Hydrophobic Effects on Complexation and Aggregation in Water

Chapter 20

Hydrophobic Effects on Complexation and Aggregation in Water-Soluble Polymers Fluorescence, p H , and Dynamic Light-Scattering Measurements Curtis W. Frank, David J. Hemker, and Hideko T. Oyama Department of Chemical Engineering, Stanford University, Stanford, CA 94305-5025 Complexation and aggregation between poly(ethylene glycol) (PEG) and either poly (acrylic acid) (PAA) or poly (methacrylic acid) (PMAA) are studied in aqueous solution using fluorescence and dynamic light scattering. Excimer fluorescence from pyrene groups terminally attached to the PEG allow study of intermolecular and intramolecular interactions. Hydrophobic attraction is shown to be important in understanding the photophysical behavior. This influences the chain configuration of PMAA, the formation of ground state interactions of pyrenes in PEG*, the sequestering of pyrenes in hydrophobic regions in PMAA:PEG* complexes and the aggregation of the complexes at low pH. A sizeable body of literature has resulted from investigations of complexation reactions between synthetic polymers (1-6). Objectives have been to describe the interaction forces (hydrogen bonding, ionic, hydrophobic), to determine structural effects (molecular weight, stoichiometry, chemical composition) and to study the effect of reaction conditions (temperature, pH, solvent). Many of these parameters have been addressed in our previous studies on complexation of poly(ethylene glycol) (PEG) with either poly(acrylic acid) (PAA) or poly(methacrylic acid) (PMAA) in water (7-9). Incorporation of probe molecules consisting of PEG containing terminal pyrene labels (denoted PEG*) has allowed intramolecular and intermolecular excimer fluorescence measurements to be used to monitor local concentration of the pyrene labels in the complexes. From this we have inferred some of the structural details occurring on the scale of individual chains and small clusters. At the same time, however, we are also interested in the existence of large scale aggregates. Tschida and co-workers observed that as the pH of a solution containing a water soluble polymer complex was lowered, the solution became more turbid as a result of aggregation of the polymer complexes (10,11). Using total intensity light scattering and turbidity measurements, they showed 0097-6156/91/0467-0303$06.00/0 © 1991 American Chemical Society

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t h a t a g g r e g a t i o n i n c r e a s e d w i t h time f o r PMAA:PEG s o l u t i o n s . A g g r e g a t i o n was a l s o enhanced b y i n c r e a s i n g the polymer c o n c e n t r a t i o n o r i n c r e a s i n g the temperature. A c r i t i c a l pH was found above w h i c h t h e complexes d i d n o t a g g r e g a t e o v e r a time s c a l e o f t e n s o f m i n u t e s b u t below w h i c h a g g r e g a t i o n was g r e a t l y e n h a n c e d . Our o b j e c t i v e i n t h i s c h a p t e r i s t o p r o v i d e some u n i t y t o t h e combined t o p i c s o f c o m p l e x a t i o n and a g g r e g a t i o n . We b e g i n b y r e v i e w i n g p r e v i o u s work from o t h e r l a b o r a t o r i e s on c o m p l e x a t i o n u s i n g c l a s s i c a l as w e l l as f l u o r e s c e n c e t e c h n i q u e s . We t h e n summarize o u r c u r r e n t t h i n k i n g on the m o l e c u l a r i n t e r a c t i o n s g i v i n g r i s e t o t h e p h o t o p h y s i c a l b e h a v i o r i n PAA:PEG* and PMAA:PEG*. F i n a l l y , we p r e s e n t a v e r y s i m p l e model t o a c c o u n t f o r t h e s i z e d i s t r i b u t i o n o f t h e a g g r e g a t e s as w e l l as t h e time dependence o f t h e i r growth. A common t h r e a d t h a t runs t h r o u g h much o f t h e d i s c u s s i o n i n v o l v e s hydrophobic i n t e r a c t i o n s o f s e v e r a l forms. We w i l l see t h a t t h e s t r u c t u r e s o f t h e i s o l a t e d PMAA c h a i n , o f t h e i s o l a t e d p y r e n e l a b e l e d PEG* c h a i n , o f t h e PMAA:PEG* complex, and o f the l a r g e s c a l e a g g r e g a t e s a r e a l l i n f l u e n c e d by h y d r o p h o b i c i n t e r a c t i o n s t h a t may dominate t h e h y d r o g e n bond i n t e r a c t i o n s . We b e g i n , however, b y p r o v i d i n g a b r i e f r e v i e w o f h y d r o g e n b o n d i n g and i t s r o l e i n complexation. BACKGROUND ON HYDROGEN BONDING AND POLYMER COMPLEXATION The p r e r e q u i s i t e s f o r a h y d r o g e n bond o f s i g n i f i c a n t s t r e n g t h are t w o f o l d : i) a h y d r o g e n atom c o v a l e n t l y bound t o an e l e c t r o n w i t h d r a w i n g atom and i i ) an a c c e p t o r w i t h d o n a t a b l e e l e c t r o n s o r i e n t e d a t about 180 w i t h r e s p e c t t o t h e f i r s t b o n d . The g e o m e t r i c c o n s i d e r a t i o n i s q u i t e i m p o r t a n t w i t h t h e energy f a l l i n g off r a p i d l y with angle. The p o t e n t i a l energy o f t h e h y d r o g e n bond may be e x p l a i n e d b y t h e Stockmayer e q u a t i o n (12) b a s e d on t h e e l e c t r o s t a t i c p o t e n t i a l , t h e L i p p i n c o t t - S c h r o d e r e q u a t i o n (13) b a s e d on c h e m i c a l b o n d s , and t h e S c h e r a g a e q u a t i o n (14) b a s e d on v a n d e r Waals and Coulombic i n t e r a c t i o n s . The h y d r o g e n bond energy i s c o m p a r a t i v e l y l o w , between 10 and 40 k J / m o l , w h i c h makes i t s t r o n g e r t h a n a t y p i c a l v a n d e r Waals bond (~1 k J / m o l ) b u t s t i l l much weaker t h a n c o v a l e n t bonds (-500 k J / m o l ) . I t i s now a c c e p t e d t h a t t h e h y d r o g e n bond i s p r e d o m i n a n t l y an e l e c t r o s t a t i c i n t e r a c t i o n ( 1 5 , 1 6 ) . W i t h few e x c e p t i o n s , t h e H atom i s n o t s h a r e d b u t remains c l o s e r t o and c o v a l e n t l y bound t o i t s p a r e n t atom. A complex c a n be formed when a p a i r o f w a t e r - s o l u b l e p r o t o n d o n a t i n g and a c c e p t i n g polymers a r e m i x e d . The p o l y ( c a r b o x y l i c a c i d ) : P E G system has been s t u d i e d b y a v a r i e t y o f c o n v e n t i o n a l methods i n c l u d i n g p o t e n t i o m e t r y ( 3 , 1 7 - 2 1 ) , v i s c o m e t r y ( 3 , 1 7 - 2 1 ) , turbidimetry (11,20), sedimentation (22), scanning e l e c t r o n m i c r o s c o p y ( 2 0 ) , conductometry (20) and e l e m e n t a l a n a l y s i s ( 4 ) . Recent a n a l y t i c a l work has been d i r e c t e d a t p r o v i d i n g a s e m i q u a n t i t a t i v e framework f o r c o m p l e x a t i o n ( 2 3 ) . Fluorescence methods have a l s o been employed o v e r t h e same time p e r i o d . I n most c a s e s , a f l u o r e s c e n t l a b e l has been a t t a c h e d t o e i t h e r t h e p o l y ( c a r b o x y l i c a c i d ) o r t h e PEG. A n t h r a c e n e ( 1 , 2 4 - 2 6 ) , d a n s y l ( 5 , 2 7 - 2 9 ) , 8 - a n i l i n o - l - n a p h t h a l e n e s u l f o n i c a c i d (ANS) (30) and p y r e n e ( 6 , 2 9 ) have been u t i l i z e d . With a n t h r a c e n e and ANS l a b e l s , the most i m p o r t a n t t e c h n i q u e i s f l u o r e s c e n c e d e p o l a r i z a t i o n from which r e l a x a t i o n times c h a r a c t e r i z i n g i n t r a m o l e c u l a r c h a i n m o b i l i t y

