Co-Ion and Counter-Ion Interactions with Sulfonated Polysaccharides

16 Co-Ion and Counter-Ion Interactions with Sulfonated Polysaccharides

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 13, 2017 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0077.ch016

MARGARET TOMASULA, NANCY SWANSON, and PAUL ANDER

1

Department of Chemistry, Seton Hall University, South Orange, NJ 07079

With t h e advent o f t h e Debye-Hückel t h e o r y and its subsequent scrutinization t o e x p e r i m e n t a l testing, a p h y s i c a l p i c t u r e emerged f o r t h e b e h a v i o r o f s i m p l e electrolyte s o l u t i o n s a l o n g w i t h its limiting laws which a r e valid f o r v e r y dilute s o l u t i o n s . T h i s model, a l o n g w i t h its f u r t h e r development by Onsager, and t h e Bjerrum i o n - p a i r concept prove u s e f u l . I t s h o u l d be noted t h a t more r e c e n t t h e o r i e s have extended o u r u n d e r s t a n d i n g o f electrolyte solutions to higher concentrations. With the particularly high electrostatic p o t e n t i a l on linear polyelectrolytes due t o c o n s t r a i n e d charges a l o n g t h e c h a i n , it is p r e s e n t l y b e l i e v e d t h a t a rod-like o r cylindrical model f o r t h e polyion w i t h " i t s i o n i c atmosphere is t h e a p p r o p r i a t e r e p r e s e n t a t i o n f o r t h e linear polyelectrolyte in solution. The most comprehensive modern t h e o r y o f polyelectrolyte b e h a v i o r in s o l u t i o n is by Manning ( 1 ) . H i s line charge model f o r t h e p o l y e l e c trolyte r e s u l t s in limiting laws f o r thermodynamic (2) , mass (2) and electrical t r a n s p o r t (3,4,5.) p r o p e r t i e s . G e n e r a l l y , t h e infinite l i n e charge i s thought t o intera c t w i t h s i m p l e i o n s via two phenomena, by ion-atmosphere interaction and by c o n d e n s a t i o n ( s i t e - b i n d i n g ) o f c o u n t e r i o n s onto t h e p o l y i o n . I f t h e charge d e n s i t y o f the polyelectrolyte, which i s p r o p o r t i o n a l t o t h e dimens i o n l e s s parameter ξ

ξ

=

ΤΈτΈ

(

1

)

where e i s the p r o t o n i c c h a r g e , ε i s t h e d i e l e c t r i c con s t a n t o f the medium, k i s t h e Boltzmann c o n s t a n t , Τ i s the a b s o l u t e temperature and b i s t h e average d i s t a n c e between a d j a c e n t charge groups on t h e p o l y e l e c t r o l y t e , i s l e s s than a c r i t i c a l charge d e n s i t y ξ , which i s given ξ = I " , where ζ i s t h e charge o f t h e σ

1

α

1

χ

Author to whom correspondence should be sent. 0-8412-0426-8/78/47-077-245$05.00/0 ©

1978 A m e r i c a n C h e m i c a l Society

Schweiger; Carbohydrate Sulfates ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CARBOHYDRATE SULFATES

