1. No category

LIOURNAL
OF
THE
ELECTROCHEMICAL
---- AND
ELEBTRDCHEMICAL
BDBIETY
SCIENCE
~i
TECHNOLOGY.
JANUARY
Composition Gradients in Molten Salt Binary Mixtures
during Electrolysis at High Current Density
C. E. Vallet,* D. E. Heatherly,and J. Braunstein*
Chemistry Division, Oak Ridge National Laboratory, Oak Eidge, Tennessee 37830
ABSTRACT
S e p a r a t i o n of components has been m e a s u r e d in b i n a r y m o l t e n salt m i x tures, AgNO3-KNO3, s u b j e c t e d to electrolysis b e t w e e n silver electrodes. The
analysis of thin slices of frozen m i x t u r e contained in silica frits gives q u a l i t a t i v e l y the composition changes b e t w e e n anode and cathode and shows the e x p e c t e d e n r i c h m e n t of potassium ions at the cathode. Changes in concentration
a t t h e electrodes a r e m e a s u r e d e l e c t r o c h e m i c a l l y in free electrolytes and in
electrolytes contained in frits. The time dependence of concentration at the
electrodes is obtained both d u r i n g electrolysis and d u r i n g r e l a x a t i o n following electrolyses of different durations. The e x p e r i m e n t a l results confirm the
predictions from a mass t r a n s p o r t m o d e l p r o p o s e d p r e v i o u s l y for systems
analogous to m i x e d m o l t e n salt b a t t e r i e s o p e r a t e d at h i g h c u r r e n t densities.
E l e c t r o l y t e composition g r a d i e n t s in aqueous fuel
cells and electrolyzers have been o b s e r v e d (2, 3) and
e x p l a i n e d in t e r m s of electrode reactions, diffusion,
and m i g r a t i o n (4-6). P r e v i o u s l y d e r i v e d equations for
(one dimensional) diffusion and m i g r a t i o n in m o l t e n
salt b i n a r y m i x t u r e s d u r i n g c u r r e n t flow p r e d i c t e d
the e s t a b l i s h m e n t of concentration g r a d i e n t s in the
electrolytes of m o l t e n salt b a t t e r i e s and fuel cells (7).
Such g r a d i e n t s h a v e been reported, b u t not analyzed,
in an A1/NaC1-KC1-A1C13/C12 b a t t e r y (8) and in the
electrolysis of L i B r - K B r m i x t u r e s for isotope s e p a r a tion (9). [Isotope s e p a r a t i o n by electrolysis of "pure"
m o l t e n salt 6LiCI-?LiCt is itself an e x a m p l e of the
d e v e l o p m e n t of composition g r a d i e n t s b y virt~,e of
difference of m o b i l i t y (of 6Li+, ~Li+)] (10). These
gradients, a l t h o u g h p o t e n t i a l l y of significant m a g n i t u d e
and consequence in actual batteries (or fuel cells),
a r e difficult to observe. R a p i d back-diffusion d u r i n g
cooling imposes severe constraints on the s a m p l i n g
of such g r a d i e n t s for chemical analysis. In m o l t e n
salt b a t t e r i e s (11, 12), variations of the potential b e t w e e n LiA1 a n d FeSz electrodes for reasons o t h e r than
changes of the L i / K ratio of the LiC1-KC1 e l e c t r o l y t e
t e n d to obscure in situ p o t e n t i o m e t r i c m e a s u r e m e n t
of the composition changes. Consequently, there is a
need for suitable analog e x p e r i m e n t s to test the v a l i d i t y
of the predictions.
This p a p e r presents the results of an e x p e r i m e n t a l
test of the predictions of the p r e v i o u s l y d e r i v e d one
dimensional equation for a system in which the electrode reaction, ion flows, and conditions of o p e r a t i o n
a r e analogous to those in a m o l t e n 'salt battery, but
which is m o r e a m e n a b l e to q u a n t i t a t i v e analysis. We
describe m e a s u r e m e n t s of the composition changes in
m o l t e n AgNO~-KNO~ m i x t u r e s s u b j e c t e d to electrolysis
b e t w e e n two silver electrodes. Since silver, one of
the two l i k e - c h a r g e d ions in the b i n a r y mixture,
reacts at b o t h electrodes, t h e ion flows a r e analogous
* E l e c t r o c h e m i c a l Society A c t i v e Member.
Key words: m o l t e n salt, transport, battery.
to those in the LiCI-KCI e l e c t r o l y t e of a L i / S b a t t e r y ,
in which Li + ion enters t h e e l e c t r o l y t e at the anode
and leaves at the cathode (11, 12). E x p e r i m e n t s w e r e
done both w i t h free e l e c t r o l y t e and with e l e c t r o l y t e
contained in a coarse silica frit, the l a t t e r configuration r e s e m b l i n g the containment of the electrolyte in
a m o l t e n salt b a t t e r y . Two kinds of m e a s u r e m e n t s
w e r e m a d e of composition changes: first, chemical
analysis, following electrolyses for differing lengths
of time and at differing c u r r e n t densities, in sections
of r a p i d l y cooled frits; second, in situ p o t e n t i o m e t r i c
analysis in cells w i t h free and w i t h f r i t - c o n t a i n e d
electrolytes. The results of b o t h kinds of e x p e r i m e n t
and both kinds of analysis d e m o n s t r a t e the depletion
of silver ions at the cathode, and confirm the p r e d i c tions of our m o d e l u n d e r the conditions studied.
