21 Determination of Thermoset Resin Cross-link Architecture by Gel Permeation Chromatography A. J. AYORINDE, C. H. LEE, and D. C. TIMM University of Nebraska, Lincoln, NE 68588-0126
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W. D. HUMPHREY Brunswick Corporation, Lincoln, NE 68504
Gel permeation chromatography is the method of choice for analysis of thermoplastic resin systems. Corrected for imperfect resolution, chromatogram interpretation yields accurate molecular descriptions, including theoretical, kinetic distributions (1,2). The current research is designed to extend the utility of this analytical tool to the analysis of thermoset resins. Kinetic mechanisms (3) are such that low molecular weight species are present in a cured resin; in fact, the molar concentration of dimers, trimers, etc. usually exceeds that for higher molecular weight species. An exception is a Poisson distribution, but oligomeric species are still abundant. If a cured thermoset resin is prepared such that a large surface area to volume ratio is achieved, solvent leaching provides an effective method for sample preparation. Analysis of extracts (4,5) provides data descriptive of monomeric content and oligomeric, molecular distributions. Such extracts contain definitive information with respect to the extent of cure as well as a description of the crosslink architecture. Average m o l e c u l a r weights between c r o s s l i n k s i t e s p l u s c r o s s l i n k d e n s i t y w i t h i n the i n s o l u b l e , r e s i n f r a c t i o n can be determined. Observations f o r cured epoxy r e s i n s and r e s i n s d e r i v e d from 1,2-polybutadiene c r o s s l i n k e d w i t h t - b u t y l s t y r e n e a r e r e p o r t e d . These r e s i n s f i n d a p p l i c a t i o n s i n aerospace i n d u s t r y , i n c l u d i n g h i g h performance, K e v l a r 49, f i l a m e n t wound, pressure v e s s e l s on Skylab and the Space S h u t t l e . P o p u l a t i o n Density D i s t r i b u t i o n s Chain-growth p o l y m e r i z a t i o n . A 1 , 2 - p o l y b u t a d i e n e polymer i s crosslinked with t-butylstyrene, u t i l i z i n g a free r a d i c a l i n i t i a t o r . Reaction r a t e s i n c l u d e 0097-6156/84/0245-0321 $06.00/0
© 1984 American Chemical Society
Provder; Size Exclusion Chromatography ACS Symposium Series; American Chemical Society: Washington, DC, 1984.
SIZE E X C L U S I O N C H R O M A T O G R A P H Y
322
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Initiation Propagation Branching Terminât i o n
I
-> 2 Â
The 1 , 2 - p o l y b u t a d i e n e i n i t i a l l y formulated i s a commercially a v a i l a b l e m a t e r i a l s u p p l i e d by Colorado S p e c i a l t y Company and Nippon Soda. An a n i o n i c p o l y m e r i z a t i o n , i n i t i a t e d by a b u t y l l i thium, i s l i k e l y used i n i t s manufacture. This r e s u l t s i n a mol ar d i s t r i b u t i o n of c o n s t i t u t i v e molecules d e f i n e d by a Poisson d i s t r i b u t i o n f o r batch p o l y m e r i z a t i o n s . Thus, the number and weight average molecular weights are n e a r l y equal. The c u r r e n t r e s e a r c h f u r t h e r assumes that t h i s d i s t r i b u t i o n i s s u f f i c i e n t l y narrow such t h a t a l l polybutadiene molecules are of the same mol e c u l a r weight, which i s described by the degree of p o l y m e r i z a t i o n n. This c o n s t r a i n t g r e a t l y s i m p l i f i e s the mathematical d e s c r i p t i o n to be developed f o r the p o p u l a t i o n of molecules during the subsequent chain-growth cure i n i t i a t e d by dicumyl peroxide. F i s h e r ( 6 ) , i n a d i s c u s s i o n of r e l a t i v e r a t e s of r e a c t i o n , s t a t e s that the s t y r e n i c f r e e r a d i c a l i s more l i k e l y to r e a c t w i t h a styrene molecule than w i t h the polyunsaturated 1,2-polybu tadiene. The r e l a t i v e r a t e s are expected to d i f f e r by orders i n magnitude. Therefore, the propagation r e a c t i o n r a t e i s expressed i n terms of the m o l e c u l a r l y mobile monomer, t - b u t y l s t y r e n e . The consequence i s t h a t the 1,2-polybutadiene w i l l be c r o s s l i n k e d p r i m a r i l y by t - b u t y l s t y r e n e segments. The e x t r a c t s from a q u a l i t y r e s i n c o n t a i n o l i g o m e r i c mole c u l e s of a degree of p o l y m e r i z a t i o n l e s s than t h a t f o r the 1,2polybutadiene. These s p e c i e s are a consequence of simultaneous propagation and t e r m i n a t i o n r e a c t i o n s . Their p o p u l a t i o n d e n s i t y d i s t r i b u t i o n i s a l s o d e s c r i p t i v e of t h a t p o r t i o n of molecules which r e a c t w i t h polymeric s p e c i e s , i n i t i a l l y forming a branched, and l a t e r a c r o s s l i n k e d , s t r u c t u r e w i t h i n the r e s i n . Research shows that the average molecular weight of the o l i g o m e r i c f r a c t i o n c o r r e l a t e s w i t h the c r o s s l i n k average molecular weight w i t h i n the i n s o l u b l e , c r o s s l i n k e d r e s i n f r a c t i o n ( 7 ) . Such i s a k i n e t i c consequence of the c o m p e t i t i o n between branching and t e r m i n a t i o n r e a c t i o n s i n the above r e a c t i o n model. For f r e e r a d i c a l species of degree of p o l y m e r i z a t i o n l e s s than that f o r the 1,2-polybutadiene used i n the f o r m u l a t i o n , a k i n e t i c r e a c t i o n a n a l y s i s r e s u l t s i n the f o l l o w i n g r e l a t i o n s h i p s expressed i n terms of the molar c o n c e n t r a t i o n of primary f r e e radicals A . ο dA dt
Provder; Size Exclusion Chromatography ACS Symposium Series; American Chemical Society: Washington, DC, 1984.
