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Its Aqueous Solution onto a Solid KARMA
M.
VAN
DOLSEN
and M A R J O R I E
J.
VOLD
The University of Southern California, Los Angeles, Calif. 90007
The charge density, the diffuse
Volta
double
1:1 electrolyte
layer
from
potential, formed
aqueous
solution
The experimental
isotherm
isotherms
the common
without
for the electrolyte
reached
layer
toward
properties,
aqueous
electrolyte. stability
sodium
of kT/e =
potential
assumption.
That sur
and equilibrium from
two
at
con "zero"
Unity is closely
In dispersions
β-naphthalene are useful
but
of Sterling
sulfonate
7 (170 mv.) is reached
The results
of the
individual
10 for spheres of 1000 A. radius
is still about 1.3 for plates. in
particles.
into
unity with rising potential.
near kT/e =
for strong
Guggenheim-Adam
The ratio: σ0/Г2N declines
centrations. potential
monolayer
relating
of a
onto solid
can be resolved
permits
face excess, double
etc., are calculated
by adsorption
a
maximum
at 4 X
in interpretation
FTG 10- M 3
of
the
dispersions.
T t has b e e n r e c o g n i z e d since the n i n e t e e n t h c e n t u r y t h a t s p a r i n g s o l u b l e particles o f l a r g e surface area h a v e b e e n k n o w n to b e m a i n t a i n e d for l o n g times i n s o l u t i o n of sufficiently l o w i o n i c strength. T h e m u t u a l r e p u l s i o n of the l i k e charge b o r n e b y the p a r t i c l e s counterbalances the v a n d e r W a a l s attraction. T w o classes of s o l i d / l i q u i d i n t e r f a c e h a v e b e e n extensively s t u d i e d : the c o m p l e t e l y p o l a r i z e d ( 3 ) r e v e r s i b l e i n t e r f a c e (9, 12, 13).
a n d the c o m p l e t e l y
T h e o r i g i n of the influence of electrolyte
is, as is w e l l k n o w n , p a r t i a l e x p u l s i o n ( n e g a t i v e a d s o r p t i o n ) of s i m i l i o n s near the surface a n d c o n c o m i t a n t increase i n c o n c e n t r a t i o n of c o u n t e r ions.
T h e s i t u a t i o n w a s t r e a t e d as analogous to a condenser w i t h the
c h a r g e p e r u n i t area of the c o l l o i d a l surface a n d the e q u i v a l e n t net charge i n the s u r r o u n d i n g s o l u t i o n b e i n g d e s i g n a t e d " e l e c t r i c d o u b l e 145
Weber and Matijevi; Adsorption From Aqueous Solution Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
146
ADSORPTION F R O M
AQUEOUS SOLUTION
l a y e r " as e a r l y as 1879 b y H e l m h o l z . S h o r t l y thereafter the d i s t r i b u t i o n of b o t h s i m i l i o n s a n d counterions i n the p o t e n t i a l field w a s t r e a t e d b y the statistical B o l t z m a n n expression b y G u o y a n d C h a p m a n ( 5 ) to a l l o w for the t h e r m a l m o t i o n of the ions. T h e c o n c e p t of c a p a c i t y of the e l e c t r i c d o u b l e l a y e r r e m a i n e d , apart f r o m the d e s i g n a t i o n "diffuse d o u b l e l a y e r . " F o r a r e v e r s i b l e interface, s u c h as A g l / a q u e o u s s o l u t i o n , the electro static p o t e n t i a l i n the s o l u t i o n just outside the surface r e f e r r e d to z e r o at regions of s o l u t i o n i n f i n i t e l y remote f r o m c o l l o i d a l particles, the V o l t a p o t e n t i a l , is c a l c u l a t e d f r o m the N e r n s t e q u a t i o n , the c o n c e n t r a t i o n of p o t e n t i a l d e t e r m i n i n g ions, a n d the zero-point-of-charge
