Correlation Networks in Polymeric Materials Determined by Small

6

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Correlation Networks in Polymeric Materials Determined by Small-Angle Neutron Scattering L. H. SPERLING, A. M. FERNANDEZ, and G. D. WIGNALL

1

Materials Research Center No. 32, Lehigh University, Bethlehem, PA 18015

Two nonclassical methods of aggregation as detected by small-angle neutron scattering, SANS, are examined. In one case, deuteropolyethylene separates from poly ethylene on slow cooling from the melt, because of a six degree difference in their melting tempera tures. In the second case, polystyrene crosslinked with divinyl benzene was examined. The network had a delta fraction of deuterated polystyrene inserted at various points in the reaction via a substitution method. Both cases of aggregation were shown to f i t the Schelten correlation network concept, where no real center of mass motion takes place. For the polystyrene-DVB network case, the SANS experiments make i t possible to distinguish networks formed during the polymerization from those vulcanized after polymerization is complete. Polymer networks may be brought about by a c t u a l chemical c r o s s l i n k s between the polymer chains, or through a v a r i e t y of p h y s i c a l mechanisms which serve to a t t a c h the chains to each other, e i t h e r permanently or temporarily. As an example o f the p h y s i c a l a t t a c h ment o f chains, Schelten and coworkers (1-3) found t h a t , on blending hydrogenated polyethylene (H-PE) and deuterated polyethy lene (D-PE) i n the melt, unusually high molecular weights were observed by small-angle-rieutron s c a t t e r i n g , SANS, when samples were slowly cooled from the melt. Normal molecular weights were observed when the samples were r a p i d l y cooled from the melt. One of the major purposes f o r t h i s e n t i r e s e r i e s of experiments (1-3) was to study the c h a i n - f o l d i n g - r e e n t r y problem i n l a m e l l a c r y s t a l l i z e d from the bulk. I t was pointed out by S t e h l i n g , Ergas, and Mandelkern (4) that H-PE and D-PE had m e l t i n g temperatures of about 135°C and 1

Current address: Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, TN 37830.

0097-6156/84/0243-0071S06.00/0 © 1984 American Chemical Society Labana and Dickie; Characterization of Highly Cross-linked Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

72

HIGHLY CROSS-LINKED POLYMERS

129°C r e s p e c t i v e l y , about s i x degrees a p a r t . I t was f i r s t thought that on slow c o o l i n g , the d i f f e r e n c e i n m e l t i n g p o i n t caused a s i g n i f i c a n t aggregation of the deuterated chains i n the c r y s t a l l i n e m a t e r i a l r e s u l t i n g i n the high molecular weights recorded. Commonly, molecular weights were found i n the range of ten to one thousand times the primary c h a i n molecular weights. When the samples were quenched, normal molecular weights were observed. I t was then reasoned that when the blend of the two polymers was quenched, i n s u f f i c i e n t time was a v a i l a b l e to permit a s e p a r a t i o n and the m a t e r i a l remained homogeneously dispersed even i n the c r y s t a l l i n e state. More r e c e n t l y , Schelten, et a l . (5,6) developed a theory of the phenomenon c a l l e d " c o r r e l a t i o n networks" to d e s c r i b e the soc a l l e d aggregation o f D-PE i n H-PE. As opposed to an aggregate c o n s i s t i n g of regions which are enriched i n tagged molecules formed by the motion of the centers of g r a v i t y of the i n d i v i d u a l molecules, a c o r r e l a t i o n network i s formed by i n d i v i d u a l segments of d i f f e r e n t chains touching each other i n above s t a t i s t i c a l average numbers of c o n t a c t s . More r e c e n t l y , Fernandez, et a l . (7) found that the concept of the c o r r e l a t i o n network best explained t h e i r data on chemically c r o s s l i n k e d polystyrenes c o n t a i n i n g a d e l t a f r a c t i o n of deuterated p o l y s t y r e n e . In t h i s l a s t study (7) as w e l l as i n S c h e l t e n s work, very high molecular weights were found by SANS, correspond ing to a s t a t e of aggregation ranging from two to about f o r t y molecules. The purpose of t h i s paper w i l l be to d e s c r i b e the works of Schelten et a l . and Fernandez e t a l . and i l l u s t r a t e how the concept of the c o r r e l a t i o n network can provide a p h y s i c a l model f o r s i m i l a r r e s u l t s i n two very d i v e r s e m a t e r i a l s . 1

Theory The p r i n c i p l e s of neutron s c a t t e r i n g theory as a p p l i e d to the s o l u t i o n of polymer problems have been described i n a number of papers and review a r t i c l e s (8-23). The coherent i n t e n s i t y i n a SANS experiment i s given by the s c a t t e r i n g c r o s s - s e c t i o n dE/dfi, which i s the p r o b a b i l i t y that a neutron w i l l be s c a t t e r e d i n t o a s o l i d angle, Ω, f o r u n i t volume of the sample. The q u a n t i t y dE/dfi expresses the neutron s c a t t e r i n g power of a sample and i s the counterpart of the Rayleigh r a t i o , R(6), used i n l i g h t scattering. For homopolymer blends c o n s i s t i n g of deuterated (labeled) polymer molecules randomly d i s p e r s e d or d i s s o l v e d i n a protonated polymer matrix, small-angle neutron s c a t t e r i n g i n the G u i n i e r region a r i s e s from the c o n t r a s t between the l a b e l e d (deuterated) and the protonated s p e c i e s . The s c a t t e r i n g c r o s s - s e c t i o n can be expressed

Labana and Dickie; Characterization of Highly Cross-linked Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

6.