Ion Flowsin AgNO3-KN03
The ion flows considered in our previous analysis
(7) of mass t r a n s p o r t in electrolyzed m o l t e n salt
m i x t u r e s were: (i) the f a r a d a i c flow across the elect r o d e - e l e c t r o l y t e interface arising from the electrode
reactions; (ii) t h e e l e c t r o m i g r a t i o n a l flow of ions
c a r r y i n g the c u r r e n t t h r o u g h the electrolyte; and
(iii) the diffusional flow d r i v e n b y the concentration
changes p r o d u c e d b y the two p r e c e d i n g flows. In a
constant volume system the diffusion-migration e q u a tion d e r i v e d for the ion not r e a c t i n g at the electrodes
(cation K +) was shown to be, neglecting convection
OCKO[DOCK~
o~o5 \
I
F
dtKN~
acK
oCK
oz
[1]
CK is the ionic concentration of K + in eq cm -a, x
is the distance from the anode (5 ----- d at c a t h o d e ) , I
is the c u r r e n t density, D is the b i n a r y diffusion coefficient in the AgNOa-KNOa mixture, and tKN~ is the
t r a n s f e r e n c e n u m b e r of the cation K + r e l a t i v e to the
n i t r a t e anion; the b o u n d a r y conditions at both electrodes (x = 0, x = d) a r e
Downloaded on 2015-04-01 to IP 149.156.116.7 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).
J. Electrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y
aCK
IrKN~
a=
FD
January 1980
[2]
A l t h o u g h convection terms and frit porosity m a y a l t e r
the predictions, and are being t r e a t e d currently, our
e x p e r i m e n t a l results indicate that these effects a r e
p r o b a b l y not large u n d e r the conditions studied here.
E q u a t i o n [1] t o g e t h e r w i t h Eq. [2] can be n u m e r i c a l l y solved (13) for the cases w h e r e D and (or)
tKNO~ are composition dependent. The computation
gives the entire composition profile b e t w e e n the two
electrodes at any t i m e and the t i m e dependences of
concentration at both electrodes. F i g u r e 1 shows the
analogy of the t h r e e ion flows considered in the m o d e l
in a L i / S b a t t e r y on charge or on discharge and in
t h e KNO3-AgNOs m i x t u r e during electrolysis w i t h
s i l v e r electrodes. Only the two l i k e - c h a r g e d cations
are indicated, since the c o m m o n anions (C1- or N O 8 - )
are taken as r e f e r e n c e frame.
BATTERY
ANODE
ELECTROLYSIS
OF KNOs-AgNO 3
....( ~
:ATHODE
i
A9
Ag
I~KNO~-AgNOs
ANODE
GATHODE
DISCHARGE: ELi
2L +2e
2 e + E L I ++ S ~ L i E S
CHARGE: LiES ~ 2 L i + + S + Ee ELi++ 2 e ~ 2Li
Ag--~Ag + + e
Ag++
~Ag
0 Li*OR Ag+
9 K+
DIFFUSIVE FLOW
> FARADAIC FLOW
> MIGRATIONAL FLOW (ULiORUAg>UK)
Fig. 1. Ion flow analogies in battery and in electrolysis cell
Experimental
Chemicals.--The silver nitrate was crystal certified
A.C.S. f r o m F i s h e r Scientific Company. The potassium
nitrate was analytical r e a g e n t crystal f r o m M a l linckrodt, Incorporated. It was dried in an o v e n at
300~ prior to weighing. The solutions w e r e p r e p a r e d
by weighing the a p p r o p r i a t e amounts of both components.
Electrolysis cells.--A typical silica cell for electrolysis of free e l e c t r o l y t e and e l e c t r o c h e m i c a l m e a s u r e m e n t of the concentration changes at both electrodes
is shown in Fig. 2. The silver electrodes 1 and 2 are
m o u n t e d in two pieces of Macor 1 (or of Teflon in
e x p e r i m e n t s at t e m p e r a t u r e below 250~
A and B
in order to provide g e o m e t r i c a l l y w e l l - d e f i n e d areas.
The holders A and B are placed in the silica tube C,
whose bore is m a c h i n e d to p r o v i d e a tight fit to the
bottom electrode support A. Two apertures, E and F,
in the tube C, p e r m i t filling of alI the space b e t w e e n
the two electrodes w i t h the m o l t e n salt w h e n the
t u b e C ( m a i n t a i n e d at the t e m p e r a t u r e of the melt)
is inserted in the large tube D containing the binary
n i t r a t e melt. The silver electrode 3, dipping in the
outer tube, is used as a reference electrode r e l a t i v e
to the electrodes 1 and 2. The electrode separations
w e r e of the o r d e r of 1-2 cm and the electrode areas
w e r e of the order of 0.5 cm 2. The height of the m e l t
in tube D was of the order of 4-5 cm. U n i f o r m i t y of
the t e m p e r a t u r e in the m e l t was obtained by inserting
the assembly in an a l u m i n u m block G. A Leeds and
N o r t h r u p E l e c t r o m a x Controller was used to m a i n tain the furnace to within +__O.I~ of the desired
temperature.
1
Machinable Glass-Ceramic f r o m
Corning.
Fig. 2. Electrolysis cell with free electrolyte: A, B, Motor insulators; C, inner silica tubing; D, outer silica tubing; E, F, apertures in the internal silica tubing; G, aluminum block; 1, 2, silver
electrodes for electrolysis; 3, silver reference electrode.
F i g u r e 3 shows an electrolysis cell w i t h the m o l t e n
electrolyte contained in a coarse silica frit B. Silica
frits 0.25-0.4 cm thick are sealed at one end of the
silica tube A. Two p l a n a r silver electrodes 1 and 2,
of 0.5 cm 2 area are placed against opposite faces of
the frit. Electrode 2, i n t r o d u c e d into tube A, has a
k n o w n area in contact w i t h the m e l t w h i c h i m p r e g nates the frit. Electrode 2 is used as anode or as
cathode. The electrolyses are done b e t w e e n the electrodes I and 2. S i l v e r electrode 3, dipping in the
m e l t contained in the outer tube B, is used as a r e f erence electrode. The l e v e l of the m o l t e n m i x t u r e i n
tube C is adjusted to touch the bottom of the u p p e r
electrode 2. This cell also is contained in an a l u m i n u m
block for u n i f o r m i t y of the t e m p e r a t u r e .