21.
Thermoset Resin Cross-link
AYORINDE E T A L
_i..
ο - km
0
p
ΤΟΤ
p
l - A Ck M)V(k M +
A
+ Ι^Ρ
_ n. The consequence i s t h e formation of a f r e e r a d i c a l of molecular s i z e j + m. Furthermore, due t o the r e l a t i v e l y h i g h c o n c e n t r a t i o n i n i t i a l l y of t h e 1,2-polybutadiene c o n s t i t u e n t a t j = n, the d e r i v a t i o n assumes that a l l polymeric species o f s i z e j >_ η a r e unsaturated and a r e capable of branch and/or c r o s s l i n k formation. Polymeric species a r e denoted by Ρj; f r e e r a d i c a l intermediates a r e described by A j . Therefore, the f i r s t a c t i v a t e d intermediate capable of formation by branching r e a c t i o n s i s A i r i a A Q + P + A . Conservation laws y i e l d T Q T
T Q T
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+
Q
n
N
n
dA IT
=
° - p n - l -V k
m
VTOT
+
V W
+
A
n
+
W n
n V o V V ® As the degree of p o l y m e r i z a t i o n i n c r e a s e s , a l l p o s s i b l e combina t i o n s of r e a c t i o n s forming a f r e e r a d i c a l v i a branching must be considered. Thus dA A
+
Ί
- 3 P - 0 - k MA -(k M + p
n
p
ν
τ
0
Γ
V
+
^
A
^
V V n
+
l
+
A
l V
Previous expressions f o r A^ and A^ can be s u b s t i t u t e d , y i e l d i n g A k. A 2P n+1
^n+1 D
k MD ρ
v
n+1
D
}
Provder; Size Exclusion Chromatography ACS Symposium Series; American Chemical Society: Washington, DC, 1984.
SIZE EXCLUSION CHROMATOGRAPHY
324
The f a c t o r 2 i s a consequence o f the second term i n the expres s i o n f o r An and the term k A ] P i n t h e c o n s e r v a t i o n expression n+l/ * degree o f p o l y m e r i z a t i o n j = η + 2 dA b
d A
d t
A
n
t a
9
S u b s t i t u t i o n of the s e v e r a l expressions f o r Α^χ» Αχ, A£ and a c o l l e c t i o n of s i m i l a r terms y i e l d s A Downloaded by COLUMBIA UNIV on September 19, 2017 | http://pubs.acs.org Publication Date: March 30, 1984 | doi: 10.1021/bk-1984-0245.ch021
n+2
D
k, A
n+2
+
k MD
3V
2P
1
n+2
p
D
n
D
2'
This type of r e c u r r i n g formula represents the molar concen t r a t i o n o f f r e e r a d i c a l s up t o a degree of p o l y m e r i z a t i o n j = 2 n - l . At molecular weights twice t h a t of t h e i n i t i a l 1,2-polybutadiene, j=2n, the i n i t i a l s u b s t i t u t i o n o f the expression f o r A i n t h e r a t e of formation due t o branching occurs and r e s u l t s i n a second major change i n t h e o v e r a l l f u n c t i o n a l i t y o f t h e d e s c r i p t i v e r e l a t i o n s h i p f o r the c o n c e n t r a t i o n of a c t i v a t e d i n t e r m e d i a t e s . Consider the c o n s e r v a t i o n laws a t t h i s degree of p o l y m e r i z a t i o n n
d A
2n 1 Γ Λ
^
ΐ
Λ
^
^
W
o
W 2 n - 1 + A
P
+
+ A
n-l n l nV +
S o l v i n g t h i s expression f o r a f t e r expressing A j , 1 n '
D
D
Ρ
Thus, the a d d i t i o n of a t h i r d f u n c t i o n occurs f o r the f i r s t time at j=2n. C o n t i n u a t i o n o f the d e r i v a t i o n w i l l r e s u l t i n a s e r i e s of r a t h e r complex f u n c t i o n a l i t y , but one which w i l l be mathema t i c a l l y defined. The degree o f p o l y m e r i z a t i o n i n t e r v a l s of i n t e r e s t a r e , t h e r e f o r e , comprised of d i s t i n c t r e g i o n s determined by the i n i t i a l molecular weight of the 1,2-polybutadiene, n. j \