246

c o u n t e r i o n and s i s the charge o f a s i n g l e c h a r g e - s i t e on the p o l y i o n , no c o n d e n s a t i o n o f c o u n t e r i o n s o c c u r s and b o t h c o u n t e r i o n s and c o i o n s ( i f a s i m p l e s a l t i s p r e s e n t ) i n t e r a c t w i t h charges on the p o l y i o n by DebyeHuckel f o r c e s , i . E . , the p o t e n t i a l a t any p o i n t in the i o n i c atmosphere s u r r o u n d i n g the p o l y i o n i s g i v e n by the Debye-Huckel s c r e e n i n g p o t e n t i a l . If ξ i s greater than ξ f o r a p o l y e l e c t r o l y t e , an i n s t a b i l i t y i s shown t o e x i s t which i s r e l i e v e d by c o n d e n s a t i o n o f c o u n t e r i o n s onto the p o l y i o n so as t o reduce ξ t o i t s e f f e c t i v e value ξ . A l l uncondensed c o u n t e r i o n s and c o i o n s in the i o n i c atmosphere i n t e r a c t w i t h the p o l y i o n by DebyeHlickel f o r c e s . S i n c e | s | = 1 f o r almost e v e r y p o l y e l e c t r o l y t e , then f o r ζ>\ζ \~ , and the f r a c t i o n o f con densed (site-bound) c o u n t e r i o n s i s ( 1 - | ζ \ ~ ζ ~ ) . The Manning"model has been t e s t e d e x p e r i m e n t a l l y u s i n g d i f f e r e n t p o l y e l e c t r o l y t e s ( 6 . - 2 J 3 ) . S i n c e the model demands a r o d - l i k e geometry f o r the p o l y i o n , i o n i c p o l y s a c c h a r i d e s have been used because o f t h e i r r e l a t i v e l y s t i f f s t r u c t u r e as compared t o the more f l e x i b l e synthetic polyelectrolytes. For s u l f o n a t e d p o l y s a c c h a r i d e s , a c t i v i t y c o e f f i c i e n t measurements f o r the s i m p l e i o n s gave e x c e l l e n t agreement w i t h Manning's t h e o r e t i c a l r e s u l t s o v e r a l a r g e c o n c e n t r a t i o n range f o r sodium c h o n d r o i t i n s u l f a t e (_12) , the sodium s a l t o f s u l f a t e d p r o t e o g l y c a n from b o v i n e i n t e r v e r t e b r a l d i s c (12^) , d e x t r a n s u l f a t e ( 1 J . , _ 2 2 , 2 _ 3 ) and i o t a , kappa and lambda c a r r a g e e n a n s a l t s o f sodium, p o t a s s i u m and c a l c i u m (ISO . S e l f - d i f f u s i o n measurements o f N a Ca and S r + in the p r e s e n c e o f c h o n d r o i t i n s u l f a t e have e s t a b l i s h e d the v a l i d i t y o f the c o n d e n s a t i o n phenomena p r e d i c t e d by Manning's t h e o r y (10,24) . S i m i l a r s t u d i e s w i t h sodium i o t a c a r r a g e e n a n in aqueous s o l u t i o n s o f NaCl, Na^O^ and Na^FeiCN) i n d i c a t e t h a t w h i l e the Manning t h e o r y c o r r e c t l y p r e d i c t 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 s f o r monovalent C I " i o n , i t c l e a r l y overemphasized the e l e c t r o s t a t i c i n t e r a c t i o n s between the d i v a l e n t SO "", the t e t r a v a l e n t F e ( C N ) g ~ and the p o l y i o n , e x c e p t f o r the good agreement a t low r a t i o s o f p o l y e l e c t r o l y t e t o s i m p l e s a l t c o n c e n t r a t i o n s (6_) . With our r e c e n t emphasis on the i n t e r a c t i o n s of c o i o n s w i t h p o l y e l e c t r o l y t e s , i t was o f i n t e r e s t t o examine the e f f e c t o f the charge d e n s i t y o f s e v e r a l c o i o n s on t h i s i n t e r a c t i o n by p o t e n t i o m e t r i c and s e l f - d i f f u s i o n t e c h n i q u e s . Here we r e p o r t r e s u l t s f o r s i n g l e i o n a c t i v i t y c o e f f i c i e n t s f o r Na , CI", B r " and I " in aqueous s o l u t i o n s o f sodium i o t a c a r r a g e e n a n (NaCarr) and sodium d e x t r a n (NaDS) a t 25°C. The r e s u l t s w i l l be d i s c u s s e d in l i g h t o f modern Manning theory of p o l y e l e c t r o l y t e s o l u t i o n s .


α

α

p

1

ι

1

+

1

1

+ 2

2

f

2

+


16.

TOMASULA E T A L .

Co-Ion

and Counter-Ion

Interactions

247


Experimental Section Materials. Sodium iota-carrageenan, an extraction of the red algae Eueheuma Spinosum was kindly supplied by Marine C o l l o i d s , Inc. I t consists of β-D-galactose4-sulfate and 3,6-anhydro-a-D-galactose-2-sulfate r e s i dues with an average distance between charges on the chain of b = 4.4A. Analysis of the carrageenan (sample Re 7275) by the manufacturer indicated that t h i s sample has a weight average molecular weight of 291,000 and a number average molecular weight of 191,000. No con taminating cations or anions were present in the sample; the c r i t e r i a f o r contamination being that the cation or anion i s present in the sample in excess of 0.5%. The sample has an equivalent weight of 255.2 ± O.lg. Chem i c a l analysis of the p u r i f i e d iota-carrageenan gave a sulfate-hexose r a t i o of 0.99; therefore, one s u l f a t e group i s assumed per sugar unit. The sample was p u r i f i e d by the manufacturer by washing of the unpurified carrageenan with a 1 Ν NaCl solution in 50% isopropyl alcohol. This procedure was repeated four times. This was followed by four p l a i n alcohol washes to remove r e s i d u a l s a l t . The product was then dried and ground. Solutions were prepared by adding weighed amounts of the carrageenan, which were dried in vacuo at 40°C f o r at l e a s t 24 hours, to a volumetric f l a s k and an aliquot of the appropriate s a l t from a stock s a l t s o l u t i o n . The f l a s k was d i l u t e d to the mark with deionized water. Dried reagent grade NaCl, NaBr, and Nal were used to prepare a l l solutions. Dextran s u l f a t e , a sulfated d e r i v a t i v e of dextran, was kindly supplied by Pharmacia Fine Chemicals, Inc. The sample had a molecular weight of 500,000. Foreign ions were removed from the sample by passing the sample through appropriate ion exchange columns. The equi valent weight of the sample was found to be 180.5 ± 0.5 g/equiv., i n d i c a t i n g 2.06 s u l f a t e groups per sugar u n i t . This gives an average spacing between charges on the NaDS sample of b = 2. 5Â (11). The concentration of the NaDS solutions were determined by converting the NaDS to the hydrogen form followed by t i t r a t i o n . Electromotive Force Measurements. The counterion a c t i v i t i e s of the i o n i c polysaccharide solutions with added simple s a l t were determined using the Orion Model #94-11 sodium s e l e c t i v e s o l i d - s t a t e electrode in conjunction with a calomel electrode. Coion a c t i v i t i e s of the i o n i c polysaccharide solutions with added simple s a l t were determined using the appropriate anion select i v e s o l i d state electrode. Orion Model #97-17 chloride