Composition Changes
M e a s u r e m e n t s w e r e m a d e of the composition changes
at the electrode surfaces and across the electrolyte
b e t w e e n anode and cathode (concentration profiles)
induced by electrolyses at 0.15 A - c m -~ of 1-2 rain
duration. Both kinds of m e a s u r e m e n t s showed the
t r e n d towards separation of the m i x t u r e components
predicted by the mass t r a n s f e r analysis. T h e concentration profiles, w h i c h w e discuss first, show this effect
qualitatively, and h i g h e r analytical precision' is needed
for a m o r e q u a n t i t a t i v e test of the model. The c o n -
Downloaded on 2015-04-01 to IP 149.156.116.7 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).
Vol. 127, No. I
COMPOSITION
GRADIENTS
3
Table I. Weight losses (mg) of flit slices during extraction by hat
0.01N HNO~ so(utlon
Washing /
Na.
NO~sHc e
No,
1
2
3
4
1
2
3
60.4
0.1
--
30.8
0.6
0.1
45.5
0.7
0.1
58.2
- O.1
t a i n e d i n t h e slice. T h e w a t e r s o l u t i o n s , w h i c h t y p i c a l l y
c o n t a i n e d 1 • 1 0 - 3 g o f s a l t p e r c m ~, a r e a n a l y z e d
both for potassium and for silver. The potassium
a n a l y s i s is d o n e b y f l a m e s p e c t r o s c o p y , s i l v e r b y s p a r k
s o u r c e s p e c t r o s c o p y . T h e a c c u r a c y of t h e s e m e t h o d s
is u s u a l l y e s t i m a t e d to b e --+5%. I n o r d e r to t e s t t h e
analytical results and the extraction procedure from
t h e frit, s t a n d a r d s a m p l e s w e r e p r e p a r e d f o r a n a l y s i s
b y d i l u t i n g i n 0.01N HNO~ s o l u t i o n e i t h e r a p r e v i o u s l y
m o l t e n m i x t u r e of k n o w n c o m p o s i t i o n o r t h e m i x t u r e
extracted from a quartz frit impregnated with a molten
m i x t u r e of k n o w n c o m p o s i t i o n . I n m o s t of t h e cases,
both Ag and K analyses indicate a lower concentration
of p o t a s s i u m . T h e r e s u l t s f r o m s i l v e r a n a l y s i s a r e
f o u n d to b e w i t h i n 6% of t h e k n o w n c o m p o s i t i o n s .
R e s u l t s f r o m p o t a s s i u m a n a l y s i s a r e w i t h i n 10% o f
t h e k n o w n c o m p o s i t i o n s . T h e e x t r a c t i o n of t h e s a l t
f r o m t h e f r i t does n o t i n c r e a s e s i g n i f i c a n t l y t h e d i s c r e p a n c y b e t w e e n t h e r e s u l t s of t h e a n a l y s i s a n d
t h e k n o w n c o m p o s i t i o n of t h e m e l t .
Fig. 3. Electrolysis cel! with the Mectrotyte contam~cl m a silica
flit. A, Inner silica tubing; B, coarse silica frit sealed at the
end of A; C, outer silica tubing; D, aluminum block; 1, 2, silver
electrodes for electrolysis; 3, silver reference electrode.
centrations at the electrode surfaces and their change
with time, however, are very well explained by the
p r e d i c t i o n s of t h e m a s s t r a n s p o r t m o d e l .
Experimental procedure.--A d i r e c t d e t e r m i n a t i o n of
the composition changes across the electrolyte was
attempted after electrolyzing the AgNOa-KNQ mixt u r e , c o n t a i n e d i n t h e p o r o u s m a t r i x i n t h e cell s h o w n
i n Fig. 3, a t c o n s t a n t c u r r e n t f o r d i f f e r i n g t i m e s . A s
s o o n as t h e c u r r e n t is c u t off, t h e t u b e A (Fig. 3)
is r e m o v e d f r o m t h e m e l t a n d r a p i d l y c o o l e d i n a
cold h e l i u m flow. T h e frit, B, is t h e n s e c t i o n e d i n t o
slices 15-20 t h o u s a n d t h s of a n i n c h t h i c k u s i n g a
Buehler low speed saw equipped with a diamondf a c e d b l a d e 15 t h o u s a n d t h s of a n i n c h t h i c k . A s i l i c o n e
c u t t i n g oil is u s e d to i n c r e a s e t h e c u t t i n g speed. T h e
slices a r e w a s h e d w i t h c o l d b e n z e n e to r e m o v e t h e
s i l i c o n e c u t t i n g oil. T h e n i t r a t e m i x t u r e is e x t r a c t e d
f r o m t h e f r i t slices b y a h o t (90~
0.01N HNO~ s o l u tion. T h e h o t s o l u t i o n is d r o p p e d o n t o t h e slice i n a
B u c h n e r f u n n e l as v a c u u m is a p p l i e d to t h e c o l l e c t i n g
flask. T h e f r i t slices, d r i e d i n a n o v e n , w e r e w e i g h e d ,
and then reweighed after each washing. Table I gives
t y p i c a l w e i g h t losses ( i n r a g ) o b s e r v e d f o r f o u r slices.