SPERLING ET AL.

Small-Angle Neutron Scattering

[

^

(K>rl =

sk

73

ts0 0 1 - 1

(1)

The q u a n t i t y M represents the weight-average molecular weight o f the deuterated polymer, and % i s a c a l i b r a t i o n constant given by w

(a -a ) C

J

N » -

L

2

Ν. ρ (l-X)X

5

"

2

1

"Ό where and ap a r e the s c a t t e r i n g lengths of normal (hydrogenated) and deuterated ( l a b e l e d ) monomer s t r u c t u r a l u n i t s . The quantity ρ i s the d e n s i t y o f the polymer, X i s the mole f r a c t i o n of l a b e l e d chains, m^ i s the mass o f the deuterated monomer s t r u c t u r a l u n i t and N^ i s the Avogadro's number. The q u a n t i t y S(k) i s the s i n g l e c h a i n form f a c t o r [ i d e n t i c a l with the Ρ(θ) f u n c t i o n used i n l i g h t s c a t t e r i n g ] , which d e s c r i b e s the conformation o f an i n d i v i d u a l l a b e l e d c h a i n . T h i s molecular s t r u c t u r e f a c t o r becomes independent of p a r t i c l e shape as the angle o f s c a t t e r θ approaches zero, and under these l i m i t i n g c o n d i t i o n s (Guinier r e g i o n , K R | < i ) becomes a measure of the r a d i u s of g y r a t i o n , R . A f t e r r e a r r a n g i n g , equation (1) becomes: 2

g

2

t f ^

-

1

- ^ -
and the polymer molecular weight, M^, may be obtained from the slope and i n t e r c e p t respec t i v e l y of a Zimm p l o t of [dZ/dft]"" v s . K . The values of ^ and Rg were evaluated a f t e r a p p r o p r i a t e s u b t r a c t i o n o f the s c a t t e r i n g from an unlabeled polymer m a t r i x (blank) from the samples c o n t a i n ing d i f f e r e n t f r a c t i o n s of l a b e l e d molecules. In the above d e r i v a t i o n i t was assumed t h a t the l a b e l e d molecules a r e f u l l y deuterated. Thus, c o n s i d e r i n g the s t r u c t u r a l u n i t s o f the hydrogenated and deuterated polystyrene as CgHs and CoDg, r e s p e c t i v e l y , a = 2.328 1 0 " cm, and a = 10.656 10~i2 cm. Thus, the d i f f e r e n c e i n s c a t t e r i n g lengths between hydrogenated and deuterated monomer repeat u n i t s (mers), (an-a ) i s 8.328 1 0 ~ cm. Equation (3) i s a p p l i c a b l e to m i s c i b l e homopolymer blends i n which the molecular s i z e d i s t r i b u t i o n o f the l a b e l e d and unlabeled polymer molecules are i d e n t i c a l . I f the s i z e d i s t r i b u t i o n s a r e d i f f e r e n t , the SANS s c a t t e r e d i n t e n s i t y contains i n f o r m a t i o n of both species; t h e r e f o r e , c o r r e c t i o n s to the measured values o f R and M a r e needed. These c o r r e c t i o n s g w 2

g

1

2

1 2

H

D

1 2

D


74


have been developed by Boue et a l . (17), and p r e v i o u s l y used by other authors (14,18). In the G u i n i e r range, the s c a t t e r i n g c r o s s - s e c t i o n under c o n d i t i o n s of mismatch i n molecular s i z e s i s given by (17): r U

W

m

i

- l

K ) 1

_

f

{

- c'

(l-X)

~¥~"

Ν

2

X +

FT

wD

2

K a +

N Z

"is"

D

( 1

"

[

~FZ—

wH

X )

, +

X N

ZH

ΤΓΓ

wD

n

(4)

]}

wH

where (a - a „ )

2

ρ N_ χ m

(1-X)

D

The weight average, N , and the Z-average, N , degree of polymer i z a t i o n of the l a b e l e d (D) and unlabeled (H) polymer chains, are r e l a t e d by: w

z

N

wH

" wD

N

( 1

+

A W )

( 6 )

N

ZH

" ZD

N

( 1

+

Δ

( 7 )

Ζ

)

9

S u b s t i t u t i n g N i n terms of N , equation (4) becomes: H

r

dE.