American Chemicaf Society Library

1155 IGth St. N. W. Schweiger; Carbohydrate Sulfates W*htigtoii, D, 6. Society: 20036 Washington, DC, 1978. ACS Symposium Series; American Chemical


248


i o n e l e c t r o d e s , O r i o n Model #94-35 bromide i o n e l e c t r o d e s and O r i o n Model #94-53 i o d i d e e l e c t r o d e s were used t o determine the a p p r o p r i a t e c o i o n a c t i v i t i e s . A l l the above a n i o n e l e c t r o d e s were used in c o n j u n c t i o n w i t h a standard calomel e l e c t r o d e . The e l e c t r o m o t i v e f o r c e was measured u t i l i z i n g a C o r n i n g Model 12 pH meter o r an O r i o n Model 801A pH meter w i t h an a c c u r a c y o f ± 0.1 mv. A l l measurements were c a r r i e d out in a c o n s t a n t temperature water b a t h t h e r m o s t a t e d a t 25.00 ± 0.01°C. A i r was bubbled through a l l s o l u t i o n s . A c o n s t a n t p o t e n t i a l r e a d i n g over a 20 minute p e r i o d was r e g a r d e d as a r e l i a b l e emf. Stable p o t e n t i a l s were o b t a i n e d in 2 minutes f o r d i l u t e p o l y e l e c t r o l y t e s o l u t i o n s w i t h added s a l t and 10 minutes f o r the more v i s c o u s s o l u t i o n s . R e p r o d u c i b i l i t y o f ± 0.1 mv was o b t a i n e d which c o r r e s p o n d s t o an u n c e r t a i n t y o f ± 0.002 a c t i v i t y c o e f f i c i e n t u n i t s . The c a l i b r a t i o n o f e l e c t r o d e s was c a r r i e d out r e p e a t e d l y d u r i n g each run u s i n g s o l u t i o n s of the a p p r o p r i a t e simple s a l t w i t h o u t p o l y e l e c t r o l y t e p r e s e n t . in the c o n c e n t r a t i o n range s t u d i e d , the s l o p e s of the emf in mv v s . l o g a were found t o always g i v e c l o s e t o N e r n s t i a n b e h a v i o r . The d a t a i s r e p o r t e d as Y-j/Y^/ the r a t i o o f the e x p e r i mental i o n a c t i v i t y c o e f f i c i e n t s in the p r e s e n c e o f p o l y e l e c t r o l y t e t o t h a t in the absence of p o l y e l e c t r o lyte . +

R e s u l t s and

Discussion

A p r i n c i p a l aim o f t h i s study was t o examine the e f f e c t o f the charge d e n s i t y o f the c o i o n on i t s i n t e r a c t i o n w i t h the p o l y i o n . Thus the s i n g l e i o n a c t i v i t y c o e f f i c i e n t s f o r C l ~ , Br~ and I ~ i o n s were determined in aqueous s o l u t i o n s c o n t a i n i n g NaCarr and NaDS a t 0.00100 M, 0.00500M and 0.0100M N a C l , NaBr and Nal a t 25°. The r e s u l t s are g i v e n in T a b l e s I and I I f o r NaCarr and NaDS, r e s p e c t i v e l y , where γ / γ i s the r a t i o of the c o i o n a c t i v i t y c o e f f i c i e n t s in the p r e s e n c e o f p o l y e l e c t r o l y t e t o t h a t in the absence o f p o l y e l e c t r o l y t e and X = η / n , where n and n a r e the e q u i v a l e n t con c e n t r a t i o n s o f p o l y e l e c t r o l y t e and simple s a l t , r e s p e c tively. The g e n e r a l t r e n d f o r the NaCarr r e s u l t s shows that γ / γ i s f a i r l y c o n s t a n t a t u n i t y f o r X < 1 and d e c r e a s e g r a d u a l l y t o f a i r l y c o n s t a n t v a l u e s f o r X > 4, w i t h the e x c e p t i o n f o r 0.0010Af NaCl and NaBr where the Y / Y r a t i o s are c o n s t a n t a t about 0.9 f o r X < 0.5 p r i o r to t h e i r gradual decrease. The γ / γ ° r a t i o s f o r 0.00100M and 0.00500M NaCl and NaBr are almost i d e n t i c a l a t c o r r e s p o n d i n g simple s a l t c o n c e n t r a t i o n s and X v a l u e s , in d i c a t i n g t h a t the C l ~ and B r " i o n s i n t e r a c t w i t h the 2

s

2

2

p

2

s

2

2

2


Schweiger; Carbohydrate Sulfates ACS Symposium Series; American Chemical Society: Washington, DC, 1978. 1 .000 1 .000 0 .976