U s u a l l y t h r e e w a s h i n g s a r e s u ~ c i e n t to r e a c h a s t e a d y
w e i g h t . T h e t o t a l w e i g h t loss of t h e s~ice is i d e n t i f i e d
w i t h t h e t o t a l w e i g h t of A g N O 3 - K N O 8 m i x t u r e c o n -
Composition profiles in AgNO3-KNO3.--A 0.2
A g N O s - 0 . 8 KNOB m i x t u r e a t 310~ w a s e l e c t r o l y z e d
a t 0.15 A - c m - 2 d u r i n g 40 sec. T h e u p p e r p a r t of
T a b l e II g i v e s t h e r e s u l t s of t h e a n a l y s i s of t h e s a l t
i n five slices o f t h e 0.5 c m - t h i c k frit. S l i c e 1 w a s
a d j a c e n t to t h e a n o d e a n d slice 5 w a s c l o s e s t to t h e
c a t h o d e . T h e t h i c k n e s s of f r i t lost f r o m e a c h c u t h a s
b e e n e s t i m a t e d to b e a b o u t 0.05 cm, a n d t h e s u b s e q u e n t
p o s i t i o n s ( r e l a t i v e to t h e a n o d e ) of t h e m i d p o i n t s
o f t h e slices a r e r e p o r t e d i n t h e t h i r d c o l u m n . T h e
l o w e r p a r t of T a b l e II g i v e s t h e r e s u l t s of t h e a n a l y s i s
o f p o t a s s i u m a n d of s i l v e r i n f o u r slices of a 0.378
c m - t h i c k f r i t i n w h i c h a 0.5 KNO~-0.5 A g N O 3 m i x t u r e
h a s b e e n e l e c t r o l y z e d f o r 90 sec a t 0.I5 A - c m -2. T h e
results in Table II for both initial compositions show
a c l e a r t r e n d of i n c r e a s i n g A g / K r a t i o f r o m c a t h o d e to
a n o d e . T h i s is s t r e n g t h e n e d b y a c o m p a r i s o n of s t a n d a r d d e v i a t i o n s of fit c a l c u l a t e d f o r t w o m o d e l s : ( a )
n o effect of e l e c t r o l y s i s , i.e., t h e a n a l y t i c a l r e s u l t s f o r
Table II. Composition from analysis of potassium and of silver in
slices of electrolyzed frits
~
= 0.6; time of electrolysis = 40 see, current density ~ 0.15
A-cm-~; thickness of the frit = 0.5 cm
since
No.
Thickness
(cm)
Distance of
midpoint
from anode
(cm)
XK
From K
analysis
From Ag
analysis
1
2
43
5
0.065
0,079
0.053
0.061
0.040
0.0325
0.154
0.270
0.377
0.478
0.75
0.77
0.81
0.84
0.87
0.81
0.82
0.85
0.88
0.91
~K = 0.5; time of electrolysis = 90 sec, current density = 0.15
A-cm-~; thickness of the frit = 0.376 c m
Slice
No.
Thickhess
(cm)
Distance of
midpoint
from anode
(cm)
X•
From K
analysis
From Ag
analysis
1
23
4
0.066
0.034
0.058
0.054
0.033
0.133
0.229
0.335
0.48
0.513
0.539
0.527
0.45
0.43
0.49
0.53
Downloaded on 2015-04-01 to IP 149.156.116.7 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).
January 1980
J. Electrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y
sections at differing positions are r a n d o m l y distributed
about the m e a n value, and (b) a systematic change
of composition with position; for this, a least squares
fit with a linear dependence on distance was assumed,
although the solution of the diffusion-migration equation is not linear, since uncertainties in the data did
not w a r r a n t a more complex function. Table I I l summarizes the standard deviation, CN-~, about the m e a n
composition < X K > of the different sections, a n d the
s t a n d a r d deviation of fit, r
based on the l i n e a r
least squares fit. Table HI also lists the difference,
aXK, b e t w e e n the values of XK at the cathode and
at the anode as calculated from the linear regression.
I n all the cases the s t a n d a r d deviation of fit of a
linear dependence on distance are smaller t h a n the
standard deviation about a n assumed constant value.
For 0.8 KNO3-0.2 AgNOs, r
is sixfold smaller for
the silver analysis and twentyfold smaller for the
potassium analysis t h a n ~N-1. For 0.5 KNO3-0.5 AgNO~,
~N-2 is about half ~N-1. Figure 4 shows the least
squares fits to both K and Ag analyses in the two
melts together with the e x p e r i m e n t a l results reported
for the midpoint of each slice. (The middle lines are
the fits to the average of the data from both analyses.)
The differences i n composition at the cathode and
at the anode calculated from the l i n e a r regression
are larger t h a n twice the s t a n d a r d deviations of fit
(~N-2), the electrolyte near the cathode being richer
in KNO3.
The results thus show that the direction a n d m a g n i t u d e of the composition changes at the two electrodes
are consistent with those predicted (7) from solution
of the diffusion migration equation in a b i n a r y melt
with electrode reactions involving one of the likecharged ions. A more accurate m e a s u r e m e n t of the
composition profile, r e q u i r i n g both better resolution
of the distance and improved analytical accuracy, is
u n d e r way.
Concentration changes at electrode surfaces.--The
most striking evidence for the predicted gradients is
obtained from m e a s u r e m e n t s of the composition
changes at the electrodes d u r i n g electrolysis, and of
their rates of decay after electrolysis.
I n this second kind of experiment, the concentrations at the electrode surfaces and their time dependence were measured potentiometrically. The composition (XAg) at the silver cathode (or anode) of
the concentration cell with transference containing
molten AgNO~-KNO~ mixtures, Ag/AgNO~-KNO3
(X~
AgNO3-KNO3(XAg)/Ag, is related to the
open-circuit potential difference b e t w e e n the cathode
(or anode) and a reference electrode dipped in a
m i x t u r e of k n o w n composition (X~
by (14)
1 ~'xA,
F "~X~
tKNOs
1
--
d~AgNO3
dX'Ag
X'Ag
dX'Ag
[3]
Table HI. Standard deviation about the average value <XK>,
and of the linear regression
(a)
0.8
0.5
Ag analysis
(b)
0.0416 0.007
0.0465 0 . 0 2 4
XK from K analysis
(a)
0.014
0.048
0.0492
0.0255
(b)
0.0026
0.017
,,~/i
s/--
/
0.85
0.80
.
