Determination of Cluster Size in Polyelectrolyte ... - ACS Publications

Chapter 27 Determination of Cluster Size in Polyelectrolyte Solutions by Small-Angle Neutron Scattering 1

2

3

Hideki Matsuoka , Dietmar Schwahn, and Norio Ise 1

Department of Polymer Chemistry, Kyoto University, Kyoto 606-01, Japan Institut für Festkörperforschung, Forschungszentrum Jülich, Postfach 1913, D-5170 Jülich, Germany Fukui Research Laboratory, Rengo Company Ltd., 10-8-1, Jiyugaoka, Kanazu-cho, Sakai-gun, Fukui 919-06, Japan

Downloaded by UNIV LAVAL on June 24, 2014 | http://pubs.acs.org Publication Date: December 13, 1993 | doi: 10.1021/bk-1994-0548.ch027

2

3

Small-angle neutron scattering measurements were performed for sodium polystyrenesulfonate-D O solutions. A steep upturn behavior was observed at very small-angle regions below 0.01 Å which could not measured by our previous X-ray experiments. This upturn reflects the existence of ordered cluster and i t s size was estimated to be around 400 - 1000 Å by Guinier, Debye-Bueche, and Porod analyses. Model calculations were also performed to estimated the number density of the clusters by using absolute scattering intensity. 2

-1

Small-angle X-ray scattering (SAXS) and neutron s c a t t e r i n g (SANS) c u r v e s f o r p o l y e l e c t r o l y t e s o l u t i o n s at low i o n i c s t r e n g t h s showed a s i n g l e , broad but distinct p e a k . ( 1 - 4 ) T h i s p e a k was t a k e n as i m p l y i n g a more o r l e s s o r d e r e d arrangement of i o n i c s o l u t e s , though i n s o l u t i o n s . In o t h e r words, t h i s was an i n t e r p a r t i c l e interference p e a k a l t h o u g h t h e d e g r e e o f o r d e r was n o t h i g h . The a v e r age i n t e r p a r t i c l e d i s t a n c e ( 2 0 ^ - ) was c a l c u l a t e d f r o m t h e peak p o s i t i o n by the Bragg Equation. A t low p o l y m e r concentrations, 2D v a l u e was s m a l l e r t h a n t h e average d i s t a n c e c a l c u l a t e d f r o m t h e c o n c e n t r a t i o n ( 2 D ) when t h e c h a r g e number and m o l e c u l a r w e i g h t o f t h e p o l y m e r were h i g h . ( 1 , 2 ) T h i s r e l a t i o n i m p l i e s t h a t the ordered r e g i o n s were n o t f o r m e d t h r o u g h o u t t h e s o l u t i o n b u t e x i s t e d as l o c a l i z e d c l u s t e r s . We h a v e b e e n c a l l i n g this structure a "two-state s t r u c t u r e " ( 1 , 2 ) . A s i m i l a r kind of structure was o f t e n o b s e r v e d d i r e c t l y f o r i o n i c l a t e x d i s p e r s i o n s by ultramicroscope technique.(1,2) However, no f u r t h e r s i g n s o f t h e c l u s t e r s t r u c t u r e have b e e n d e t e c t e d i n c o n v e n t i o n a l s c a t t e r i n g measurements o f i o n i c p o l y m e r s o l u t i o n s . I n a p r e v i o u s s t u d y , we p e r f o r m e d SANS measurements by a s c a t t e r i n g camera which c o u l d d e t e c t s c a t t e r i n g at v e r y s m a l l a n g l e s t h a t were n o t c o v e r e d by t h e convene X D

Q

0097-6156y94A)548-0349$06.00A) © 1994 American Chemical Society

In Macro-ion Characterization; Schmitz, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1993.