1 .004 1 .004

1 .00 1 . 60

0 .996

0 .949

0 .966 0 .955 0 .948 0 .948 0 .948

0 .961 0 .957 0 .938 0 .938 0 .938

1 .004 0 .985 0 .965 0 .906 0 .884

2 .00 3 .00 4 .00 6 .00 8 .00

0 .961 0 .942

-0 .981 0 .927

0 .942 0 .925

-0 .882 0 .888

0 .854 0 .822 0 .725 0 .765 0 .773

1 . 92 3 . 20 4 . 00 6 . 00 8 . 00

0. 891

0 . 868

0. 860

0. 863

0. 879

0. 913

0. 880

0. 878

0. 893

0. 863

0 .809

0 .803

0 .800

0 .765

0 .741

1 .96

3 .00

4 .00

6 .00

8 .00

0 .978

0 .981

0 .947

0 .854

1 . 60

0 . 902

0. 926

0 .831

888

1 .48

0 .

0 . 96

0. 922

0. 928

0 .

0 .98

835

1 .000

0 .966

0 .896

0 . 80

0. 958

0. 962

0 .845

1 .004 1 .009 1 .004 0 . 80

0 .70

1 .044 1 .036

1 .012

0 .52

1 .025

0 .985

0 .900

0 . 48

0. 958

0. 962

0 .883

0 .48

1 .047 1 .036 0 .965

0 .28

000

1 .028

1 .

0 .907

0 . 22

1 . 000

1 . 003

0 .894

0 .28

-

1 .012 1 .015

1 .004

0 .12

1 .040

0 .957

0 . 10

1 . 000

χ

ο

ο ο

ο

ο ο

ο ο LO ο ο ο

ο ο .Η ο ο ο

Nal

ο

1 . 003

ο ο LO ο ο

0 .914

ο

ο ο

ο ο ιΗ ο ο ο

0 .080

Ο ο LO Ο ο ο

NaBr

2

R a t i o γ / Υ 2 Dependence on X f o r

ο

ο ο fH Ο Ο

NaCl

The C o i o n A c t i v i t y C o e f f i c i e n t Sodium I o t a Carrageenan,

χ

Table I.


CD

to

2:

ο

3

ο

α

Ο

ι

ο

Η Η

>

>

8

CARBOHYDRATE

250

U Ο

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M-l

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00 ο ο

Γ Ι Ο^

ιΗ 00 σ>

σ\ σ>

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ο

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00 σ>

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(Ν σ>

CM (Ts as

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SULFATES

16.

TOMASULA E T A L .

Co-Ion

and

Counter-Ion

Interactions

251

NaCarr p o l y i o n t o t h e same e x t e n t . A l s o , f o r the 0.00100M NaCl and NaBr s o l u t i o n s , t h e Y / Y r a t i o s are c o n s i s t e n t l y lower a t each X v a l u e when compared t o t h e 0.00500M and 0.0100M s o l u t i o n s , which i s p r o b a b l y due t o l e s s s c r e e n i n g o f t h e charges on t h e p o l y i o n a t t h e lowest simple s a l t c o n c e n t r a t i o n . The Y / Y ° r a t i o s f o r the t h r e e N a l c o n c e n t r a t i o n s c l o s e l y approximate one another f o r each X v a l u e and t h e r a t i o s f o r t h e 0.0100M N a l a r e c l o s e t o t h e r a t i o s f o r O.OlOOAf NaBr and NaCl f o r each X v a l u e . A t t h e two lower s i m p l e s a l t concen t r a t i o n s t h e C l ~ and B r ~ i o n s i n t e r a c t w i t h NaCarr t o the same e x t e n t , w h i l e a t t h e h i g h e s t s i m p l e s a l t con c e n t r a t i o n t h e C l ~ , B r " and I " i o n s i n t e r a c t t o t h e same extent with t h i s p o l y e l e c t r o l y t e . Except f o r 0.00100M NaCl and NaBr, t h e γ / γ r a t i o s approximate u n i t y a t low X v a l u e s , i n d i c a t i n g t h a t t h e c o i o n i n t e r a c t s in s o l u t i o n as i f t h e p o l y e l e c t r o l y t e were not present. I t s h o u l d be noted t h a t c o i o n a c t i v i t y c o e f f i c i e n t s were a l s o determined f o r NaCarr in 0.000500M simple s a l t s . They were found t o be c l o s e t o t h e v a l u e s found f o r 0.00100M s i m p l e s a l t s and w i l l be d i s c u s s e d below. The Y / y r e s u l t s f o r NaDS a r e l i s t e d in T a b l e I I f o r 0.00100M, 0.00500M and 0.0100M NaCl, NaBr and N a l . With t h e e x c e p t i o n o f 0.00100M N a l , all the Y / Y ° r a t i o s c l o s e l y approximate u n i t y f o r t h e whole X range from one to ten. S i m i l a r r e s u l t s were o b t a i n e d w i t h sodium p o l y phosphate f o r a l l t h r e e simple s a l t c o n c e n t r a t i o n s (_25) . From t h e s e c o i o n a c t i v i t y c o e f f i c i e n t measurements, i t appears t h a t t h e monovalent c o i o n s i n t e r a c t w i t h t h e p o l y i o n only a t v e r y low simple s a l t c o n c e n t r a t i o n s , where t h e Debye-Huckel atmosphere i s l a r g e s t . The Manning t h e o r y 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 g i v e s f o r monovalent c o i o n a c t i v i t y c o e f f i c i e n t s (2) 2

