Pure & Appl. Chern.,Vol. 63,No. 5,pp. 71 1-734, 1991
Printed in Great Britain.
@ 1991 IUPAC
I
ADONIS
206922209100080K
INTERNATIONAL UNION OF PURE
AND APPLIED CHEMISTRY
PHYSICAL CHEMISTRY DIVISION
COMMISSION ON ELECTROCHEMISTRY*
REAL SURFACE AREA MEASUREMENTS
IN ELECTROCHEMISTRY
Prepared for publication b y
S . TRASATTI' and 0. A. PETRI12
'Dipartimento di Chimica Fisica ed Elettrochimica, Universith di Milano, Italy
2Faculty of Chemistry, Lomonosov Moscow State University, USSR
*Membership of the Commission during the period the report was prepared (1985-1989) was
as follows:
Chairmen: K. Niki (Japan; 1985-1987); G. Gritzner (Austria; 1987-1991); Vice Chairman:
L. R. Faulkner (USA; 1985-1987); Secretaries: G. Gritzner (Austria; 1985-1987); G. S. Wilson
(USA; 1987-1991); Titular Members: B. E. Conway (Canada; 1985-1989); L. R. Faulkner
(USA; 1983-1989); G. Gritzner (Austria; 1983-1991); D. Landolt (Switzerland; 1983-1991);
V. M. M. Lob0 (Portugal; 1985-1993); R. Memming (FRG; 1983-1987); K. Tokuda (Japan;
1987-1991); Associate Members: C. P. Andrieux (France; 1987-1991); J. N. Agar (UK; 19791987); A. Bewick (UK; 1983-1987); E. Budevski (Bulgaria; 1979-1987); Yu. A. Chizmadzhev
(USSR; 1987-1991); K. E. Heusler (FRG; 1983-1987); J. C. Justice (France; 1983-1987);
J. Koryta (Czechoslovakia; 1983-1991); B. Miller (USA; 1979-1987); 0. A. Petrii (USSR;
1983-1991); D. Pletcher (UK; 1987-1991); J. A. Plambeck (Canada; 1979-1987); W. Plieth
(FRG; 1987-1989); M. Sluyters-Rehbach (Netherlands; 1985-1989); K. Tokuda (Japan; 19851987);M. J. Weaver (USA; 1987-1991); A. Yamada (Japan; 1983-1987); National Representatives:
A. J. Arvia (Argentina; 1980-1991); M. L. Berkem (Turkey; 1987-1991); T. Biegler (Australia;
1985-1991); A. K. Covington (UK; 1979-1991); D. DraiiC (Yugoslavia; 1981-1991); E. Gileadi
(Israel; 1983-1991); C. Gutierrez (Spain; 1987-1991); G. Horinyi (Hungary; 1979-1991);
H. D. Hunvitz (Belgium; 1985-1991); R. W. Murray (USA; 1985-1989); K. Niki (Japan; 19871989); R. L. Paul (RSA; 1983-1989); D. Pavlov (Bulgaria; 1987-1991); S. Trasatti (Italy; 19851991); G. A. Wright (New Zealand; 1985-1991); Z. Zembura (Poland; 1983-1989); B. E.
Conway (Canada; 1979-1985).
Republication of this report is permitted without the need for formal IUPAC permission on condition that an
acknowledgement, with full reference together with IUPAC copyright symbol (0
1991 IUPAC), is printed.
Publication of a translation into another language is subject to the additional condition of prior approval from the
relevant IUPAC National Adhering Organization.
Real surface area measurements in
electrochemistry
Abstract - Electrode reaction rates and most double layer parameters are
extensive quantities and have to be referred to the unit area of the
interface. Knowledge of the reel surface area of electrodes is therefore
needed. Comparison of experimental data with theories or of experimental
results for different materials and/or from different laboratories to each
other is physically groundless without normalization to unit reel area of
the electrode surface. Different methods have been proposed to normalize
experimental data specifically with solid electrodes. Some of them are not
sufficiently justified from a physical point of view. A few of them are
definitely questionable. The purpose of this document is to scrutinize the
basis on which the various methods and approaches rest, in order to assess
their relevance to the specific electrochemical situation and, as far as
possible,
their absolute reliability.
Methods and approaches are
applicable to ( a ) liquid electrodes, (b) polycrystalline and single
crystal face solids, ( c ) supported, compressed and disperse powders. The
applicability of the various techniques to each specific case is to be
verified. After an introductory discussion of the "concept" of real
surface area, fifteen methods, eleven applied in situ and four ex situ,
are scrutinized. For each of them, after a description of the principles
on which i t is based, limitations are discussed and recomnendations are
given.
CONTENTS
1.
Introduction
1.1 Generalities
1.2 General concepts
71 2
71 2
713
2.
In Situ Methods
2.1 Drop weight (or volume)
2.2 Capacitance ratio
2.3 Parsons-Zobel plot
2.4 Hydrogen adsorption from solution
2.5 Oxygen adsorption from solution
2.6 Underpotential deposition of metals
2.7 Voltammetry
2.8 Negative adsorption
2.9 Ion-exchange capacity
2.10 Adsorption of probe molecules from solution
2.1 1 Mass transfer
71 5
71 6
71 7
719
720
721
722
723
724
724
725
Ex Situ Methods
3.1 Adsorption of Probe molecules from gas phase
3.2 X-ray diffraction
3.3 Porosimetry
3.4 Microscopy
3.5 Other methods
726
728
729
730
731
References
73 1
3.
4.
1.
INTRODUCTION
1.1 Generalities
T h e s u r f a c e a r e a w h i c h c a n b e d e t e r m i n e d w i t h o r d i n a r y t o o l s d e s i g n e d to
m e a s u r e a l e n g t h i s t h e g e o m e t r i c s u r f a c e a r e a , A s . It i s d e f i n e d ( r e f . 1 ) a s
the projection of the real surface o n a plane parallel to the m a c r o s c o p i c ,
712
Real surface area measurements in electrochemistry
713
visible p h a s e boundary..
T h u s , A= is calculated o n the b a s i s of k n o w n
geometric
dimensions
of
the
object
constituting
the
electrode,
whose
resolution is normally that of m a c r o s c o p i c m e a s u r e m e n t s . O n l y for liquids d o e s
the real s u r f a c e coincide in p r i n c i p l e w i t h the g e o m e t r i c s u r f a c e . In the case
of s o l i d s , a s p e r i t i e s are n o r m a l l y present w h o s e height m a y be o r d e r s of
m a g n i t u d e greater than the atomic o r m o l e c u l a r s i z e , though lower than the
v i s i b l e r e s o l u t i o n . in t h i s case the real s u r f a c e area is h i g h e r than AK and
experimental data must b e n o r m a l i z e d to the real s u r f a c e to b e c o m e u n i v e r s a l l y
comparable.
Electrode
quantities
Knowledge
Comparison
different
physically
surf ace.
r e a c t i o n r a t e s and most d o u b l e layer p a r a m e t e r s are e x t e n s i v e
and h a v e to be referred to the unit area of the interface.
of
the real s u r f a c e area of e l e c t r o d e s is t h e r e f o r e n e e d e d .
of experimental data w i t h t h e o r i e s o r of experimental r e s u l t s for
m a t e r i a l s a n d / o r f r o m different
l a b o r a t o r i e s to e a c h o t h e r is
g r o u n d l e s s w i t h o u t n o r m a l i z a t i o n to unit real area of the e l e c t r o d e
W h i l e the s u r f a c e a r e a , A , is n o r m a l l y e x p r e s s e d a s a s q u a r e d length (SI
U n i t s : mz), i t is o f t e n expedient to report specific v a l u e s referred e i t h e r to
unit m a s s ( A a / m 2 g-1). o r to unit v o l u m e ( A v / m z m - 3 E m - 1 ) ; they are r e l a t e d
by the f b l l o w i n g equation:
Av = A / V = A p / m = A m p
(1)
w h e r e p is the m a s s d e n s i t y , m the m a s s and V the v o l u m e of the system. N o t e
that the ( r e a l ) s u r f a c e area per unit g e o m e t r i c s u r f a c e area i s c a l l e d the
r o u g h n e s s factor, fr = A / A K ( c f r e f . 1 )
Different m e t h o d s h a v e b e e n proposed to n o r m a l i z e experimental data specifically w i t h solid e l e c t r o d e s . S o m e of them are not s u f f i c i e n t l y justified f r o m a
physical point of view. A f e w of them a r e d e f i n i t e l y q u e s t i o n a b l e .
T h e p u r p o s e o f t h i s document is to s c r u t i n i z e the b a s i s o n w h i c h the v a r i o u s
m e t h o d s and a p p r o a c h e s r e s t , in o r d e r to a s s e s s their r e l e v a n c e to the
specific electrochemical s i t u a t i o n a n d , a s far a s p o s s i b l e , their a b s o l u t e
reliability. M e t h o d s and a p p r o a c h e s are a p p l i c a b l e to ( a > liquid e l e c t r o d e s ,
(b) p o l y c r y s t a l l i n e and s i n g l e crystal f a c e s o l i d s , ( c ) s u p p o r t e d , c o m p r e s s e d
and d i s p e r s e powders. T h e a p p l i c a b i l i t y of the v a r i o u s t e c h n i q u e s to each
specific case is to b e verified.
T h i s document i s related to p r e v i o u s IUPAC p u b l i c a t i o n s , s u c h a s the Manual of
S y m b o l s and T e r m i n o l o g y ( r e f . a ) , its A p p e n d i x 1 1 ( r e f . 3), A p p e n d i x 1 1 1 ( r e f .
4 ) , and the p a p e r s o n a d s o r p t i o n from s o l u t i o n ( r e f . 5 ) and o n i n t e r p h a s e s
between c o n d u c t i n g p h a s e s (ref. 1 ) . T h e final list of r e f e r e n c e s g i v e n is not
intended to be exhaustive: o n l y a f e w i l l u s t r a t i v e and e x e m p l i f i c a t i v e p a p e r s
have been chosen for q u o t a t i o n .
1.2 General concepts
T h e m e a n i n g of real s u r f a c e area d e p e n d s o n the m e t h o d of m e a s u r e m e n t of A , o n
the theory of t h i s m e t h o d , and o n the c o n d i t i o n s of a p p l i c a t i o n of the method.
T h u s , for a g i v e n s y s t e m , v a r i o u s "real s u r f a c e areas" can in p r i n c i p l e b e
defined, d e p e n d i n g o n the c h a r a c t e r i s t i c d i m e n s i o n of the p r o b e u s e d . T h i s is
so even if phenomena of s u r f a c e r e c o n s t r u c t i o n , r e l a x a t i o n and faceting. w h i c h
o f t e n o c c u r d u r i n g a d s o r p t i o n o r electrochemical m e a s u r e m e n t s , should not be
taken into account. T h e most a p p r o p r i a t e is the o n e e s t i m a t e d u s i n g a m e t h o d
w h i c h best a p p r o a c h e s the experimental s i t u a t i o n to w h i c h the area d e t e r m i n e d
is to be applied.
