Linear polymers are usually characterized in solution. How ever, if enough crosslinking has occurred, such as in the vulcan ization of elastomers, the polymer will swell but cannot dissolve in typical solvents. Then, it is impossible to derive molar mass (molecular weight) information from solution behavior. However, the average molar mass of the chains in the polymer network can be determined from swelling (1,2). If a polymer network attains an equilibrium degree of swell ing, one can relate the number of "effective" chains per unit vol ume (v*) or the average molar mass between crosslinks (M ) to the degree of swelling (q ), if certain assumptions are made; namely, a constant polymer/solvent interaction parameter (x) and a refer ence degree of swelling in the unperturbed state (q ) equal to unity for polymerization in bulk. However, we have calculated that M derived from swelling measurements did not agree with values determined analytically by labelling crosslinks with C (3). In deed, M derived from swelling was about ten times that derived analytically. The origin of this discrepancy is examined in this c

i

o

c

14

c

paper. Selected polyurethane networks are swelled over polymer s o l u t i o n s w i t h v a r i e d s o l u t e c o n c e n t r a t i o n i n order to determine the e q u i l i b r i u m degree of s w e l l i n g as a f u n c t i o n of solvent a c t i v i t y . From these d a t a , M , χ and q can be independently d e t e r mined . In a d d i t i o n , swollen networks are subjected t o s t r e s s r e l a x a t i o n i n t e n s i o n . The i n i t i a l and e q u i l i b r i u m s t r e s s are r e l a t e d to M and q . c

c

Q

Q

Experimental D e t a i l s Materials Two commercial polypropylene g l y c o l s ( p o l y o l s ) of d i f f e r e n t f u n c t i o n a l i t y were used. The t r i f u n c t i o n a l p o l y o l i s Union Carbide ΝIAX 16-56, and the d i f u n c t i o n a l p o l y o l i s Union Carbide NIAX 2025. Each has an equivalent weight approximating 1.00 kg. The p o l y o l s were d r i e d w i t h bubbling dry n i t r o g e n w h i l e 0097-6156/81/0172-0373$05.00/0 © 1981 American Chemical Society Edwards et al.; Urethane Chemistry and Applications ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

374

URETHANE CHEMISTRY AND APPLICATIONS 1


heating to 110°C. S o l i d MDI (4-4 -diphenylmethane d i i s o c y a n a t e ) was s u p p l i e d by the Upjohn Company. MDI was p u r i f i e d by vacuum d i s t i l l a t i o n . Since MDI d i m e r i z e s on s t o r a g e , samples were always f r e s h l y d i s t i l l e d before use. The c a t a l y s t was d i b u t y l t i n d i l a u r ate from Witco Chemical. Dioxane solvent was obtained from Union Carbide, and p o l y s t y r e n e "standards" from Pressure Chemicals. Network S y n t h e s i s (4) S o l i d MDI was weighed i n t o a f l a s k and an e q u i v a l e n t amount of p o l y o l added. The mixture was heated to about 40°C to d i s s o l v e the MDI. The mixture was then cooled to room temperature and degassed f o r s e v e r a l minutes under vacuum i n order to remove d i s s o l v e d a i r . C a t a l y s t was then added and the contents of the f l a s k mixed under vacuum to ensure u n i f o r m i t y and then poured i n t o a mold. A l l o p e r a t i o n s were c a r r i e d out i n a dry glove bag to minimize r e a c t i o n w i t h atmospheric water. The c r o s s l i n k i n g process was a l s o c a r r i e d out i n dioxane s o l u t i o n at 70% volume f r a c t i o n of s o l i d s . Polyurethane networks w i t h d i f f e r e n t c r o s s l i n k d e n s i t i e s were prepared by v a r y i n g the r a t i o of d i f u n c t i o n a l and t r i f u n c t i o n a l p o l y o l s . A l l samples were e x t r a c t e d w i t h dioxane to remove unreacted and u n c r o s s l i n k e d m a t e r i a l b e f ore swelling. S w e l l i n g A temperature c o n t r o l l e d a i r bath, a balance and s m a l l m o d i f i e d weighing b o t t l e s were used to study s w e l l i n g . Polymer network samples were suspended over p o l y s t y r e n e s o l u t i o n s . Vapor a b s o r p t i o n was measured by gravimetry and by m o n i t o r i n g the weight of the b o t t l e s , c o r r e c t i o n could be made f o r changes i n solute concentration. Stress Relaxation Polyurethane networks were a l s o polymer i z e d i n a mold w i t h a c y l i n d r i c a l c a v i t y . Uniform r i n g s were cut from the c y l i n d e r s and weighed. The c r o s s s e c t i o n a l area was then d e r i v e d from the sample diameter and polymer d e n s i t y and a p p r o x i mated 0.05 cm . S t r e s s r e l a x a t i o n was measured a t s e v e r a l s t r a i n s between 10 and 43% w i t h an I n s t r o n t e n s i l e t e s t e r . During s t r e s s r e l a x a t i o n , the samples were immersed i n dioxane and swelled to equilibrium. 2