w h i c h is not
u s u a l l y the s t o i c h i o m e t r i c e q u i v a l e n c e p o i n t . T h e characteristics of the diffuse electric d o u b l e l a y e r at a c o m p l e t e l y p o l a r i z e d interface, s u c h as at a m e r c u r y / a q u e o u s
electrolyte s o l u t i o n
interface are essentially i d e n t i c a l w i t h those f o u n d at the r e v e r s i b l e i n t e r face. W i t h the p o l a r i z a b l e interface the p o t e n t i a l difference is a p p l i e d b y the experimenter, a n d , together w i t h the electrolyte, specifically a d s o r b e d as w e l l as l o c a t e d i n the diffuse d o u b l e layer, results i n a m e a s u r a b l e c h a n g e i n i n t e r f a c i a l tension a n d a m e a s u r a b l e c a p a c i t y . It c a n b e o b s e r v e d that the a b o v e t w o types of electric d o u b l e l a y e r , w h i c h h a v e b a s i c a l l y s i m i l a r properties, differ p r i n c i p a l l y i n the m a n n e r of e s t a b l i s h i n g the p o t e n t i a l difference across the electric d o u b l e layer. O n e t y p e is fixed b y the s o l u b i l i t y a n d other interactions of the s o l i d i n contact w i t h s o l u t i o n of electrolyte. I n the other t y p e , p o l a r i z a b l e i n t e r face, the e x p e r i m e n t e r a p p l i e s a n y d e s i r e d p o t e n t i a l difference one l i q u i d surface a n d a reference electrode.
between
T h e resulting V o l t a poten
t i a l is fixed b y the specific a d s o r b a b i l i t y of the electrolyte. A t h i r d t y p e of electric d o u b l e l a y e r , h i t h e r t o b u t s l i g h t l y i n v e s t i g a t e d i n m o d e r n times, derives its V o l t a p o t e n t i a l f r o m the specific
adsorba
b i l i t y of a n i o n w h i c h is c h e m i c a l l y u n r e l a t e d to the s o l i d . T h i s t y p e , w h i c h is the subject of the present p a p e r ( u s i n g b e t a - n a p h t h a l e n e s u l fonate i o n a n d a h o m o g e n e o u s n o n p o l a r g r a p h i t i z e d c a r b o n ) also has q u a l i t a t i v e s i m i l a r i t i e s to the t w o c l a s s i c a l ones. T h e results of this s t u d y are i n t e n d e d for use i n c o m p a n i o n studies of the e l e c t r o k i n e t i c properties a n d s t a b i l i t y factors of the same system.
Although graphitized carbon
b l a c k ( a n d also c a r b o n a c e o u s m a t e r i a l of v a r y i n g , sometimes composition)
has
been
( l a r g e l y as a result of
investigated its i m p o r t a n c e
as
sols
unknown
i n hydrocarbon
media
to the p e t r o l e u m a n d r e l a t e d
i n d u s t r i e s ) , a n d to a lesser extent as aqueous sols to s i m u l a t e " d i r t " i n studies of detergency,
precise d a t a a n d c a r e f u l i n t e r p r e t a t i o n of
them
are b o t h l a c k i n g . O n e of the most significant results is that negative a d s o r p t i o n of s i m i l i o n s ( t h e i r p a r t i a l e x p u l s i o n f r o m the surface r e g i o n ) , w h i c h has b e e n r e c o g n i z e d b u t not e m p h a s i z e d , e v e n i n the earliest days of G u o y -
Weber and Matijevi; Adsorption From Aqueous Solution Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
12.
