23 Hydration Control of Ion Distribution in Polystyrene Sulfonate Gels and Resins J A C O B A . M A R I N S K Y , M . M . R E D D Y , a n d R. S. B A L D W I N 1
2
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Chemistry Department, State University of New York, Buffalo, N Y
14214
Numerous a t t e m p t s t o f o r m u l a t e i o n - e x c h a n g e e q u i l i b r i a have been r e p o r t e d ( 1 - 1 2 ) and a r a t h e r c o m p l e t e d i s c u s s i o n o f t h e s p e c t r u m o f t h e o r e t i c a l a p p r o a c h e s and models t h a t have been employed f o r t h i s p u r p o s e has been p r e s e n t e d by H e l f f e r i c h ( 1 3 ) . One o f t h e most s u c c e s s f u l o f t h e s e i s t h e G i b b s - D o n n a n ( 1 4 , 1 5 ) model. In t h i s m o d e l , Κ M, t h e s e l e c t i v i t y c o e f f i c i e n t , i . e . , N the m o l a l i t y product r a t i o at e q u i l i b r i u m f o r the Ζ » - , Z^-valent c a t i o n e x c h a n g e r e a c t i o n , i s e x p r e s s e d by P
t x
K N
Ex
M
=
A
"
where π i s
"
+
the s w e l l i n g
are the p a r t i a l molal
?
-
.- ,
exp [ - , [ Z V - Z V ] / R T N
pressure of the r e s i n ,
M
M
(1)
N
(1>2_ 6_) 5
and
5
volumes o f t h e e x c h a n g i n g i o n s i n t h e
V
N
resin
phase and γ± and γ± a r e t h e mean m o l a l a c t i v i t y c o e f f i c i e n t s o f Μ Ν salts jvi X and N X . Barred symbols denote the r e s i n M H H 7
7
7
7
L
phase,
and γ
Ν
corresponding
t o t h e mean m o l a l
e f f i c i e n t s of the exchanging p a i r s charge of the coion of s a l t s
M
of
activity
ions i n the g e l .
co
The
X and N X i s designated ^X M ^X H The v a l i d i t y o f t h i s model has been f u l l y d e m o n s t r a t e d by 7
7
7
7
L
by Ζ . χ
us i n e a r l i e r s t u d i e s w i t h z e o l i t e s (]J5) t o s u p p o r t i t s f u r t h e r a p p l i c a t i o n t o t h e e x a m i n a t i o n o f t h e i o n - e x c h a n g e phenomenon i n organic resins. Our e f f o r t s i n t h i s d i r e c t i o n have been c o n c e r n e d w i t h t h e e v a l u a t i o n o f t h e π(Δ\Γ) and Ύ Μ / Ύ Μ t e r m s o f E q u a t i o n 1. With t h e i r assessment Κ Ν i s c a l c u l a b l e f o r comparison £ χ
with experiment, ( 17.).