350

MACRO-ION CHARACTERIZATION

tional SAXS apparatus.(5) Sodium p o l y s t y r e n e s u l f o n a t e (NaPSS) having a narrow molecular weight d i s t r i b u t i o n was chosen as a sample s i n c e we c a r r i e d out e a r l i e r SAXS measurements f o r the same m a t e r i a l and found an i n t e r f e r ence peak.(6) The SANS curves obtained f o r NaPSS i n D«0 s o l u t i o n s showed a steep upturn behavior i n very s m a l l angle regions while an i n t e r f e r e n c e peak was a l s o observed at the same p o s i t i o n s as i n our previous SAXS r e s u l t s . According to b a s i c s c a t t e r i n g theory, the strong s c a t t e r ing at very small angles i s due to a d e n s i t y f l u c t u a t i o n of a very l a r g e s i z e i n the system. T h i s upturn i s compat i b l e with the l o c a l i z e d c l u s t e r s i n the two-state s t r u c ture; other model proposed e a r l i e r , ( 7 ) cannot account f o r the upturn s i n c e i t assumes a uniform d i s t r i b u t i o n of solutes. In the present paper, the upturn behavior was con firmed at v a r i o u s polymer and s a l t c o n c e n t r a t i o n s . G u i n i er method, Debye-Bueche method and model c a l c u l a t i o n s with the absolute s c a t t e r e d i n t e n s i t y were employed to analyze the upturn behavior and to estimate the s i z e and other s t r u c t u r a l parameters of the c l u s t e r s t r u c t u r e . Experimental S e c t i o n Materials NaPSS was purchased from Pressure Chemicals ( P i t t s b u r g h , PA). The molecular weight was 100,000 by the s u p p l i e r . The sample was p u r i f i e d by u l t r a f i l t r a t i o n u n t i l the f i l t r a t e showed no UV absorbance. The p u r i f i e d sample was f i l t e r e d by a g l a s s f i l t e r of mesh G3 and then f r e e z e dried. D 0 used as s o l v e n t was Merck Art.2919 (99.75%, Darmstadt, FRG). Sodium c h l o r i d e used as an added s a l t was a l s o of Merck, pro analyze grade, l o t 527K785404. 2

SANS Measurements The SANS apparatus used was a KWS 2 system i n Forschungszentrum J u l i e n . T h i s has a long camera d i s t a n c e of 20m, which enables us to cover very s m a l l angle r e g i o n s . The d e t a i l s of the system were f u l l y de scribed elsewhere, (β) The SANS c e l l used was made of quartz, Hellma Prâzisions-Kuvetten, thickness 5.00 mm. The c e l l s were washed with detergents and a l s o cleaned by u l t r a s o n i c a t i o n before use. The s c a t t e r e d i n t e n s i t i e s were c o l l e c t e d at three or four detector d i s t a n c e s (say, 2m, 4m, 8m, and 20m). Those data were gathered and analyzed by a computer system (ELLAVAX system). The absorption c o r r e c t i o n was done using the r e s u l t s of t r a n s m i s s i o n measurements. The c a l i b r a t i o n f o r the absolute i n t e n s i t y was performed by u s i n g a standard Lupolen sample. Results Figure 1 shows the polymer c o n c e n t r a t i o n dependence of the SANS curves of NaPSS-D«0 solutions. The ordinate (d2(q)/dQ = I ( q ) ) i s the absolute i n t e n s i t y of s c a t t e r e d neutrons, and the a b s c i s s a , q, i s the s c a t t e r i n g v e c t o r i n 8 : q=47rsin0/A (20 : the s c a t t e r i n g angle, λ : wave l e n g t h ) . An i n t e r f e r e n c e peak was observed at p r a c t i c a l l y the same q as our previous SAXS measurements ( 6). In the very small-angle regions, i . e . q
w

c

for D 0 2

(Pj)2o)

u

h

i

c

h

s

a

n

d

t

h

a

t

*

o r

NaPSS m o l e c u l e s

(P^aPSS^*

I

n

the d i s o r d e r e d regions, some m a c r o i o n s a r e d i s t r i b u t e d , and t h i s r e g i o n has an a v e r a g e s c a t t e r i n g l e n g t h d e n s i t y of Ρ I n g e n e r a l , the s c a t t e r e d i n t e n s i t y of neutrons a t q=6 i s g i v e n by E q u a t i o n 2. For t h e model shown above, η corresponds to the number d e n s i t y o f t h e o r d e r e d c l u s t e r , V t o t h e volume o f


