IonPolyion Interactions in Chondroitin Sulfate Solutions - American

27 Ion—Polyion Interactions in Chondroitin Sulfate Solutions H. MAGDELENAT—Service de Radiopathologie, Institut Curie, 26, rue d'Ulm, 75005 Paris, France P. TURQ—Laboratoire d'Electrochimie, Université P. et M . Curie, 4, place Jussieu, 75230 Paris, France

Downloaded by UNIV LAVAL on July 14, 2016 | http://pubs.acs.org Publication Date: April 21, 1981 | doi: 10.1021/bk-1981-0150.ch027

P. TIVANT and M . DRIFFORD—Laboratoire de Spectroscopic Optique, C.E.N. Saclay, 91190 Gif-sur-Yvette, France

The Nernst-Einstein

relationship

(1),

U° / D° = Ζ e/kT

(1)

s

relates the electrical mobility U° and the self-diffu sion coefficient D° of an ionic species in solution through the structural charge Ζ (e = elementary charge, kT = Boltzman factor). It allows the determination of the structural charge of individual species such as simple or complex ions, since the transport parameters, U°and D° can be obtained experimentally, for instance with radioactive tracers (2). This relationship is strictly valid only in the limit of infinite dilution, i.e., in the absence of interactions between the ionic species. In the presence of such interactions, for instance in semi-dilute solutions, one can however define the apparent charge, Ζ , by the following equation : s

ap

Ζ

ap

= (U/D) (kT/e)

(2)

where U and D are the observed transport parameters. In many cases Ζ is a good approximation to the effec tive charge (2). It is the aim of this presentation to show how the determination of U, D, and subsequently Z, reflects the nature and the extent of ion-polyion ap

ap

0097-6156/81/0150-0387$05.00/0 © 1981 American Chemical Society Brant; Solution Properties of Polysaccharides ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

SOLUTION

388 interactions salts.


Theoretical

i naqueous

PROPERTIES

solutions

with

OF

POLYSACCHARIDES

or without

added

Background.

I n t h e frame o f e l e c t r o c h e m i s t r y , polyelectrolytes are defined as macromolecular s t r u c t u r e s bearing a g r e a t n u m b e r o f c h a r g e d s i t e s . We c o n s i d e r t h e case where these s i t e s a r e s i m i l a r i nn a t u r e ( n e g a t i v e i n m o s t b i o l o g i c a l p o l y e l e c t r o l y t e s s u c h a s DNA, RNA o r sulfated polysaccharides), so that t h ep o l y e l e c t r o l y t e , or p o l y i o n , a c q u i r e s a high charge density. Counterions are present i n s o l u t i o n i norder t o m a i n t a i n e l e c t r o n e u t r a l i t y o r as c o n s t i t u e n t s o f a n added simple s a l t which, i nturn, introduces a co-ion. The transport parameters U and D o f t h e d i f f e r e n t i o n i c s p e c i e s i n trie p o l y e l e c t r o l y t e s o l u t i o n depend both on t h e e q u i l i b r i u m p r o p e r t i e s and on s p e c i f i c e f f e c t s w h i c h a p p e a r i nr e l a t i o n w i t h t h e m o t i o n o f ions, i . e . , "relaxation" and "electrophoresis". Ion-polyion interactions and equilibrium proper ties. The high charge density o f t h ep o l y i o n gives p o l y e l e c t r o l y t e solutions t h e i r unique properties : a) e l e c t r o s t a t i c r e p u l s i o n b e t w e e n c h a r g e d s i t e s gives t h epolyion an extended conformation a t low or semi-low i o n i c s t r e n g t h . The p o l y i o n c a n thus be con s i d e r e d as almost l i n e a r , a t l e a s t over a distance o f several charged s i t e s . b) c o n s e q u e n t l y , t h e e x c e s s f r e e e n e r g y ( o f e l e c t r o s t a t i c o r i g i n ) c a n be d e r i v e d -andsubsequently a l l the e q u i l i b r i u m p r o p e r t i e s , from a c y l i n d e r , o r r o d - l i k e , o r l i n e a r chain model o f d i s t r i b u t i o n o f charges, by s o l v i n g a P o i s s o n - B o l t z m a n n e q u a t i o n w i t h cylindri c a l symmetry f o r t h e p o t e n t i a l . The c e n t r a l parameter o f modern p o l y e l e c t r o l y t e theories i s £ , t h e l i n e a r charge density parameter i n t h e m o d e l o f b a n n i n g (3_) : £

g

= e

2

/ ekTb

(3)

where e = d i e l e c t r i c c o n s t a n t a n d b = a x i a l distance between charged s i t e s . When £ i ss u f f i c i e n t l y high, condensation of counterions on t h e p o l y i o n s h o u l d be observed, a n d i s e f f e c t i v e l y observed, so that £ i s reduced t o [ z , z. b e i n g t h e v a l e n c e o f t h e c o u n t e r i o n (3.). The r e s i dual charge o f t h ep o l y i o n i sa f r a c t i o n of the struc t u r a l charge Ζ ,

Brant; Solution Properties of Polysaccharides ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

MAGDELENAT

27.