20.

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are determined. The i n t e n s i t y o f e m i s s i o n from t h e d a n s y l l a b e l i s v e r y s e n s i t i v e t o t h e environment w i t h an i n c r e a s e i n i n t e n s i t y o c c u r r i n g upon complexation. F i n a l l y , p y r e n e e x c i m e r f l u o r e s c e n c e and t h e m o d i f i c a t i o n o f t h e monomer v i b r o n i c band s t r u c t u r e p r o v i d e a n i n d i c a t i o n o f l o c a l probe c o n c e n t r a t i o n and d i e l e c t r i c c o n s t a n t . I t i s s u r p r i s i n g t h a t complexes a r e a b l e t o form so r e a d i l y i n aqueous s o l u t i o n s where t h e r e i s s u c h s t r o n g c o m p e t i t i o n f o r h y d r o g e n bonds from t h e water ( 3 1 ) . I n f a c t , f o r wholy s m a l l molecules i t appears t h a t the complexation i s o n l y m a r g i n a l l y favored. However, when t h e i n t e r a c t i n g components a r e p o l y m e r s , t h e summation f o r s u c c e s s i v e u n i t s a l o n g t h e two c h a i n s g i v e s a s u f f i c i e n t l y f a v o r a b l e e n t h a l p y change t o outweigh t h e u n f a v o r a b l e e n t r o p y c o n t r i b u t i o n from a l i g n i n g t h e two c h a i n s i n f o r m i n g t h e complex ( 3 , 3 2 ) . O b v i o u s l y , complex f o r m a t i o n i s c a u s e d b y t h e c o o p e r a t i v e i n t e r a c t i o n s o f l o n g c o n t i n u o u s sequences o f f u n c t i o n a l groups on t h e polymer c h a i n . A n t i p i n a concluded that i n order f o r a complex t o be formed between PMAA and PEG, t h e PEG m o l e c u l a r w e i g h t s h o u l d n o t be l e s s t h a n 2000, w h i l e any s i g n i f i c a n t i n t e r a c t i o n between PAA and PEG s t a r t e d o n l y when the m o l e c u l a r w e i g h t was a r o u n d 6000 ( 3 ) . I n a d d i t i o n , Ikawa d i d n o t o b s e r v e any change i n v i s c o m e t r i c d a t a when t h e PEG m o l e c u l a r w e i g h t was l e s s t h a n 1760 f o r t h e PMAA: PEG complex o r 8800 f o r t h e PAA: PEG complex ( 3 2 ) . C o m p l e x a t i o n i s a l s o s t r o n g l y a f f e c t e d by t h e degree o f d i s s o c i a t i o n o f the a c i d . The e x i s t e n c e o f a c e r t a i n number o f u n d i s s o c i a t e d c a r b o x y groups i s n e c e s s a r y f o r PMAA and PEO t o form a s t a b l e complex t h r o u g h h y d r o g e n b o n d s . This dissociation i s suppressed i n the presence o f p o l y ( e t h y l e n e oxide) (PEO). F o r example, t h e d i s s o c i a t i o n c o n s t a n t (pK ) 7.5 f o r PMAA:PEO (MW o f PEO = 1300) and 7.9 f o r PMAA:PEO (MW o f PEÔ *= 2 5 , 0 0 0 ) , whereas i t i s 7.3 f o r PMAA ( 2 ) . A t h i g h pH where the number o f a c t i v e s i t e s i s i n s u f f i c i e n t , i t i s assumed t h a t t h e e n t h a l p y a f f o r d e d b y h y d r o g e n bonds does n o t compensate f o r t h e d e c r e a s e i n e n t r o p y ; t h i s c r i t i c a l pH i s about 5.7 f o r PMAA and about 4.8 f o r PAA. EXPERIMENTAL The s o u r c e and p u r i f i c a t i o n o f t h e PMAA and PAA a r e d e s c r i b e d elsewhere. (7,8) The v i s c o s i t y average m o l e c u l a r w e i g h t s were 9500 f o r t h e PMAA and 1850 f o r t h e PAA. Narrow d i s t r i b u t i o n ( p o l y d i s p e r s i t y < 1.10) PEG o f m o l e c u l a r w e i g h t 9200 was o b t a i n e d from P o l y s c i e n c e s . S o l u t i o n s o f PEG were made w i t h g l a s s - d i s t i l l e d deionized water. The pH was measured upon a d d i t i o n o f e i t h e r PMAA o r PAA u s i n g a Beckman P h i 44 pH Meter c a l i b r a t e d t o w i t h i n 0.02 pH units. F o r b l a n k pH measurements i n w h i c h no c o m p l e x a t i o n c a n o c c u r , d i s t i l l e d , d e i o n i z e d water was u s e d i n p l a c e o f t h e PEG solution. A l l f l u o r e s c e n c e measurements were p e r f o r m e d on a SPEX F l u o r o l o g 212. To date we have examined e m i s s i o n and e x c i t a t i o n s p e c t r a , l i f e t i m e s and a b s o r p t i o n s p e c t r a . Only s e l e c t e d measurements w i l l be d e s c r i b e d i n t h i s c h a p t e r , however. I n the dynamic l i g h t s c a t t e r i n g a p p a r a t u s , t h e i n c i d e n t r a d i a t i o n i s s u p p l i e d by a L e x e l two w a t t a r g o n - i o n l a s e r o p e r a t i n g a t 514.5 nm. A l l measurements were done u s i n g 12 mm c y l i n d r i c a l c u v e t t e s and a s c a t t e r i n g a n g l e o f 90 . The a u t o c o r r e l a t o r r e c e i v e s a s i g n a l from