27. MATSUOKAETAL.

359

Cluster Size in Polyelectrolyte Solutions

3

p

T

h

e

a

n

the c l u s t e r (=47rR /3), and Δ ρ = ρD20~ NaPSS' scatter ing length d e n s i t y f o r each r e g i o n i s represented as f o l l o w s by those of solvent ( Ρ o l v ^ D 2 0 ^ polymer po lymer NaPSS * * =/0

d

S

( p

(= p

;

"cluster p

=

dis

=

+

^c^polym p

*d polym

+

(

1 _

=

p

cluster "

= (*

" *d

c

) ( p

p

dis ( 9 )

p o l y m " "solv*

where φ and ^ are volume f r a c t i o n s of polymer i n c l u s t e r s and i n The d i s o r d e r e d region, r e s p e c t i v e l y . By using Equation 9, Equation 2 becomes

the


0

I(0)=d^a η V and

2

(* -* ) c

Φ

can be w r i t t e n as

0

= (N Mw

0

C

/ (N

A

2

(Opolym-Osolv)

d

2

'

10

( >

d))/ V

(11),

where Ν i s the number of polymers i n one cluster (= V/(2D^ ) ) , Mw the molecular weight of polymer, N the AvogaSrô number, and d the d e n s i t y of ^the polymer. The t o t a l number of polymer i n c l u s t e r s (N ) and the t o t a l number of polymers i n d i s o r d e r e d regions ( N ) are A

d i s

Ν* = η Ν N

(12)

N

N

( 1 3 )

dis = tot " *

where N i s the t o t a l number of polymers i n the system. The volume f r a c t i o n of d i s o r d e r e d regions, V , is t o t

d i s

V

dis = 1 " V η

(14)

Hence, N

*d=< dis

Mw

N

d

/ < A >>/

By using Equations ^ W ^ l V I f we a

define = (Mw

2

2

v

N

dis=< dis

11,12

and

( (N/V-(N

/ (N

A

d) )

2

Mw

14,

N

/< A d))/(l-Vn) Equation

10 reduces to;

-N* )/( 1-Vn) ) ( ρ 2

tQt

(p

(15)

p

o

l

y

m

-ρ

„ - Psolv) 2

p

o

l

y

m

) (16)

2

s o l v

17

< >>

then d

Kj

0 )

= α

When we β

η V

2

((N/V)-(N

tot

-Nn)/(l-Vn))

2

(18)

define

= Ν - V N

t Q t

then


(19),

360


1

n

/

2

a ±/a 0 + 4 Y ( d Z (0)/dQ ) ) /(2(άΣ(0)/dQ) V) 1/2

^ - *

2

1 / 2

By be

(20)

E q u a t i o n 20, t h e number d e n s i t y o f estimated. Here^, we J i s e d 0 =6.Ο5 η 9 Π

2

*NaPSS= -

0 9

x

1

0

c

m

the cluster, χ 10 , and

n,

can

·


The r e s u l t s a r e summarized i n T a b l e I I I . The g e n e r a l trend of this model calculation is as follows; A t low p o l y m e r c o n c e n t r a t i o n , a l a r g e number o f r e l a t i v e l y small er c l u s t e r s a r e d i s t r i b u t e d i n the system. The difference i n t h e number d e n s i t i e s o f t h e p o l y m e r s between t h e c l u s ters and the disordered regions are rather large. With increasing polymer concentration, the size of the cluster becomes l a r g e r . However, t h e number d e n s i t y of the clus t e r s become smaller. V o i d M o d e l A s i s w e l l known f r o m t h e B a b i n e t p r i n c i p l e , i t cannot be determined by simple s c a t t e r i n g experiments that the density d i f f e r e n c e ( Δ ρ ) is positive or negative. For the present case, i t i s c e r t a i n that there e x i s t s a large scale density fluctuation i n the system, b u t we cannot claim conclusively that the upturn is solely due t o a c l u s t e r of high polymer density: the opposite case, i.e. v o i d s t r u c t u r e o f low polymer d e n s i t y , cannot be e x c l u d e d . Actually, f o r some c a s e s , void structures were observed by u l t r a m i c r o s c o p e f o r i o n i c p o l y m e r l a t e x d i s p e r s i o n s at l o w i o n i c s t r e n g t h s . ( 2 0 , 2 1 ) H e n c e , we p e r f o r m e d a s i m i l a r model c a l c u l a t i o n f o r a v o i d s t r u c t u r e . F i g u r e 9 shows a model o f t h e v o i d s t r u c t u r e u s e d i n t h i s calculation. For simplicity, we a s s u m e d t h a t no p o l y m e r s were c o n t a i n e d i n voids and they coexisted with ordered p a r t i c l e s . Voids a r e spheres of radius R. F o r the case o f void structure, E q u a t i o n 2 i s a l s o v a l i d w i t h t h e number density of voids, n y ^ j , and t h e volume o f t h e v o i d , V . Δ ρ f o r t h i s case i s a e r i n e d by Δ