ET AL.

Chondroitin

Sulfate

389

Solutions

-1 α = ( £ ζ.) (4) s i The a b o v e e x p r e s s i o n s a p p l y t o p o l y i o n s w i t h u n i v a l e n t charged s i t e s . I n the absence o f added s a l t α i s a l s o the f r a c t i o n f o f c o u n t e r i o n s which are not condensed onto the p o l y i o n . The observed transport parameters f o r the counterions should t h e r e f o r e be the f r a c t i o n - a v e r a g e d mean o f t h e t r a n s p o r t p a r a m e t e r s o f t h e uncondensed (u) a n d condensed ( c ) e n t i t i e s . with

D

-p V I· υ

_


U -

(u)

A( ξ , r . )

+

(1-f)

(c)

(5)

Ion-polyion interactions andtransport properties. Relaxation effect.In equation( 5 ) A ( ξ ,r.) represents the c o r r e c t i o n f o r r e l a x a t i o n . The r e l a x a t i o n e f f e c t i s due t o the temporary asymmetry o f t h e i o n i c atmosphere around a given i o n . The e l e c t r i c field w h i c h a p p e a r s f r o m c h a r g e s e p a r a t i o n s l a c k e n s t h e mo t i o n o f the i o n · A( ξ , r.) h a sbeen c a l c u l a t e d b y M a n n i n g 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 (k) · O n l y a t zero o r low added s a l t c o n c e n t r a t i o n can A( ξ , r . ) be s i g n i f i c a n t l y l o w e r t h a n 1. E l e c t r o p h o r e t i c e f f e c t . I ti s due t o the mutual hydrodynamic t r a n s m i s s i o n o f v e l o c i t y between moving ions · Material

and

Method.

The p o l y i o n . C h o n d r o i t i n s u l f a t e was e l e c t e d f o r t h i s work because o f i t s b i o l o g i c a l i n t e r e s t : i t i s the main component o f c a r t i l a g e a n dp l a y s a r o l e i n b i o l o g i c a l c a l c i f i c a t i o n and r e t e n t i o n o f m u l t i v a l e n t c a t i o n s (see paper b y Rosenberg, t h i s symposium) C h o n d r o i t i n s u l f a t e (ChSO,) i s a p o l y m e r o f g l u curonic a c i d andglucosaminosulfate with two isomeric p o s i t i o n s f o r t h e s u l f a t e g r o u p ( F i g . 1 ) . We h a v e mostly worked w i t h the 4-isomer. I t i s a n adequate model o f p o l y e l e c t r o l y t e w i t h r e l a t i v e l y high charge density. I ti s almost l i n e a r i n s o l u t i o n a s shown b y e l e c t r o n m i c r o s c o p y (5) o r by p h y s i c o - c h e m i c a l determinations (6). The a v e r a g e d i s t a n c e b e t w e e n c h a r g e d s i t e s c a n be e s t i m a t e d t o b e n e a r 6 A, w h i c h makes £ a b o u t 1.2. s As a c o m p a r i s o n w i t h o t h e r b i o l o g i c a l a n i o n i c p o l y s a c c h a r i d e s , h y a l u r o n i c a c i d i s l e s s charged ( b 2 0 A) w h i l e h e p a r i n i s more ( b ~ 3 - 4 A ) . The m o l e c u l a r w e i g h t o f t h e p o l y i o n i s 29-30,000 D a l t o n s l e a d i n g t o a s t r u c t u r a l c h a r g e o f a b o u t -120 a n d a c o n t o u r l e n g t h o f a b o u t 600 A . H o w e v e r , t h e


390

SOLUTION

polyion - 1 0 0

i snot exhaustively

PROPERTIES

OF

POLYSACCHARIDES

s u l f a t e d and Ζ

i s about S

.