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the PMT p r o p o r t i o n a l t o t h e l i g h t s c a t t e r i n g i n t e n s i t y and computes the s e c o n d - o r d e r t e m p o r a l c o r r e l a t i o n f u n c t i o n ( 3 3 - 3 5 ) . After n o r m a l i z a t i o n b y t h e measured b a s e l i n e , t h e s e c o n d - o r d e r f u n c t i o n may be r e l a t e d t o t h e f i r s t - o r d e r c o r r e l a t i o n f u n c t i o n t o y i e l d

g \x)= f"F(/?)exp{l

Jo

q kT 2

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(1)

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where q i s t h e s c a t t e r i n g v e c t o r , k i s B o l t z m a n n ' s c o n s t a n t , Τ i s a b s o l u t e temperature, e t a i s the s o l v e n t v i s c o s i t y , η i s the r e f r a c t i v e i n d e x o f t h e s o l u t i o n and F(R) i s t h e amount o f l i g h t s c a t t e r e d b y p a r t i c l e s o f s i z e R. The p r i m a r y g o a l o f t h e DLS d a t a a n a l y s i s i s t o o b t a i n a r e a s o n a b l e e s t i m a t e o f F(R) g i v e n a s e r i e s o f measured s e c o n d - o r d e r temporal c o r r e l a t i o n f u n c t i o n s . We u s e d t h e program CONTIN d e v e l o p e d b y P r o v e n c h e r ( 3 6 , 3 7 ) t o p e r f o r m an i n v e r s e L a p l a c e t r a n s f o r m o f E q u a t i o n (1) y i e l d i n g t h e smoothest n o n n e g a t i v e s o l u t i o n f o r F(R) t h a t i s c o n s i s t e n t w i t h the s i g n a l to n o i s e r a t i o f o r the data (38). The a b i l i t y o f CONTIN t o d e t e r m i n e t h e r e l a x a t i o n times o f b i m o d a l systems a c c u r a t e l y has been d e m o n s t r a t e d (35) a l o n g w i t h i t s a b i l i t y t o d e t e r m i n e F(R) c o r r e c t l y f o r p o l y d i s p e r s e monomodal e x p e r i m e n t a l systems w i t h known p a r t i c l e s i z e d i s t r i b u t i o n s (39). RESULTS AND DISCUSSION COMPLEXATION FLUORESCENCE MEASUREMENTS F i g u r e 1 shows e a r l i e r r e s u l t s f o r t h e n o r m a l i z e d i n t r a m o l e c u l a r and i n t e r m o l e c u l a r I / I r a t i o s f o r pyrene e n d - t a g g e d PEG upon t h e a d d i t i o n o f PMAA o r PAA ( 7 , 8 ) In general, the i n t r a m o l e c u l a r Î Q / I ^ d e c r e a s e s and t h e i n t e r m o l e c u l a r I p / I i n c r e a s e s as p o l y a c i a i s a d d e d . The PMAA d a t a show a much s t r o n g e r i n i t i a l dependence on m o l a r r a t i o , [ P M A A ] / [ P E G ] . During the i n i t i a l s t a g e s o f c o m p l e x a t i o n , t h e i n t r a m o l e c u l a r e x c i m e r i n t h e PMAA:PEG* system i s o v e r twenty times more s e n s i t i v e t o a d d i t i o n a l p o l y a c i d t h a n i n t h e PAA:PEG* s y s t e m . S i m i l a r l y , the i n t e r m o l e c u l a r e x c i m e r i s i n i t i a l l y o v e r n i n e t i m e s more s e n s i t i v e t o t h e a d d i t i o n o f PMAA, as compared t o t h e PAA. To g a i n a b e t t e r u n d e r s t a n d i n g o f t h e c o m p l e x a t i o n i n PMAA:PEG and PAA:PEG s y s t e m s , we r e c e n t l y have examined t h e i r pH b e h a v i o r (40). Such measurements a l l o w c a l c u l a t i o n o f t h e c o m p l e x a t i o n e q u i l i b r i u m c o n s t a n t and t h e degree o f c o m p l e x a t i o n . In order to make c o m p a r i s o n s o f t h e pH measurements w i t h t h e e a r l i e r s p e c t r o s c o p i c work, we f o l l o w e d t h e i d e n t i c a l e x p e r i m e n t a l p r o c e d u r e t h a t was u s e d e a r l i e r . To be s u r e , t h i s p r o t o c o l was q u i t e complex, w i t h s i m u l t a n e o u s v a r i a t i o n s i n s t o i c h i o m e t e r y and i n degree o f d i s s o c i a t i o n o c c u r r i n g as t h e p o l y ( c a r b o x y l i c a c i d ) was added t o t h e PEG s o l u t i o n . ( B u f f e r e d s o l u t i o n s c o u l d n o t be u s e d b e c a u s e o f i n s o l u b i l i t y o f the pyrene l a b e l e d PEG). N e v e r t h e l e s s , the a d d i t i o n o f pH r e s u l t s p e r m i t a c o n s i s t e n t p i c t u r e t o emerge t h a t u n i f i e s a l l of the f l u o r e s c e n c e d a t a . n

M

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20. FRANK ET AL.