0.75
"/
.
.
.
.
.
CATHODE-~
,Iv/
Z
0
(2
n-
./
/ / 6 -
re~
0
.
4'~ANOOE
0.70
--
.
bJ
,
.
.FROM.
0 - - . . . .
FROM
•
hg ANALYSIS
K ANALYSIS
0
0.55
--
o.5o
9
. ~
.
~
0.45
o
/
.
.
.
.
.
.
//CATHODE--P-
/
o
/
o.,o
I
0
OA
I
0.2
I
I
0.3
0.4
0.5
DISTANCE FROM ANODE. (cm)
Fig. 4. Least squares fit of a linear dependence on instance to
compositions from silver analysis ( Q ) and from potassium analysis
(O).
t e m p e r a t u r e - i n d e p e n d e n t (15). A least squares fit
of a second-order polynomial that represents the
absolute values of the K + a n d Ag + mobilities, i n
cm ~ sec-1 V -1, was reported (16) as
UK -- (4.83 XK2 -- 6.86 XK + 4.49) X 10 -4
[4a]
UAg ~- (--3.87 XK2 + 2.73 XK -t- 3.71) X 10 -4
The transference n u m b e r of the potassium cation relative to n i t r a t e ions is
tKNO. =
Cz(uz + U~os)
[4b]
CK(UK ~- UNO3) ~- CAg(UAg JC UNO3)
where X'Ag is the mole fraction of AgNO3 in the melt
a n d gAgno3 the chemical potential of AgNO3. The
needed i n t e r n a l t r a n s f e r e n c e n u m b e r m a y be calculated from the external mobilities of the Ag +, K +,
and NO3- ions which have been d e t e r m i n e d b y Duke
and Owens (15) at 350~
They report that the
external mobility of nitrate ion is composition-independent, with absolute value 1.55 X 10 -4 cm2 see-1
V -~, and that the mobilities of all the three ions are
XK-from
0.90
0 . 0 0 5 2 0.13
0.034
0.091
F i g u r e 5 shows, i n curve 1, the transference n u m b e r
tKNO~ calculated from Eq. [4]. These values are confirmed by more recent m e a s u r e m e n t s (17) of concentration cells with transference. The transference n u m ber of potassium relative to nitrate anions differs
slightly from the KNO3 mole fraction, ~20% at XK
= 0.5, and ,--10% at XK -- 0.7. Its composition dependence is well represented i n the composition range
0 < XK < 0.55 by a second degree polynomial
tK NO8 - - 0.6 XK -~ 0.4 XK 2
[5]
or by the assumption of a constant mobility ratio (18)
UAg/UK = 1.5, as shown in curve 2 of Fig. 5.
The activity coefficients of KNOa and AgNO3 have
been found (19) to be larger t h a n 0.8 at all concentrations. They are v i r t u a l l y u n i t y around XK ---- 0.8,
the composition studied here. Therefore, in our calculations of the emf of the concentration cells (with
X~
----0,2) w e m a y assume with very little error
that the mixture is ideal The emf of the concentration
cell with transference becomes
Downloaded on 2015-04-01 to IP 149.156.116.7 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).
V o i 127, No. I
tO
I
COMPOSITION GRADIENTS
I
I
]
TIME (rain)
0.5 t
5
t0
t5
20
30
ooo6o [ - ~ - - [ - - I - - [ - - 7 - - - 7 - - 7 - -
0.9 --
I
40
50
,L'~---/---I 9 4 0 0 m A
; F////_i =200mA CATHODE
0.8
~
0.7
T = 200*0
0.0050
m"
V
r-.'~/'
80m%AgNO3-2Om% KN03
Jk~%
Electrode Area 0.5 cm 2
Electrode Separation, t.5 cm
L~
AN Oo
0,00401-, % .
0.6
E
z~05
I
z
W 0,0030[---
",
\
',,
~0
0
0.5
0.40.1i
0.2
,,,,
2; 0 . 0 0 2 0
~
0
I
I
I
I
I
I
I
0 --//I / I
0 0.1 0.2 0 5 0.4 0.5 0.6 0 7 0.8 0.9 LO
MOLEFRACTIONKNO3
RT
XAg
In
F
SYMBOLS REFER TO
EXPERIMENTAL RUNS IN
~.\
FREE ELECTROLYTE
~'~. <,~I = 2OO rnA
""
"-.e,,I =400 rnA
20
10
0
"-...
50
40
50
60
( s '/2 )
Fig. 6. Time dependence of concentration at electrodes during
the electrolysis of 0.8 AgNO3-0.2 KNO3 free electrolyte, with
constant current. + , A , • O current = 200 mA; ~ current =
400 mA.
RT
+ 0.4
X~
.....
____CALCULATED
o o o
0 , 0 0 | 0 --
O_
E' =
\\
L
Fig. 5. Composition dependence of transterence number of potassium relative to nitrate in AgNO3-KNO3. Curve 1, calculated
from the external mobilities of Ref. (15); curve 2, fit assuming a
constant mobility ratio UAg/UK ~ 1.5; curve 3, transference number assumed equal to the mole fraction (uAg = uK).
o
A
+
\,,, o xz,
o
(X~
-- XAg)
[6]
F
,so
Note t h a t the second t e r m on the R H S results f r o m
the difference of the t r a n s f e r e n c e n u m b e r f r o m the
m o l e fraction.
o
=
E
i
II
II
i
I
I
30
Time dependence of concentration in free electrolyte.--A 0.8 K N Q - 0 . 2 AgNO3 m i x t u r e was electrolyzed
at constant currents of 0.2 and 0.4A in the cell shown
in Fig. 2. D u r i n g electrolysis, the c u r r e n t was i n t e r r u p t e d periodically for short periods of time in o r d e r
to record the o p e n - c i r c u i t potential of cathode and
anode (electrodes 1 and 2) r e l a t i v e to the r e f e r e n c e
electrode, 3, in the m e l t of initial composition. The
separation b e t w e e n the electrodes was 1.5 cm and
the t e m p e r a t u r e 200~ F i g u r e 6 shows concentrations
of potassium calculated w i t h Eq. [6] f r o m the m e a sured potentials. As the electrolysis progresses, the
c o n cen t rat i o n of potassium increases at the cathode
and decreases at the anode. The dashed curves are
the concentrations p r e d i c t e d by the m o d e l assuming
an interdiffusion coefficient of 5 X 10 -5 cm 2 se c- 1
and the t r a n s f e r e n c e n u m b e r tg No~ g iv e n in Eq. [4].