V A N DOLSEN A N D VOLD
Composite
147
Isotherm
C h a p m a n theory, is i n fact a q u a n t i t y o f c o n s i d e r a b l e i m p o r t a n c e . A l r e a d y v a n d e n H u l a n d L y k l e m a (18) h a d r e a l i z e d this s i t u a t i o n . T h e y s h o w e d that t h e m e a s u r e d negative a d s o r p t i o n o f p h o s p h a t e ions a n d o f sulfate ions c o u l d b e u s e d to d e t e r m i n e t h e surface area o f t h e p a r t i c l e s i n n e g a t i v e sols o f A g l , i n reasonable agreement w i t h results o b t a i n e d f r o m c a p a c i t a n c e measurements. Poisson-Boltzmann
I n t h e present case, a first i n t e g r a t i o n o f t h e
e q u a t i o n gives
t h e charge
d e n s i t y a t t h e surface
c o r r e s p o n d i n g i n p o s i t i o n to that of t h e V o l t a p o t e n t i a l . B u t t h e a d s o r p t i o n m e a s u r e d b y c h a n g e i n c o n c e n t r a t i o n of s o d i u m b e t a - n a p h t h a l e n e sulfonate refers t o t h e n u m b e r o f ions o n t h e surface m i n u s t h e n u m b e r of ions w h i c h are n e g a t i v e l y a d s o r b e d i n t h e diffuse d o u b l e layer. T h e t w o q u a n t i t i e s a r e n o t i d e n t i c a l a n d differ b y a factor o f t w o , i f t h e ( d u b i o u s l y justifiable) D e b y e - H i i c k e l a p p r o x i m a t i o n is u s e d . the r a t i o b e t w e e n n e g a t i v e a d s o r p t i o n a n d t o t a l surface c h a r g e
Happily, appears
Symbol Table a A C e k m rii N
2
b
8
0
N 1 L r T u u Vi V Xi Zi r
0
s
2
R a d i u s o f a sphere ( m e t e r s ) . A r e a o f t h e surface ( m e t e r s ) . M o l a r c o n c e n t r a t i o n o f electrolyte i n t h e b u l k s o l u t i o n . C h a r g e o f a n e l e c t r o n (e.s.u.). B o l t z m a n n constant. W e i g h t of adsorbent ( g r a m s ) . Moles of component i i n the surface-containing region. T o t a l moles o f a l l c o m p o n e n t s present i n t h e s o l u t i o n before d i s p e r s i n g t h e adsorbent. Avogadro's number. Distance (meters). L i n e a r extent of t h e s u r f a c e - c o n t a i n i n g r e g i o n m e a s u r e d p e r pendicularly o u t w a r d from the interface (meters), D i s t a n c e f r o m t h e center o f a sphere ( m e t e r s ) . Absolute temperature, R e d u c e d p o t e n t i a l , x&^/kT. R e d u c e d surface p o t e n t i a l . P a r t i a l m o l e c u l a r v o l u m e of c o m p o n e n t i ( m i l H l i t e r s / m o l e c u l e ) . V o l u m e of the surface-containing region (meters ). M o l e f r a c t i o n of c o m p o n e n t i . V a l e n c e o f the i i o n t y p e . G u g g e n h e i m - A d a m " N c o n v e n t i o n " surface excess of c o m p o nent i ( i = 1 for w a t e r , i = 2 f o r electrolyte, i n m o l e s / m e t e r ) , B u l k d i e l e c t r i c constant of w a t e r . C h a r g e d e n s i t y o n t h e surface ( m o l e s / m e t e r ) . Specific surface area of adsorbent ( m e t e r s / g r a m ) . Electrostatic potential (millivolts). C o n c e n t r a t i o n of ions ( i o n s / m l . i = c f o r c o u n t e r i o n s , 1 = s f o r s i m i l i o n s , i = b f o r b o t h i n t h e b u l k solution). 3
t h
( N )
2
c (T 2 \ff vi 0
2
2
American Chemical Society Library 1155 16th St, N.W.
Weber and Matijevi; Adsorption From Aqueous Solution WasMnfton, D.CWashington, 20038 DC, 1968. Advances in Chemistry; American Chemical Society:
148
ADSORPTION F R O M
AQUEOUS SOLUTION
DISTANCE
Figure 1. Schematic: Diffuse double layer formed as a result of anion adsorption, showing the effect of negative adsorption of similions on the bulk concentration. A. Initial electrolyte concentration. B. Final electrolyte concentration. C. Final concentration if there were no negative adsorption of similions (19)
to b e i n d e p e n d e n t of electrolyte c o n c e n t r a t i o n a n d depends o n l y o n
the V o l t a p o t e n t i a l .