D

-1

,

1

g

XAw ι ,

f

2

Nza^/6 by R ,

K

2 2 g

R

and m^N^

by

/Q\

, X(AZ-Aw^

n

M^,

The c o r r e c t i o n terms i n the square brackets depend on the mis match i n the s i z e d i s t r i b u t i o n . The curve of [dE/dfi(K)I" v s . K , y i e l d s apparent values of and R . The c o r r e c t e d values may be obtained: 1

2

2

M

R

2

g

w

= M

= R

w app

2

g app

[1 +

[1 =

,

X

£ x

l+(l-X)M w

(9)

l+Aw

]

1

J

M

(10)

w

I t should be pointed out that when the molecular s i z e s of the two species are equal, Aw = ΔΖ = 0, and equation (8) reduces to (3), as expected. Experimental The method of s y n t h e s i s of the d e l t a f r a c t i o n of deuterated p o l y styrene (D-PS) i n polystyrene w i l l be b r i e f l y reviewed (7). In


6. SPERLING ET AL.


75

the f o l l o w i n g , hydrogenated and deuterated styrène, H-S and D-S, r e s p e c t i v e l y , stand f o r the o r d i n a r y monomer and the monomer with deuterium atoms i n p l a c e o f hydrogen atoms. The monomers have not been hydrogenated i n the sense of being saturated or reduced. Figure 1 i l l u s t r a t e s two d i f f e r e n t methods o f s y n t h e s i s . In the f i r s t method, hydrogenated styrene (H-S) monomer, d i v i n y l benzene (DVB), (1 mole %) and benzoin, 0.4% by weight, were sub j e c t e d to f r e e r a d i c a l p o l y m e r i z a t i o n v i a UV l i g h t exposure. The s y n t h e s i s was permitted to continue u n t i l about s i x t y to seventy per cent (60% to 70%) conversion. At that p o i n t , the remaining styrene and DVB were removed by evaporation and replaced by an e x a c t l y equal amount of deuterated styrene (D-S) and f r e s h DVB and i n i t i a t o r . The p o l y m e r i z a t i o n was then permitted to continue for another s e v e r a l per cent. D e l t a f r a c t i o n s i z e s o f 5 to 20% were obtained. A f t e r the d e l t a f r a c t i o n had been synthesized i n p l a c e , the remaining D-S and DVB were again removed by evapora t i o n , and replaced by an e x a c t l y equal amount of H-S, DVB and new i n i t i a t o r . Then the r e a c t i o n was permitted to continue to comple t i o n v i a UV exposure. In a second s y n t h e t i c method (7), D-PS was formed from a mixture o f D-S and DVB by p e r m i t t i n g the r e a c t i o n to proceed to about t e n (10%) per cent. The r e s u l t a n t s t i l l s o l u b l e polymer was then p r e c i p i t a t e d and recovered. Two per cent (2%) by weight of t h i s deuterated polymer was then d i s s o l v e d i n H-S, DVB, and benzoin. T h i s s o l u t i o n was then permitted to polymerize u n t i l the e n t i r e mixture was f u l l y r e a c t e d . As before, f r e e - r a d i c a l chemistry was employed i n the p o l y m e r i z a t i o n v i a UV i n i t i a t i o n . It must be s t r e s s e d that f r e e - r a d i c a l p o l y m e r i z a t i o n was used, and not an a n i o n i c p o l y m e r i z a t i o n . The l a t t e r , o f course, has been used widely i n the s y n t h e s i s o f polymers f o r SANS experiments. The two methods r e s u l t i n q u i t e d i f f e r e n t polymers, the f r e e r a d i c a l synthesis y i e l d i n g a broader molecular weight d i s t r i b u t i o n than the a n i o n i c method. C o r r e l a t i o n Networks As mentioned above, a long-standing problem i n polymer science has been the supermolecular o r g a n i z a t i o n of polymeric c r y s t a l s . A f t e r K e l l e r (24) discovered the presence o f s i n g l e c r y s t a l s of polyethylene i n 1957, people became i n t e r e s t e d i n the concept of c h a i n - f o l d i n g . Several models evolved. These included the switch board model, which suggests that r e - e n t r y o f polymer molecules i n t o a p a r t i c u l a r l a m e l l a i s random. Another model suggested that r e g u l a r f o l d i n g and r e - e n t r y was more probable. While i n f r a red s t u d i e s (25) were used t o c h a r a c t e r i z e the c r y s t a l r e - e n t r y problem, b a s i c a l l y t h i s remained an incompletely solved problem u n t i l the advent of small-angle neutron s c a t t e r i n g . ( I t must be remarked that a f t e r t e n years o f small-angle neutron s c a t t e r i n g research, the problem i s s t i l l unresolved although we know much more about i t . )


76


One o f the main c o n c l u s i o n s from these experiments (8,9,24) was that when the blend of hydrogenated and deuterated p o l y e t h y lene was cooled slowly from the melt, SANS experiments showed molecular weights many times the s i z e o f the molecular weight of the primary c h a i n s . In c o n t r a s t , the expected molecular weights were obtained when the polymers were quenched from the melt. Schelten e t a l . (5,6) showed that the r a d i u s o f g y r a t i o n , Rg, depended on the apparent s t a t e o f aggregation, N, (R ) = (R ) , N g agg g single

1 / 2

Ί

(11)

where M

agg

= NM . , single

(12)

and M gg i s the aggregate molecular weight determined by SANS and ^ s i n g l e * ^ P * a r y c h a i n molecular weight, as determined by GPC or i n t r i n s i c v i s c o s i t y . Equation (11) can be expressed d i r e c t l y i n terms of the aggregated molecular weight, g g > a

s t

i e

r

m

M

a

1 / 2

(R ) = Κ'Μ 8 agg agg

(13)