Th e e x p e r i m e n t a l points fall on the predicted curves
initially, b u t for times longer t h a n 3 m i n the concent rat i o n at the anode is closer to the initial c o n c e n t r a tion t h a n the p r e d ic te d values. This m a y arise p a r t l y
f r o m c u m u l a t i v e errors introduced by the successive
c u r r e n t interruptions, b u t is in the direction e x p e c t e d
for c o n v e c t i v e m i x i n g in the free electrolyte. F i g u r e 7
is a reco rd i n g of the potentials of the anode and of
the cathode during the c u r r e n t i n t e r r u p t io n s shown
in the u p p er p a r t of the figure. A f t e r c u r r e n t i n t e r r u p tion, t h e potential decreases rapidls; w i t h time, hence
t h e r e is a v e r y fast c o n c e n tr a ti o n change at the electrodes. At the end of a c u r r e n t i n t e r r u p t i o n step the
concentration profile b e t w e e n the two electrodes, consequently, is different f r o m that at the b e g i nn i n g of
the interruption, and leads to a different concentration
at t h e electrodes at the time of the n e x t c u r r e n t
interruption. F e w e x p e r i m e n t a l points w e r e obtained
at the cathode because of silver d e n d r i t e formation.
The initial portion of the curves yields a high v al u e
of the a p p a r e n t interdiffusion coefficient (5 X 10 -5
II
J
0
25
I
I
--
\
\
;e
20
--
.J
~t5 -Z
uJ
k0
o-
t0
l
5 --
o
\
\
\
2"
\
--
o
\
I
I
~0
20
30
40
\\
I
I
I
50
60
70
\
1
80
TIME ( s )
) and of
Fig. 7. Time dependence of potential of ( + ) anode (
(--) cathode ( - - ) during interruptions of electrolysis with constant
current in 0.2 AgNO~-0.8 KNO3 at 310~
cm 2 s e c - 1 ) , w h i ch is in the direction expected for
errors resulting f r o m convection in the melt. Results
f r o m analogous e x p e r i m e n t s using silica frits (Fig. 3)
to reduce convection yield a m o r e reasonable, 2 lower,
interdiffusion coefficient, 1.5-2 X 10 -5 cm 2 sec -1.
Relaxation of the polarization emf in frits.--Since
successive c u r r e n t i n t er r u p t i o n s disturb the d e v e l o p m e n t of concentration gradients in the electrolyte,
another, r e l a t e d e x p e r i m e n t was performed. Th e m e l t
confined in a fr.it is electrolyzed at constant c u r r e n t
for a k n o w n period of time, t h e c u r r e n t is cut off,
2 A t 300~
the interdiffusion coefficient i n AgNOs-NaNO3 m i x t u r e s h a s b e e n r e p o r t e d as Z x 10-~ cm~ s e c -1 ( 2 0 ) .
Downloaded on 2015-04-01 to IP 149.156.116.7 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).
January 1980
J. EIectrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y
a n d the relaxation to the u n i f o r m initial composition
is followed by m e a s u r i n g the potentials of cathode
a n d of anode (relative to a reference electrode i n
the melt of initial composition) as they decay back
towards zero. The recording on a X - Y recorder starts
a few seconds after the cutoff, allowing complete
discharge of the double layer. Extrapolation of the
recorded curves to zero time of relaxation, and the
use of Eq. [6], gives the composition at both electrodes
at the end of each electrolysis. Typical relaxations,
at 320~
are indicated b y the emf measurements,
shown as points i n Fig. 8, of anode a n d cathode after
1 m i n of electrolysis of a 0.2 AgNO~-0.8 KNO3 melt
at 0.15 A - c m -2. The lines in Fig. 8 are the calculated
diffusional relaxations (Fick's second law) from the
concentration profiles at the end of electrolysis. These
t r a n s i e n t concentration profiles d u r i n g electrolysis were
calculated b y n u m e r i c a l solution of Eq. [1] and [2],
with Eq. [3] for the emf at the end of electrolysis
and d u r i n g the relaxation. A square root of time scale
is used in order to separate the points i n the fast
initial portion of the r e l a x a t i o n curve. The solid line
curves are predicted potentials, with Eq. [5] for the
transference n u m b e r , the dashed curves are the predictions with the assumption of a transference n u m ber equal to the mole fraction, which provides a
simpler b u t slightly less accurate computation. In all
the computations the interdiffusion coefficient is t a k e n
to be 1.5 X I 0 - 5 cm 2 sac - t . I n the three experiments,
shown in Fig. 8, the thickness of the frit was about
0.5 cm. Extrapolation of the e x p e r i m e n t a l curves to
zero r e l a x a t i o n time leads to a composition of XAg
-- 0.30 at the anode and of XAg ---- 0.08 at the cathode
at the end of electrolysis. The e x p e r i m e n t a l curves
have the general shape of the predicted curves and
the time scale of the predicted curves agrees with
the time scale of the e x p e r i m e n t a l curves. Neglecting
the deviations of the transference n u m b e r from the
mole fraction (dashed line curves) gives predicted
composition changes slightly larger t h a n those observed. A t short times of relaxation, the measured
emf values at the cathode differ more from the predictions t h a n those at the anode. The measured curves
correspond to less negative potentials, i.e., the cornTIME
II
I
--
20
08
~
I
KNO 3-
9 ""
30~
I
02
,o
I
50 eo
I
to
--
~,~.~.