B e s i d e s the concept of real s u r f a c e area. other a s p e c t s should be t a k e n into
c o n s i d e r a t i o n w h e n d e a l i n g w i t h s o l i d electrodes:
( a > s u r f a c e topography
(macro- and m i c r o r o u g h n e s s ) ; (b> homogeneity/heterogeneity of the s u r f a c e ; (c)
d i s p e r s i o n of the a c t i v e m a t e r i a l , including (d) d i s t r i b u t i o n law of the
d i s p e r s e d a c t i v e m a t e r i a l . T h e s e a s p e c t s are closely interrelated and a r e to
be thoroughly c o n s i d e r e d in o r d e r to a c h i e v e a correct c o m p r e h e n s i o n of the
m e a n i n g of n o r m a l i z a t i o n of data to t h e unit real area of the e l e c t r o d e
surf ace.
Note thmt if the surfmce includes a macroscopic verticml step between two planar regions, a l s o the phmse boundary
haa a step whose ares is thus obviouely counted in the calculetion of A=. If the step is microscopic, i t turns out
not to be included into tho g8Omet?iC surface.
714
COMMISSION ON ELECTROCHEMISTRY
S u r f a c e h e t e r o g e n e i t y and s u r f a c e r o u g h n e s s a r e crucial a s p e c t s of solid
surfaces. T h e d i f f e r e n c e between the two c o n c e p t s lies in the fact that
p e r i o d i c i t y is not required for s u r f a c e h e t e r o g e n e i t y w h i l e for s u r f a c e
r o u g h n e s s i t b e c o m e s a d e t e r m i n i n g c o n d i t i o n . S u c h i r r e g u l a r i t i e s w h i c h should
not b e considered a s r o u g h n e s s d u e to their non-periodic c h a r a c t e r m a y be
important in the d e f i n i t i o n of surface quality. T h e concept of r o u g h n e s s is
well illustrated by the a b o v e d i s t i n c t i o n b e t w e e n real and g e o m e t r i c s u r f a c e
area. A surface is ideally h o m o g e n e o u s a s i t s p r o p e r t i e s d o not depend o n the
p o s i t i o n o n the s u r f a c e at the atomic s i z e resolution. T h e s u r f a c e of liquids
s i m u l a t e s homogeneity at the best s i n c e the local p r o p e r t i e s a r e s m o o t h e d by
thermal f l u c t u a t i o n s . F o r s o l i d s , ideally ordered s i n g l e crystal f a c e s m a y be
r e p r e s e n t a t i v e of h o m o g e n e o u s surfaces.
s u r f a c e is h e t e r o g e n e o u s a s its p r o p e r t i e s depend o n the position. T h e
simplest example of a h e t e r o g e n e o u s s u r f a c e i s a s i n g l e crystal f a c e w i t h
randomly d i s t r i b u t e d point defects. T h e commonest e x a m p l e is a p o l y c r y s t a l l i n e
s u r f a c e w h e r e the periodicity o f d i s t r i b u t i o n o f a t o m s d i f f e r s f r o m place to
place. In both c a s e s the surface, though h e t e r o g e n e o u s , m a y be ideally smooth.
H o w e v e r , pits o n a
s i n g l e crystal
face entail
both h e t e r o g e n e i t y and
roughness. C o n s i s t e n t l y , a r o u g h s u r f a c e m a y in p r i n c i p l e be h o m o g e n e o u s .
H o w e v e r , a rough single crystal face i m p l i e s also s u r f a c e h e t e r o g e n e i t y .
A
In v e r y general t e r m s , s u r f a c e r o u g h n e s s m a y be treated in c e r t a i n c a s e s u s i n g
the
theory
of
fractal
geometry
( r e f . 6). Recent
developments
in
the
u n d e r s t a n d i n g of the fractel n a t u r e of ( e s p e c i a l l y ) s u r f a c e r o u g h n e s s and of
its c o n s e q u e n c e s for a l l extensive interfacial q u a n t i t i e s , c o m p l i c a t e the
phenomenological a p p r o a c h adopted in the p r e v i o u s p a r a g r a p h s . F o r i n s t a n c e ,
the d i m e n s i o n of a " s u r f a c e area" is n o longer the s q u a r e of length in the
theory of fractals. Also "bulk properties" such a s electrical c o n d u c t i v i t y a r e
n o longer m e r e l y bulk but they b e c o m e ( p a r t l y ) interfacial. S i n c e t h i s
document is devoted to the experimental d e t e r m i n a t i o n of the s u r f a c e area and
not to its mathematical d e s c r i p t i o n , the c u s t o m a r y phenomenological a p p r o a c h
to the problem will be f o l l o w e d in the v a r i o u s sections.
P o l y c r y s t a l l i n e solid m a t e r i a l s consist of a n e n s e m b l e o f randomly o r i e n t e d
c r y s t e l l i t e s , w h i c h a r e the smallest u n i t s of single c r y s t a l s . In the c a s e of
a d i s p e r s e m a t e r i a l , two or m o r e c r y s t a l l i t e s m a y a g g r e g a t e through g r a i n
b o u n d a r i e s to f o r m particles. T h e s e are c h a r a c t e r i z e d by their d i m e n s i o n
(size), s h a p e and s i z e d i s t r i b u t i o n f u n c t i o n . P a t c h w i s e m o d e l s s i m u l a t e
h e t e r o g e n e o u s s u r f a c e s a s a c o l l e c t i o n of h o m o g e n e o u s patches. H e t e r o g e n e i t y
is t h u s expressed in t e r m s of a spatial d i s t r i b u t i o n f u n c t i o n .
T h e p a r t i c l e ( c r y s t a l l i t e ) s i z e is n o r m a l l y g i v e n in terms of a length, d,
w h o s e g e o m e t r i c s i g n i f i c a n c e d e p e n d s o n the p a r t i c l e s h a p e . H o w e v e r , d is
customarily referred to a s the p a r t i c l e (crystallife) diameter. F o r a g i v e n
m a t e r i a l , the experimental v a l u e of d is a l w a y s an a v e r a g e over the n u m b e r of
p a r t i c l e s examined.
V a r i o u s k i n d s of d m a y b e defined ( r e f . 7 ) . F o r c r y s t a l l i t e s of d i a m e t e r di
and n u m b e r n i , the n u m b e r a v e r a g e d i a m e t e r for a g i v e n p a r t i c l e s i z e
d i s t r i b u t i o n is g i v e n b y :
d = Znidi/Pni
(2)
the s u r f a c e a v e r a g e d i a m e t e r b y :
and the v o l u m e a v e r a g e d i a m e t e r by:
dv = Pni did /2ni di3
W h i c h of the three d i a m e t e r s a b o v e are e x p e r i m e n t a l l y obtained d e p e n d s o n the
technique and the procedure used for the d e t e r m i n a t i o n .
O t h e r e x a m p l e s illustrating the a b o v e a s p e c t s are: ( a > m e c h a n i c a l l y treated
p o l y c r y s t a l l i n e solid e l e c t r o d e s , a l w a y s involving a disturbed s u r f a c e layer
w h o s e atomic arrangement d i f f e r s from the e q u i l i b r i u m one in the b u l k ; ( b >
dispersed electrode m a t e r i a l s usually involving an u n k n o w n s i z e d i s t r i b u t i o n
o f p a r t i c l e s w h o s e s h a p e and c r y s t a l l o g r a p h i c o r i e n t a t i o n m a y depend o n the
n a t u r e of the m a t e r i a l , and w h o s e s u r f a c e s t r u c t u r e m a y include different
d e f e c t s d e p e n d i n g o n the kind o f preparation procedure.
Real surface area measurements in electrochemistry
715
The above paragraphs, while not exhausting the problem, are illustrative of
the fact that the simple concept of "real surface area" may be misleading if
not related to the numerous other parameters which depend on the surface
structure and determines the reactivity of an electrode surface.
2.
IN SlTU METHODS
2.1 Drop weight (or volume)
This method is that classically used with liquid metal electrodes (refs. 8-11)
such a s Hg, G a , amalgams, and gallium liquid alloys (In-Ga, TI-Ga, etc.).
Electrodes may be static (hanging or sessile drop) or dynamic (falling drop).
In general terms, the area of such drop electrodes can be calculated as the
surface of rotation on the basis of diameters of sections which belong to
different fixed levels on the drop drawing. More specific approaches are
described below.
2.f.f Principles. For dropping electrodes, the rate of flow ( m ) of the liquid
metal down a glass capillary is measured by weighing the mass of metal dropped
in a given period of time. The area A of the extruded drop at a selected time
t of the drop life is calculated, assuming spherical shape, from the equation
(refs. 9,12,13):
A = 4n(3mt/4np)z/3
(1.1)
where p is the density of the dropping liquid. With m in g
in g cm-3 the resulting surface area is in cmz.
s-1,
t
in s and p
2 . 1 . 2 Limitations. Equation ( 1 . 1 )
is strictly valid only for the area of a
single drop at the end of the drop life. I t may be valid at a different moment
of the drop life only if i t is allowed to assume that the flow rate is not
significantly depending on time. However, the assumption of constant flow rate
is rendered invalid by the effect of the back pressure (refs. 12-16) given by
2y/r where y is the surface tension of the liquid metal and r the drop radius.
Thus, the action of the back pressure is maximum at the moment of drop
detachment. Consequently, the flow rate increases during the growth of a drop.
The back pressure is seen to decrease with drop size and drop life. Its
relative effect becomes smaller with increasing height of the liquid metal
head (pressure) over the capillary. The quantity m , measured as indicated
above, will be the average of the time-dependent flow rate, m ( t ) , over the
whole drop life, r , ie m = (l/r)J;rn(t)dt.
At T = r the area is correctly
calculated by eqn.(l.l). but a t t < r the real area will be smaller than the
calculated one. Since y is potential dependent, the back pressure effect is
also expected to depend on potential, being greatest at the potential of zero
charge ref. 3). On the other hand, there is a compensating effect caused by
the inertia of the Hg stream downwards the Capillary.
These problems do not occur if the weight of the drop is measured at exactly
the time where the electrochemical quantity is recorded, for instance, at
mechanically knocked-off electrodes and at the hanging-drop electrode.
The condition of perfect sphericity of the drop is not met toward the end of
the drop life especially with capillaries of relatively large bore. Under
similar circumstances the drop will become pear-shaped (refs. 11,12,17).
Part of the surface of the (assumed) sphere is actually excluded at the place
where the drop connects with the column in the capillary. Under similar
circumstances, the drop can be treated as a "truncated" sphere (refs. 18,19).
The excluded area is approximately equal to 7rrc2, where rc is the radius of
the capillary at the orifice (refs. 12,20).
An experimental approach to the determination of the excluded area resting on
the assumption of constant flow rate with drop life is the following. Under
similar circumstances i t is possible to write:
T C I / ( A I - A X ) = T C Z / ( A Z - A ~=)
...
= T C ~ / ( A ~ - A
= ~const(€)
)
(1.2)
where T C ~ ,T C Z , . . .TC,, are the total capacitances (ie not referred to unit
surface area) measured at some times t i , t z . . . t n of the drop 1 ife. Ai , Az
.An
are the surface areas determined at the various times by means of eqn.(l.l)
and Ax is the excluded area. By solving eqn.(l.l), an average value < A x > can
..