The s e l f - d i f f u s i o n c o e f f i c i e n t a n d e l e c t r i c a l m o b i l i t y o f t h e p o l y i o n ( i n e x c e s s s o d i u m s a 1 t j 2 a r ç -1 r e s p e c t i v e l y 3 & +CVt F i c k s a n d ( 5 . 7 + 0 . 5 ) 1 0 " c m s " V " . Transport parameter measurements. Transport parameters o f small counterions were measured by r a d i o a c t i v e t r a c e r methods, t h e l a b e l e d i o n i c s p e c i e s moving amidst a c h e m i c a l l y homogeneous solution : - s e l f - d i f f u s i o n , by t h e "open and c a p i l l a r y " method d e s c r i b e d p r e v i o u s l y ( 7 , 8 ) - e l e c t r i c a l m o b i l i t y , by electrophoresis on c e l l u l o s e a c e t a t e s t r i p s (9.). Transport parameters o f the macromolecular ionic s p e c i e s were measured b y dynamic l i g h t s c a t t e r i n g : - a p p a r e n t d i f f u s i o n c o e f f i c i e n t was d e r i v e d from t h e broadening o f t h e Rayleigh d i f f u s i o n line m e a s u r e d b y homodyne o r h e t e r o d y n e o p t i c a l b e a t i n g ( 1 0 ) . I f Γ i s t h e l i n e w i d t h o f t h e power spectrum o f R a y l e i g h d i f f u s i o n , and k t h e modulus o f t h e a s s o c i a t e d w a v e v e c t o r , k = ( 2 ττ η / λ ) s i n ( Θ / 2 ) , t h e n : o

Γ = D k

2

t

.

- the e l e c t r i c a l m o b i l i t y o f the macroion i s pro p o r t i o n a l t o t h e s h i f t o f t h e h e t e r o d y n e power s p e c trum i n t h e presence o f an e x t e r n a l e l e c t r i c field(10). The o p t i c a l m o u n t i n g s h a v e b e e n d e s c r i b e d previously Results. We d e f i n e r . a s t h e r a t i o o f e q u i v a l e n t concentra t i o n z.n. o f t h e added c o u n t e r i o n i o f charge z. t o the e q u i v a l e n t c o n c e n t r a t i o n o f t h e p o l y i o n η ( r . = Ζ.n./n ) . χ χ χ e Transport parameters of counterions. One c o u n t e r i o n s p e c i e s : F i g u r e ( 2 ) s h o w s t h a t the s e l f - d i f f u s i o n c o e f f i c i e n t o f Na i n chondroitin sulfate salt solution, D , i s lowered from i t s value i n absence o f p o l y e l e c t r o l y t e ( + - 1 3 3 Ficks) to a l i t t l e l e s s than 1 0 0 F i c k s i n t h e absence o f added N a C l ( r . = 0 ) . Since h a l f o f t h i s 3 0 percent d e c r e a s e c a n Èe a c c o u n t e d f o r b y t h e r e l a x a t i o n e f f e c t , i t means t h a t a r o u n d 1 5 p e r c e n t o f t h e p o l y i o n c h a r g e i s n e u t r a l i z e d by condensed N a ions. This i s i n agreement w i t h t h e p r e d i c t e d l o w e r i n g o f £ f r o m ξ 1 . 2 to ξ f = 1 = [Zi] · N o s i g n i f i c a n t s p e c i f i c e f f e c t , a s regards condensation, was o b s e r v e d n e i t h e r between Na +

+

D

a

+

+


ET AL.

Chondroitin

Sulfate

Solutions

391


MAGDELENAT

Figure 2.

Variation of T> + when NaCl is added to: (1) ChSO^-Na (Φ); (2) ChSO^N(CHs)^ (O) (n = 3.4 χ 10 equiv/L. Na