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[Polyacid]/[PEG] Figure 1. Normalized intermolecular and intramolecular contributions to I / I for complexes between P E G and either P M A A or P A A as a function of the stoichiometry. (Reprinted from Ref. 40. Copyright 1990 American Chemical Society.) D

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308


pH MEASUREMENTS F i g u r e 2 shows t h e change i n pH o f a 10 ml s o l u t i o n o f 2x10" M o r 5x10 M PEG when 2x10 M PAA i s a d d e d . The monotonie drop i n pH i s s o l e l y due t o t h e i n t r i n s i c a c i d i t y o f t h e added p o l y a c i d . Most o f t h e c o m p l e x a t i o n i n t h i s system i s e x p e c t e d t o o c c u r between m o l a r r a t i o s o f z e r o and one b e c a u s e PAA and PEG form a 1:1 complex ( 2 ) . PAA was a l s o added t o 10 ml o f d i s t i l l e d water and t h e pH was m o n i t o r e d . I f c o m p l e x a t i o n were t o o c c u r between PAA and PEG, t h e pH o f t h e s o l u t i o n c o n t a i n i n g PAA:PEG would be h i g h e r t h a n t h a t o f t h e P A A : H 0 s o l u t i o n a t a g i v e n m o l a r ratio. T h i s i s b e c a u s e some o f t h e a c i d i c h y d r o g e n atoms i n t h e PAA w i l l be p a r t i c i p a t i n g i n c o m p l e x a t i o n h y d r o g e n b o n d s , r a t h e r t h a n being free i n s o l u t i o n . However, t h e r e i s no d i f f e r e n c e between e i t h e r o f t h e PAA:PEG m i x t u r e s and t h e PAA:H^O s o l u t i o n i n F i g u r e 2, i n d i c a t i n g t h a t e i t h e r PAA and PEG do n o t complex under t h e s e c o n d i t i o n s , o r t h a t c o m p l e x a t i o n i s n o t d e t e c t a b l e f o r PAA:PEG u s i n g pH measurements. We f e e l t h a t t h e l a t t e r c o n c l u s i o n i s t h e c o r r e c t one. The same s e t o f e x p e r i m e n t s were a l s o done on PMAA:PEG. The change i n pH o f 10 ml o f 1x10" M PEG upon t h e a d d i t i o n o f 1 x 1 0 ' M PMAA i s shown i n F i g u r e 3. A b l a n k r u n was a l s o done t o d e t e r m i n e whether c o m p l e x a t i o n c o u l d be m o n i t o r e d under t h e s e c o n d i t i o n s . A g a i n , no d i f f e r e n c e between t h e PMAA:PEG and the PMAA:H 0 r e s u l t s f o r t h e low PEG c o n c e n t r a t i o n was o b s e r v e d . However, f o r PEG c o n c e n t r a t i o n o f 5x10 M c o m p l e x a t i o n was d e t e c t a b l e w i t h p H . These pH r e s u l t s may be u s e d t o show t h a t a t m o l a r r a t i o s above above 0 . 1 , about 80% o f t h e a v a i l a b l e h y d r o g e n b o n d i n g s i t e s a r e p a r t i c i p a t i n g i n c o m p l e x a t i o n h y d r o g e n b o n d s . (40) 9

2

INTERPRETATION OF FLUORESCENCE AND PH MEASUREMENTS Fluorescence d a t a p r e v i o u s l y o b t a i n e d f o r PMAA:PEG* a r e c r o s s p l o t t e d a g a i n s t pH i n F i g u r e 4. We f o c u s on t h e s e r e s u l t s because o f t h e i r s t r o n g e r dependence on pH t h a n t h e PAA:PEG* system and because DLS measurements (41) o f l a r g e a g g r e g a t e s have r e c e n t l y b e e n made f o r PMAA:PEG and PMAA:PEG*. Our c u r r e n t t h i n k i n g on t h e m o l e c u l a r l e v e l i n t e r a c t i o n s a s s o c i a t e d w i t h t h e p h o t o p h y s i c a l measurements a n d , i n d i r e c t l y , t h e c o m p l e x a t i o n p r o c e s s p l a c e s c o n s i d e r a b l e emphasis on h y d r o p h o b i c e f f e c t s , as d i s c u s s e d i n t h e f o l l o w i n g . We f i r s t c o n s i d e r t h e i s o l a t e d PMAA c h a i n s . The h y d r o p h o b i c n a t u r e o f PMAA due t o t h e m e t h y l s i d e group has been o b s e r v e d e x p e r i m e n t a l l y i n many d i f f e r e n t systems (42-44) and has been s u c c e s s f u l l y modelled (45-47). One m a n i f e s t a t i o n o f t h e h y d r o p h o b i c n a t u r e o f PMAA i s t h a t i t undergoes a r a t h e r sharp c o i l c o n t r a c t i o n as t h e pH i s l o w e r e d , l e a d i n g t o the f o r m a t i o n o f r e g i o n s o f g r e a t e r h y d r o p h o b i c i t y than the surroundings. F o r example, Chu and Thomas (47) s t u d i e d PMAA u s i n g p y r e n e p r o b e s c o v a l e n t l y a t t a c h e d a t random p o i n t s along the c h a i n . A t h i g h pH t h e p y r e n e s p r o d u c e d a s m a l l amount o f f l u o r e s c e n c e , i n d i c a t i n g t h a t t h e p y r e n e s were i n a w a t e r r i c h environment. C o n v e r s e l y , a t low pH t h e r e was a s t r o n g p y r e n e e m i s s i o n i n d i c a t i n g t h a t t h e p y r e n e s were i n a h y d r o p h o b i c environment. T h i s a b r u p t change i n c h a i n c o n f i g u r a t i o n , o c c u r r i n g between pH 6 and 4, was a t t r i b u t e d t o t h e f a c t t h a t a t h i g h pH a s i g n i f i c a n t f r a c t i o n o f t h e c a r b o x y groups a r e i o n i z e d . The tendency t o maximize t h e s e p a r a t i o n between t h e i o n i c c h a r g e s thus

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0 2M PAA added toIQml of; t

•

distilled water (blank)

Δ 2x10^ PEG ?