COMMISSION ON ELECTROCHEMISTRY
thus be estimated. S t r i c t l y , i t should result to be a function of potential
( c f above). T h e order of magnitude of Ax is about 1 % of the d r o p surface area.
Other complications which h a v e to be mentioned are shielding effects and
solution creeping. if the g l a s s of t h e capillary s h i e l d s a part of the drop
surface. a non-linear relationship m a y result b e t w e e n , eg capacitance or
c u r r e n t , and the surface area derived f r o m the d r o p w e i g h t . O n the other hand,
solution may creep into the capillary causing an o p p o s i t e effect. T h e
occurrence of solution creeping is usually shown by the erratic formation of
drops.
2 . 1 . 3 Evaluations. T h e back pressure effect is important only at the birth of
a drop. I t is observable at short times of the drop life. I t is minimized by
using relatively high v a l u e s of t , h i g h pressure over the capillary and
relatively high f l o w rates.
T h e non-sphericity of the d r o p becomes important only toward the end of the
drop life and is minimized by working at short t v a l u e s compared to the d r o p
time and with n a r r o w capillaries.
Back-pressure and non-sphericity are usually not a problem w i t h dropping H g
electrodes with f l o w r a t e s of the order of 0.2 m g s - 1 and time of measurement
of about 7-9 s over a d r o p life of 12-15 s. Both e f f e c t s can h a v e some
importance w i t h oxidizable liquid electrodes, s u c h a s G a and its a l l o y s , for
which h i g h f l o w rates,
low o v e r p r e s s u r e , and short drop times c a n be
necessary.
Excluded area e f f e c t s h a v e been reported (refs. 1 3 , 2 0 1 and h a v e been claimed
to be more important than the other two, u p to ca 1%. H o w e v e r , its bearing is
greater at short times and decreases rapidly with the expanding drop surface
area. I t is minimized by using very n a r r o w capillary and large drops. W i t h the
characteristics specified above, the d r o p surface area is of the order of 1-2
mm2. T h e excluded area effect becomes negligible with respect to the intrinsic
accuracy of the measured quantities (<O.l%) a s the r a d i u s of the o r i f i c e is
<20-25 pm. A g a i n , this effect m a y be a problem with oxidizable liquid m e t a l s
for which large bore c a p i l l a r i e s m a y b e necessary.
T h e recommended procedure to check whether any of the above e f f e c t s are
operative is to carry out measurement at different times with the same
capillary under otherwise constant conditions. Corrections for the screened
area can be m a d e w h e r e necessary by measuring re by a suitable technique.
2.2 Capacitance ratio
T h i s method is normally used w i t h solid electrodes, but i t is also applicable
to liquid m e t a l s and disperse systems. I t is widely adopted for the estimation
of the surface area ratio for different s a m p l e s of the same electrode material
( e g ref. 21-24>.
2.2.1 Principles. T h e experimental differential capacitance of the electrode
under investigation in aqueous s o l u t i o n s is divided by 15-17 pF c m - 2 , the
empirically established range of capacitance per unit area measured w i t h a H g
electrode at moderately n e g a t i v e charges (around -12 p C c m - 2 ) where C g o e s
through a s h a l l o w minimum. T h i s implies assuming that the structure of the
double layer is exactly the s a m e for the investigated electrode a s for H g . T h e
potential of measurement should be the same on the rational scale. v i z
referred to the potential of z e r o charge.
A variant of this method c o n s i s t s in m e a s u r i n g the capacitance in very dilute
s o l u t i o n s ((10-3
mol d m - 3 ) and in assuming that the m i n i m u m v a l u e at the
potential of z e r o charge is entirely governed by the diffuse layer capacitance
so that the surface area can be obtained by dividing the experimental v a l u e by
that calculated by m e a n s of the Gouy-Chapman theory. T h i s modification implies
that the position of the potential of z e r o charge (the point of zero charge in
the case of ionic solids) is experimentally identifiable.
2.2.2 Limitations. Although there is s o m e evidence that the capacitance f a l l s
in a n a r r o w range of v a l u e s at negative charges in the region -10 to -15 pC
c m - 2 , this v a l u e m a y span f r o m 15 f o r Hg to 25 for the ( 1 1 1 ) face of Ag.
Moreover, the capacitance is potential dependent in a w a y which d e p e n d s
dramatically o n the n a t u r e of the metal. In m a n y c a s e s the position of the
potential of zero cCharge is not known, hence the observation of a plateau d o e s
717
Real surface area measurements in electrochemistry
not n e c e s s a r i l y m e a n that i t m a y
m i n i m u m of H g at n e g a t i v e charges.
be
treated
as
equivalent
to
the
shallow
In the case of the c a p a c i t a n c e m i n i m u m at the potential of z e r o charge, t a k i n g
i t a s d e t e r m i n e d e n t i r e l y by the d i f f u s e layer i s tantamount to a s s u m i n g that
the inner layer c a p a c i t a n c e i s as low a s that o n H g . R e s u l t s for A g , A u , G a
and In-Ga h a v e s h o w n that t h i s is d e f i n i t i v e l y not a general case. T h i s
approach
is e v e n
less
reliable with
ionic
solids, whose
inner
layer
capacitance and its potential d e p e n d e n c e a r e a s a r u l e u n k n o w n ( c f s e c t i o n
7.2).
S i n c e t e c h n i q u e s based o n a l t e r n a t i n g e l e c t r i c s i g n a l s are used for the
measurement.
for rough
solid
s u r f a c e s the c a p a c i t a n c e u s u a l l y s h o w s a
frequency d i s p e r s i o n w h i c h p r e v e n t s the assignment to i t of a p h y s i c a l l y
significant v a l u e . A l s o , m e a s u r e d c a p a c i t a n c e s are o f t e n v i t i a t e d b y s o m e
faradaic c o m p o n e n t s d u e to the fact that most electrochemical i n t e r f a c e s are
not ideally p o l a r i z a b l e ( r e f . 5).
2.2.3 E v a l u a t i o n s . T h i s method h a s n o physical b a s i s ; i t cannot e v e n b e
defined a s empiric s i n c e i t g o e s against the experimental e v i d e n c e . A p a r t f r o m
the n a t u r e of the e l e c t r o d e , the e l e c t r o l y t e m a y h a v e u n p r e d i c t a b l e effects.
F o r i n s t a n c e , F - ions a r e not s p e c i f i c a l l y a d s o r b e d o n H g but they are o n A g
and o t h e r sp-metals. T h e potential of z e r o c h a r g e of d-metals is m a i n l y
unknown and the b e h a v i o u r o f the d o u b l e layer c a p a c i t a n c e w i t h potential h a s
not been investigated. In the case of o x i d i z a b l e t r a n s i t i o n m e t a l s like Ni and
F e , the C a p a c i t a n c e d e p e n d s d r a m a t i c a l l y o n the p r e s e n c e of o x i d e films. In
non-aqueous s o l v e n t s
the d i f f e r e n c e b e t w e e n H g and d-metals ( c f Pt and Pd in
D M S O and A C N ) is even m o r e s t r i k i n g and u s e of t h i s m e t h o d to e s t i m a t e s u r f a c e
a r e a s m a y be in error by e v e n a n o r d e r of m a g n i t u d e .
T h e m e t h o d is m o r e r e a s o n a b l e in its v a r i a n t . H o w e v e r , the a p p r o x i m a t i o n of
constancy in the inner layer c a p a c i t a n c e must be v e r i f i a b l e and c a n anyway
lead to inaccuracy of 10-20%. T h e m e t h o d is a c c e p t a b l e a s an internal check
( o r for the e s t i m a t i o n of the r e l a t i v e s u r f a c e a r e a ) for different s a m p l e s of
the s a m e metal
or of
the s a m e
ionic
solid
( e g oxide),
provided
the
r e p e a t i b i l i t y of the experimental r e s u l t s is a s c e r t a i n e d at a g i v e n constant
f r e q u e n c y of the a l t e r n a t i n g signal. W i t h liquid m e t a l s , i t i s a correct w a y
to n o r m a l i z e experimental data to unit s u r f a c e a r e a , provided . a c c e p t e d v a l u e s
for e x a c t l y the s a m e s y s t e m and the s a m e c o n d i t i o n s a r e a v a i l a b l e , and the
measuring
apparatus
is
known
to
give
correct
results.
Experimental
d i f f i c u l t i e s m a y a r i s e f r o m the h i g h o h m i c r e s i s t a n c e d u e to the low
e l e c t r o l y t e c o n c e n t r a t i o n s n e e d e d . M o r e o v e r , d o u b l e layer c h a r g i n g m a y b e c o m e
a . d i f f u s i o n - c o n t r o l l e d process.
2.3 Parsons-Zobel plot
T h i s m e t h o d r e s t s o n the c o m p a r i s o n of the experimental data w i t h the d o u b l e
layer t h e o r y . T h e d i f f e r e n c e w i t h respect to the p r e v i o u s o n e i s that t h i s is
a multiple-point and not a single-point method.
2.3.1 P r i n c i p l e s . O r i g i n a l l y , the m e t h o d stemmed f r o m the a p p l i c a t i o n o f the
Gouy-Chapman-Stern theory of the d o u b l e layer r e f i n e d by G r a h a m e ( G C S G model),
according to w h i c h the interface is d e p i c t e d a s equivalent to t w o c a p a c i t o r s
in s e r i e s . T h e interfacial c a p a c i t a n c e per unit s u r f a c e area is g i v e n by (ref.
25):
l / C = 1/Ci
+
l/cS
(3.1)
w h e r e Cd is the c a p a c i t a n c e associated w i t h the d i f f u s e layer ( o n the s o l u t i o n
side of the interface) end Ci is the inner layer c a p a c i t a n c e a s s o c i a t e d w i t h
an ion-free
layer of s o l u t i o n adjacent to the s o l i d surface. T h e model
p r e d i c t s that cS d e p e n d s o n the e l e c t r o l y t e c o n c e n t r a t i o n w h i l e 0 is not
d i r e c t l y m e a s u r a b l e but i t can be derived f r o m eqn.(3.1) provided the ions a r e
not s p e c i f i c a l l y a d s o r b e d . If the interface h a s an area A . eqn.(3.1) m a y be
r e w r i t t e n as:
(3.2)
w h e r e Cd is g i v e n by the Gouy-Chapman theory in t e r m s of the unit s u r f a c e area
(Sl u n i t s : F m-2). Subscript T h a s b e e n introduced - c f eqn(l.2) - to d e n o t e
the total c a p a c i t a n c e , ie T C = CA (SI u n i t s : F). T h e experimental e v i d e n c e
indicates that Ci is in fact independent of e l e c t r o l y t e c o n c e n t r a t i o n in the
COMMISSION ON ELECTROCHEMISTRY
absence of ionic specific adsorption (refs. 25,26). Thus, a plot of 1 / T C
(experimental quantity) vs 1 1 0 (calculated for different concentrations of
the electrolyte) will result in a straight line whose slope and intercept give
1/A and T C ~ respectively
,
(refs. 27.28).