2
L
5
h
10
]
210
30
L
410
510
60
-0.56
-0.34
-0.32
0.8 KNO~- 0.2 AgNO 3
/ = 350~
[ = 0.t50 A cm-2
20
--0.30
0.28
~5
AgNO 3
, II
,0 ~ ' ~ , II l
i , o , - - - - t0 s
m, D, - - - - 20 s
L-~--J ~--y-J
EXPERIMENTALJ
L PRED[CTED
ANODE
--0.26
--0.24
--
-o.22 g
EXPERIMENTAL
~ , ~ o ' - . . . . . . JL._.i_
o
~
Z
0.51
I L
25
PREDICTED
"'~,
TIME (min)
(min)
I
T=320~
position change at the cathode seems to be smaller
t h a n predicted. Possible causes of the deviation m a y
include convection, dendrite formation at the cathode
reducing the real c u r r e n t density, formation of a
saturated solution, or the onset of a mixed electrode
reaction. At 320~ the liquidus composition is XAg -0.08 (21), corresponding to an emf of --44 inV. The
extrapolated emf at zero time from the two sets of
e x p e r i m e n t a l points is close to the emf corresponding
to saturation. I n order to eliminate the possibility of
saturation, similar experiments were carried out a t
a higher temperature, 350~
The e x p e r i m e n t a l results obtained at 350~ after
5, 10, and 20 sac of electrolysis are presented in Fig. 9,
together with the corresponding predicted emf curves
calculated as above, with Eq. [5] for the transference
n u m b e r and D = 2 X 10 -5 cm 2 sac -1. The compositions corresponding to the emf's are shown on the
r i g h t - h a n d ordinate. After 20 sac of electrolysis at
0.15 A - c m -2 with a 0.4 cm electrode separation, the
measured silver n i t r a t e concentration has increased
b y 60% at the anode and decreased by 42% at the
cathode. Table IV compares the predicted compositions
at anode a n d cathode at the end of electrolysis with
the e x p e r i m e n t a l compositions, the latter obtained b y
extrapolation to zero relaxation times. E x p e r i m e n t a l
and predicted composition agree w i t h i n 4-15%. As
with the 320 ~ results, the predicted anotyte composition changes at 350~ are smaller t h a n those observed
while the predicted catholyte changes are larger. This
t r e n d appears to increase with increasing electrolysis
time, and cannot be a t t r i b u t e d to s a t u r a t i o n at the
cathode (at 350~
nor to convection or u n c e r t a i n t y
in D, which would affect predicted cathode and anode
composition changes in the same direction. The difference b e t w e e n predicted and observed composition
changes is in a direction that could correspond to a
higher c u r r e n t density at the anode t h a n at the cathode,
-
-
9 __-::_o:~___o v
D
-0.20 ~
[]
ANODE
~
-5
n
0. t8 ~
n
,5-
uJ
c,.
a2
-0.16
0
7
-15
~A
~/
CATHODE
-0.t4
-20
I
u_ - t o
-25
td
__
_ olq
0
20
30
TI~
40
50
I
I
I
5
I0
~5
2O
,I
I
25
I
30
35
Is v2)
i
I
I
I
40
45
5O
55
-
-0.t2
Fig. 9. Relaxation of polarization emf following electrolysis in
0.2 AgNO3-0.8 KNOa at 0.15 A-era - 2 for three different times.
Temperature, 350~ Experimental:
I I I I I I I I
t0
-
I
60
(s Va )
Fig. 8. Relaxation of polarization emf following electrolysis in
0.2 AgN08-0.8 I(NO,~ at 0.15 A-cm - 2 for 1 min. Effect of the
transference number on the predicted curves: ~
with emf
calculated from Eq. [6]; - - with emf calculated assuming
IKNO8 : XK. Frit thickness: 0.5 cm.
Electrolysis time: 5 sac
Electrolysis time: 10 sec
Electrolysis time: 20 sec
;
9 anode;
9 anode;
0 cathode
0 cathode
[ ] cathode
Predicted (anodic and cathodic):
Electrolysis time: 5 sac
Electrolysis time: 10 sac - - Electrolysis time: 20 sac - - -
Downloaded on 2015-04-01 to IP 149.156.116.7 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).
Vol. 127, No. I
COMPOSITION G R A D I E N T S
Table IV. Measured and predicted compositions at the anode and
at the cathode from electrochemical measurement after electrolyses
at 0.15 A-crn - 2 of a 0.2 AgNO~-0.8 KNO~ mixture at 350~ *
Composition at
the anode, (XA~)
JOURNAL. All discussions for the December 1980 Discussion Section should be submitted by Aug. 1, 1980.
Publication costs of this article were assisted by
Oak Ridge National Laboratory.
Composition a t
the c~Lhooe (XA~)
T i m e of
electrolysis (sec)
0
5
10
20
Mea-
Pre-
Mea-
sured
dicted ~*
sured
Predicted**
-0.27
0.30
0.200
-0.257
0.279
0.16
0.14
0.123
0.200
0.154
0.135
0.107
CK
D
d
E
F
I
R
T
9 T h e s e e x p e r i m e n t s w e r e m a d e w i t h frits of t h i c k n e s s bet w e e n 0.35 and 0.5 cm.
9* C a l c u l a t e d w i t h D = 2 x 10-~ cm~ sec-1 a n d t h e g e o m e t r i c
electrode area.
which could result from dendrites at the cathode.
Experiments are under way to determine the effects
of frit porosity (i.e., tortuosity, partial blocking of
the electrode, etc.) and longer electrolysis times on
the validity of the model predictions, in a system for
which the interdiffusion coefficient (as well as the
transference number) is better known.