Theory The s w e l l i n g behavior of polymer networks i s de s c r i b e d by s e v e r a l network parameters: Xg, a polymer networks o l v e n t i n t e r a c t i o n parameter; υ*, the c o n c e n t r a t i o n of e l a s t i c a l l y e f f e c t i v e network c h a i n s ; and q , a r e f e r e n c e degree of s w e l l i n g which i s r e l a t e d to the unperturbed end-to-end d i s t a n c e of the polymer c h a i n s during network f o r m a t i o n . At an e q u i l i b r i u m degree of s w e l l i n g , the chemical p o t e n t i a l s of mixing and of e l a s t i c deformation of the network balance, so that: Q

(1)

,d

Δ G 3 Ν

mixings

,3 A G 3 Ν

elastic. ;

_ "

Λ U

Edwards et al.; Urethane Chemistry and Applications ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

24.

Polyurethane

ERSHAGHI ET AL.

Networks

375

where, AG . . and AG „. are the Gibbs f r e e energies due * mixing elastic ° Λ

mixing and e l a s t i c i t y , r e s p e c t i v e l y , and Ν i s the number of moles of s o l v e n t . O r d i n a r i l y , a s i n g l e s w e l l i n g t e s t i s combined w i t h assumed v a l u e s f o r χ and q to determine υ* or M , the molecular weight between c r o s s l i n k s ( 2 ) . A d d i t i o n a l i n f o r m a t i o n can be de r i v e d by studying v a r i a t i o n s i n the e q u i l i b r i u m degree of s w e l l i n g as a f u n c t i o n of solvent a c t i v i t y , a^. I f μ^, i s the chemical p o t e n t i a l of s o l v e n t , then Q


to

(2)

c

= μ^

μ

0

+ k Τ lna

] L

and the s w e l l i n g of a c r o s s l i n k e d network may follows (5): (3)

( l n a ^ In ( l - q

_! ±

) q

2

=

±

X

. * - Vj_ Βυ q

g

be expressed as + ν

±

χ

Αυ

*

q

~ Q

2 / 3

5 / 3

q

±

q i i s the degree of s w e l l i n g , expressed as the swollen volume/dry volume, V i s the molar volume of the s o l v e n t , A and Β are a r b i t r a r y constants from the theory of rubber e l a s t i c i t y . Values f o r A and Β have been suggested (6,7,8). Another method of v a r y i n g the e q u i l i b r i u m degree of s w e l l i n g i s to s t r e t c h the polymer during s w e l l i n g . Then, the chemical p o t e n t i a l of the solvent i n s i d e the g e l w i l l decrease so that the degree of s w e l l i n g i n the s t r e t c h e d s t a t e i n c r e a s e s . For a s w o l l en network, one can c a l c u l a t e the degree of s w e l l i n g i n the s t r e t c h e d s t a t e (q) from the i n i t i a l ( f ) and e q u i l i b r i u m ( f ^ ) f o r c e s and the s t r e t c h r a t i o i n the swollen s t a t e ( Λ ) . If is the f o r c e per u n i t dry u n s t r a i n e d c r o s s - s e c t i o n a l a r e a , then x

Q

χ

(4)

a

d

=

Ak

Tu*

q o

2 / 3

-

1 / 3 q i

( Λ

3_

)

s i n c e f o r a swollen network, the r e t r a c t i v e f o r c e i n s t r e s s r e l a x a t i o n i s almost purely e n t r o p i e . Then, A U*q can be c a l c u l a t e d and compared to v a l u e s from s w e l l i n g . Since the i n t e r a c t i o n parameter (χ) i n most polymer s o l u t i o n s i s c o n c e n t r a t i o n dependent (10), we can w r i t e : 2

3

Q

( 5 )

x

g

=

Xi

+

x

2

{

i"

2

In order to evaluate χ, we can combine data from s t r e s s r e l a x a t i o n and s w e l l i n g . From s t r e s s r e l a x a t i o n , the v a l u e of Alfq Ρ can be c a l c u l a t e d (equation 4) and s u b s t i t u t e d i n t o equation i . I f we represent a l l of the q u a n t i t i e s i n equation 3 which are d e t e r mined experimentally by D, then we can w r i t e : 2

(6)

D -

X i

+ χ

2

q

2

+

V^BuSi


376

URETHANE CHEMISTRY AND APPLICATIONS

The v a l u e s of χ , programming.