In more recent theories the physical separation of the interface into an inner
and a diffuse layer is not included as a necessary concept (ref. 29). The
reciprocal of the capacitance of the electrode/solution interface turns out to
be described by a power series with respect to the Debye length, x-1:
If the surface area is made explicit, eqn.(3.3)
~ / T =C ax-i/A
+
bxo/A
+
cxl/A
+.....
becomes:
(3.4)
The first term depends on the square root of the electrolyte concentration as
in the Gouy-Chapman theory, the second term is independent of the electrolyte
concentration a s the inner layer capacity does in the GCSG model, and the
third term becomes important only at high electrolyte concentrations, say
> 1 mol dm-3.
Although some evidence for the importance of the third term is experimentally
available (ref. 30),
in the electrolyte concentration range up to ca
1 mol dm-3 eqn.(3.4) is equivalent to eqn.(3.2) and can be used to derive the
real surface area. Thus, this method is in fact not bound to the validity of
any existing specific double layer theory.
2.3.2 Limitations. Equation (3.2) has been verified in the case of liquid
electrodes, including Ga. I t is however inconvenient for such electrodes since
a single-point experiment at the diffuse layer minimum may be sufficient ( c f
section 2). For liquid electrodes conformation to eqn.(3.2) is often used to
verify the absence of specific adsorption (ref. 25).
For the applicability of the method to solid electrodes the electrode surface
must be absolutely homogeneous and the measured capacitance must be frequency
face
independent. Thus, i t is strictly valid only for single crystal
electrodes (ref. 31).
lnhomogeneities on the surface result in a marked curvature of the plot of
l/TC v s 1 / C a (refs. 31.32). Paradoxically, the method is useful to measure
surface
roughness,
but
rough
surfaces
of
single
crystal
faces
are
inhomogeneous so that the requirements for the applicability of the method are
lost. In any case the asperities which can be "seen" by this method are those
of
height
greater
than
the
diffuse
layer
thickness
at
the
highest
concentration (normally 1 mol dm-3 since the mod,el probably breaks down in
more concentrated solutions). ie of the order of 1 nm.
Eveluetions. While the method is unacceptable for polycrystalline
surfaces in principle, i t can be reasonably used with polycrystalline metals
of low melting points (soft surfaces) since inhomogeneities are of minor
effect on the electronic structure of these surfaces. Thus, the method is to a
first approximation acceptable with P b , S n , Cd, In, Bi.
2.3.3
With single crystal faces the applicability of the method depends on the
extent of the surface defects. If the surface is perfect, the method serves to
give an exact measure of the geometric surface which in case of complex
electrode shape is difficult to determine optically. If the surface shows only
small deviations from ideality (roughness factor < l.l), the method will give
the real surface within a few percent (2-3X). Better resolution is probably
possible by a somewhat different approach based on trials (refs. 26.32). The
most probable roughness factor is that resulting in the most regular variation
of Ci with potential. The approach is more empiric because i t is not based on
a model but on an intuitive view of how a capacitance curve should be as a
function of potential around the zero charge. I t seems to work with silver,
but there are problems with Au. At the moment the latter approach lacks the
general validity necessary to be recommended here. I t necessitates further
investigation.
The applicability of the method to disperse systems (mainly ionic solids) is
still under evaluation (refs. 33.34).
Real surface area measurements in electrochemistry
2.4
719
Hydrogen adsorption from solution
T h e m e t h o d is used a s a rule w i t h a f e w transition m e t a l s s h o w i n g h y d r o g e n
adsorption
in
potential
regions
prior
to
massive
Hz
evolution.
The
experimental technique m a y be cyclic v o l t a m m e t r y o r current s t e p ( c h r o n o potentiometry) (refs. 35,36). T h e m e t h o d h a s b e e n e s t a b l i s h e d m a i n l y w i t h Pt
e l e c t r o d e s ( r e f . 37), but i t h a s b e e n extended to R h and lr ( r e f s . 3 8 , 3 9 ) , and
to Ni ( r e f s . 40.41).
2.4.1
Principles. T h e c h a r g e under
the v o l t a m m e t r i c p e a k s for h y d r o g e n
adsorption or d e s o r p t i o n ( o r a s s o c i a t e d w i t h the a p p r o p r i a t e s e c t i o n of the
potential-time curves). corrected for d o u b l e layer c h a r g i n g ( i e the c a p a c i t i v e
component), is assumed to correspond to a d s o r p t i o n of o n e h y d r o g e n a t o m o n
each metal a t o m of the s u r f a c e ( 9 ) . T h e c h a r g e a s s o c i a t e d w i t h a one-to-one
H-M c o r r e s p o n d e n c e per unit s u r f a c e area ( Q s )
is c a l c u l a t e d o n the b a s i s of
the d i s t r i b u t i o n of metal a t o m s o n the s u r f a c e . T h i s i s well d e f i n e d for a
perfect s i n g l e crystal f a c e (ref. 42), w h e r e a s i t is taken a s a n a v e r a g e v a l u e
between the m a i n low-index f a c e s for p o l y c r y s t a l l i n e s u r f a c e s . T h e r e s u l t i n g
value is a s a rule v e r y c l o s e to that p e r t a i n i n g to the ( 1 0 0 ) f a c e ( r e f . 43).
T h e true s u r f a c e area is t h u s d e r i v e d f r o m :
A =
Q/Qs
(4.1)
In the c a s e of p o l y c r y s t a l l i n e Pt the accepted v a l u e is 2 1 0 pC c m - 2 , based o n
the a s s u m p t i o n that the density of a t o m s o n s u c h a s u r f a c e is 1 . 3 1 ~ 1 0 1 5 c m - 2
(refs. 4 4 , 4 5 ) .
T h e v a l i d i t y of the m e t h o d i m p l i e s that the point w h e r e h y d r o g e n a d s o r p t i o n is
complete can be exactly i d e n t i f i e d , and that the c o v e r a g e is completed b e f o r e
the rate of h y d r o g e n e v o l u t i o n b e c o m e s s i g n i f i c a n t . In a d d i t i o n , i t r e s t s o n
the a s s u m p t i o n that t h e r e is a d e f i n i t e q u a n t i t a t i v e r e l a t i o n b e t w e e n the
charge m e a s u r e d and the amount of s u b s t a n c e d e p o s i t e d , i e total
charge
transfer t a k e s place from the a d s o r b a t e to the m e t a l . F i n a l l y , n o a l t e r a t i o n
of the s u r f a c e upon a d s o r p t i o n is assumed to t a k e place. T h e s e a s s u m p t i o n s are
common a l s o to m e t h o d s 5 and 6.
2.4.2 L i m i t a t i o n s . S o m e of the a s s u m p t i o n s o n w h i c h the m e t h o d r e s t s m a y not
be valid.
In p a r t i c u l a r , a d s o r p t i o n may take place w i t h partial
charge
t r a n s f e r , and phenomena r e l a t e d to s u r f a c e a l t e r a t i o n m a y a l s o o c c u r u p o n
d e p o s i t i o n of s p e c i e s f r o m the solution.
T h e completion of the m o n o l a y e r probably t a k e s place o n l y w i t h Pt e l e c t r o d e s
w h e r e a s w i t h R h and lr s u c h c o n d i t i o n is not f u l f i l l e d . T h i s i n v o l v e s s o m e
independent d e t e r m i n a t i o n of coverage by pseudo-capacitance m e a s u r e m e n t s w h i c h
introduces additional u n c e r t a i n t i e s . T h e i d e n t i f i c a t i o n of the end-point for
a d s o r p t i o n is a l s o a p r o b l e m s i n c e i t s p o s i t i o n d e p e n d s o n the o p e r a t i n g
c o n d i t i o n s ( e g the partial p r e s s u r e of Hz gas). I t h a s b e e n s u g g e s t e d that
t h i s point is better s e e n at v e r y low t e m p e r a t u r e s ( r e f . 39), w h i c h i n t r o d u c e s
the a s s u m p t i o n that the temperature d o e s not m o d i f y the s i t u a t i o n e s s e n t i a l l y .
A l t e r n a t i v e l y , the end-point c a n be attained by e x t r a p o l a t i n g Q to infinite
s w e e p rate w h i c h e n a b l e s a s e p a r a t i o n b e t w e e n a d s o r p t i o n and f a r a d a i c c h a r g e s
for Hz e v o l u t i o n to b e achieved ( r e f . 46).
T h e m e t h o d cannot be u s e d w i t h m e t a l s a b s o r b i n g h y d r o g e n such a s Pd. H y d r o g e n
absorption a t low potential s w e e p r a t e s ( e g < 5 m V s - 1 ) is a l s o a p r o b l e m w i t h
highly p o r o u s e l e c t r o d e s ( r e f . 47). T h e i n d e p e n d e n c e of Q o n the s w e e p r a t e
should
be
ascertained
to
find
out
the
best
experimental
conditions.
E x t r a p o l a t i o n to infinite s w e e p rate ( o r current p u l s e ) could in p r i n c i p l e
separate a d s o r p t i o n f r o m a b s o r p t i o n . H o w e v e r , d i s t o r s i o n of the v o l t a m m o g r a m
due to o h m i c d r o p s a n d / o r kinetic r e s t r i c t i o n s m a y a p p e a r at high s w e e p r a t e s ,
especially w i t h highly p o r o u s materials. T h e p r o b l e m of the o v e r l a p p i n g of the
h y d r o g e n and o x y g e n a d s o r p t i o n r e g i o n s is m o r e s e r i o u s and p r e v e n t s the
a p p l i c a t i o n of the m e t h o d to easily o x i d i z a b l e t r a n s i t i o n metal such a s N i .
F e , R u , Os, etc.
T h e m e t h o d h a s been applied a l s o to finely d i v i d e d p o w d e r s ( r e f . 48). In the
case of s u p p o r t e d m e t a l s , the H a t o m s deposited o n the m e t a l l i c p a r t i c l e s m a y
diffuse
along
the
surface
to r e g i o n s w h e r e
the
support
is u n c o v e r e d
(spillover). S p i l l o v e r e f f e c t s m a y r e n d e r the r e s u l t s of h y d r o g e n a d s o r p t i o n
ambiguous, t h u s invalidating the q u a n t i t a t i v e s i g n i f i c a n c e of the m e a s u r e d Q .
T h e a b s o l u t e s i g n i f i c a n c e of the accepted Q s i s q u e s t i o n a b l e . Apart f r o m the
d i s t r i b u t i o n of the a d s o r b a t e w h i c h might b e v e r i f i e d s p e c t r o s c o p i c a l l y (but
COMMISSION ON ELECTROCHEMISTRY
720
adsorption in solution d o e s d i f f e r from the g a s phase situation because of the
competition w i t h solvent molecules), the assumption that the surface density
of a t o m s is a constant for a given metal is inconsistent w i t h the widely
d i f f u s e idea of basic unreproducibility of polycrystalline surface structures.
T h e adsorbability of hydrogen v a r i e s very m u c h on different crystal f a c e s
(refs. 42,49). In a d d i t i o n , the double layer c o r r e c t i o n , a s usually m a d e , is
arbitrary. Besides being in principle unfeasible, the separation of "faradaic"
and the capacitive charges r e s t s o n the assumption that the interfacial
capacitance is constant o v e r the potential region of hydrogen adsorption, and
equal to its magnitude in the potential region prior to hydrogen discharge.