3

e


SOLUTION

392 and N(CH3 ) 4

(Fig.2),

+

PROPERTIES

n o rbetween N a

+

OF

POLYSACCHARIDES

and C s

+

The v a r i a t i o n o f U + , t h e e l e c t r i c a l m o b i l i t y o f Na i n c h o n d r o i t i n s u l f a t e s o l u t i o n s w h e r e N a C l i s a d d e d i s q u i t e s i m i l a r t o t h a t o f DNa ( F i g . 2 ) . T h e apparent charge f o r Na equation (2) i salways close to 1 ( T a b l e I ) . Counterions with d i f f e r e n t charges. I f we a d d divalent cations, l i k e Ca2 , Sr2 or Co t o ChSO4-Na s o l u t i o n s . £ £ b e i n g i n i t i a l l y 1 a n d Z. = 2 , c o n d e n s a tion of occurs i n order t o lower ξ · The observed transport parameters, and , s h o u l d be a s l o w as the t r a n s p o r t c o e f f i c i e n t s o f t h e p o l y i o n . T h i s i s almost true for ( F i g . 4:) a n d i t c a n b e d e r i v e d t h a t up t o a b o u t 50 p e r c e n t o f t h e p o l y i o n c h a r g e c a nb e n e u t r a l i z e d when s u f f i c i e n t d i v a l e n t c a t i o n s a r e added. No s i g n i f i c a n t s p e c i f i c e f f e c t i s o b s e r v e d b e t w e e n the three d i v a l e n t counterions (Fig. k and reference (12)). F i g u r e 5 shows t h e v a r i a t i o n o f when CoCl2 i s a d d e d t o ChSO4-Na. T h e c u r v e s f o r and U a r e q u i t e s i m i l a r . They a l l show a n a n i o n i c behavior at l o w added s a l t c o n c e n t r a t i o n , so that an a n i o n i c a p p a r e n t charge i s o b s e r v e d , w h i c h becomes p o s i t i v e and t e n d s t o w a r d + 2 i n e x c e s s added s a l t ( T a b l e I I ) . However t h e apparent charge o f t h e c o u n t e r i o n s at l o w added s a l t i sn o t as negative as expected , since i t should be c l o s e t o t h e charge o f t h e p o l y i o n (about -100). Therefore some d e g r e e s o f f r e e d o m r e m a i n for t h e c a t i o n s w h i c h a r e a l l o w e d t o move r a p i d l y a l o n g t h e p o l y i o n . I n d e e d n.m.r. e x p e r i m e n t s h a v e s h o w n , a t l e a s t f o r c o b a l t , t h a t l e s s t h a n kO p e r c e n t of t h e condensed ions a r e site-bound ( 1 3 ) · We h a v e a l s o s h o w n p r e v i o u s l y ( l j 2 ) b y m e a s u r i n g when CaCl2 i s added t o ChS0,-Na t h a t t h e s m a l l f r a c t i o n (15 p e r c e n t ) o f t h e s o d i u m i o n s i n i t i a l l y condensed a r e e x p e l l e d from t h e condensation layer by t h e n e w l y c o n d e n s i n g C a 2 i o n s , which c a nbe expec ted from Manning s theory. On t h e c o n t r a r y , t h a t a n e x c e s s o f m o n o v a l e n t i o n s can compete w i t h condensed d i v a l e n t ones i s o u t o f t h e range o f v a l i d i t y o f Manning's model. However, t h e m o d e l o f I w a s a (13.) w h i c h i n t r o d u c e s a n e n t r o p i e t e r m c o n t r i b u t i n g t o t h e free energy o f p o l y e l e c t r o l y t e systems c a n e x p l a i n that an excess NaCl d i s p l a c e s condensed d i v a l e n t counterions. I n t h e experiment d e s c r i b e d i nF i g . 6 , N a C l was added t o a s o l u t i o n o f chondroitin sulfate containing Sr2 counterions, a f r a c t i o n o f w h i c h a r e c o n d e n s e d . T h e v a r i a t i o n o f Dg shows t h a t Sr2+ a r e "decondensed" b y a n e x c e s s NaCl, i n good agreement w i t h I w a s a s model. N

+

+

+

2

+

e


(Fig.3).

+

1

+

1


MAGDELENAT

27.

ET AL.

Chondroitin

Sulfate

Solutions

393

TABLE

Apparent charge added N a C l r

Na+

D

o f N a i n ChSO,-Na ^

Na+ 7

U

2

Na"

solutions

/ U

Cl-

with

Z

Na

+

1


(I0" cm s" )

0

1 0 0

0 . 5 0

0 , 9 0

0 . 2 5

10k

0 . 5 5

0 . 9 2

0 . 5

1 1 0

0 . 5 8

0 . 9 7

1

1 1 5

0 . 6 0

1 . 0 0

r +=n / n : U -f/UCl — : o b s e r v e d e l e c t r i c a l m o b i l i t y Na s e NëT C l o f Nâf" r e l a t i v e t o t h a t o f C l i n C h S O 4 - N a s o l u t i o n s ; ΖNaμ= a p p a r e n t c h a r g e o f Na+ X T

A T


SOLUTION PROPERTIES OF

394

8

POLYSACCHARIDES

P-

7

U)

'4-'

·

X

2+ •

Ca

+

Sr

•

Co

2+ 2+


• in

r

2 +

M 2+

2

2

Figure 4. D o/ C A * , Sr , Co * counterions on adding CaCl , SrCl , or CoCl (τ * = 2n /n ). Upper lines refer to the variation of D of Sr * (+) and Co * (Φ) in the absence of polyelectrolyte. 2

2

8

2

2

Μ

2

e

+ 0.6h

Figure 5.

Variation of O

Co

(relative to the electrical mobility of CI') when CoCl is added to ChSO^-Na


2

27.

MAGDELENAT

ET AL.

Chondroitin

Sulfate

Solutions

395

TABLE I I 2+ Apparent charges Ζ o f t h e d i v a l e n t c o u n t e r i o n s Ca , Sr2+ a n d C o i n C n 2 S O 2 N a s o l u t i o n s (ne= 5 . 4 1 0 ~ 3 e q / l ) as a f u n c t i o n o f t h e i r c o n c e n t r a t i o n ( r . = 2 n / n ) . Ζ 2+ i s t h e a p p a r e n t c h a r g e o f t h e c a t i o n s i n tËe absence o f p o l y e l e c t r o l y t e s , a t i o n i c strengths corresponding to r i . 2 +

Apparent

r.