Ο 5x10 M PEG

ώ-—ύ I

15

10

20

Molar Ratio Figure 2. Dependence of pH on stoichiometry for addition of PAA to distilled water or PEG solutions. (Reprinted from Ref. 40. Copyright 1990 American Chemical Society.)

0.4

0.6

Molar Ratio

Figure 3. Dependence of pH on stoichiometry for addition of PMAA to distilled water or PEG solutions. (Reprinted from Ref. 40. Copyright 1990 American Chemical Society.)

310

WATER-SOLUBLE P O L Y M E R S

2

4

6

8

pH Figure 4. Dependence of intramolecular and intermolecular for addition of P M A A to 1 Χ ΙΟ" M P E G . (Reprinted from Ref. Copyright 1990 American Chemical Society.)

o n

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p r o d u c e s an expanded c h a i n . As the pH i s l o w e r e d , the c a r b o x y l a t e groups become p r o t o n a t e d and the c h a i n r e l a x e s i n t o a more compact structure. They a l s o showed t h a t as the pH was l o w e r e d , i t became more d i f f i c u l t f o r f l u o r e s c e n c e quenchers t o r e a c h the p y r e n e s . A sharp t r a n s i t i o n i n q u e n c h i n g a b i l i t y w i t h pH was f o u n d , f u r t h e r c o n f i r m i n g the c o l l a p s e o f PMAA w i t h d e c r e a s i n g p H . N e x t , we c o n s i d e r the i n t e r a c t i o n s p o s s i b l e i n aqueous PEG* s o l u t i o n s c o n t a i n i n g no PMAA. We have shown e a r l i e r (8) t h a t a t low c o n c e n t r a t i o n e x c i m e r f o r m a t i o n was c o n s i d e r a b l y enhanced i n water compared to the e x p e c t e d v a l u e r e s u l t i n g from i n t r a m o l e c u a r e n d - t o end c y c l i z a t i o n i n an o r g a n i c s o l v e n t . We a t t r i b u t e d t h i s o b s e r v a t i o n t o h y d r o p h o b i c a t t r a c t i o n between the p y r e n e groups and modeled the a t t r a c t i o n i n terms o f a " h y d r o p h o b i c c a p t u r e r a d i u s " . (47). T h i s r a d i u s was about 20 Angstroms i n pure w a t e r , b u t c o u l d be r e d u c e d to about 6 Angstroms upon a d d i t i o n o f 30% m e t h a n o l . Knowledge o f the tendency f o r the pyrene groups to seek a h y d r o p h o b i c environment i s i m p o r t a n t f o r u n d e r s t a n d i n g c o m p l e x a t i o n and a g g r e g a t i o n i n t h e s e l a b e l l e d p o l y m e r s , as we w i l l s e e . We a r e now i n a p o s i t i o n t o d i s c u s s complex f o r m a t i o n . When the f i r s t PMAA i s added t o the PEG s o l u t i o n , two e v e n t s o c c u r simultaneously. Not o n l y do h y d r o g e n bonds form between the a c i d and PEG, b u t some p y r e n e s on the e n d - t a g g e d PEG a r e e x p e c t e d t o be a t t r a c t e d to the h y d r o p h o b i c r e g i o n s o f the PMAA. B o t h phenomena w i l l l e a d to a r e d u c e d e n d - t o - e n d c y c l i z a t i o n r a t e and a much more r a p i d d e c r e a s e i n i n t r a m o l e c u l a r 1^/1^ f o r the PMAA:PEG* complex t h a n f o r the PAA:PEG* complex, where o n l y c o m p l e x a t i o n h y d r o g e n bonds o c c u r . Differences i n i n i t i a l intermolecular I / 1 increases for PMAA:PEG* and PAA:PEG* a l s o may be r e l a t e d t o the h y d r o p h o b i c effects. F o r PMAA:PEG* n o t o n l y i s t h e r e an i n c r e a s e i n l o c a l p y r e n e c o n c e n t r a t i o n due t o c o m p l e x a t i o n , b u t t h e r e i s a l s o a c o n t r i b u t i o n t o t h a t i n c r e a s e from the h y d r o p h o b i c a t t r a c t i o n o f p y r e n e groups t o the h y d r o p h o b i c r e g i o n s i n the PMAA complex. I t i s i n t e r e s t i n g to n o t e t h a t the i n c r e a s e i n i n t e r m o l e c u l a r I p / I ^ o c c u r s a p p r e c i a b l y p a s t the p o i n t a t w h i c h PMAA c o i l c o l l a p s e i s e x p e c t e d , as shown i n F i g u r e 3. T h i s i m p l i e s t h a t the p y r e n e s w h i c h a r e " h y d r o p h o b i c a l l y a g g r e g a t i n g " a r e s t i l l m o b i l e enough, o r a r e l o c a t e d c o r r e c t d i s t a n c e s a p a r t , to form i n t e r m o l e c u l a r e x c i m e r s . As more PMAA i s a d d e d , however, t h e s e h y d r o p h o b i c r e g i o n s w i l l most l i k e l y i n c r e a s e i n l o c a l d e n s i t y and thus the s t e r i c c o n s t r a i n t on the i n t e r m o l e c u l a r e x c i m e r s r e s u l t i n g from l o s s o f p y r e n e m o b i l i t y w i l l c o n t i n u e to i n c r e a s e . I f t h i s t r e n d c o n t i n u e s , e v e n t u a l l y the e x c i m e r s c o u l d become so d e s t a b i l i z e d t h a t the e x c i m e r c o n f i g u r a t i o n i s d e s t r o y e d c a u s i n g the i n t e r m o l e c u l a r I^/I^. t o d e c r e a s e . A d d i t i o n a l p h o t o p h y s i c a l parameters c a n De u s e d t o s u p p o r t the g e n e r a l p i c t u r e o f c o m p l e x a t i o n t h a t we have d e s c r i b e d . For example, r e d s h i f t s i n the monomer e x c i t a t i o n s p e c t r a i n the complexes have b e e n i n t e r p r e t e d i n terms o f ground s t a t e i n t e r a c t i o n s o f the pyrene groups i n the h y d r o p h o b i c c l u s t e r s (48). When the c a r b o x y groups o f the PMAA were 30% i o n i z e d by the a d d i t i o n o f NaOH, no monomer e x c i t a t i o n s h i f t was o b s e r v e d i n e i t h e r the 100% o r 1% t a g g e d s y s t e m s . The n e u t r a l i z a t i o n o f some o f the c o m p l e x a t i o n bonds e f f e c t i v e l y b r e a k s up the PMAA h y d r o p h o b i c r e g i o n s by f o r c i n g the PMAA c h a i n s i n t o a more e x t e n d e d configuration. W i t h o u t t h e s e c o n s o l i d a t e d h y d r o p h o b i c domains, n