For a l l polymers studied i n the bulk amorphous s t a t e , the r a d i u s o f g y r a t i o n was found t o go as the molecular weight to the 1/2 power, s u b s t a n t i a l l y the same as was found i n F l o r y - t h e t a s o l v e n t s . Equations (11) and (13) express a circumstance where i n d i v i d u a l chains a r e connected together to form a much longer super c h a i n . Schelten and coworkers (5,6) pointed out that r e l a t i v e l y few deuterated i n t e r m o l e c u l a r contacts above that expected s t a t i s t i c a l l y a r e r e q u i r e d to produce s u b s t a n t i a l l y higher mole c u l a r weights than would be expected f o r the i n d i v i d u a l primary chains. To i l l u s t r a t e the e f f e c t o f slow-cooling and quenching from the melt on the apparent molecular weight and s i z e of the chain, some of the data o f Schelten, e t a l . (4) a r e reproduced i n Table I. I t i s seen that the aggregated molecular weights can be as high as s e v e r a l hundred times the primary molecular weight. Schelten and coworkers expressed the one-half power molecular weight dependence o f the r a d i u s o f g y r a t i o n f o r the aggregates, equations (11) and (13), i n terms of a new type o f network which they c a l l e d a " c o r r e l a t i o n network". As opposed to a r e g u l a r aggregation o r phase s e p a r a t i o n , a c o r r e l a t i o n network merely r e q u i r e s that the chains o f one of the components has a g r e a t e r p r o b a b i l i t y of touching other members o f the same component above that of the other components. In touching each other s t a t i s t i c a l l y on an above average frequency, the SANS instrument "sees" a l a r g e r molecule.


6. SPERLING ET AL. Table I .


D-Polyethylene i n Η-Polyethylene: SANS Results f o r D i f f e r e n t Thermal H i s t o r i e s

H-PE Sample No.

77

c (gm/gm)

ΡΕ31

0.31

PE35

0.053

PE37

0.051

M xlO" w 217

D-PE 3

M xlO" w

Quenched 3

Slow Cooled

Ν

Ν

R (A) β

15.5

1130

510

0.99

399

41.5

54

1.00

131

140

913

15.7

17

1.80

100

721

2000

In order to t e s t t h e i r hypothesis o f a c o r r e l a t i o n network being formed, Schelten e t a l . (6) prepared s e v e r a l H-PE and D-PE blended samples and gamma-irradiated them i n the melt and a l s o i n the quenched c r y s t a l l i n e s t a t e . Of course, gamma i r r a d i a t i o n causes a c t u a l chemical c r o s s l i n k i n g . Schelten and coworkers t h e o r i z e d that i f aggregates were b u i l t up by the c o r r e l a t i o n mechanism, they should occur o r disappear on c o o l i n g and heating r e s p e c t i v e l y , i r r e s p e c t i v e o f the extent o f gamma i r r a d i a t i o n . On the other hand, i f r e a l aggregates i n the sense o f phase separation were forming, then center-of-mass motion would be taking p l a c e which would be hindered by the presence o f r e a l chemical c r o s s l i n k s . The major f i n d i n g of t h i s paper (6) was that the degree o f "aggregation" was not a f f e c t e d a t a l l by the extent o f i r r a d i a t i o n or by i t s absence. Thus Schelten concluded that the chain's center o f mass could not be moving very f a r during the formation of the c o r r e l a t i o n networks. The D e l t a Deuterated F r a c t i o n Method More r e c e n t l y , Fernandez and coworkers (7) prepared networks o f polystyrene with DVB, i n s e r t i n g a d e l t a - f r a c t i o n o f deuterated m a t e r i a l as d e s c r i b e d i n the experimental s e c t i o n . The o r i g i n a l o b j e c t i v e of t h i s experiment was t o provide a study o f p o l y s t y r e n e conformation i n network form before going on t o preparing i n t e r penetrating polymer networks out of t h i s m a t e r i a l . T h i s was the p r i n c i p a l reason that the H-S or D-S was replaced during the syn t h e s i s i n q u a n t i t i e s e x a c t l y equal t o that removed so that the network s t r u c t u r e already formed would not be d i s t u r b e d , and the o r i g i n a l unperturbed dimensions would be r e t a i n e d . As i t was, the major method of s y n t h e s i s employed, that of i n s e r t i n g a d e l t a f r a c t i o n of 5% t o 20% of D-PS somewhere a f t e r 60% of polymeriza t i o n of Η-PS, r e s u l t e d i n a s t a t e of aggregation which was