2


2

2

2

2

2

2

γ

2

= exp[-|

Γ ' χ / ί ζ - ' Χ

+ 2)]

(2)

where o n l y Debye-Hiickel i n t e r a c t i o n s w i t h t h e p o l y e l e c t r o l y t e are considered. For a given p o l y e l e c t r o l y t e ζ i s f i x e d , so eqn (2) p r e d i c t s t h a t γ d e c r e a s e s as X i n c r e a s e s u n t i l h i g h v a l u e s o f X cause γ t o l e v e l o f f . S i n c e o n l y 0.00100M NaCl and NaBr s o l u t i o n s o f NaCarr i n d i c a t e c o i o n - p o l y i o n i n t e r a c t i o n over an extended range, t h e s e r e s u l t s w i l l be used t o t e s t eqn ( 2 ) , a l o n g w i t h v a l u e s f o r 0.000500M NaCl and NaBr. F o r 0.000500M N a l c o n t a i n i n g NaCarr i t was found t h a t Y / Y approxi mated u n i t y over t h e whole X range. The r e s u l t s f o r 0.000500M and 0.00100M NaCl and NaBr s o l u t i o n s con t a i n i n g NaCarr a r e p r e s e n t e d in F i g u r e s 1 and 2, r e s p e c t i v e l y , where b = 4 . 4 Â and ξ = 1.62. I t s h o u l d be noted t h a t t h e s m a l l i o n - s m a l l i o n c o r r e c t i o n o f W e l l s (26) 2

2

2

2


252

CARBOHYDRATE

need n o t be a p p l i e d because t h e r a t i o Υ / Ύ used. A l s o , t h e somewhat d i f f i c u l t e x t r a p o l a t i o n o f t h e d a t a t o z e r o i o n i c s t r e n g t h a t a g i v e n X v a l u e suggests t h a t o n l y t h e lowest s i m p l e s a l t c o n c e n t r a t i o n s be c o r r e l a t e d t o t h e t h e o r y when an i o n i c s t r e n g t h dependence i s p r e sent. The agreement between Manning's p r e d i c t e d v a l u e s and e x p e r i m e n t a l v a l u e s i s q u i t e good over most o f t h e range o f X. Using c l u s t e r expansion theory 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 , Iwasa and Kwak (_27) r e c e n t l y p r e d i c t e d an a p p r e c i a t e d i f f e r e n c e between t h e a c t i v i t y c o e f f i c i e n t s o f c o u n t e r i o n s and c o i o n s . From t h e c o n t r i b u t i o n o f h i g h e r o r d e r c l u s t e r terms t o t h e a c t i v i t y c o e f f i c i e n t o f s m a l l i o n s in p o l y e l e c t r o l y t e s o l u t i o n s , i t was shown t h a t f o r ζ > 1 c o n s i d e r a b l e asymmetry between y and γ v a l u e s , w i t h t h e v a l u e s o f y a p p r o x i mating u n i t y . While t h i s t h e o r y might b e t t e r e x p l a i n our r e s u l t s f o r y , f u r t h e r e v a l u a t i o n awaits near future publications. C h l o r i d e i o n and sodium i o n s e l f - d i f f u s i o n measure ments were performed on aqueous s o l u t i o n s o f NaCarr ((5) and NaDS (28) in 0 . 0 0 0 5 0 M , 0 . 0 0 1 0 M , 0 . 0 0 5 0 M and 0 . 0 1 0 M NaCl. The same i o n i c p o l y s a c c h a r i d e samples were used as t h o s e employed in t h e p r e s e n t study. When compared t o t h e c o i o n d i f f u s i o n c o e f f i c i e n t s in t h e absence o f p o l y e l e c t r o l y t e D°, t h e c o i o n d i f f u s i o n c o e f f i c i e n t s D f o r C I " i o n showed t h e same t r e n d f o r NaCarr and NaDS. The D /D° r a t i o s d e c r e a s e d from u n i t y f o r X < 1 and l e v e l e d o f f at approximately # / £ ° = 0 . 9 f o r X < 1 . The p r e d i c t e d v a l u e s from Manning's t h e o r y were c l o s e l y obeyed over t h e whole X range. I t s h o u l d be noted t h a t f o r NaDS, t h e D /D° v a l u e s were below u n i t y f o r a l l NaCl c o n c e n t r a t i o n s , w h i l e t h e γ / γ ? v a l u e s were u n i t y f o r almost e v e r y c o n c e n t r a t i o n . T h i s p r o b a b l y r e f l e c t s t h e g r e a t e r s e n s i t i v i t y o f t h e d i f f u s i o n measurements in m o n i t o r i n g Debye-Huckel atmosphere i n t e r a c t i o n s as com pared t o a c t i v i t y c o e f f i c i e n t measurements. It i s dif f i c u l t t o d e t e c t t h e e f f e c t o f t h e i n t e r a c t i o n s between c o i o n s and p o l y e l e c t r o l y t e s w i t h a c t i v i t y c o e f f i c i e n t measurements because o f t h e h i g h background l e v e l due to small i o n - s m a l l i o n i n t e r a c t i o n s . Sodium i o n a c t i v i t y c o e f f i c i e n t s Y]sj + were d e t e r mined in aqueous NaCarr s o l u t i o n s c o n t a i n i n g 0 . 0 0 0 5 0 0 M , 0.00100M, 0 . 0 0 5 0 0 M and 0 . 0 1 0 0 M N a C l , NaBr and N a l a t 25°C. The r e s u l t s a r e p r e s e n t e d in F i g u r e s 3 , 4 and 5 , where i t can be seen t h a t f o r each s i m p l e s a l t concen t r a t i o n ΎΝ3+/ΎΝΛ+ d e c r e a s e s as X i n c r e a s e s and l e v e l s o f f approximately X > 5 . While t h e e x p e r i m e n t a l p o i n t s are c l o s e in v a l u e f o r X > 2 , t h e s i m p l e s a l t c o n c e n t r a t i o n dependence i s e v i d e n t f o r h i g h e r X v a l u e s , where a t a g i v e n X v a l u e Y ^ a d e c r e a s e s as t h e n o r m a l i t y o f w