ρ

=

p

order

p

"

solv(D20) =

since

φ

o

r

d

e

is

r

border Equation Δ

given =

c

(

"

=

c

d

/

21 c a n b e

(

border

p

polym

" ^solv*

(

2

1

)

by

> /

v

o r d e r

=

c

/
>

'

written

/
>

·

Then, =

where which Table

a=

n

v

void

( void>

( c / d ) ( p

p

o

l

y

m

-

« / p

D

2

Q

d e v o i d * )

(25),

g i v e s us n values. The r e s u l t s a r e summarized i n III. The η v a l u e d e c r e a s e d w i t h i n c r e a s i n g p o l y m e r c o n c e n tration, which i s e a s i l y acceptable, while n ^ i j was n o t so s e n s i t i v e towards salt concentration under xne c o n d i tions studied here. Certainly, with the experimental data available now, i t is definitely impossible to conclude whether the void structure really contributes to the v

r

ν

i

ο

i

ι

H

α


27. MATSUOKA E T A L

Cluster Size in Pofyelectrofyte Solutions

Ordered

361

Disordered

C l u s t e r

Region

Ο

/

οο ο \

/ Ο Ο Ο Ο Θ\ · •


2 R

ι

\ °

Ο Ο ο

\ο ο ο χ.ο Ο

^ s o

0

20

°τ

ex ρ

ο

/

ο

1 ν ."

PdiS.

— ]|

Δ ρ

^ c l u s t e r @ ρο Ίym .

Figure 8 S t r u c t u r a l model used f o r absolute calculation.

intensity

Void Structure

i o o o o o o o o yo

ο ο

Ο

Ο

Ο

ο

ο ο

s—\ (

]

ο

ο

Ο

Ο

ri

r — P i ΔΡ

Porder Ppolym.

F i g u r e 9 Void calculation.

model

used

f o r absolute

intensity



362

Table III Number Density (n) of Clusters and Voids [NaPSS]


(g/ml)

[NaCl] (M)

0.01 0.02 0.04 0.08

0 0 0 0

0.04 0.04 0.04 0.04

0.05 0.1 0.3 0.5

η

n (10

1 2

v o i d

3

cm" )

346 14.9 4.1 1.46

838 269 117 51.5

8.50 (110)

95.2 86.2 67.4 88.9

appearance of the upturn, although the model c a l c u l a t i o n d i d not provide unacceptable r e s u l t s . Judging from the microscopic observation of the l a t e x d i s p e r s i o n s , c l u s t e r s and v o i d s t r u c t u r e are simultaneously present i n r e a l s o l u t i o n s . Further study i s necessary and i n progress i n order to c l a r i f y the true nature of i o n i c d i s t r i b u t i o n i n polyelectrolyte solutions. Conclusions A steep upturn at very small-angle regions was observed f o r NaPSS i n D 0 s o l u t i o n s . This upturn r e f l e c t s the e x i s t e n c e of l a r g e s c a l e d e n s i t y f l u c t u a t i o n such as ordered c l u s t e r s . The s i z e of the c l u s t e r was estimated by both G u i n i e r and Debye-Bueche analyses. The radius was i n the range of 200 - 1000 8 , and increased with i n c r e a s i n g polymer c o n c e n t r a t i o n . The r a d i i estimated by the simple G u i n i e r method and by using the Porod a n a l y s i s agreed very w e l l . The l i n e a r i t y of the Debye-Bueche p l o t was e x c e l l e n t . The number d e n s i t y of the c l u s t e r , n, was a l s o c a l c u l a t e d by using absolute s c a t t e r e d i n t e n s i t y and decreased with i n c r e a s i n g polymer c o n c e n t r a t i o n . Both the radius and the number d e n s i t y of c l u s t e r s were independent of added s a l t i n the c o n c e n t r a t i o n range s t u d i e d here. The p o s s i b i l i t y of v o i d s t r u c t u r e was a l s o considered. 2