Theory T h e presence of a n a d s o r b e d l a y e r at the s o l i d / s o l u t i o n interface is i n f e r r e d f r o m a n o b s e r v e d c o n c e n t r a t i o n c h a n g e w h e n c o l l o i d a l s o l i d is p l a c e d i n contact w i t h s o l u t i o n . I f one of the ions adsorbs p r e f e r e n t i a l l y , the interface becomes c h a r g e d , a n d a diffuse d o u b l e
l a y e r is
spontaneously e x t e n d i n g o u t w a r d f r o m the c h a r g e d surface.
formed
Since c o u n
terions are a t t r a c t e d to the c h a r g e d interface, t h e i r c o n c e n t r a t i o n i n the diffuse d o u b l e l a y e r is greater t h a n i n the b u l k s o l u t i o n a n d t h e y are s a i d to b e p o s i t i v e l y a d s o r b e d . S i m i l i o n s are r e p e l l e d f r o m the surface a n d are s a i d to b e n e g a t i v e l y a d s o r b e d .
T h e n e u t r a l i z a t i o n of the surface charge
is a c c o m p l i s h e d b y the c o m b i n a t i o n of the p o s i t i v e a d s o r p t i o n of c o u n t e r ions a n d the negative a d s o r p t i o n of s i m i l i o n s . S i n c e p o s i t i v e a d s o r p t i o n is i n f e r r e d f r o m a decrease i n c o n c e n t r a t i o n of the b u l k s o l u t i o n , a n d negative a d s o r p t i o n is i n f e r r e d f r o m a n increase i n c o n c e n t r a t i o n , the net change w i l l b e s m a l l e r i n m a g n i t u d e t h a n the larger of the t w o effects. T h e s i t u a t i o n is s c h e m a t i z e d i n F i g u r e 1. This measured concentration
change
is u s u a l l y c o n v e r t e d
into a
surface excess q u a n t i t y , analogous to that u s u a l l y c a l c u l a b l e f r o m surface tension d a t a for a d s o r p t i o n at the l i q u i d / v a p o r interface. I n the case of
Weber and Matijevi; Adsorption From Aqueous Solution Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
12.
V A N DOLSEN
A N D
Composite
VOLD
149
Isotherm
the s o l i d / l i q u i d interface i n w h i c h the s o l i d is i m p e n e t r a b l e to solvent a n d solute a l i k e , the surface of contact b e t w e e n the s o l i d a n d s o l u t i o n is a l o g i c a l c h o i c e f o r the d i v i d i n g surface. A n a r b i t r a r y surface m u s t b e chosen to separate the b u l k s o l u t i o n f r o m the s u r f a c e - c o n t a i n i n g r e g i o n . A H extensive q u a n t i t i e s of the i n t e r f a c i a l r e g i o n w i l l b e d e p e n d e n t
on
the p o s i t i o n of this second surface. A n y c o n v e n t i o n chosen s h o u l d satisfy the f o l l o w i n g c r i t e r i a : ( 1 )
give a v a l u e of the surface excess w h i c h is
i n d e p e n d e n t of the c h o i c e of p o s i t i o n of the second
d i v i d i n g surface;
( 2 ) c l e a r l y s h o w the r e l a t i v e presence of b o t h solvent a n d solute i n t h e i n t e r f a c i a l r e g i o n ; a n d ( 3 ) a l l o w a c o n c e p t of this r e g i o n w h i c h facilitates a p p l i c a t i o n of diffuse d o u b l e l a y e r theory. T h e G i b b s surface excess,
r
(1)
2
,
is c o n c e p t u a l l y difficult, a n d has the
f u r t h e r d i s a d v a n t a g e that the extent of the surface r e g i o n m u s t change as the c o m p o s i t i o n of the surface r e g i o n changes A d a m " N " c o n v e n t i o n surface excess, r , 2
N
(4).
The Guggenheim-
is a l o g i c a l c h o i c e i n a s m u c h
as i t satisfies the a b o v e c r i t e r i a a n d also a l l o w s r e s o l u t i o n of the composite i s o t h e r m i n t o i n d i v i d u a l isotherms ( 8 ) .