78


detected i n two independent runs a t Oak Ridge using the 30-meter SANS instrument. Results The extent of conversion of the p o l y s t y r e n e network was examined as a f u n c t i o n of time, see F i g u r e 2. [In t h i s experiment, l i n e a r polystyrene was employed r a t h e r than d e c r o s s l i n k e d polystyrene (26).] The major p o i n t o f i n t e r e s t i n the p o l y m e r i z a t i o n curve, Figure 2, i s the onset of the Trommsdorff e f f e c t , sometimes c a l l e d a u t o a c c e l e r a t i o n . As i s w e l l known, the molecular weight i n creases r a p i d l y a f t e r the onset of the Trommsdorff e f f e c t . Molecular weights were determined as a f u n c t i o n of conversion by gel-permeation chromatography, GPC. T h i s data i s i l l u s t r a t e d i n Table I I . Of p a r t i c u l a r i n t e r e s t i n Table I I are the weightaverage molecular weights and the d i s p e r s i o n , which i s weightaverage molecular weight d i v i d e d by number-average molecular Table I I . Molecular Weights as f u n c t i o n of Conversion by Gel Permeation Chromatography, GPC. Extent of

% 9.51

Conversion

4

M

10~ η gms/mol

M

10~* w gms/mole

D w

3.9

6.1

1.57

20.6

3.9

6.4

1.67

39.0

4.0

6.5

1.63

60.0

4.1

6.5

1.61

70.8

4.3

7.4

1.71

74.6

4.5

7.8

1.74

90.7

5.5

10.0

1.85

96.9

5.3

19.0

3.53

99.1

5.7

23.0

4.02

99.3

6.6

35.0

5.24

η

weight. I t w i l l be noted that the weight average molecular weight i s i n the range of 60,000 to 100,000 up to 90% conversion. Above about 90% conversion, molecular weight increases very r a p i d l y . The d i s p e r s i o n l i k e w i s e remains n e a r l y constant i n the range of about 1.6 up t o about 90% conversion. The value of 1.6 f o r M /M means that two major p o l y m e r i z a t i o n mechanisms: c h a i n t r a n s f e r and t e r m i n a t i o n by d i s p r o p o r t i o n a t i o n together must occur i n very l i m i t e d amounts. T h i s was estimated a l g e b r a i c a l l y as being more than 25% to 40% of the t o t a l . The major termination mechanism w


n


SPERLING ET AL.

The Deuterated

Delta Fraction Synthesis

Yielded Aggregate

MW:

Η-PS

D-PS 60

Yielded Primary Chain D-PS 0

H-PS 75

100%

MW:

.Reaction Stopped

-10

Precipitated 2%wt.D-PS Redissolved in HS

0

100%

% conversion F i g u r e 1.

The deuterated

Oi 0

.

.

.

.

delta f r a c t i o n synthesis.

. 50

-

.

.

.

_ 100

TIME IN HOURS F i g u r e 2.

Rate of polymerization of l i n e a r

polystyrene.


80


f o r polystyrene f r e e r a d i c a l p o l y m e r i z a t i o n i s known to be termination by combination, which y i e l d s a weight to number average molecular weight of 1.50. The other two mechanisms of course, y i e l d molecular weight d i s p e r s i o n s i n the range of 2.0. T h i s l a t t e r w i l l be of great s i g n i f i c a n c e i n e v o l v i n g a model to d e s c r i b e the f i n a l r e s u l t s . The molecular weight as a f u n c t i o n of conversion i s f u r t h e r i l l u s t r a t e d i n F i g u r e 3. Not only are the number- and weightaverage molecular weights shown but a l s o the instantaneous mole c u l a r weight, which i s obtained from the slope of the weightaverage curve. The instantaneous molecular weight i s the molecu l a r weight of polymer a c t u a l l y being formed at that p a r t i c u l a r i n s t a n t of time. T h i s i s p a r t i c u l a r l y important because when the d e l t a - f r a c t i o n s were prepared the molecular weight a t i n s e r tion i s required. I n c i d e n t a l l y , i t should be remarked that even though l i n e a r polymers were employed i n the determination of the molecular weights i n Table I I as w e l l as the data i n F i g u r e 3, i t i s known from p r i o r experiments that the molecular weights of the primary chains are the same as they are i f they were p a r t of an a c t u a l chemical network. S p e r l i n g et a l . (26) f o r example, prepared polystyrene networks c r o s s l i n k e d with a c r y l i c a c i d anhydride which i s e a s i l y hydrolyzed with ammonia water to produce the l i n e a r polymer. In a s e r i e s of experiments, S p e r l i n g , et a l . (26) determined that the molecular weights of a p o l y s t y r e n e a c r y l i c a c i d anhydride network a f t e r h y d r o l y s i s had a weight-average molecular weight of about 350,000 grams/mole. This compares to the value obtained by Fernandez et a l . who found weight-average molecular weights of j u s t over 300,000 gms/mole i n a s i m i l a r l i n e a r polymer s y n t h e s i s , Table I I . The r e s u l t s from small-angle neutron s c a t t e r i n g are summar i z e d i n Figures 4 and 5. In F i g u r e 4, a normal molecular weight of 70,000 grams/mole and an R value of 121 A was obtained. In F i g u r e 5, a molecular weight of about 15 times that of the primary chains i s shown with the corresponding increase i n Rg v a l u e s . In a l l , a t o t a l of seven samples were examined as i l l u s t r a t e d i n Table I I I . Sample 1 was prepared by adding the 2% of preformed D-PS mix c o n t a i n i n g the DVB and benzoin. Samples 2 through 7 were prepared by the deuterated d e l t a - f r a c t i o n technique, and a l l showed molecular weights very much higher than expected. These molecular weights range from about one to n e a r l y f o r t y times the molecular weights expected from the GPC measurements performed, as described above. The s t a t e of aggregation o f these m a t e r i a l s , samples 2 thru 7, i s shown i n Table IV, i n order of i n c r e a s i n g s t a t e of aggregation. I t w i l l be observed that the s t a t e of aggregation appears to i n c r e a s e as the s i z e o f the d e l t a - f r a c t i o n decreases. An extrapo l a t i o n to zero d e l t a - f r a c t i o n s i z e was performed, data not shown, and approximately an aggregation s t a t e of f o r t y was deduced. (f course, f o r very l a r g e d e l t a - f r a c t i o n s i z e s , the sample develops g