Acknowledgments T h i s work i s supported by a G r a n t - i n - A i d f o r S p e c i a l l y Promoted Research (no.63060003) and an I n t e r n a t i o n a l S c i e n t i f i c Research Program from the M i n i s t r y of Educa t i o n , Science and C u l t u r e , Japan, and a p a r t i a l support of the t r a v e l i n g expenses from the Japanese-German C u l t u r e I n s t i t u t e , to which our g r a t i t u d e i s due. D.S. would l i k e to thank Yamada Science Foundation f o r a f e l l o w s h i p . H.M. expresses h i s s i n c e r e thanks to Ms.Rita Thomas, Messers Gerd Meier and Gunter Pohl, and other members of the I n s t i t u t e of Festkfirperforschung f o r t h e i r k i n d coopera t i o n ad support during h i s stays i n J u l i c h .



27. MATSUOKA ET AL.

Cluster Size in Polyelectrofyte Solutions

References 1) Ise,N. Angew. Chem. 1986, 25, 323. : Ise,N.;Matsuoka, H.;Ito, K. Macromolecules 1989, 22, 1 : Ise,N.; Matsuoka, H.;Ito,K.;Yoshida,H.; Yamanaka, J . Langmuir 1990, 6, 296. 2) Ise, N.; Okubo, T. Acc. Chem. Res. 1980, 13, 303. 3) Ise,N.;Okubo,T.;Yamamoto,K.;Kawai,H.;Hashimoto,Τ.; Fujimura,M.;Hiragi,Y. J. Amer. Chem. Soc. 1980, 102, 7901. 4) Plestil,J.;Mikes,J.;Dusek,K.; Acta Polym 1979, 30, 29. 5) Matsuoka, H.; Schwahn D.; Ise, N. Macromolecules 1991, 24, 4227. 6) Ise, N.; Okubo, T.; Kunugi, S.; Matsuoka, H.; Yamamoto, K.; Ishii, Y. J.Chem.Phys. 1984, 81, 3294. 7) M.Nierlich et al., J.Physique,1979, 40, 701. 8) Alefeld, Β.; Schwahn, D.; Springer, T. Nucl. Instrum. Methods Phys. Res. 1989, A274, 210. 9) Guinier, Α.; Fournet, G. "Small-angle Scattering of X -rays" Wiley, NY, 1955 10) Debye, P.; Bueche,A.M. J.Appl.Phys. 1949, 20 518. 11) Porod,G. Kolloid Z. 1951 124, 83. 12) Boue, F. et a l . , Proc. Symp. Neutron Inelastic Scattering,1977, 1, 563. 13) Schwahn,D.; Hahn,K.; Sheib,J.; Springer,T. J.Chem.Phys. 1990, 93, 8383. 14) Lin,S.-C.; Lee,W.I.; Schurr,J.M. Biopolymers, 1978, 17, 1041. 15) Drifford,M.;Dalbiez,J.P.; J.Physique, 1985 46, L-311. 16) Sedlack,M.; Amis,E. J.Chem.Phys. 1991, 96 817. 17) Sedlack,M. Macromolecules, in press. 18) Matsuoka,H; Hattori,N.; Ise,N. in preparation. 19) Matsuoka,H.; Tomita,H.; Ise,N. in preparation. 20) Ito,K.; Yoshida,Y.; Ise,N. Chem. Lett., 1992, 2081. 21) Dosho, S. et a l . , 1993 Langmuir, 9, 394. RECEIVED August 6,

1993


363

Determination of Cluster Size in Polyelectrolyte ... - ACS Publications

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