Ca

2 +

Sr

2

+

Co

charge

2 +

Ζ

ZMo-f

η


xlO 0 0.18

-

7.1 4.5

-

3.5 2.3

0.25 0.36

-

0.55

+ 0.52

0.72

+

0.88

+

1.40

1

-

1.2

-

12

2,00

0

10

1.94

5

6 4.5

1.90

10

+ 0.50

+ 0.9

1.88

15

1.40

+ 1.45

+ 1.1

1.86

19.5

1.40

+ 1.60

+ 1.50

1.85

24

+ 1.6ο

+ 1.56

+ 1.80

1.81

58

1.84

+ 1.63

+ 1.54

+ 1.95

1.78

50

2.25

+

+ 1.55

+ 1.95

1.75

60

2.58

+ 1.67

+ 1.55

+ 1.96

1.72

70

2.94

+ 1.70

+

1.54

+ 1.99

1.70

80

3.68

+ 1.75

+ 1.49

1.64

_

_

100


M

SOLUTION

396

PROPERTIES

OF

POLYSACCHARIDES

/

3+ T r i v a l e n t counterions such as L a , added t o ChSO4-Na, do condense s i n c e £ ~ i s i n i t i a l l y equal to 1 a n d s h o u l d be l o w e r e d t o t h e c r i t i c a l v a l u e o f 1/3 i n t h e p r e s e n c e o f t r i v a l e n t c a t i o n s . R e s u l t s p u b l i s h e d p r e v i o u s l y (12) c l e a r l y showed t h a t up t o about 70 percent o f t h ep o l y i o n charge c o u l d be neu t r a l i z e d by i o n s . L a 3 + i g n s n o t only c o m p e t e d w i t h Na ions b u t a l s o w i t h Ca or Sr ions and the agreement w i t h Manning's model was f a i r l y good. I t i s a general o b s e r v a t i o n that t h e higher t h e coun t e r i o n charge, t h eb e t t e r Manning's model f i t s t h e data concerning condensation. I n d e e d more a n i o n i c v a l u e s than f o r d i v a l e n t c o u n t e r i o n s were obtained (20 f o r t h e e l e c t r i c a l m o b i l i t i e s o f L a ions i n the p r e s e n c e o f C h S O 4 - N a (Zap = - 1 3 f o r L a at low added L a C l concentration* compared t o Ζ = -7 f ° Ca ) i n d i c a t i n g a more r i g i d c o n d e n s a t i o n laylr. T r i v a l e n t c o u n t e r i o n s a d d e d t o ChSO^-Ca s o l u t i o n s w e r e a l s o s h o w n t o c o n d e n s e ( l 2 ) s o t h a t ξ ef, w h i c h i s i n i t i a l l y e q u a l t o 1/2 ( Z C = 2 ) , i s l o w e r e d t o £ = l / 3 i n t h e p r e s e n c e o f t r i v a l e n t c o u n t e r i o n s . On a d d i l i o n o f L a C l 3 , t h e Ca2+ i o n s w h i c h a r e i n i t i a l l y c o n d e n s e d ( a b o u t 4θ p e r c e n t o f t h e s t o i c h i o m e t r i c c o n c e n t r a t i o n ) are e x p e l l e d from t h e condensation l a y e r a s was shown by a n i n c r e a s e o f D ( 1 2 ) · La Transport parameters o f the polyion Transport parameters o f thepolyion i t s e l f will be a f f e c t e d b y t w o t y p e s o f i o n - p o l y i o n i n t e r a c t i o n s : Condensation, which reduces s i g n i f i c a n t l y the e f f e c t i v e charge o f t h ep o l y i o n and hence, i t s e l e c t r i c a l m o b i l i t y . C o n d e n s a t i o n s h o u l d be l e s s s e n s i tive t o theself-diffusion coefficient unless great conformational v a r i a t i o n r e s u l t s from charge modifica tion. E l e c t r o k i n e t i c e f f e c t s , i . e . i n t e r a c t i o n s between the p o l y i o n and i t s i o n i c atmosphere, s i n c e counterions c a n n o t move i n d e p e n d e n t l y from t h ep o l y i o n , i n order to m a i n t a i n e l e c t r o n e u t r a l i t y . These e f f e c t s a r e h i g h l y dependent on t h e i o n i c s t r e n g t h o f t h e s o l u t i o n s and a f f e c t b o t h s e l f - d i f f u s i o n a n d e l e c t r i c a l m o b i l i t y as m e a s u r e d b y dynamic l i g h t s c a t t e r i n g s i n c e they give r i s e t o long-range s p a t i a l c o r r e l a t i o n s between i o n s . These e f f e c t s a r e expected t o be l a r g e r i n d i l u t e s o l u t i o n s because o f t h e large r e l a t i v e f l u c t u a t i o n s there· The v a r i a t i o n o f t h e t r a n s l a t i o n a l d i f f u s i o n coef f i c i e n t measured a t 20°C b y homodyne d e t e c t i o n a t a n g l e s f r o m 5 ° t o k0° o f C h S O , - N a w h e n t h e i o n i c s t r e n g t h i s e


+

2

r

3

a


f

+

27.