2


SULFATES

l

a

s

2

2

2

2

2

2

2

2

2

2

2

a

+


TOMASULA E T A L .

Co-Ion and Counter-Ion

Interactions

m Ο.Ο005 Ν α 0.0010 0.0050 ο 0.0100

•


•

ο

• _ι

• 1

1

1

I

Figure 1. The dependence of the Cl' ion activity coefficient ratio on X in NaCl solutions containing NaCarr. The solid line is predicted from Man ning's theory.

Figure 2. The dependence of the Br~ ion activity coefficient ratio on X in NaBr solutions containing NaCarr. The solid line is predicted from Mannings theory.

• • • Ο

0.9 0\

0.71

0.0005 Ν 0.0010 0.0050 0.0100

Ο .•\· Ο v

0.5\2

3

χ

Figure S. The dependence of the Na* ion activity coefficient ratio on X in NaCl solutions containing NaCarr. The solid line is predicted from Man nings theory.


254

CARBOHYDRATE

SULFATES

simple s a l t decreases. A l s o note that Y + i s f a i r l y independent o f t h e nature o f t h e coion a t a l l concen trations. I t i s g r a t i f y i n g t h a t t h e r e s u l t s f o r Yvr + r e p o r t e d b y P a s s , P h i l l i p s a n d W e d l o c k (19) f o r 0.OU50M a n d 0.010M N a C l a r e in e x c e l l e n t a g r e e m e n t w i t h o u r s . Sodium i o n a c t i v i t y c o e f f i c i e n t s were d e t e r m i n e d f o r 0.00100M, 0.00500M a n d 0.0100M N a C l , N a B r a n d N a l s o l u t i o n s c o n t a i n i n g NaDS. The r e s u l t s a r e p r e s e n t e d in F i g u r e s 6, 7 a n d 8, w h e r e i t c a n b e n o t e d t h e e x p e r i m e n t a l v a l u e s o f YNa+/Y^ + a t t h e c o r r e s p o n d i n g X values are p r a c t i c a l l y superimposable forall three simple s a l t s used. T h u s , Yvr + a p p e a r s t o b e i n d e p e n d e n t of the nature o f the monovalent coion. Also, l i t t l e i o n i c s t r e n g t h dependence i s noted a t each X v a l u e . As c o m p a r e d t o YN +/Y]sf + v a l u e s o b t a i n e d f o r N a C a r r , t h e v a l u e s a p p e a r t o b e l o w e r f o r NaDS a t c o r r e s p o n d i n g X values. T h i s i s p r o b a b l y due t o t h e h i g h e r c h a r g e d e n s i t y o f t h e NaDS c h a i n w i t h b = 2.5& a n d ξ = 2 . 8 5 . To c o r r e l a t e t h e e x p e r i m e n t a l d a t a t o t h e p r e d i c t e d v a l u e s from t h e l i n e - c h a r g e model o f Manning, t h e r e s u l t s s h o u l d b e e x t r a p o l a t e d t o z e r o i o n i c s t r e n g t h . We a v o i d e d t h i s b e c a u s e t h e two l o w e s t s i m p l e s a l t c o n c e n t r a t i o n s u s e d f o r N a C a r r a n d f o r NaDS s o l u t i o n s w e r e v e r y c l o s e in YNa+/Yïia+ l u e s f o r e a c h v a l u e o f X. A l s o , e x t r a p o l a t i n g t h e d a t a a t t h e s e v e r y low c o n c e n t r a t i o n s u s e d , i . E . , 0.000500M a n d 0.00100M s a l t , w o u l d give only a small correction. The t h e o r e t i c a l e q u a t i o n f o r t h e c o u n t e r i o n a c t i v i t y coefficient y f o r ξ > 1 i s (2) N a