T h e G u g g e n h e i m - A d a m surface
excess is defined as the n u m b e r of moles of electrolyte i n a v o l u m e of s o l u t i o n c o n t a i n i n g one square meter of surface a n d N t o t a l moles of a l l species, i n excess of the c o r r e s p o n d i n g q u a n t i t y i n a v o l u m e of b u l k s o l u t i o n c o n t a i n i n g the same t o t a l n u m b e r of moles ( 4 ) .
T h i s surface excess
q u a n t i t y is s y m m e t r i c a l w i t h respect to solvent a n d solute.
r
2
N
= -i\
N
I t is d i r e c t l y r e l a t e d to the G i b b s surface excess.
r
2
N
= x r 1
2
( 1 )
It is c a l c u l a b l e f r o m a m e a s u r e d c o n c e n t r a t i o n change r
2
= -N Ax /m2
N
0
(la)
2
i f the specific area is k n o w n , a n d the s o l i d has a w e l l c h a r a c t e r i z e d surface. Its d e f i n i t i o n gives the r e l a t i o n s h i p b e t w e e n
the composite,
T
2
N
,
and
i n d i v i d u a l isotherms, n i a n d n . R
T
2
N
2
s
= ( 1 / m S ) ( n - - x ( i V + n *)) a
2
2
(lb)
T h e extent of the s u r f a c e - c o n t a i n i n g r e g i o n is not specified b y t h e d e f i n i t i o n of the surface excess.
T h i s r e g i o n m u s t c o n t a i n a l l of
the
s o l u t i o n w h o s e c o n c e n t r a t i o n differs f r o m that of the b u l k l i q u i d a n d m a y c o n t a i n a n y a m o u n t of b u l k s o l u t i o n . T h e b u l k s o l u t i o n makes no c o n t r i b u t i o n to the v a l u e of the surface excess. N o a s s u m p t i o n is i n v o l v e d i n the d e f i n i t i o n of surface excess as to w h e t h e r either c o m p o n e n t forms a m o n o l a y e r o n t h e surface.
Weber and Matijevi; Adsorption From Aqueous Solution Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
150
ADSORPTION F R O M
AQUEOUS
SOLUTION
T h e a b o v e d e f i n i t i o n o f t h e s y m m e t r i c surface excess a n d t h e c l a s s i c a l G u o y - C h a p m a n m o d e l of t h e diffuse d o u b l e l a y e r a r e c o m b i n e d to s h o w that t h e surface excess c a n n o t b e c o n s i d e r e d a surface c o n c e n t r a t i o n i n t h e presence of a n i o n i z e d m o n o l a y e r o n a n i m p e n e t r a b l e s o l i d / l i q u i d interface. It is p o s t u l a t e d t h a t o n e o f t h e ions of t h e a d s o r b e d 1:1 e l e c t r o l y t e is surface a c t i v e a n d t h a t i t f o r m s a n i o n i z e d m o n o l a y e r at t h e s o l i d / l i q u i d interface. A l l counterions a r e a s s u m e d l o c a t e d i n t h e diffuse d o u b l e l a y e r ( n o specific a d s o r p t i o n ) . S i m i l i o n s a r e n e g a t i v e l y a d s o r b e d i n t h e diffuse double layer.
Since the surface-containing region must be electrically
n e u t r a l , t h e t o t a l moles of electrolyte a d s o r b e d , n
2
a
, equals t h e t o t a l moles
of c o u n t e r i o n s i n t h e diffuse d o u b l e l a y e r w h i c h m u s t b e e q u a l t o t h e s u m of t h e moles of s i m i l i o n s i n t h e diffuse d o u b l e l a y e r a n d t h e c h a r g e d surface, Ao- . T h e s e c o n d i t i o n s a r e expressed i n E q u a t i o n s 2a,b. 0
n «=(l/N)
Jj*
n «=(l/N)
J * dv
2
y
2
(2a)
dv
Vc
+
Vs
(2b)
A