γ± and γ± b e i n g Μ Ν
M
accessible
i n the
literature
Current addresses: State of New York, Department of Health, Environmental Health Center, Albany, N Y 12201 Hooker Chemicals and Plastics Corporation, Electrochemical Research, Niagara Falls, N Y 14302 1
2
0-8412-0559-0/ 80/ 47-127-387$05.00/ 0 © 1980 American Chemical Society
Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
388
W A T E R IN P O L Y M E R S
The w a t e r s o r p t i o n p r o p e r t i e s o f p o l y s t y r e n e s u l f o n a t e (PSS) e x c h a n g e r s w i t h d i f f e r e n t d e g r e e s o f c r o s s - l i n k i n g have been o b s e r v e d t o c o i n c i d e i n t h e l o w e r w a t e r a c t i v i t y r e g i o n where t h e irV Q term i s n e g l i g i b l y small ( 6 ) . T h e r e i s c o i n c i d e n c e as w e l l H
between o s m o t i c c o e f f i c i e n t d a t a (1J3) f o r t h e l i n e a r PSS and t h o s e o b t a i n e d by S o l d a n o f o r t h e
K
= P o - O 0 3
(kT)
K
(
5
)
where w i s a measure o f t h e e l e c t r o s t a t i c f r e e e n e r g y r e q u i r e d t o i n c r e a s e t h e c h a r g e o f t h e p o l y i o n f r o m 0 t o Z. From t h e w e l l known H a s s e l b a c h - H e n d e r s o n e q u a t i o n pK = pH - l o g ^ w h e r e , a, r e p r e s e n t s nM
Inn
pH - l o g
the degree of d i s s o c i a t i o n ; -
06
1
(6)
-
a
n
|/
- pK
2
Z
()
w
7
-
Q
thus
(
k
T
)
The p o t e n t i a l d i f f e r e n c e between t h e s u r f a c e o f a p o l y i o n and t h e r e g i o n i n w h i c h t h e p o t e n t i a l i s measured d u r i n g pH measurements i n t h e c o u r s e o f n e u t r a l i z a t i o n o f a weak p o l y a c i d w i t h s t a n d a r d base p r o v i d e s an e x p e r i m e n t a l e v a l u a t i o n o f t h i s d e v i a t i o n t e r m ( 0 . 8 6 8 6 Zw) i n s u c h p o l y m e r i c s y s t e m s . The d e v i a t i o n from i d e a l i t y of mobile H ions a t the s i t e o f the n e u t r a l i z a t i o n r e a c t i o n i s obtained from the well-known equation given below: +
pH-log
A~ HA
p K
HA
=
p K
HA
• app
p K
HA
=
" ° -
4
3
4
3
~~kT
=
-
0
·
8
8
6
kT
(
8
)
In t h i s e q u a t i o n ε i s t h e u n i t c h a r g e o f t h e p r o t o n ,
corres
ponds t o t h e p o t e n t i a l a t t h e s u r f a c e o f t h e p o l y i o n ,
is
the
i n t r i n s i c d i s s o c i a t i o n constant of the a c i d , is its a p p a r e n t d i s s o c i a t i o n c o n s t a n t and [ A " ] and [ H A ] are molar c o n c e n t r a t i o n s o f t h e d i s s o c i a t e d and u n d i s s o c i a t e d p o l y a c i d e x p r e s s e d on a monomer b a s i s . A r n o l d and Overbeek (3^) i n t h e i r p i o n e e r d e m o n s t r a t i o n o f t h i s p l o t t e d potentiometer!c t i t r a t i o n data obtained with p o l y m e t h a c r y l i c a c i d as pH- l o g α/1-α v e r s u s a. I d e a l l y pH - l o g α/1-α = p K and any d e v i a t i o n f r o m a s t r a i g h t l i n e o f z e r o s l o p e a p p
H A
Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
23.
MARiNSKY ET A L .
Polystyrene
393
Sulfonate
i n s u c h a p l o t i s presumed t o be a q u a n t i t a t i v e measure o f t h e d e v i a t i o n f r o m i d e a l b e h a v i o r o f t h e s y s t e m as t h e p o l y a c i d i s p r o g r e s s i v e l y d i s s o c i a t e d . The o f 1.48 χ 1 0 " t h a t i s d e t e r mined f r o m e x t r a p o l a t i o n o f t h e p o t e n t i o m e t r i c d a t a t o i n t e r c e p t t h e o r d i n a t e a x i s a t α = 0 i s i n good agreement w i t h t h e d i s s o c i a t i o n c o n s t a n t r e p o r t e d f o r i s o b u t y r i c a c i d , t h e r e p e a t i n g monomer u n i t i n t h i s polymer. S i n c e t h e r e i s no i o n i z a t i o n o f t h e p o l y m e r a t α = 0 t h i s number s h o u l d c o r r e s p o n d t o t h e n e g a t i v e l o g a r i t h m of the i n t r i n s i c d i s s o c i a t i o n constant of the r e p e a t i n g a c i d g r o u p o f PMA, as i t d o e s , i f t h e s o u r c e o f d e v i a t i o n i s e x c l u s i v e l y e l e c t r o s t a t i c in nature. Thus t h e change i n t h e v a l u e o f pK (ΔρΚ) w i t h a , i s a t t r i b u t e d t o t h e c h a n g e i n t h e e l e c t r o s t a t i c f r e e e n e r g y o f t h e m o l e c u l e as a c o n s e q u e n c e o f g r o u p - g r o u p i n t e r a c t i o n s accompanying the i o n i z a t i o n p r o c e s s .