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t h e r e i s no h y d r o p h o b i c a l l y enhanced p y r e n e a g g r e g a t i o n and no g r o u n d - s t a t e i n t e r a c t i o n s are observed. S i m i l a r l y , excimer e x c i t a t i o n s p e c t r a l b l u e s h i f t s are e x p l a i n e d by t h i s m o d e l . E a r l i e r work showed t h a t as PMAA was a d d e d , t h e maximum i n the e x c i m e r e x c i t a t i o n s p e c t r u m s h i f t e d by 10 nm t o s h o r t e r w a v e l e n g t h s ( 8 ) . T h i s i s evidence of i n c r e a s i n g e x c i m e r d e s t a b i l i z a t i o n w i t h i n c r e a s i n g c o m p l e x a t i o n w i t h PMAA. No s u c h s h i f t i n e x c i m e r peak was f o u n d f o r PAA:PEG. When the PMAA was 30% n e u t r a l i z e d , no e x c i m e r peak s h i f t was o b s e r v e d , f u r t h e r s u p p o r t i n g t h e more e x t e n d e d c o n f i g u r a t i o n f o r PMAA. These phenomena a r e a l s o r e f l e c t e d i n the i n t e r m o l e c u l a r I / I d a t a ( 4 8 ) . A t 30% n e u t r a l i z a t i o n , the PMAA:PEG* i n t e r m o l e c u l a r Ι / Τ i n c r e a s e s m o n o t o n i c a l l y and does n o t p a s s t h r o u g h a maximum, q u a l i t a t i v e l y v e r y s i m i l a r t o t h a t f o r PAA shown i n F i g u r e 1. Comparable r e s u l t s were o b t a i n e d f o r a d d i t i o n o f m e t h a n o l , w h i c h a l s o c a u s e s d i s p e r s a l o f the h y d r o p h o b i c r e g i o n s i n PMAA:PEG*. (48). n

M

η

Μ

AGGREGATION DYNAMIC LIGHT SCATTERING MEASUREMENTS The i n i t i a l system c h o s e n f o r e x a m i n a t i o n w i t h DLS (41) c o n s i s t e d o f a s o l u t i o n o f 2x10" M PMAA and 2x10" M u n l a b e l e d PEG i n w a t e r a t 2 5 ° C. The pH was a d j u s t e d w i t h c o n c e n t r a t e d HCI between v a l u e s o f 3.0 and 1.7 and the f r a c t i o n o f l i g h t s c a t t e r e d by p a r t i c l e s o f a g i v e n r a d i u s i n those s o l u t i o n s i m m e d i a t e l y a f t e r m i x i n g was d e t e r m i n e d by CONTIN. The s i z e d i s t r i b u t i o n i s r a t h e r b r o a d ; f o r pH - 2.75 the p a r t i c l e s range i n s i z e from ~20 nm t o -126 nm. I n o r d e r t o compare t h i s r e s u l t w i t h o t h e r a g g r e g a t i o n work, we have u s e d F l a m b e r g and P e c o r a ' s d e f i n i t i o n o f the a v e r a g e r a d i u s o f the d i s t r i b u t i o n ( 4 9 ) . B a s e d on t h i s d e f i n i t i o n , the s o l u t i o n g i v i n g r i s e t o the s c a t t e r e d l i g h t i n t e n s i t y d i s t r i b u t i o n f o r pH 2.75 has an average r a d i u s o f 48 nm, w h i c h d i d n o t s i g n i f i c a n t l y change o v e r t h e c o u r s e o f 100 m i n u t e s . F i g u r e 5 shows the i n i t i a l a v e r a g e a g g r e g a t e r a d i u s as a f u n c t i o n o f pH. T h i s f i g u r e e x h i b i t s the same g e n e r a l b e h a v i o r as the t o t a l s c a t t e r e d l i g h t i n t e n s i t y v s pH c u r v e o f T s u c h i d a , w h i c h showed a c r i t i c a l pH o f 3. I n the c a s e o f F i g u r e 5, however, t h e c r i t i c a l pH a p p e a r s t o have b e e n s h i f t e d t o the lower v a l u e o f about 1.9 b e c a u s e o f the l o w e r m o l e c u l a r w e i g h t o f our PMAA. T h e r e a r e many s t u d i e s t h a t show t h a t c o m p l e x a t i o n o c c u r s r a p i d l y , on t h e o r d e r o f m i l l i s e c o n d s ( 1 1 ) . In order to i n v e s t i g a t e t h i s a g g r e g a t i o n p r o c e s s f u r t h e r , we a t t e m p t e d t o f i n d a s e t o f c o n d i t i o n s f o r w h i c h the k i n e t i c s would be slow enough t o a l l o w us t o m o n i t o r t h e a g g r e g a t i o n w i t h DLS. When the pH o f t h e PMAA:PEG system was l o w e r e d t o the c r i t i c a l v a l u e o f 1.9, a d e f i n i t e time dependence o f the a v e r a g e r a d i u s w i t h time was o b s e r v e d . This i n c r e a s e i s p l o t t e d i n F i g u r e |> and i s m a t h e m a t i c a l l y d e s c r i b e d by a power law r e l a t i o n s h i p R - R ' t where t i s t i m e , R' - 68 nm and b 0.11. A v a l u e f o r b l e s s t h a n one i n d i c a t e s t h a t t h e r a t e o f s i z e i n c r e a s e d e c r e a s e s w i t h t i m e , whereas a v a l u e f o r b g r e a t e r t h a n one i n d i c a t e s an e v e r a c c e l e r a t i n g r e a c t i o n where the r a t e o f i n c r e a s e i n s i z e increases with time. N o t e , R' s h o u l d be t h o u g h t o f as a measure o f a g g r e g a t e s i z e a t an a r b i t r a r y time and n o t as t h e i n i t i a l aggregate s i z e . The p o w e r - l a w r e l a t i o n s h i p a c c u r a t e l y d e s c r i b e s t h e time dependence o f the a v e r a g e r a d i u s o f t h i s system o n l y o v e r a