However, the very presence of the adsorbate may modify the capacitative
parameters of the phase boundary.
Another aspect to be taken into account is the influence of ions on hydrogen
adsorption
(ref. 50). T h e height
of
the p e a k s and
their position are
influenced by
the nature
of
the electrolyte.
Ionic adsorption m a y be
significant at the potentials w h e r e hydrogen is adsorbed or even evolved.
2.4.3 Evaluations. T h i s is the only method w h i c h enables an i n s i t u approach
to the real surface area of d-metal electrodes to be attempted. T h e total
inaccuracy and unreproducibility of these m e a s u r e m e n t s can be expected to be
about + l o % (refs. 4 3 , 4 6 ) , w h i c h is quite satisfactory in this case. Although
surface area v a l u e s for different m e t a l s estimated w i t h this approach m a y not
bear the s a m e physical s i g n i f i c a n c e , the method a l l o w s a good normalization of
experimental data f o r the same metal. T h e reliability of the method d e p e n d s
very m u c h on the cleanliness of the electrode surface (hence of the solution)
which should be ascertained before conducting the specific d e t e r m i n a t i o n s f o r
the measurement of the real surface area.
2.5 Oxygen adsorption from solution
T h e method is applicable to m e t a l s showing well developed regions f o r oxide
monolayer formation and reduction. In addition to some d-metals, i t h a s been
used w i t h A u for w h i c h the previous technique cannot be applied since n o
hydrogen adsorption region is recognizable.
2.5.1 Principles.
(ref. 51). O x y g e n
0 2 evolution with
52). T h i s implies
of the layer is:
T h e method rests o n the s a m e g r o u n d s a s the p r e v i o u s one
is assumed to be chemisorbed in a monoatomic layer prior to
a one-to-one correspondence with surface metal a t o m s (ref.
that the charge associated w i t h the formation or reduction
8 = 2 e N ~ n A
(5.1)
where NA is the A v o g a d r o constant, and ro, the surface concentration of atomic
oxygen, is assumed to be equal to fi. the surface density of metal atoms. F r o m
the value of lh per unit surface a r e a , the v a l u e of a s , the reference c h a r g e ,
is calculated so that:
A = Gb/C&-
(5.2)
The approach implies that:
Ql-/Q.
= 2
(5.3)
so that the accepted value f o r polycrystalline Pt is 4 2 0 p C cm-2. A v a l u e of
390210 p C cm-2 h a s been suggested for polycrystalline A u (refs. 52.53).
Calculated v a l u e s of Q - for A u single crystal f a c e s are also available (ref.
54),
2.5.2 Limitations. O x y g e n adsorption usually r e s u l t s in o x i d e formation by a
place-exchange mechanism. T h i s leads to Q being a function of time. T h e
potential w h e r e the monolayer is completed is difficult to assess. S o m e t i m e s
overlapping of o x y g e n and hydrogen adsorption r e g i o n s occurs.
Qp may b e measured either during oxygen adsorption ( p o s i t i v e potential sweep
or positive current pulse) (ref. 52) or during adsorbed oxygen reduction
(refs. 55,56). In the former case 8 may include oxidizable impurity e f f e c t s
and some charge associated with evolved 0 2 . In the latter case, the adsorbed
monolayer may in fact be a multilayer (oxide film) of undefined stoichiometry.
The double
layer correction usually implies that G I is constant
and equal
to
Real surface area measurements in electrochemistry
721
that in the d o u b l e layer r e g i o n prior to o x i d e formation. T h e c o r r e c t i o n m a y
come out to differ d e p e n d i n g o n the d i r e c t i o n of potential s w e e p ( o r o n the
sign of the current pulse).
A s f o r the a b s o l u t e v a l u e of
comings a s Q+.
( c f section 4 ) .
8.. the m e t h o d s u f f e r s f r o m the s a m e short-
2.5.3 E v a l u a t i o n s . T h e m e t h o d
is
less r e l i a b l e than that based
on H
adsorption, but in s o m e c a s e s i t is the o n l y a p p l i c a b l e of the t w o ( e g A u ,
Pd). T h e r e l i a b i l i t y d e c r e a s e s a s the a f f i n i t y of the metal for o x y g e n
increases. T h u s , i t should b e the best f o r A u , for w h i c h h o w e v e r the
stoichiometry of the o x i d e formed is u n c e r t a i n . If anodic s w e e p s o r current
pulses are u s e d , QJ should b e d e t e r m i n e d d o w n to constant v a l u e s a s the
experimental parameter is v a r i e d . A l s o , the d e t e r m i n a t i o n of the potential
range w h e r e
eqn.(5.3)
is v e r i f i e d
(for the m e t a l s a l l o w i n g t h a t ) m a y
constitute a n indicative c r i t e r i o n of the a b s e n c e of a n o m a l o u s effects. T h i s
e n t a i l s a careful s e l e c t i o n of the limits of the potential r a n g e w h e r e QJ
should b e d e t e r m i n e d . T h e c l e a n l i n e s s of the s u r f a c e and the s o l u t i o n should
b e ensured. U s i n g c a t h o d i c s w e e p o r current p u l s e s m a y e n a b l e a single-point
experiment to s u f f i c e . H o w e v e r , the c o n d i t i o n of 80 = 1 should b e a s c e r t a i n e d
if a n accepted p r a x i s d o e s not exist.
T h e m e t h o d c a n be used w i t h A u e l e c t r o d e s s i n c e H a d s o r p t i o n d o e s not take
p l a c e , but i t is to b e b o r n e in m i n d that the treatment the s u r f a c e is
subjected to m a y not b e without any effect o n i t s s t r u c t u r e , e s p e c i a l l y in the
case of s i n g l e crystal f a c e s .
2.6 Underpotential deposition of metals
T h i s method h a s been u s e d for e l e c t r o d e s for w h i c h n e i t h e r of the p r e v i o u s
o n e s c a n be a p p l i e d , eg A g ( r e f . 57). C u (ref. 58). and for m e t a l s for w h i c h a
better s e p a r a t i o n b e t w e e n H a n d 0 a d s o r p t i o n cannot b e a c h i e v e d , e g R u (ref.
59). A n a d v a n t a g e of t h i s m e t h o d over m e t h o d 4 ( h y d r o g e n a d s o r p t i o n ) is that
n o s p i l l o v e r e f f e c t s a r e e x p e c t e d , h e n c e s e l e c t i v e d e p o s i t i o n is possible.
T h u s , the m e t h o d m a y b e particularly c o n v e n i e n t to d e t e r m i n e the ( a c t i v e )
s u r f a c e of supported e l e c t r o d e s w h e r e the ( i n a c t i v e ) support c o m e s in contact
w i t h the s o l u t i o n (ref. 60).
2.6.1 P r i n c i p l e s . T h e c h a r g e a s s o c i a t e d w i t h the underpotential d e p o s i t i o n of
a s u i t a b l e metal
ion
is m e a s u r e d u s u a l l y by v o l t a m m e t r y . T h e m a x i m u m
a d s o r p t i o n in a m o n o l a y e r is c a l c u l a t e d o n the b a s i s of a c h o s e n model so that
the s u r f a c e area of the s a m p l e is g i v e n b y :
A = Q/Q.
(6.1)
Usually, A g and C u a d a t o m s a r e u s e d .
2.6.2 L i m i t a t i o n s . T h i s m e t h o d s u f f e r s f r o m the s a m e s h o r t c o m i n g s a s m e t h o d 4,
in p a r t i c u l a r the c o r r e c t i o n for d o u b l e layer c h a r g i n g is a r b i t r a r y and the
i d e n t i f i c a t i o n of the end point for the metal a d s o r p t i o n is uncertain. In
a d d i t i o n , ( i ) the U P D r e g i o n m a y interfere w i t h h y d r o g e n o r o x y g e n a d s o r p t i o n ,
( i i ) the s u r f a c e d i s t r i b u t i o n of the U P D s p e c i e s m a y b e u n k n o w n , ( i i i ) the
adatom d e p o s i t i o n m a y o c c u r w i t h partial c h a r g e transfer t h u s m a k i n g the v a l u e
of Q * s p e c i f i c a l l y system-dependent, and ( i v ) the usual a s s u m p t i o n of one-too n e c o r r e s p o n d e n c e w i t h H and 0 a d s o r p t i o n m a y not b e valid in the c a s e o f U P D
b e c a u s e the n e w phase f o r m a t i o n m a y result in m o r e c o n d e n s e d m o n o l a y e r s .
m u l t i l a y e r s o r cluster g r o w t h (ref. 61). T h u s , in the case of P b o n C u ( 1 1 1 )
the coverage h a s b e e n found
(ref. 5 8 ) to correspond to a close-packed
c o n f i g u r a t i o n , w h i l e in the c a s e of P b o n R u the one-to-one c o r r e s p o n d e n c e
(epitaxial g r o w t h ) is m o r e probable (ref. 59). T h e o c c u r r e n c e of the o n e o r
the o t h e r p o s s i b i l i t i e s d e p e n d s o n a n u m b e r of f a c t o r s including s i z e r a t i o
b e t w e e n s u p p o r t i n g metal and UPD m e t a l , s t r e n g t h of the b o n d b e t w e e n o v e r l a y e r
and support in c o m p a r i s o n w i t h lateral i n t e r a c t i o n s in the m o n o l a y e r , 'etc.
T h e c a l c u l a t i o n of Q.
for p o l y c r y s t a l l i n e s u r f a c e s i s based o n empirical
c o n s i d e r a t i o n s . T h e s a m e is a l s o the c a s e of s i n g l e crystal f a c e s for w h i c h
the m e t h o d g i v e s s t r i c t l y the n u m b e r of s u r f a c e a c t i v e s i t e s r a t h e r than the
true s u r f a c e area. T h e response of the s i n g l e crystal
f a c e is h o w e v e r
different f r o m that o f the p o l y c r y s t a l l i n e s u r f a c e of a g i v e n metal b e c a u s e of
the p o s s i b l e p e n e t r a t i o n o f the d i s c h a r g e d a t o m s into g r a i n b o u n d a r i e s in the
latter case.
COMMISSION ON ELECTROCHEMISTRY
722
2.6.3 Evaluations. The reproducibility of the measurements is usually high. If
established knowledge about the system does not exist, the formation of a
monolayer should be checked experimentally. The surface distribution of UPD
metal atoms should be assessed also on the basis of spectroscopic data for the
same system in gas phase adsorption, where however the situation may not be
the same in view of the absence of the competitive effect of solvent
adsorption at the solid/liquid interface (ref. 62).
In the case of epitaxial growth, the value of Q s
is expected to depend on the
surface structure of the sample, whereas this is not the case i f close-packed
monolayers are formed.
The methods of monolayer formation are claimed (ref. 57) to be more sensitive
than those based on double layer charging since the charge spent in UPD is as
a rule one order of magnitude higher. However, this consideration is tenable
only in case double layer charging is operated by the same technique a s that
used to measure Q .
I t is to be borne in mind that UPD may have undesired effects on the
properties of the electrode surface owing to retention of some UPD atoms in
the metal lattice even after complete desorption. and to possible surface
reconstruction (refs. 63-65).