a

a

a

a

a

v

a

1

Y! =

1

(ξ' * 1

+ D

(Χ + D - ' e x p C - i

Γ'Χ/ίΓ'Χ

+ 2)]

χ

(3)

where ( ζ " ^ + 1)(Ζ + 1 ) ~ r e p r e s e n t s t h e f r a c t i o n o f t o t a l uncondensed c o u n t e r i o n s . When c o m p a r e d t o t h e experimental p o i n t s f o r NaCarr, the s o l i d t h e o r e t i c a l l i n e s in F i g u r e s 3, 4 a n d 5 i n d i c a t e t h a t e x c e l l e n t agreement i s o b t a i n e d f o r a l l simple s a l t c o n c e n t r a t i o n s b e l o w X = 1 a n d o v e r t h e w h o l e r a n g e o f X f o r t h e two lowest simple s a l t c o n c e n t r a t i o n s employed. Similar f i n d i n g s a r e e v i d e n t f r o m F i g u r e s 6, 7 a n d 8 f o r NaDS a t low X v a l u e s , w i t h s m a l l n e g a t i v e d e v i a t i o n s f r o m t h e theoretical values at the higher X values. W e l l s (11) r e p o r t e d t h a t t h e thermodynamic measurements o b t a i n e d f o r a q u e o u s N a C l s o l u t i o n s c o n t a i n i n g NaDS w e r e in e x c e l l e n t agreement w i t h t h e t h e o r e t i c a l v a l u e s from t h e Manning t h e o r y . T h e NaDS s a m p l e h e u s e d was a l m o s t i d e n t i c a l t o ours w i t h r e s p e c t t o charge d e n s i t y and molecular weight. Upon c o m p a r i n g t h e r e p o r t e d (11) N a C l mean a c t i v i t y c o e f f i c i e n t s t o o u r e x p e r i m e n t a l v a l u e s f o r (γ Y - . _ ) ^ , we f i n d v e r y g o o d a g r e e m e n t o v e r t h e +

r


Co-Ion and Counter-Ion Interactions


TOMASULA E T A L .

Figure 4. The dependence of the Na ion activity coefficient ratio on X in NaBr solutions containing NaCarr. The solid line is predicted from Man ning's theory. +

Figure 5. The dependence of the Na ion activity coefficient ratio on X in Nal solutions containing NaCarr. The solid line is predicted from Manning's theory. +

I

.

i

l

2

!

L.._

1 . !

4

6

I

1

8

X

O0.010N NaCl • 0.005 3 0.001

-

δ

δ

Figure 6. The dependence of the Na ion activity coefficient ratio on X in NaCl solutions containing NaDS. The solid line is predicted from Manning's theory. +

I

2

1

4

6

Χ

8

10


255



Figure 7. The dependence of the Na ion activity coefficient ratio on X in NaBr solutions containing NaDS. The solid line is predicted from Manning's theory. +

ο0.01 ON N a l

• 0.005

-

Ο 0.001

A

C

~ °\\ 9

-

a» Figure 8. The dependence of the Na ion activity coefficient ratio on X in Nal solutions containing NaDS. The solid line is predicted from Manning's theory.

S

+

1

1

1

I

ι

2

4

6

8

10

Χ


TOMASULA E T A L .

16.

Co-Ion

and Counter-Ion

257

Interactions

same X range, g i v i n g s u b s t a n t i a t i o n t o o u r s i n g l e i o n activity results. The N a i o n 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 f o r NaDS in NaCl s o l u t i o n s (2_8) f o l l o w t h e same t r e n d as does Na ^Na+ * ^ i ^ 6. The sharp i n i t i a l d e c l i n e f o l l o w e d by a l e v e l i n g o f f o f ^ + / ^ a ^ "*" ¥ 9 agreement w i t h t h e v a l u e s p r e d i c t e d from M a n n i n g s theory. This i s f u r t h e r evidence o f the v a l i d i t y o f the c o u n t e r i o n c o n d e n s a t i o n c o n c e p t and t h e i o n i c atmosp h e r e - p o l y i o n i n t e r a c t i o n c o n c e p t which a r e paramount in the t h e o r y . +