6. SPERLING ET AL.


81

36

\ CO £ Ο oc
ΔΖ 2

83


= Μ

,

l+l(l-x)Aw xAw " l+Aw

Table IV.

Sample No. 2 5 7 4 6 3

State o f Aggregation Size Delta Fraction Size, %

Μ 10" w

20.1 13.9 13.9 10.2 10.0 5.38

8.0 8.5 8.0 11.8 10.5 23.5

SANS

5

(a)

as a Function o f D e l t a F r a c t i o n

M

w

1 0

GPC

~ ( b )

5

Ν Aggregation Number

17.0 2.78 0.82 0.98 0.78 0.88

Ν Mismatch Corrected

(1) (c) 3 10 12 13 27

(1) 4 11 15 16 34

(a) M (SANS uncorrected w

f o r degree of p o l y m e r i z a t i o n mismatches,

^ I n s t a n t a n e o u s molecular weight ( f i g u r e 3 ) . (c) T h i s sample was a f f e c t e d by the Trommsdorff e f f e c t , and i t s molecular weight i s known with l e s s c e r t a i n t y than the other samples.



84

a c e r t a i n degree of c o n t i n u i t y , and one would not expect the theory to h o l d . The molecular weights shown i n the two preceding t a b l e s , i t must be remarked, were c o r r e c t e d f o r the d i f f e r e n c e s i n weightaverage molecular weight between the deuterated f r a c t i o n and the o v e r a l l m a t e r i a l , as i l l u s t r a t e d i n the t h e o r e t i c a l s e c t i o n . As i s seen from Table I I I , the c o r r e c t i o n s of the weight-average molecular weight are of the order of 5% or 10% i n most cases. Table V shows a c a l c u l a t i o n of the corresponding weightaverage r a d i i o f g y r a t i o n c a l c u l a t e d from the z-average r a d i i of g y r a t i o n . More importantly, Table V a l s o shows that the molecular weights obtained vary as equations (11) and (13) with respect to t h e i r r a d i i of g y r a t i o n .

Table V.

Comparison of weight-average r a d i i of g y r a t i o n , R from Molecular S i z e Mismatch Corrected M . W

%

W

η

7

w

R

V

g Sample

No.

From M

7 2

1 2 3 4 5 6 7 (a) R

w

8g

8

(a)

=

[R

w

= 0.275M

R i

s n

S ± n g

g

x

N b

From (a)]

S

(b)

72 272 420 279 144 288 239

272 476 328 275 305 265

g

S

, data from Table I I I . w

ο

(b) A l l values i n Angstroms. g

g

g

(c) From the r e l a t i o n R = R N (using values of • g 8 R (R , s i n g l e chain) equal to 7 2 Â , the c o r r e c t e d g g values of N, and a value of b=0.50). S

i

n

g

Equation (11) can be g e n e r a l i z e d to read: agg

R

g

m

R

sing b N

(

u

)

g

where b i s a constant to be determined by experiment. By p l o t t i n g l o g Rg v s . l o g N, data not shown, i t was determined that the expo nent b was equal to 0.50 w i t h i n experimental e r r o r , see Table V.