2.7 Voltammetry
In some cases none of methods 4-6 can be used because neither hydrogen nor
oxygen adsorption, nor UPD takes place. This may be the case of non-metallic
electrodes (refs. 66-68). Voltammetry. chronopotentiometry, current step and
potential
step techniques, differential chrono-potentiometry, etc.
(ref.
69.70). can be used to determine the apparent total capacitance of the
electrode surface. The voltammetric approach, which is the most popular, is
described in some details below.
2.7.1 Principles. Voltammetric curves are recorded in a narrow potential range
(a few tens of mV) at different sweep rates (ref. 69). The current in the
middle of the potential range is then plotted as a function of the sweep rate.
Under the assumption that double layer charging is the only process, a
straight
line should be obtained, whose slope gives the differential
capacitance (total value) of the interface:
r C = dQ/dE = Idt/dE = I/(dE/dt)
(7.1)
The capacitance thus obtained is then compared to some reference value 0 so
that the surface area is obtained from:
A = r C / 0
(7.8)
The method is not different in substance from that in sec. 2 except for the
fact that the technique used is not specific for capacitance measurement and
is generally applied to large surface area and porous electrodes.
2.7.2 Limitations. This method has been several times applied to oxide
electrodes. The assumption of 0 = 60 pF cm-2 for the capacitance of the unit
true surface area of an oxide (irrespective of its nature) (ref. 67) is not
established. The dependence of capacitance on potential for oxides is unknown,
so that the error may be very large. Since voltammetric curves of oxides show
maxima related to surface redox processes, the value of capacitance may differ
in different potential regions (ref. 71).
Porous materials or oxide electrodes usually show a dependence of I on sweep
rate due to exclusion of some less accessible surface at the highest rate
(ref. 71). The mechanism of charging of oxide electrodes is more complex than
that of metals since i t is also governed by pH through surface proton exchange
(ref. 72). The state of charge of a surface is thus strongly dependent on the
solution pH. Therefore, the determinations should at least be normalized to a
reference pH.
2.7.3 Evaluations. The method has no universal significance since 0 has only
is quantitatively
possible between
an empiric validity. No comparison
different oxides since the physical meaning of the charge may change in the
different cases. Nevertheless, the method is useful for an internal comparison
for a given material, provided the technique is normalized to appropriate
Real surface area measurements in electrochemistry
723
experimental conditions.
The comparison of capacitance values between different oxides is also
invalidated by the fact that the fraction of surface sites being oxidised or
reduced in a given potential range may differ for different systems. The
determination of an absolute capacity has been attempted in some cases by
using an independently determined BET surface area (ref. 68). However, while
this approach does not add anything to the validity of an internal comparison,
i t adds the vexing question of the relative meaning of in situ and ex situ
surface area determinations, relevant also to other methods dealt with in this
document .
2.8 Negative adsorption
The method has been proposed for large surface area solids suspended or
colloidal ly dispersed in an electrolyte solution (ref. 73). In principle, i t
can also be used with massive systems.
2 . 8 . 1 Principles. The method assumes the validity of the diffuse layer model.
Ions are repelled from surfaces carrying charges of like sign. The GouyChapman theory predicts that their negative surface excess (depletion) is
charge (potential) dependent and reaches asymptotically an almost constant
value at relatively small charges ( a t potentials in the OHP, outer Helmholtz
plane, not too far from zero). A s a consequence of the repulsion into the
solution, the concentration level of these species is increased in the bulk
since they are excluded from all the interfacial regions (refs. 7 4 - 7 6 ) .
The method usually employed involves the analytical determination of the
change in the concentration of the negatively adsorbed ion in the solution.
The surface area is proportional to the measured A c through the following
equation:
A =
B Vt (Ac/c)c1/2
(8.1)
Vt is the total liquid volume where the solid is suspensed and B is a constant
for a given electrolyte type and charge sign on the solid surface. Normally,
negative adsorption is measured at negatively charged surface since the
probability of specific adsorption of cations is more remote.
2 . 8 . 2 Limitations. Since the increase in concentration (Ac) is usually small,
this sets a lower size limit to the specific area that can be measured. The
potential at the OHP or the charge of the diffuse double layer must be known
to apply the method not far enough from the zero charge condition where
negative adsorption has not yet reached its limiting value. With porous
solids, the negative adsorption from the pores is incomplete because of double
layer overlap. In some cases the response of the method is unreliable because
the technique is extremely sensitive to the release of traces of impurities
from the solid.
Different equations have to be used depending on whether flat or spherical
double layers are best approximated (ref. 77). The results can be unreliable
i f inhomogeneous suspensions are dealt with. In any case, being a double layer
technique, i t can reveal surface asperities whose height is comparable to the
diffuse layer thickness.
2 . 8 . 3 Evaluations. The particle size of the disperse solid should be as
homogeneous as possible. The method is best suited for crystalline non-porous
solids. In general, negative adsorption measurements can be performed at one
concentration, but a check of the applicability of the technique is obtained
by plotting VtB(Ac/c) vs c-112. A straight line of slope A should be obtained.
The potential a t the OHP should not be < 1 5 0 m V , otherwise i t should be fairly
accurately known ( c f sec. 8 . 2 ) ; the surface area to be measured must be
greater than 1 m2 g - 1 ; the interparticle distance in the suspension should be
more than 10 times the diffuse layer thickness. The analytical technique to
determine Ac should be precise owing to the small value of Ac. A method to
alleviate the strict analytical requirements has been proposed (ref. 78).
However, i f all recommended conditions are met, the accuracy may be of the
order of f l O X .
The method is not a routine one and must be assessed case by case.
COMMISSION ON ELECTROCHEMISTRY
724
2.9 Ion-exchange capacity
T h i s m e t h o d h a s been s p e c i f i c a l l y s u g g e s t e d for s o m e o x i d e s s u c h a s MnOz ( r e f .
7 9 ) and tested a l s o for SiOz ( r e f . 80). C o m p a r e d to the p r e v i o u s m e t h o d , i t i s
still a d o u b l e layer a p p r o a c h , but based o n p o s i t i v e adsorption.
2.9.1 P r i n c i p l e s . S p e c i f i c a d s o r p t i o n o n o x i d e s is s u b s t a n t i a l l y a n ione x c h a n g e p r o c e s s (ref. 72). S u r f a c e c o m p l e x a t i o n of the s u r f a c e OH g r o u p s
takes p l a c e through the r e l e a s e of a c i d i t y ( r e f . 81). F o r instance:
I
MnloH
I
+
Znz+
+
‘OH
I
0
M n / ‘Zn
I
‘o/
+
2H+
(9.1)
The method
is based
o n the d e t e r m i n a t i o n ( r a d i o c h e m i c a l l y or b y o t h e r
analytical m e a n s ) of the amount of c o m p l e x i n g ions taken u p by the o x i d e
surface. T h e s u r f a c e area i s then c a l c u l a t e d by assigning a g i v e n crosss e c t i o n to the a d s o r b a t e (ref. 82).
2.9.2 L i m i t a t i o n s . S p e c i f i c a d s o r p t i o n d o e s not n e c e s s a r i l y g o to c o m p l e t i o n ,
i e not all a v a i l a b l e s u r f a c e s i t e s u n d e r g o ion e x c h a n g e ( c f 9.3). T h i s h a s
b e e n a s c e r t a i n e d e v e n in the case of M n O z . T h e m a x i m u m amount taken u p by the
o x i d e s u r f a c e d e p e n d s o n the n a t u r e of the s o l i d , presumably o n its acid-base
p r o p e r t i e s ( r e f . 81). T h e p H of the s o l u t i o n p l a y s a paramount role and the
amount adsorbed will depend o n i t (ref. 79).
T h e cross-sectional
area assigned to the a d s o r b a t e ( Z n + + is that usually
r e c o m m e n d e d ) will depend o n the d i s t r i b u t i o n of the a d s o r b i n g s i t e s o n the
o x i d e s u r f a c e and h a s n o d e f i n i t e physical m e a n i n g , s i n c e i t is a s a rule
established so a s to b r i n g the c a l c u l a t e d area into agreement w i t h the B E T
surface area. T h i s m a k e s the m e t h o d not an a b s o l u t e o n e , s i n c e the r e s u l t s are
complicated by the p r o b l e m of identity b e t w e e n B E T and in s i t u wet s u r f a c e
area.
2.9.3 Evelustions. T h i s m e t h o d h a s b e e n scrutinized o n l y for MnOz and the
procedure h a s b e e n n o r m a l i z e d to t h i s p a r t i c u l a r o x i d e . T h e m a x i m u m s u r f a c e
coverage o n A1203 h a s been found to b e lower than o n MnOz ( r e f . 81). A n
attempt w i t h RuOz h a s resulted in a s u r f a c e area t h r e e times lower than the
B E T v a l u e ( r e f . 83). M o r e o v e r , a l s o in the case of M n O z , the claimed 1 to 1
correlation between B E T and Z n + + a d s o r p t i o n s u r f a c e area d e v i a t e s at h i g h
s u r f a c e area v a l u e s p r o b a b l y b e c a u s e of p o r e e x c l u s i o n (ref. 81). F i n a l l y , the
a d s o r b a b i l i t y of Z n + + d e c r e a s e s w i t h i n c r e a s i n g c a l c i n a t i o n t e m p e r a t u r e , a
fact w h i c h m a k e s t h i s m e t h o d fully a p p l i c a b l e ( r e l i a b i l i t y a p a r t ) o n l y w i t h
h y d r o u s o x i d e s (ref. 80).
Since this method
routine u s e .
is
insufficiently
established,
it
is not
recommended
for
2.10 Adsorption of probe molecules from solution
T h e m e t h o d is u s u a l l y applied to h i g h s u r f a c e area a n d / o r d i s p e r s e s o l i d s
(refs. 84-86). W h i l e ionic s p e c i e s are used a s probe s p e c i e s in p r e v i o u s
m e t h o d s , neutral c o m p o u n d s a r e e s s e n t i a l l y u s e d here. T h e amount of a d s o r b a t e
may
be
detected
directly
or
indirectly
using
electrochemical
or
nonelectrochemical techniques.
2 . 1 0 . 1 Principles. A
probe m o l e c u l e is adsorbed o n the solid in s o l u t i o n and
the extent of a d s o r p t i o n is determined a n a l y t i c a l l y f r o m the d e p l e t i o n in the
solution. Dyes,
s u r f a c t a n t s , f a t t y a c i d s and p o l y a l c o h o l s are g e n e r a l l y
s u g g e s t e d a s s u i t a b l e probe m o l e c u l e s (refs. 81.88).
F r o m the ( a p p a r e n t )
m o n o l a y e r s u r f a c e c o n c e n t r a t i o n the s u r f a c e area of the solid is d e r i v e d by
the e q u a t i o n :
A = f. NAA.
w h e r e f. is the s a t u r a t i o n coverage in mol
assigned to o n e adsorbed probe molecule.
(10.1)
c m - 2 and A*
is the p r o j e c t e d area
In the electrochemical v a r i a n t , for i n s t a n c e , C O and 1 2 h a v e b e e n u s e d a s
probe m o l e c u l e s ( r e f s . 45.89-91). A m o n o l a y e r of atomic iodine is assumed to
f o r m in the c a s e o f 12 a d s o r p t i o n . T h e amount of a d s o r p t i o n is d e t e r m i n e d from
the c h a r g e required to anodically o x i d i z e the a d s o r b a t e ( a n o d i c stripping).