χ , and ν Β υ * may then be obtained by l i n e a r

χ

2

χ


R e s u l t s and D i s c u s s i o n A polyurethane g e l network prepared w i t h 80% d i o l and 20% t r i o l showed the h i g h e s t degree of s w e l l i n g i n dioxane among p o l y urethane s prepared from the b u l k p o l y m e r i z a t i o n of d i f f e r e n t p o l y o l m i x t u r e s . Compositions higher than 80% d i o l y i e l d e d s o l u b l e p o l y mers. When an 80/20 p o l y m e r i z a t i o n was run i n dioxane s o l u t i o n , the degree of s w e l l i n g of the r e s u l t a n t network was i n c r e a s e d . Dioxane solvent produced maximum s w e l l i n g of the polyurethane n e t works when compared t o v a r i o u s s o l v e n t s . From s w e l l i n g s t u d i e s i n a s e r i e s of s o l v e n t s , the s o l u b i l i t y parameter (δ) of a p o l y urethane network prepared w i t h 100% t r a f u n c t i o n a l p o l y o l was e s t i mated t o equal 11. The s w e l l i n g of polyurethane networks was a l s o conducted i n dioxane vapor. Such experiments g e n e r a l l y take a l o n g time to reach e q u i l i b r i u m . The d i f f u s i o n time was reduced by u s i n g t h i n (50μ) samples. The v a r i a t i o n of the degree of s w e l l i n g w i t h the volume f r a c t i o n of p o l y s t y r e n e s o l u t e i n dioxane i s shown i n F i g u r e 1. The s t r e s s r e l a x a t i o n of s w o l l e n polyurethane networks i s i l l u s t r a t e d i n F i g u r e 2. The Flory-Rehner equation (2,13) was used t o i n t e r p r e t the s w e l l i n g of the polyurethane networks i n pure dioxane i n order to c a l c u l a t e MQ, the molecular weight between c r o s s l i n k s . Here, we set q = 1 and χ , the network-solvent i n t e r a c t i o n parameter, con s t a n t and assumed equal to 0.35 ( 3 ) . Networks w i t h degrees of s w e l l i n g (q ) of 6.41, 11 and 21.1 y i e l d e d M v a l u e s of 7,700, 23,000, and 76,500, r e s p e c t i v e l y . Values of M approximating 10^ were d e r i v e d from measurements of the s o l f r a c t i o n s of these networks (11) . Such r e s u l t s d i d not c o r r e l a t e w i t h the degree of s w e l l i n g and are b e l i e v e d to be i n accurate. The s w e l l i n g data i n F i g u r e 1 were analyzed by l i n e a r program ming i n order to determine v a l u e s of M , q , and χ , assuming t h a t X i s constant f o r each network. R e s u l t s f o r the t h r e e networks are shown i n Table I . Values of q are much l a r g e r and M much s m a l l e r than expected. S t r e s s r e l a x a t i o n c a l c u l a t i o n s on the s w o l l e n networks ( F i g ure 2) a r e summarized i n Table I I . The v a l u e s of AU*q ~ / are i n f a i r l y good agreement w i t h those d e r i v e d from s w e l l i n g over p o l y mer s o l u t i o n s (Table I ) . I t i s p o s s i b l e to determine M by s e t t i n g q = 1. Then, from s t r e s s r e l a x a t i o n , the networks w i t h degrees of s w e l l i n g 6.41, 11, and 21.1 gave M v a l u e s of 14,000, 21,000, and 31,500, r e s p e c t i v e l y . An a l t e r n a t i v e and, perhaps, p r e f e r a b l e treatment of these data i n v o l v e s the method d e s c r i b e d i n the s e c t i o n on theory. In t h i s case, the i n t e r a c t i o n parameter, χ , i s assumed t o be a simple f u n c t i o n of c o n c e n t r a t i o n and s t r e s s r e l a x a t i o n and s w e l l Q

±

C

C

C

Q

Q

c

2

Q

Q

C


3

ERSHAGHI ET AL.

Polyurethane Networks

311


24.

Figure L

The degree of swelling (q) of polyurethane networks in dioxane over polystyrene solutions of various volume fractions (Φ ). 8


URETHANE CHEMISTRY AND APPLICATIONS


378

300

200

1001

Ι ο

ί

Days Time

Figure 2. Stress relaxation of a swollen polyurethane network.

Table I S w e l l i n g of Polyurethane Networks over P o l y s t y r e n e S o l u t i o n s i n Dioxane

X

q

6.41

0.720

7.92 x l O "

11.1

0.642

5.717xl0"

21.1

0.436

4.810x1ο*"*

5

5

5

M 0

c

19.4

1800

17.8

2600

16.8

3260



24.

ERSHAGHI ET AL.

Polyurethane Networks

379

Table I I S t r e s s R e l a x a t i o n of Swollen Polyurethane Networks a (gm/cm )

f (gm)

foo(gm)

q

"1.10

61

56

6.58

960

8.16xl0"

5

< 1.25

114

110

6.62

1886

6.85xl0~

5

1.32

154

147

6.79

2520

7.5 x l O "

5

1.065

50

41.5

11.38

415

4.85xl0"

5

1.24

150

144

11.41

1440

4.74xl0~

5

1.324

201

194

11.51

1940

4.78xl0"

5

1.432

272

263.6

11.65

2636

5.15xl0"

5

1.10

31

26

22.22

542

3.35xl0"

5

1.14

40

35.5

22.24

739

3.19xl0"

5

1.21

62

57

22.41

1187

3.46xl0"

5

1.32

78

73

22.86

1570

3.08xl0"

5

A

v

x

Q

2

d

qi=11.00^

qi=21.10

Urethane Chemistry and Applications - ACS Publications - American

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