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5
ii.
Equivalence
in the D e v i a t i o n
from I d e a l i t y
of
Counter-Ions:
We have shown t h a t t h e f u n d a m e n t a l d e v i a t i o n t e r m , exp-εΨζ χ/kT, d e r i v e d f r o m t h e s t u d y o f H i o n i n weak p o l y a c i d s y s t e m s , a l s o p r o v i d e s an a c c u r a t e b a s i s f o r e s t i m a t e o f t h e d e v i a t i o n from i d e a l i t y o f o t h e r m o b i l e M counterions present c o n c u r r e n t l y i n these complicated systems: The d e v i a t i o n t e r m t h e n i s exp-ΖεΨζ x/kT where Ζ i s t h e c h a r g e o f t h e m e t a l , M , \ / 2 +9 +2 counter-ion. In a s t u d y o f c o m p l e x a t i o n o f Ca , Co and Zn by p o l y m e t h a c r y l i c and p o l y a c r y l i c a c i d as a f u n c t i o n o f A made i n our l a b o r a t o r y (29) the d i s t r i b u t i o n o f t r a c e - l e v e l c o n c e n t r a t i o n s o f t h e s e r e s p e c t i v e m e t a l i o n s between a c a t i o n - e x c h a n g e r e s i n ( N a - i o n f o r m ) and s o l u t i o n (M NaCIO*) i n t h e a b s e n c e and presence of v a r i o u s c o n c e n t r a t i o n s of the r e s p e c t i v e p o l y a c i d s was measured a t d i f f e r e n t d e g r e e s o f n e u t r a l i z a t i o n t o d e m o n s t r a t e this. The p a r t i t i o n c o e f f i c i e n t D ( a b s e n c e o f p o l y a c i d ) and D ( p r e s e n c e o f l i g a n d ) b e a r t h e f o l l o w i n g r e l a t i o n s h i p t o 3 and A for M 2-polyligand systems: +
+ z
+ z
a
+
0
+
D-D p2_= Analysis
3 (θχρ-2εΨ 1
( ά )
/^)
+ 3 A(exp-2 ¥ 2
of the d i s t r i b u t i o n r e s u l t s ,
£
( a )
/kT)
(9)
w i t h exp-e¥^ ^/kT a
and A
v a l u e s d i r e c t l y a v a i l a b l e f r o m pH measurements ( b i n d i n g o f t r a c e m e t a l i o n does n o t a f f e c t t h e s t o i c h i o m e t r y o f t h e s y s t e m ) made c o n c u r r e n t l y w i t h t h e d i s t r i b u t i o n measurements p r o v i d e d u n a m b i g uous v e r i f i c a t i o n o f t h e g e n e r a l a p p l i c a b i l i t y o f t h e n o n - i d e a l i t y t e r m so o b t a i n e d i n t h e s e s y s t e m s . The e x p e r i m e n t a l v a l u e o f D -D/DA were p l o t t e d v e r s u s A. The d a t a were e x t r a p o l a t e d and Q
the i n t e r c e p t of the o r d i n a t e d e f i n e d the value o f β-,. A p l o t of l o g D -D/DA3 versus pH-log a/1-a -pK then y i e l d e d a l i n e Q
1
H A
w i t h a slope o f 2 which i n t e r s e c t e d the o r i g i n .
The
ordinate,
Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
394
WATER IN P O L Y M E R S
l o g D -D/DAe Q
is
1
the abscissa
equal
to - 2 ε ψ ^ 2 . 3 Ι < Τ
pH-log α/1-α - p K
is
H a
+ log
equal
(1 + β Α / β ) w h i l e 2
Ί
to εψ^^/2.3Ι