Real surface area measurements in electrochemistry
725
The electrode surface area is obtained by the equation:
A = (Q
-
@)/nFr.
(10.2)
where Q is the charge associated with the anodic oxidation of the probe
molecule, Gb is the charge spent in the same potential range in the absence of
adsorbate (background charge), n is the charge number of the oxidation
reaction ( C O + C 0 2 ; 1 + 1 0 3 - 1 , F the Faraday c o n s t a n t , and r. the c a 1 c u l e t e d
saturation coverage in mol c m - 2 .
2.10.2 Limitations. In the non-electrochemical
version of this method, the
major drawback is that the orientation and conformation of the adsorbate may
depend o n surface charge, on surface c o v e r a g e , and on the nature of the
adsorbent and of the solvent (refs. 6 2 , 9 2 ) . T h e r e f o r e the value of A* d o e s not
possess a certain physical significance. In a d d i t i o n , the adsorbing s p e c i e s
may produce m i c e l l e s in solution and at the surface, a s well a s multilayers,
so that i t is often necessary to introduce a correcting factor (refs. 9 3 , 9 4 ) .
The value of r. is usually derived f r o m extrapolation procedures based on a
specific isotherm. T h e obtained v a l u e may not correspond to a complete
monolayer if the competition with the solvent is strong. F i n a l l y , adsorption
of hydrophilic m o l e c u l e s o n hydrophobic surfaces is generally w e a k and g i v e s
no practical b a s i s for surface area determinations.
The electrochemical detection of the adsorbate by "anodic stripping" ( i n the
case of CO and 1 2 ) s u f f e r s from the s a m e shortcomings a s the m e t h o d s based on
H, 0 and metal adsorption ( m e t h o d s 4 to 6 ) with the additional problem that
the "background charge" usually includes processes of surface oxidation w h i c h
may be affected by the presence of the adsorbate. T h e surface stoichiometry of
the adsorbed layer h a s been found to depend o n the metal n a t u r e and o n the
crystallite size in the case of C O ( r e f . 45). T h e assumption of a close-packed
monolayer
of
unassociated
atoms
of
iodine
or
of
CO
may
not
be
straightforwardly extensible to all systems.
2.10.3 Eveluetions. L a r g e molecules m a y generally not h a v e access to p o r e s ,
cracks or grain boundaries so that different surface a r e a s can be obtained by
using different m o l e c u l e s ( r e f . 87). T h i s m a y enable the external f r o m the
internal surface area to be separated. Another possibility is to f o l l o w the
rate of a d s o r p t i o n ; the area accessible to the adsorbate can then be evaluated
a s a function of time.
A s in previous c a s e s , this method can be used to assess the relative s i z e of
two or more solids of the same nature. T h e absolute v a l u e s of surface area are
vitiated by the assumption of complete coverage at saturation or of a given
molecular orientation and conformation. T h i s m a k e s the comparison of the
results for different s o l i d s rather difficult.
T h e electrochemical variant should be used only w i t h electrode m a t e r i a l s for
which the s u r f a c e stoichiometry of adsorption and the structure of the
adsorbed layer have been reliably e s t a b l i s h e d , bearing in mind t h a t , due to
its n a t u r e ,
the approach
is particularly
affected by
the presence of
oxidizable organic impurities.
2.1 1 Mass transfer
T h i s method h a s been particularly suggested for surface area determination of
complicated objects in galvanic depositions ( r e f . 9 5 ) but i t is in fact used
much m o r e frequently, even in research situations. I t can in principle be used
for any system irrespective of the extent of the surface area.
2.11.1 Principles. Under the assumption of homogeneous current d i s t r i b u t i o n ,
the current associated with the charge transfer to a reactant w h o s e supply is
controlled by diffusion is given by (refs. 96-99):
I = nFADc/S
(11.1)
where D is the diffusion coefficient, c the bulk concentration and d the
thickness of the diffusion layer. Under the proviso that c = c at t = 0 and c
= 0 at the electrode surface at t > 0 , S at time t is g i v e n by:
(11.2)
COMMISSION ON ELECTROCHEMISTRY
726
From ( 1 1 . 1 )
and (11.2) the measured current is related to the surface area by:
A = I(nDt)l/2/nFDc
(11.3)
The measurement is carried out potentiostatically by recording the current a s
a function of time.
Equation (11.3) is strictly valid only for linear diffusion a t a plane
electrode. For non-linear dif usion the complete equations are the following:
I = nFADcC(nDt)-1/2
I = nFADcC(nDt)-i/2
I = nFADcC(nDt)-1/2
+
+
+
(spherical electrode)
..I (disk electrode)
O.5r-1
..I (cylindrical electrode)
1-11
r-1
+
-
(11.4)
(11.5)
(11.6)
where r is the radius of the sphere, the disk or the cylinder, respectively.
Thus, a plot of I vs t - 1 1 2 wi 1 give a straight line of slope nFAcCD/n)1/2 for
linear diffusion ( c f eqn.Cll.3)). while i t can be approximated to a straight
line with the same slope for non-linear diffusion.
~
A variant of this method
(mainly applied to voltammetric situations) makes use
of
a
linear potential-time
scan
instead of
stationary potentiostatic
conditions. If the solution is quiescent, the current as a function of
potential goes through a maximum (j,) given by (ref. 100):
j,
= A(kn3/2&1/2cg)v1/2
(11.7)
where & and CB are the diffusion coefficient and the bulk concentration of
the reacting species B , respectively. n is the charge number of the electrode
reaction, v the potential sweep rate and k a numerical constant which is
determined empirically. The method is tested by checking the functional
dependence of j, on the two parameters, A and v.
Equation (11.7) was originally derived for one-dimensional convection-free
linear diffusion, but i t is also obeyed in experiments with unshielded
electrodes possessing a hemispherical diffusion domain in chronopotentiometry
and chronoamperometry for short transition times.
2 . 1 1 . 2 Limitations. The method is not limited by the surface size but simply
by the sensitivity of the measuring apparatus. Nevertheless, the applicability
calls for an homogeneous distribution of current which is difficult to achieve
precisely a t surface asperities. Since the diffusion layer thickness has a
macroscopic order of magnitude, the surface roughness detected by this
technique is of the same order of magnitude, ie >lo-100 pm.
The current measured may contain an unknown contribution from surface
modifications of the electrode, although cathodic polarization is usually
suggested. For the correct applicability of the method, the current yield of
the probe reaction must be strictly unity.
For purely diffusive systems, the thickness of the diffusion layer varies with
time; this may be a problem for rough and porous electrodes, in that different
effective surface areas may be determined a t different times. Using convective
systems ( e g pipe flow, rotating disc, etc) for which the thickness of the
diffusion layer can be controlled although i t will depend on the convection
conditions. This will make the experimental approach simpler but the ambiguity
of the physical meaning of the measured surface area remains.
2.11.3 Evaluations.
This
method
is
not
suitable
for
surface
area
determinations to be used in systems where atomic roughness is important. I t
is applicable to systems for which knowledge of a self-consistent macroscopic
surface area, which may be higher than A s , but lower than the real surface
area, (eg large electrode surfaces of complicated shapes) is all that is
needed.
3.
EX SlTU METHODS
3.1 Adsorption of probe molecules from gas phase
The well-known BET (from Brunauer, Emmett and Teller) (ref. 101) method
belongs to this category; i t is undoubtedly the most popular technique to
measure surface areas in all branches of surface chemistry.
Real surface area measurements in electrochemistry
727
3 . 1 . 1 P r i n c i p l e s . P r o b e m o l e c u l e s a r e a d s o r b e d f r o m t h e g a s phase o n t o the
solid s u r f a c e a s a f u n c t i o n of g a s pressure. T h e amount adsorbed in a monolayer ( s a t u r a t i o n s u r f a c e c o n c e n t r a t i o n , r.) i s d e r i v e d f r o m a n a p p r o p r i a t e
treatment of the a d s o r p t i o n data o n the b a s i s of a s p e c i f i c a d s o r p t i o n
isotherm. F i n a l l y , the s u r f a c e area is c a l c u l a t e d f r o m fr a f t e r assignment of
a n effective cross-sectional area A* to the a d s o r b a t e m o l e c u l e (ref. 102).
T h e most popular treatment m a k e s use of the B E T isotherm to derive r r , but
v a r i a n t s h a v e b e e n suggested and used ( r e f . 103). In p a r t i c u l a r , f. is derived
from the first m o n o l a y e r region, but
i t c a n a l s o be o b t a i n e d f r o m the
m u l t i l a y e r r e g i o n ( r e f . 104). S e l e c t i v e a d s o r p t i o n o n s o m e specific s i t e s can
be
achieved
by
using
molecules
undergoing
chemisorption
instead
of
physisorption a s implied in the B E T treatment. In t h i s case the experimental
data are a s a rule w o r k e d out o n the b a s i s of different isotherms ( e g
F r e u n d l i c h ' s ) ( r e f . 105).
3 . 1 . 2 L i m i t a t i o n s . I t is not the purpose of t h i s document to d i s c u s s the basic
validity of t h i s m e t h o d . Being a n e x s i t u technique, what i s to b e assessed i s
its r e l e v a n c e to the electrochemical situation.
V a r i o u s k i n d s of probe m o l e c u l e s can b e used: N 2 , K r , Ar m o s t l y ( r e f . 106),
but a l s o H2O ( r e f s . 1 0 7 , 1 0 8 ) and n-butane ( r e f . 109). and for c h e m i s o r p t i o n
C 0 2 , 0 2 . CO. N 2 0 , ( r e f s . 1 0 5 , 110,111) etc. Different s u r f a c e area v a l u e s are
usually o b t a i n e d w i t h different adsorbates. T h i s is especially true for p o r o u s
s o l i d s s i n c e the a c c e s s i b i l i t y of probe m o l e c u l e s to inner s u r f a c e s d e p e n d s of
course o n their size. T h u s , the s u r f a c e area o n the b a s i s of N2 ( a s s i g n e d area
0.162 n m 2 ) ( r e f . 102.109), the classic probe m o l e c u l e in t h i s technique, m a y
be lower than that w i t h K r o r HzO. A c c o r d i n g l y , h y d r o c a r b o n s are large
m o l e c u l e s and c a n only g i v e the external s u r f a c e . T h e u s e of two j u d i c i o u s l y
chosen probe m o l e c u l e s can e n a b l e external
and internal s u r f a c e s to b e
distinguished ( r e f . 107).
T h e most v e x i n g q u e s t i o n in t h i s m e t h o d is o b v i o u s l y the v a l u e of A*
(ref.