Y

+//

v

s

X

n

F

u

r

e

+

s

nv

e

r

o o d

a


1

Acknowledgement. The a s t u t e c o n t r i b u t i o n s o f Dr. M. Kowblansky a r e g r e a t l y a p p r e c i a t e d . T h i s p r o j e c t was s u p p o r t e d by Grant No. GM 21234, awarded by t h e P u b l i c H e a l t h S e r v i c e , DHEW. Abstract. C h l o r i d e , bromide, i o d i d e and sodium ion a c t i v i t y coefficients have been determined a t 25°C for aqueous s o l u t i o n s o f sodium i o t a c a r r a g e e n a n and sodium d e x t r a n s u l f a t e o v e r a l a r g e range o f i o n i c p o l y s a c c h a r i d e c o n c e n t r a t i o n s f o r 0.000500M, 0.00100M, 0.00500M NaCl, NaBr and N a I . The e q u i v a l e n t c o n c e n t r a t i o n r a t i o s o f i o n i c p o l y s a c c h a r i d e t o s i m p l e salt was v a r i e d from 0.10 t o 8.0 for sodium i o t a c a r r a g e e n a n and 1.0 t o 10.0 f o r sodium d e x t r a n s u l f a t e . The e x p e r i m e n t a l r e s u l t s a r e d i s c u s s e d in l i g h t o f t h e monovalent c o i o n and mono v a l e n t c o u n t e r i o n i n t e r a c t i o n s w i t h t h e polyelectrolyte a c c o r d i n g t o t h e modern t h e o r y o f p o l y e l e c t r o l y t e s o l u t i o n s by Manning. Literature Cited 1.

2. 3. 4. 5. 6. 7. 8. 9. 10.

Manning, G. S., Annu.

Rev.

Phys.

Chem.

(1972) 23,

117. Manning, G. S., J. Chem. Phys. (1969) 51, 924, 934. Manning, G. S., J. Phys. Chem. (1975) 79, 262. Devore, D. I . and Manning, G. S., J. Phys. Chem. (1974) 78, 1242. Ross, P. D., Scruggs, R. L. and Manning, G. S., Biopolymers, in press. Kowblansky, Α., Sasso, R., Spagnuola, V. and Ander, P., Macromolecules (1977) 10, 78. Kowblansky, M. and Ander, P., J. Phys. Chem. (1976) 80, 297. D i x l e r , D. S. and Ander, P., J. Phys. Chem. (1973) 77, 2684. Menezes-Affonso, S. and Ander, P., J. Phys. Chem. (1974) 78, 1756. Magdelenat, Η., T u r q , P. and Chemla, Μ., Biopolymers



258

11. 12. 13.


14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

(1974) 1 3 , 1 5 3 5 . W e l l s , J. D., Proc. R. Soc. London, Ser Β (1973) 183, 3 9 9 . P r e s t o n , Β . Ν., Snowden, J. McK. a n d H o u g h t o n , K.T., Biopolymers (1972) 1 1 , 1 6 4 5 . Kwak, J. C. Τ . a n d H a y e s , R. C., J. Phys. Chem. (1975) 7 9 , 2 6 5 . S z y m c z a k , J., H o l y k , P. a n d A n d e r , P., J. Phys. Chem. (1975) 19, 2 6 9 . Kwak, J. C. T. a n d J o h n s o n , A. J., Can. J. Chem. (1975) 5 3 , 7 9 2 . H o l y k , P. a n d S z y m c z a k , J., J. Phys. Chem. (1976) 80, 1 6 2 6 . Tuffile, F. M. a n d A n d e r , P., Maoromolecules (1975) 8, 7 8 9 . K o w b l a n s k y , M. a n d A n d e r , P. J. Phys. Chem., in press. P a s s , G., Phillips, G. O. a n d W e d l o c k , D. J., Macromolecules (1977) 1 0 , 1 9 7 . Kwak, J. C. T . , J. Phys. Chem. (1973) 7 7 , 2 7 9 0 . Kwak, J. C. T., O'Brien, M. C. a n d M a c l e a n , D. Α . , J. Phys. Chem. (1975) 7 9 , 2 3 8 1 . S a t a k e , I . et al., J. Polym. Sci., Phys. Ed. (1972) 10, 2 3 4 3 . N o g u c h i , H., G e k k o , K. a n d M a k i n o , S., Macromole cules (1973) 6, 4 3 8 . M a g d e l e n a t , Η . , Turq, P. a n d C h e m l a , Μ . , Biopoly mers (1976) 1 5 , 1 7 5 . K o w b l a n s k y , M. a n d A n d e r , P., t o b e published. W e l l s , J. D., Biopolymers (1973) 1 2 , 2 2 3 . I w a s a , K. a n d Kwak, J. C. T . , J. Phys. Chem. (1977) 81, 4 0 8 . G a n g i , G. a n d A n d e r , P., to b e published.

RECEIVED F e b r u a r y 6, 1 9 7 8 .


Co-Ion and Counter-Ion Interactions with Sulfonated Polysaccharides

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