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Figure 5. Average aggregate radius as a function of p H for P M A A i P E G immediately after mixing. (Reprinted from Ref. 41. Copyright 1990 American Chemical Society.)

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Time (min) Figure 6. Rate of growth of P M A A : P E G aggregate radius for p H = (Reprinted from Ref. 41. Copyright 1990 American Chemical Society.)

1.9.

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r e s t r i c t e d time r a n g e . N e v e r t h e l e s s , the c o n s t a n t s c a n be u s e d t o compare r a t e d a t a f o r d i f f e r e n t s y s t e m s . F o r example, from o u r e a r l i e r d i s c u s s i o n on h y d r o p h o b i c e f f e c t s i n the complexes we a r e v e r y i n t e r e s t e d i n the i n f l u e n c e o f the p y r e n e l a b e l s on the o v e r a l l aggregation process. To examine t h i s , an i d e n t i c a l s o l u t i o n u s e d t o o b t a i n F i g u r e 6 was made w i t h the e x c e p t i o n o f u s i n g l a b e l e d PEG r a t h e r than u n l a b e l e d . However, when the f i r s t DLS measurement was made on the s o l u t i o n , a p p r o x i m a t e l y one minute a f t e r m i x i n g , the s o l u t i o n h a d a l r e a d y a g g r e g a t e d so r a p i d l y t h a t the average r a d i u s h a d r e a c h e d -1000 nm. I n o r d e r t o slow down the a g g r e g a t i o n p r o c e s s , a new s o l u t i o n w i t h pH o f 3.0 was p r e p a r e d . The k i n e t i c d a t a f o r t h i s s o l u t i o n a l s o f o l l o w a p o w e r - l a w w i t h c o n s t a n t s R' — 123 nm and b = 0 . 3 1 . DIFFUSION LIMITED CLUSTER-CLUSTER AGGREGATION MODEL. In c o n s i d e r i n g the b a s i c p r o b l e m o f a g g r e g a t i o n , t h e r e a r e two q u e s t i o n s t h a t must be answered. The f i r s t c o n c e r n s the l i m i t i n g s t e p i n the aggregation. The g e n e r a l p r o c e s s o f a g g r e g a t i o n i n v o l v e s two p a r t i c l e s d i f f u s i n g toward each o t h e r . When t h e y a r e some c h a r a c t e r i s t i c distance a p a r t , there i s a c e r t a i n p r o b a b i l i t y that the i n t e r a c t i o n f o r c e s between the two p a r t i c l e s w i l l be such t h a t the p a r t i c l e s s t i c k t o g e t h e r v i a e . g . a h y d r o g e n b o n d . I f the s t i c k i n g p r o b a b i l i t y i s h i g h i n c o m p a r i s o n to the d i f f u s i o n r a t e o f the p a r t i c l e s , the p r o c e s s i s known as d i f f u s i o n l i m i t e d a g g r e g a t i o n (DLA). I f , on the o t h e r h a n d , the d i f f u s i o n r a t e i s h i g h i n c o m p a r i s o n t o the s t i c k i n g r e a c t i o n r a t e , the p r o c e s s i s known as r e a c t i o n l i m i t e d aggregation (RLA). The s e c o n d q u e s t i o n c o n c e r n s the r e l a t i v e m o b i l i t y o f aggregates. A g a i n , two l i m i t i n g c a s e s e x i s t . I n the f i r s t , o n l y the i n d i v i d u a l s u b - p a r t i c l e s t h a t make up a l l l a r g e r a g g r e g a t e s a r e allowed to d i f f u s e . T h i s model was f i r s t i n v e s t i g a t e d i n a computer s i m u l a t i o n by W i t t e n and Sander ( 5 0 ) . A g g r e g a t e s grow v i a the a d d i t i o n of i n d i v i d u a l s u b - p a r t i c l e s . T h i s p r o c e s s i s known as p a r t i c l e - c l u s t e r aggregation. The second l i m i t i n g c a s e a l l o w s b o t h i n d i v i d u a l p a r t i c l e s and a l l l a r g e r a g g r e g a t e s t o d i f f u s e f r e e l y . I n t h i s m o d e l , a g g r e g a t e s grow by the c o m b i n a t i o n o f two a g g r e g a t e s o f any s i z e . T h i s p r o c e s s i s known as c l u s t e r - c l u s t e r a g g r e g a t i o n . As a s t a r t i n g p o i n t f o r the development o f our m o d e l , we have assumed t h a t our a g g r e g a t i o n system i s d e s c r i b e d by the d i f f u s i o n l i m i t e d a g g r e g a t i o n , and t h a t c l u s t e r - c l u s t e r a g g r e g a t i o n i s the dominant mode f o r a g g r e g a t e growth. This implies that aggregates a r e n o n i n t e r a c t i n g u n t i l t h e y s t i c k t o g e t h e r i r r e v e r s i b l y on contact. The e f f e c t s on a g g r e g a t i o n o f l o n g range i n t e r a c t i o n s , s u c h as d i p o l e o r s c r e e n e d Coulomb, have been i n v e s t i g a t e d by Hurd (51) and a r e assumed to be n e g l i g i b l e . The time dependence o f a g g r e g a t e mass, assuming c l u s t e r - c l u s t e r aggregation, for a solution i n i t i a l l y consisting of Ν p a r t i c l e s of r a d i u s R c a n be d e s c r i b e d by the g e n e r a l i z e d Smoluchowski e q u a t i o n s (52,53). F o r DLA the d i f f u s i o n k e r n e l i s e q u a l t o the sum o f the c a p t u r e r a d i i f o r the two c l u s t e r s times the sum o f t h e i r d i f f u s i o n c o e f f i c i e n t s (54). I f we assume t h a t the c a p t u r e r a d i u s s c a l e s w i t h the c l u s t e r r a d i u s and t h a t the c l u s t e r s undergo S t o k e s - E i n s t e i n d i f f u s i o n , the r a t e o f a g g r e g a t i o n o f an i - m e r w i t h a j - m e r w i l l be independent o f c l u s t e r s i z e . U s i n g the c o n s t a n t k e r n e l a s s u m p t i o n , the Smoluchowski