MAGDELENAT ET AL.

Chondroitin

Sulfate

397

Solutions

i n c r e a s e d by a d d i t i o n o f NaCl i s r e p o r t e d i n Table I I I . Figure 7 represents the experimental v a r i a t i o n (lower v a l u e s , ) together with other v a l u e s d e r i v e d from three models, assuming an e f f e c t i v e charge o f t h e polyion Ζ = - 8 8 . (ChSO.-Na : l O g / l ) . + : t h e model o f S t e p h e n ( l A ) where t h e f l u c t u a t i o n s o f t h e m a c r o i o n s a r e t h e o n l y ones t o be t a k e n into account gives : Z

D,

p


X

ef ef ) 1 + 2r

(1 +

= D *

(6)

w h e r e Dp i s t h e s e l f - d i f f u s i o n c o e f f i c i e n t o f t h e p o l y ion and r = η / η i s the r a t i o o f the equivalent cons e c e n t r a t i o n o f t h e added s a l t t o t h a t o f t h e p o l y i o n . Δ : t h e m o d e l o f T u r q ( 1 1 , 15) , w h e r e t h e f l u c t u a t i o n s o f t h e t h r e e components o f t h e system a r e c o n s i d e r e d . T h i s model l e a d s t o t h e f o l l o w i n g expres sion for D (11) : (Z 1 2r) D D e

(Z

e

f

+

1

+

f

+

+

r)D

p

D

l

+

p D l

(Z

e f +

2

r)D D p

2

+

(Z

e

f

+

2r

(7) and are the s e l f - d i f f u s i o n c o e f f i c i e n t s of the counterion and the coion r e s p e c t i v e l y . φ : a m o d e l o f s c r e e n e d c h a r g e , t h a t we p r o p o s e o r i g i n a l l y h e r e ( 1 5 . ) · T h e two p r e c e d i n g m o d e l s based on t h e Debye-Onsager treatment o f i o n t r a n s p o r t , c o n s i d e r t h e e n t i r e charge o f t h e p o l y i o n t o be con centrated i n a point charge. T h i s i s t o t a l l y mislea d i n g s i n c e t h e l e n g t h o f t h e p o l y i o n c h a i n c a n b e one h u n d r e d times t h a t o f t h e D e b y e - s c r e e n i n g l e n g t h (K-1) a t s u c h i o n i c s t r e n g t h s . We p r o p o s e t h a t t h e e f f e c t i v e c h a r g e o f t h e p o l y i o n Zef b e r e p l a c e d i n e q u a t i o n ( 7 ) by a s c r e e n e d c h a r g e , Ζ D , o f t h e f o r m : -Kb Z = 1 e (8) -Kb 1 - e b b e i n g the d i s t a n c e between charged s i t e s and Κ t h e Debye s c r e e n i n g p a r a m e t e r . E a c h u n i t c h a r g e on t h e p o l y i o n c h a i n , a t a d i s t a n c e nb f r o m a c e n t r a l c h a r g e , c o g t g i b u t e s to i h i s c e n t r a l charge by a s c r e e n i n g f a c t o r e s o t h a t t h e sum o f c o n t r i b u t i o n s g i v e s equation (8). I n order t o maintain the t o t a l concentration, n must be r e p l a c e d b y n = n e Z /ZD i n e q u a t i o n ( 7 ) · T h e a g r e e m e n t o f t h i s mocïel w i t h t h e e x p e r i m e n t a l v a l u e s i s much b e t t e r t h a n b y t h e o t h e r m o d e l s . 1

+

n

f


SOLUTION

PROPERTIES

OF

POLYSACCHARIDES


398

Figure 7.

Variation of D of ChSO -Na f

k

with added NaCl concentration


27.

MAGDELENAT

ET AL.