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85

Discussion Several models could be imagined which could e x p l a i n the above polystyrene data. Four p o s s i b i l i t i e s are i l l u s t r a t e d i n F i g u r e 6. F i r s t of a l l , one very long chain a c t u a l l y having a molecular weight of one to two m i l l i o n might be imagined. However, the GPC values which y i e l d e d molecular weights of 60,000 to 70,000 gm/mole b e l i e t h i s model, and hence i t was d i s c a r d e d . Chain t r a n s f e r might be considered a l s o . Then one would have s e v e r a l long chains which are placed end on end. In a network s y n t h e s i s , they would be h e l d more or l e s s i n p l a c e . These super chains would have the c o r r e c t r e l a t i o n s h i p between the r a d i u s of g y r a t i o n and the molecular weight. However, i t i s known that the extent of chain t r a n s f e r permitted by the molecular weight d i s t r i b u t i o n i s f a r too small to e x p l a i n the r e s u l t s by t h i s mechanism. A t h i r d mechanism i s due to Bobalek et a l . (37) and Labana et a l . (28), who p o s t u l a t e d that there are s e r i e s of small g e l s which are formed during the e a r l y p a r t of a network p o l y m e r i z a t i o n . I t i s w e l l v e r i f i e d experimentally that i n the e a r l y stage of polymerization of a network, one has a c o l l e c t i o n of microgels, l i n e a r polymer, and monomer. Of course, by f r e e r a d i c a l polymeri z a t i o n , there i s very l i t t l e l i v i n g or growing polymer at any point i n time, while by condensation p o l y m e r i z a t i o n a l i g i o m e r i c species may dominate at a c e r t a i n p e r i o d of time. The presence of small g e l s dispersed i n monomer suggests regions of r e l a t i v e l y high and low monomer c o n c e n t r a t i o n i n a p a r t l y polymerized network. If the deuterated monomer i s added i n the d e l t a f r a c t i o n manner, the deuterated polymer w i l l tend to form s p h e r i c a l shaped regions which would have a super molecular weight dependence of the r a d i u s of g y r a t i o n of o n e - t h i r d . However, the molecular weight depen dence of the r a d i u s of g y r a t i o n i s 0.50, r a t h e r than o n e - t h i r d . Therefore, t h i s mechanism was a l s o set a s i d e . As explained above, Schelten et a l . (5,6) have developed a c o r r e l a t i o n network which p r e d i c t s the 0.5 power behavior of the exponent b. In f a c t , an exact q u a n t i t a t i v e agreement with the Schelten c o r r e l a t i o n network was obtained. The mechanism of c o r r e l a t i o n network formation i s described i n Figure 7. The c o r r e l a t i o n network of D-PE i s formed on c o o l i n g from the melt through the formation of an above-average number of contacts, s t a t i s t i c a l l y , between deuterated chains. This a r i s e s as f o l l o w s . In a formation of a D-PS d e l t a - f r a c t i o n , the chains have an a b o v e - s t a t i s t i c a l average p r o b a b i l i t y of being connected to each other, because chains r e c e n t l y formed have a l a r g e r than average number of pendant v i n y l groups. Of course as time passes, these v i n y l groups are reacted to form p a r t of the network. Thus, chains polymerized w i t h i n a short time of each other have a g r e a t e r than average p r o b a b i l i t y of being reacted with each other, and hence t h i s i s picked up by small-angle neutron s c a t t e r i n g to g i v e an apparent increase i n molecular weight. I t must be emphasized that the aggregation noted i n the


86


One long chain (but GPC shows M~7 HOT)

Shelten's correlation network R - M * 0

Figure 6.

5

Several short chains by chain transfer (but chain transfers25-40%)

Bobalek- Labana gel (but R - M ^ ) 3

Models f o r p o l y m e r i z a t i o n aggregation.

Melt Crystalline Formation of Systematic Points of Contact

Free Radical Synthesis Crosslinked Network Crosslinks Can Form Systematic Point of Contact F i g u r e 7. C o r r e l a t i o n networks f o r s e m i - c r y s t a l l i n e polymers and f o r d e l t a f r a c t i o n chemical networks.


6.

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87

present system i s h i g h l y unusual. P r e v i o u s l y , blends of a t a c t i c Η-PS and D-PS have been examined by SANS techniques (13,29), and these s t u d i e s r e p o r t the expected s i n g l e chain molecular weights. Thus, the phenomenon i s caused by the d e l t a f r a c t i o n sample prepa r a t i o n technique, r a t h e r than being a general phenomenon. Conclusions The term c o r r e l a t i o n network d e s c r i b e s v a r i o u s polymer systems where the chains have a g r e a t e r than average p r o b a b i l i t y of being i n contact with each other. In the case of c r y s t a l l i z i n g blends of D-PE and H-PE a c o r r e l a t i o n network i s caused by the s l i g h t l y d i f f e r e n t c r y s t a l l i z i n g temperatures of D-PE and H-PE. Extensive center of mass motion of the deuterated chains towards each other i s not r e q u i r e d . In the case of the PS-DVB networks, aggregates of from about 1 to 34 D-PS molecules were formed with r a d i i of g y r a t i o n ranging upwards to 350 to 400Â. The Schelten c o r r e l a t i o n network model seems to f i t the present data b e t t e r than other models at t h i s time. I t should be noted that these chains are a c t u a l l y chemically c r o s s l i n k e d to each other. The higher than s t a t i s t i c a l p r o b a b i l i t y of chemically connecting two chains that are reacted at n e a r l y the same p o i n t i n time during the p o l y m e r i z a t i o n leads to a very high molecular weight by SANS instrumentation. In t h i s system, l i k e w i s e , i t i s not necessary f o r the centers of mass of the chains to have moved. Thus, i t i s concluded that the system i s not aggregated i n any r e a l sense of the term, except that there i s a preference f o r chains that are polymerized i n the same time period to be chemically attached to each other. Since deuterated chains were formed i n the d e l t a - f r a c t i o n method, t h i s l e d to the apparent increase i n the molecular weight. Most importantly the present experiment provides a new method of e v a l u a t i n g the proba b i l i t y of two chains being l i n k e d during a network p o l y m e r i z a t i o n . This experiment a l s o d i s t i n g u i s h e s between a network formed by v u l c a n i z a t i o n , i . e . , c r o s s l i n k i n g a f t e r p o l y m e r i z a t i o n , and c r o s s l i n k i n g during p o l y m e r i z a t i o n . To t e s t the ideas i n t h i s paper f u r t h e r , PS d e l t a f r a c t i o n polymerizations should be conducted with the c r o s s l i n k e r systema t i c a l l y omitted from the v a r i o u s p a r t s of the p o l y m e r i z a t i o n shown i n F i g u r e 1. Acknowledgment s The authors wish to acknowledge f i n a n c i a l support through the Polymers Program of the N a t i o n a l Science Foundation, Grant Number DMR-8106892. The SANS experiments were performed at NCSAR, funded by NSF Grant Number DMR-7724458 through interagency agreement Number 40-637-77 with DOE.