316


e q u a t i o n s c a n be i n t e g r a t e d t o g i v e t h e time dependence o f a n a g g r e g a t i o n number d i s t r i b u t i o n f o r c l u s t e r - c l u s t e r , diffusion l i m i t e d aggregation.

N

A

t

—

=

N

( i _ 1 )

(2)

(1+A)

0

(i+1)

where A - k N t . The c o n s t a n t k i s t h e r a t e c o n s t a n t f o r t h e a g g r e g a t i o n o ? any two c l u s t e r s . The n e x t s t e p i s t o w r i t e E q u a t i o n (2) i n terms o f a g g r e g a t e r a d i u s , R . , r a t h e r t h a n number o f s u b - p a r t i c l e s . A g e n e r a l s c a l i n g to accomplish t h i s i s p r o v i d e d by S

5 5

(3)

where D i s t h e s c a l i n g d i m e n s i o n a l i t y o f t h e s y s t e m . By a l l o w i n g D t o v a r y i n t h e f i t t i n g p r o c e d u r e , a b e s t - f i t e s t i m a t e o f t h e system d i m e n s i o n a l i t y c a n be o b t a i n e d . E q u a t i o n (3) c a n be i n s e r t e d i n t o E q u a t i o n (2) t o g i v e a n e x p r e s s i o n f o r t h e number d i s t r i b u t i o n o f p a r t i c l e s i n terms o f radius. T h i s number d i s t r i b u t i o n c a n n o t , however, be d i r e c t l y compared w i t h t h e l i g h t s c a t t e r i n g i n t e n s i t y d i s t r i b u t i o n c a l c u l a t e d by CONTIN. I n o r d e r t o r e l a t e t h e two d i s t r i b u t i o n s , we f o l l o w t h e method o f F l a m b e r g and P e c o r a (49) t o o b t a i n

F(R)=R

l

M

(4)

(1+Aj f o r the normalized i n t e n s i t y d i s t r i b u t i o n . When E q u a t i o n (4) was f i t t o t h e CONTIN o u t p u t , convergence was o b t a i n e d . This leasts q u a r e s f i t t i n g p r o c e s s was r e p e a t e d f o r a l l d i s t r i b u t i o n s and an average d i m e n s i o n a l i t y o f 1.7 + / - 0.25 was f o u n d . T h i s exponent was found i n b o t h t h e PMAA:PEG and PMAA:PEG* systems and was c o n s t a n t i n time. The n o n - i n t e g r a l exponent i m p l i e s a system w i t h d i l a t i o n a l symmetry, i . e . , t h e a g g r e g a t e s c a n be d e s c r i b e d as h a v i n g " f r a c t a l " dimensionality (55). S e v e r a l computer s i m u l a t i o n s (56-58) have shown t h a t c l u s t e r - c l u s t e r a g g r e g a t i o n i n t h e DLA regime s h o u l d produce a d i m e n s i o n a l i t y o f 1.8. M i c r o s c o p y e x p e r i m e n t s on d i f f u s i o n l i m i t e d c o l l o i d a l g o l d a g g r e g a t e s done by W e i t z (54) produced a f r a c t a l dimension o f 1.7. L i k e w i s e , n e u t r o n and l i g h t s c a t t e r i n g done on t h e same p a r t i c l e s gave r i s e t o a f r a c t a l

20. FRANK ET AL.


exponent of 1.8. However, under reaction limited aggregation conditions, Weitz (59) found a fractal dimension of 2.0. The close agreement between these studies and our data supports our proposal that the PMAA:PEG aggregates are fractal in nature and grow via DLA and cluster-cluster aggregation. SUMMARY As either PMAA or PAA is added to an aqueous PEG solution, complexation occurs and is stabilized by the hydrogen bonds between the polyacid and the PEG chains. Additionally, in the PMAA system, some pyrenes covalently attached to the ends of PEG chains are attracted to hydrophobic regions. The pyrenes interact in the ground state and participate in preformed excimers. This phenomenon manifests itself in red-shifted monomer excitation and absorption spectra, blue shifted excimer excitation spectra, increases in monomer lifetimes, the absence of excimer transient rise times (not discussed here), a rapid i n i t i a l decrease in intramolecular I p / ^ and a rapid i n i t i a l increase in intermolecular I / I . Since there are no hydrophobic regions in the analogous PAA:PEG systems, none of the non-hydrogen bonding phenomena are observed. In fact, a l l of these observations can be eliminated by destroying the consolidated hydrophobic regions in PMAA complexes. This has been experimentally accomplished by the ionization of the carboxy groups in PMAA or by adding methanol. At sufficiently low pH, macroscopic flocculation occurs with a power law dependence of the average particle size on time. Interestingly, the pyrene labeled PEG exhibits much faster aggregation with PMAA than does the unlabeled PMAA. A diffusion limited cluster-cluster aggregation model with fractal dimension of 1.7 has been shown to be adequate to interpret the data. 1

ACKNOWLEDGEMENT This work was supported by the Polymers Program of the National Science Foundation Division of Materials Research under DMR 8407847. REFERENCES 1. 2. 3. 4. 5. 6. 7.

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RECEIVED July 2, 1990

Hydrophobic Effects on Complexation and Aggregation in Water

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