Chondroitin

Sulfate

399

Solutions

T h e v a r i a t i o n o f t h e e l e c t r i c a l m o b i l i t y o f ChSO^ -Na m e a s u r e d b y d y n a m i c l i g h t s c a t t e r i n g ( h e t e r o d y n e d e t e c t i o n a t an angle o f 5 ° ) , i s r e p o r t e d i n F i g u r e 8 . The m o b i l i t y d e c r e a s e s w i t h t h e f i r s t a d d i t i o n o f N a C l , t h e n k e e p s a c o n s t a n t v a l u e f r o m 2 10~"-> t o 1 0 ~ Μ a d d e d NaCl. The i n i t i a l value i s compatible with an e f f e c t i v e charge o f the p o l y i o n Ζ - - 4 2 (corresponding t o a s t r u c t u r a l c h a r g e Ζ = -$Ό. T h e i n i t i a l d e c r e a s e can be d e s c r i b e d by t h e t l o r i n - H e n r y model ( l 6 ) f o r the e l e c t r i c a l m o b i l i t y o f c y l i n d r i c a l m a c r o i o n s according to : 2 Ζ . Ko ( K a ) ώ

r

Λ

U

=

λ


ττη

1

F

(

+

m

SLJLJL)

Ka K l (Ka)

( ) 9

a

where

of

a i s the radius of the c y l i n d e r 1 i t s length ο r thehydration radius of the counterion (1.5A) Ko e t K l t h e z e r o t h a n d f i r s t o r d e r s o l u t i o n s the modified Bessel function (17) F : Henry's f a c t o r being

the ionic

strength.

1000ckt ο

The

best

f i t i s obtained

for values

of 1 a Z

: 300 A : 25 A o

:

5

ef " ° The l e v e l i n g o f t h e e x p e r i m e n t a l v a l u e s a t h i g h e r i o n i c s t r e n g t h c a n be a s c r i b e d t o a c o n f o r m a t i o n a l change o f t h e macromolecule, t h e p o l y i o n b e i n g less a n d l e s s r i g i d a n d g e t t i n g a more a n d more s p h e r i c a l c o n f o r m a t i o n when t h e i o n i c s t r e n g t h i n c r e a s e s . Conclusion F r o m t h e e x p e r i m e n t a l r e s u l t s t h a t we h a v e j u s t p r e s e n t e d , w h i c h were o b t a i n e d b y v a r i o u s indépendant techniques, i t i s obvious that e l e c t r o s t a t i c intera c t i o n s have a predominant i n f l u e n c e on i o n - p o l y i o n i n t e r a c t i o n s i n aqueous s o l u t i o n s . T h i s i n f l u e n c e i s exerted a t three d i f f e r e n t l e v e l s : l ) Coulombic f o r c e s give r i s e , i n i o n i c systems i n v o l v i n g species with high charge d e n s i t i e s , t o short range i n t e r a c t i o n s such as condensation i n t h e sense of Manning and t o l o n g range i n t e r a c t i o n s i n t h e sense of Debye-Huckel. T h i s leads t o a s e p a r a t i o n o f the c o u n t e r i o n s i n t o two t y p e s : - f r e e counterions i n t e r a c t i n g only weakly with the p o l y i o n through l o n g range Debye-Huckel i n t e r a c t i o n s .


400

SOLUTION

PROPERTIES

OF

POLYSACCHARIDES

TABLE I I I


Variation

o f D^(ChSO^-Na)

[NaCl] :

1 θ "

D : (Ficks)

lk.5

5.10~

2

9.4

2

with

10"

the ionic

1

8.9

strength

:

0.25

0.5

0.75

1

5.0

4.0

3.5

3*4

> "ε υ

-

5 | X

D

Λ

. . χ

0.5 10

x

CNaCH

Ceq/l.D

Figure 8. Variation of the electrical mobility of ChSO -Na (1.5 g/L) with added NaCl concentration: (A) experimental values; (\) values derived from Equation 9. u



27.

MAGDELENAT ET AL.