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Literature Cited 1. Schelten, J.; Wignall, G. D.; Ballard, D. G. H. Polymer. 1974, 15, 682. 2. Schelten, J.; Wignall, G. D.; Ballard, D.G.H.; Schmatz, W. Colloid Polymer Sci. 1974, 252, 749. 3. Wignall, G. D.; Ballard, D. G. H.; Schelten, J. J. Appl. Phys. 1976, (B)12, 75. 4. Stehling, F. S.; Ergos, E.; Mandelkern, L. Macromolecules. 1971, 4, 672. 5. Schelten, J.; Wignall, G. D.; Ballard, D. G. H.; Longman, G. W. Polymer. 1977, 18, 1111. 6. Schelten, J.; Zinken, Α.; Ballard, D. G. H. Colloid Polym. Sci. 1981, 259, 260. 7. Fernandez, A. M.; Widmaier, J. M.; Sperling, L. H.; Wignall, G. D. submitted, Polymer. 1983. 8. Sperling, L. H.; submitted, Poly. Eng. Sci. 1983. 8a. Maconnachie, Α.; Richards, R. W. Polymer, 1978, 19, 739. 9. Higgins, J.S.; Stein, R. S. J. Appl. Cryst. 1978, 11, 346. 10. Schmitt, B. J. Angew. Chem. Int. Ed. Eng. 1979, 18, 273. 11. Kirste, R. G. Kruse, W. Α.; Schelten, J. J. Makromol. Chem. 162, 299. 12. Ballard, D.G.H.; Wignall, G.D.; Schelten, J. Europ. Polym. J. 1983, 9, 965. 13. Wignall, G. D.; Ballard, D. G. H.; Schelten, J. Eur. Polym. J. 1974, 10, 861. 14. Benoit, H.; Decker, D.; Duplessix, R.; Picot, C.; Rempp, P.; Cotton, J. P.; Farnoux, B.; Jannick, G.; Ober, R. J. Polym. Sci., Polym. Phys. Ed. 1976, 14, 2119. 15. Clough, S.; Maconnachie, Α.; Allen, G. Macromolecules. 1980, 13, 774 16. Hinkley, J. Α.; Han, C.C.; Mozer, B.; Yu, H. Macromolecules. 1978, 11, 836. 17. Ullman, R. in "Elastomers and Rubber Elasticity"; Mark, J.E.; Lal, J., Eds.; ACS SYMPSOIUM SERIES No. 193, American Chemi cal Society: Washington, DC, 1982. 18. Ullman, R. Macromolecules. 1982, 15, 1395. 19. Ullman, R. Macromolecules. 1982, 15, 582. 20. Wignall, G. D.; Child, H. R.; Samuels, R.J. Polymer. 1982, 23, 957. 21. Koehler, W. C.; Hendricks, R. W.; Child, H.R.; King, S. P.; Lin, J.S.; Wignall, G.D. Proceedings of NATO Advanced Study Institute on Scattering Techniques Applied to Supramolecular and Nonequilibrium Systems. 1981, p. 75. 22. Boue, F.; Nierlich, M.; Leiber, L. Polymer. 1982, 23, 29. 23. Crist, B.; Graessley, W. W.; Wignall, G. D. Polymer. 1982 23, 1561. 24. Keller, Α.; Phil. Mag. 1957, 2, 1171. 25. Tatsumi, M.; Krimm, J. J. Polym. Sci. 1968, A-2,6, 995.


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26.

Sperling, L. H.; Ferguson, Κ. Β.; Manson, J. Α.; Corwin, Ε. M.; Siegfried, D. L. Macromolecules. 1976, 9, 743. 27. Bobalek, E. G.; Moore, E. R.; Levy, J. S.; Lee, C. C. J. Appl. Polym. Sci. 1964,8,625. 28. Labana, S. S.; Newman, S.; Chompff, A. J., in "Polymer Networks: Structure and Mechanical Properties"; Chompff, A. J.; Newman, S., Eds; Plenum. 1971. 29. Cotton, J.P.; Decker, D.; Benoit, H.; Farnoux, B.; Higgins, J.A.; Jannink, G.; Ober, R.; Picot, C.; desCloizeaux, J. Macromolecules. 1974, 7, 863. RECEIVED November 3, 1983


Correlation Networks in Polymeric Materials Determined by Small

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