Conclusions
Electrolysis of AgNO~-KNO3 mixtures between
silver electrodes, under conditions similar to those
in a molten sal{ battery (e.g., Li (A1)/LiC1-KC1/FeSx),
demonstrates the development of significant currentinduced composition gradients, as predicted from a
consideration of the migrational, diffusional, and faradaic processes in binary molten salt mixtures. Chemical analysis of sections of salt quenched after electrolysis shows composition changes of direction and magnitude predicted, but with insufficient resolution for
a rigorous test of the one dimensional model. Potentiometric analysis of compositions at the electrode
surfaces after electrolysis and during diffusional relaxation are more precise than the chemical analysis;
for short electrolysis times, they confirm strikingly
the predicted end points of the composition profiles,
but they cannot test the predicted shape of the profile
in the bulk electrolyte. For longer electrolysis times,
deviations occur between the predicted relaxations
and the measurements, although the genera1 features
of the predicted gradients are observed. The deviations
at long times are not attributable to convection alone,
but probably also entail contributions from flit porosity, dendrite formation, and other effects. Work is
in progress to resolve these contributions to the observed composition gradients and to incorporate them
into the model, as well as to improve the analytical
precision. The experimental demonstration of electrochemical composition charJges in binary molten salt
mixtures and the test of the model for predicting
their extent are of importance because composition
changes of the magnitude observed here may affect
significantly the performance of fuel cells or batteries
(8, 22).
Acknowledgments
We are pleased to acknowledge for their assistance
W. H. F a r m e r (Metals and Ceramics Division) for
cutting the frits, J. C. Franklin (Analytical Chemistry
Division) for the analysis of silver, and P. L. Howell
(Analytical Chemistry Division) for the analysis of
potassium. Research sponsored by the Division of
Materials Sciences, Office of Basic Energy ~Cciences,
U.S. Department of Energy under Contract W-7405eng-25 with the Union Carbide Corporation.
Manuscript submitted June 14, 1978; revised manuscript received J u l y 9, 1979.
Any discussion of this paper will appear in a Discussion Section to be published in the December 1980
tKNO8
Ui
X~
XA~
X'Ag
XK
<_xK>
XK
X
~AgNO3
CrN-- 1
~N--2
LIST O F SYMBOLS
ionic concentration of K + (eq cm -3)
binary diffusion coefficient (cm 2 sec -~)
distance between cathode and anode (cm)
open-circuit potential difference (V)
faraday (96,487C)
current density (A-cm -2)
gas constant
temperature (~
transference number of K+ relative to NO3absolute value of mobility of ion i
mole fraction of AgNOa (reference)
mole fraction of AgNO~ at anode (or cathode)
mole fraction of AgNO~ in the melt
mole fraction of KNOz
mean composition (mole fraction of KNO3)
initial composition (mole fraction of KNOs)
distance from electrodes
chemical potential of AgNO3
standard deviation about the mean composition
standard deviation based on the linear least
squares fit
REFERENCES
1. D. E. Heatherly, P r e l i m i n a r y results presented at
the Council Committee on Technician Activities,
American Chemistry Society Meeting, Chicago,
Aug. 28-Sept. 2, 1977.
2. M. L. Miller and H. J. Fornasan, This Journal, 115,
330 (1968).
3. J. T. Lundquist and M. Vogel, ibid., 116, 1066
(1969).
4. F. R. McLarnon, R. H. Muller, and C. W. Tobias,
Electrochim. Acta., 21, 101 (1976).
5. L. Hsueh and J. Newman, Ind. Eng. Chem. Fundam.,
10, 4, 615 (1971).
6. C. G. Smith and R. H. Muller, Lawrence Berkeley
Laboratory Annual Report LBL-6016, p. 209
(1976).
7. C. E. Vallet and J. Braunstein, This Journal, 125,
1193 (1978); C. E. Vallet and J. Braunstein,
ibid., 126, 527 (1979).
8. G. L. HolIeck and J. Giner, ibid., 119, 1161 (1972).
9. Y. Yamamura, J. Nucl. Sci. Technol., 6, 698 (1969);
Y. Yamamura and S. Suzuki, ibid., 7, 36 (1970).
10. M. Chemla, Discuss. Faraday Soc., 32, 63 (1961).
11. Progress Report, Argonne National Laboratory,
ANL 76-98 (Dec. 1976).
12. R. K. Steunenberg and M. F. Roche, in "Electrode
Materials and Processes for Energy Conversion
and Storage," J. D. E. McIntyre, S. Srinivasan,
and F. O. Will, Editors, p. 869, The Electrochemical Society Proceedings Series, Princeton, N.J.
(1977).
13. C. E. Vallet and J. Braunstein, J. Phys. Chem., 81,
2438 (1977).
14. J. Braunstein and H. Braunstein, in "Experimental
Thermodynamics," B. LeNeindre and B. Vodar,
Editors, Chap. 18, p. 915, Butterworths, London
(1975).
15. F. R. Duke and B. Owens, This Journal, 105, 476
(1958).
16. G. L. Duret, R. J. Hassan, Jr., and M. P. Rill, Oak
Ridge National Laboratory, ORNL/MIT-249
(Feb. 1977).
17. M. Okada and K. Kawamura, Electrochim. Acta.,
15, 1 (1970).
18. C. E. Vallet and J. Braunstein, This Journal, 126,
960 (1979).
19. Y. Doucet and C. Naccache, C. R. Acad. Sci. Ft.,
259, 2838 (1964).
20. J. Richter, Ber. Bunsenges. Phys. Chem., 80, 92
(1976).
21. A. Ussow, Z. Anorg. Chem., 38, 419 (1904).
22. C. A. Melendres, C. C. Sy, and B. Tani, This Journal, 124, t080 (1977).
Downloaded on 2015-04-01 to IP 149.156.116.7 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).