Chondroitin Sulfate Solutions

401

- condensed counterions, entrapped i n the close atmosphere of the polyion, some of them being s i t e bound (as seen by n . m . r . ) , the other moving f r e e l y along the polyion. These short range interactions are mostly e v i denced by the v a r i a t i o n laws of transport coefficients of the counterions while the long range interactions affect the e l e c t r i c a l mobility of the polyion, as measured by dynamic l i g h t s c a t t e r i n g . 2) The e l e c t r o n e u t r a l i t y states that negative and positive charges cannot be macroscopically sepa rated ; this leads to great variations between macro scopic transport parameters and i n d i v i d u a l ion trans port parameters. Such effects appears s i g n i f i c a n t l y at low ionic strength. The case of the t r a n s l a t i o n a l d i f f u s i o n coefficient of ChSO,-Na as measured by dyna mic l i g h t scattering i l l u s t r a t e s the amplitude of the v a r i a t i o n and the need for new t h e o r e t i c a l approach. 3) Ionic strength is responsible for conforma t i o n a l e f f e c t s , the screening of coulombic repulsion between charged s i t e s on the polyion leading to less extended conformation. A l l these effects have to be considered when interpreting equilibrium properties or i r r e v e r s i b l e phenomena of polyelectrolyte solutions. Abstract The charge effects on ion-polyion interactions i n chondroitin-sulfate solutions were studied by both tracer and dynamic l i g h t scattering techniques. The experimentally available quantities are therefore the transport coefficients of both counterions and polyions. The tracer techniques have provided the s e l f - d i f f u s i o n coefficients (D) and e l e c t r i c a l mobi lities (U) of counterions. The dynamic l i g h t scattering techniques with or without an applied e l e c t r i c f i e l d lead to the s e l f - d i f f u s i o n coefficient (D) and to the e l e c t r i c a l mobility (U) of the polyion itself. An extensive use of the Nernst-Einstein r e l a t i o n expres sed as Ζ = (U/D).(e/kT) provides the apparent charges of the different ionic e n t i t i e s i n solutions of mix tures of chondroitin sulfate with different added s a l t s . The effects of counterion condensation are separated from those due to e l e c t r o n e u t r a l i t y condi tions and long range Coulomb i n t e r a c t i o n s , especially for the polyion.


402

SOLUTION

Literature

Cited

PROPERTIES

O F POLYSACCHARIDES

.

1 . Robinson, R.A.;Stokes, R.H. "Electrolyte Butterworths : London, 1970.

Solutions"

2 . Magdelénat, Η.; Turq, P.; Tivant, P.; Chemla, M.; Menez, R.; Drifford, M. J. Chem. Educ., 1978, 55, 12-17. Apparent ionic charge in electrolyte and polyelectrolyte solutions.


3 . Manning, G.S. J. Phys. Chem., 1969, 51, 924-933. Limiting laws and counterion condensation in poly electrolyte solutions.I Equilibrium properties. 4 . Manning, G.S. J. Phys. Chem. ,1969, 51, 934-938 . Limiting laws and counterion condensation in polyelectrolyte solutions .II Self-diffusion of the small ions. 5 . Thierry,

J.P. Personnal communication.

6 . Tanaka, K. J. Biochem., 1978, 83, 647-653 & 655659. Physicochemical properties of chondroitin sulfate. I Ion binding and secondary structure. 7 . Anderson, J.S.; Saddington, K. J. Chem. Soc., 1949, Sup 2, 381-386. The use of radioactive isotopes in the study of the diffusion of ions in solution. 8 . Magdelenat, H.; Turq, P.; Chemla, M. Biopolymers, 1974, 13, 1535-1548. Study of the self-diffusion coefficients of cations in the presence of an anionic polysaccharide. 9 . Magdelénat, H.; Turq, P.; Chemla, M.; Para, B. Biopolymers, 1976, 15, 175-186. Electric mobility of bivalent cations in the presence of an anionic polysaccharide. 10 . Berne, B.J.; Pecora, R. "Dynamic Light John Wiley & sons :New York, 1976. 11 . Gouesin-Menez, R. "Applications de la quasi-élastique de la lumière à l'étude priétés dynamiques de macromolécules Thesis, Paris, 1979.

Scattering" diffusion des pro chargées",


27.

MAGDELENAT

E T AL.

Chondroitin

Sulfate

Solutions

403

12 . M a g d e l é n a t , H . ; Turq, P . ; T i v a n t , P . ; Chemla, M . ; Menez, R . ; D r i f f o r d , M. Biopolymers, 1979, l 8 , 187-201. The effect of counterion s u b s t i t u t i o n on the transport properties of p o l y e l e c t r o l y t e solutions. 13 . T i v a n t , P . ; Turq, P . ; M a g d e l é n a t , H . ; Spegt, P . ; W e i l l , G. Biopolymers, 1979, 18, 1849-1857. Condensation of Co ions on chondroitin sulfate from transport c o e f f i c i e n t s and protons NMR measurements i n aqueous s o l u t i o n s .


2+

14 . Stephen, M.J. J. Chem. Phys., 1974, 61, 15981599. Doppler s h i f t s i n l i g h t scattering from macroion i n s o l u t i o n . 15 . T i v a n t , P . ; Turq, P . ; D r i f f o r d , M . ; M a g d e l é n a t , H.; Menez, R. submitted to Biopolymers. 16 . Abramson, H . A . ; Gorin, M . H . ; Moyer, L . S . Chem. Rev., 1939, 24, 345-366. 17 . Abramovitz, M . ; Stegun, I.A."Handbook of Mathematical functions", Dover : New York, 1965. RECEIVED October 21, 1980.


IonPolyion Interactions in Chondroitin Sulfate Solutions - American

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