102,112). Hexagonal close p a c k i n g is usually assumed to c a l c u l a t e the crosssectional area:
A*
= 1.091( M / P N A 1 2 1 3
(12.1)
where 1.091 is a packing f a c t o r , M is the m o l a r m a s s of the a d s o r b a t e , p is
its density and NA the A v o g a d r o constant ( a cube of s p a c e w a s instead
originally s u g g e s t e d by Emmett and B r u n a u e r to b e o c c u p i e d by each a d s o r b a t e
molecule). H o w e v e r , there is the possibility o f c h o o s i n g b e t w e e n the d e n s i t y
of the liquid and the d e n s i t y of the s o l i d , d e p e n d i n g o n the d e g r e e of
localization of a d s o r p t i o n . T h i s is tantamount to implying that the crosssectional area of the a d s o r b a t e m a y d e p e n d o n the s t r e n g t h of the interaction
w i t h the solid a d s o r b e n t . Despite the usual c l a i m that in the case of N2 the
constancy of A* can be taken w i t h c o n f i d e n c e o v e r a large c l a s s of s o l i d
s u r f a c e s , i t is n o w well established ( r e f s . 1 0 9 , 1 1 2 ) that there e x i s t s an
inverse p r o p o r t i o n a l i t y b e t w e e n A*
and the C constant in the B E T e q u a t i o n
( w h i c h i s a m e a s u r e of the d e g r e e of interaction b e t w e e n adsorbent and
adsorbate). T h e r e f o r e the s a m e v a l u e of A* might not be valid w i t h different
surfaces. M o r e o v e r , for sufficiently s t r o n g i n t e r a c t i o n , a d s o r p t i o n m a y b e c o m e
localized so that also the a s s u m p t i o n of c l o s e a r r a n g e m e n t s m a y break down.
3.1.3 E v a l u a t i o n s .
If
disperse
solids
are
the
working
systems
under
i n v e s t i g a t i o n , the B E T s u r f a c e area m a y b e too low d u e to s o m e packing of the
g r a i n s d u r i n g the s u r f a c e area m e a s u r e m e n t . T h e s i t u a t i o n m a y b e o p p o s i t e if a
packed layer is scraped f r o m the support to m e a s u r e its specific area, o r if
the powder o n w h i c h the B E T m e a s u r e m e n t h a s been carried out i s then u s e d to
prepare pellets, s i n c e p a c k i n g m a y b e lower u n d e r the c o n d i t i o n s of s u r f a c e
area d e t e r m i n a t i o n .
U s e of H2O a s the probe m o l e c u l e m a y a p p e a r as most a p p r o p r i a t e for s t u d i e s
relevant to electrochemical interfaces. H o w e v e r , H2O is r e a c t i v e t o w a r d s most
c a t a l y s t s so that localized a d s o r p t i o n , and s o m e t i m e s d e c o m p o s i t i o n , m a y take
place. M o r e o v e r , liquid w a t e r m a y h a v e a different a c c e s s to the m o r e internal
s u r f a c e than the v a p o u r at relatively low pressure d u e to s u r f a c e tension and
h y d r o s t a t i c p r e s s u r e effects.
I t is v e r y difficult to e s t a b l i s h a f i r m c o r r e l a t i o n b e t w e e n the B E T ( o r
o t h e r ) s u r f a c e area and the electrochemical a c t i v e s u r f a c e a r e a , e a c h m e t h o d
m e a s u r i n g a s u r f a c e w h i c h r e s p o n d s to the specific probing. H o w e v e r , the B E T
is a r o u t i n e m e t h o d and its u s e for a first a p p r o x i m a t i o n assessment is a l w a y s
COMMISSION ON ELECTROCHEMISTRY
welcome. C a u t i o n should be exerted in treating the o b t a i n e d v a l u e s o n a
q u a n t i t a t i v e ( o r semi-quantitative) b a s i s . A t t e m p t s should a l w a y s be m a d e to
complement
the
BET
surface
area
measurements
with
other
independent
approaches.
I t is to be m e n t i o n e d in t h i s context that m o d e r n s u r f a c e s p e c t r o s c o p i c
t e c h n i q u e s such a s A E S , h a v e b e e n recently u s e d to extract information about
a d s o r b a t e a b s o l u t e p a c k i n g density
( r e f . 113).
A l t h o u g h not
explicitly
developed
for s u r f a c e area m e a s u r e m e n t s ,
the a p p r o a c h c o n t a i n s such a
p o t e n t i a l i t y implicitly ( r e f . 92).
3.2 X-ray diffraction
T h e m e t h o d , w h i c h g i v e s information o n c r y s t a l l i t e s i z e , is a s a r u l e applied
to c r y s t a l l i n e p o w d e r s (refs. 1 1 4 , 1 1 5 ) a l t h o u g h i t can b e extended
to
supported m i c r o c r y s t a l l i n e layers ( r e f . 116). A v a r i a n t , the small-angle X-ray
s c a t t e r i n g (SAXS), will not b e treated h e r e b e c a u s e its u s e is not c o m m o n w i t h
electrode s y s t e m s .
3.2.1 P r i n c i p l e s . X-ray
diffraction
lines b r o a d e n
(ref.
117) w h e n
the
c r y s t a l l i t e s i z e f a l l s b e l o w about 100 nm: at t h i s s i z e b r o a d e n i n g in e x c e s s
of the instrumental w i d t h is a s a r u l e not obtained. If G a u s s i a n s h a p e is
assumed for the d i f f r a c t i o n lines, then ( r e f . 118):
we.2
= Win2
+
Wpr2
(13.1)
w h e r e s u b s c r i p t s refer to e x p e r i m e n t a l , instrumental and particle-size w i d h t ,
respectively. win is usually o b t a i n a b l e by a c a l i b r a t i o n p r o c e d u r e . T h u s , ~ p .
can be derived. T h e a v e r a g e c r y s t a l l i t e d i a m e t e r d i s then o b t a i n e d by the
classical S c h e r r e r e q u a t i o n ( r e f s . 119,120):
d = KX/W.~ c o s
e
(13.2)
w h e r e X is the X-ray w a v e l e n g t h , wax i s h e r e expressed in r a d i a n s and K
( S c h e r r e r ' s c o n s t a n t ) d e p e n d s o n h o w the peak w i d t h i s m e a s u r e d ; a s a r u l e ,
the full w i d t h at half m a x i m u m ( F W H M ) is m e a s u r e d , f o r w h i c h K takes a v a l u e
close to 0.9. M o r e s o p h i s t i c a t e d d e c o n v o l u t i o n p r o c e d u r e s h a v e a l s o b e e n
proposed ( r e f . 121).
O n c e d is k n o w n , A can b e calculated by a s s u m i n g a p a r t i c u l a r g e o m e t r y for the
p a r t i c l e s (refs. 122,123). T h u s , for cubic p a r t i c l e s , the s u r f a c e area is a
max imum :
A
= 6&
(13.3)
w h e r e a s i t is a m i n i m u m for spherical p a r t i c l e s :
A
= n&
(13.4)
3.2.2 L i m i t a t i o n s . T h e m e t h o d i s r e s t r i c t e d t o c r y s t a l l i n e s o l i d s of about
3.5-60 n m p a r t i c l e size. B e l o w 3.5 n m the d i f f r a c t i o n line is v e r y broad and
d i f f u s e o r even a b s e n t , w h i l e a b o v e c e 60 n m the change in lineshape is too
small. T h e c r y s t a l l i t e s i z e obtained w i t h t h i s approach is a v e r a g e d o v e r the
sample v o l u m e penetrated by the incident r a d i a t i o n , t h e r e f o r e the r e s u l t i n g
value is a v o l u m e a v e r a g e d i a m e t e r ( c f m e t h o d 15). S t r i c t l y , the s u r f a c e area
calculated by m e a n s o f eqns.(13.3) and ( 1 3 . 4 ) is t h u s not the true s u r f a c e
area s i n c e the latter i s r e l a t e d to the s u r f a c e a v e r a g e c r y s t a l l i t e size.
O t h e r f a c t o r s m a y c o n t r i b u t e to the o b s e r v e d linewidth, e g d i f f e r e n c e in
lattice
parameters
of
the
individual
particles.
Moreover,
the
exact
geometrical s h a p e of the p a r t i c l e s is not known. T h e s i z e d i s t r i b u t i o n m a y be
v e r y w i d e (ref. 124).
In the c a s e o f supported m a t e r i a l , p e l l e t s and layers the w h o l e s u r f a c e of
each s i n g l e p a r t i c l e is not exposed to the environment. A p a c k i n g f a c t o r is to
be adopted to t a k e account of the e x c l u d e d area (ref. 122). A l s o in the case
of d i s p e r s e s y s t e m s and p o w d e r s , the g r a i n s m a y b e composed of m o r e than o n e
c r y s t e l l i t e w h i c h c a u s e s the real s u r f a c e area to d e v i a t e f r o m the c a l c u l a t e d
one the m o r e t h e smaller the p a r t i c l e s i z e (ref. 125).
3.2.3 Evaluations. T h i s t e c h n i q u e is v e r y useful to o b t a i n rapid information
about the d i s p e r s i o n d e g r e e of a catalyst present at the s u r f a c e of a support
Real surface area measurements in electrochemistw
729
or even embedded in i t (ref. 126). H o w e v e r , for s u r f a c e area m e a s u r e m e n t s i t
should be used o n l y in c o n j u n c t i o n w i t h o t h e r m o r e a p p r o p r i a t e t e c h n i q u e s ,
mainly to o b t a i n a m o r e complete a n a l y s i s of the m o r p h o l o g y of a solid
surf ace.
3.3 Porosimetry
T h e m e t h o d s considered a b o v e m a k e i t p o s s i b l e to e s t i m a t e the specific area of
solids and a l s o in principle to find the p o r e d i s t r i b u t i o n a c c o r d i n g to the
radius. T h e s e m e t h o d s could b e n a m e d m o l e c u l a r o r atomic probe m e t h o d s ( r e f .
127). In a d d i t i o n , a n u m b e r of n o n a d s o r p t i v e m e t h o d s of p o r o s i t y d e t e r m i n a t i o n
have b e e n developed to e s t i m a t e the real s u r f a c e area.
3.3.1 P r i n c i p l e s . T h e m e t h o d is based o n the r e l a t i o n b e t w e n the real
area of a s a m p l e and i t s p o r o s i t y 8 :
surface
(14.1)
where r m i n and r m a x a r e the minimal and maximal pore r a d i i , and
Bf is the
shape f a c t o r . F o r c y l i n d r i c p o r e s , Bf = 2 , for p o r e s b e t w e e n g l o b u l a , Br =
1.45. Av is the s u r f a c e area per unit v o l u m e of the m a t e r i a l . T h e r e f o r e , ( 1 B o ) is the true v o l u m e o c c u p i e d by the solid phase (total v o l u m e m i n u s p o r e
volume). P o r o s i t y B0 i s the r a t i o of the v o l u m e of o p e n p o r e s ( c o n n e c t e d w i t h
the o u t e r surface of a s o l i d ) to the total v o l u m e of the p o r o u s solid.
According to the eqn.(l4.1), the real s u r f a c e area c a n b e calculated f r o m the
integration of the integral curve of r a d i u s p o r e d i s t r i b u t i o n 8(r). S u c h a
curve is called a n integral porosimetric curve o r a porogram.
A c t u a l l y there are m a n y m e t h o d s for m e a s u r i n g p o r o g r a m s : ( 1 ) the m e t h o d of
pressing m e r c u r y into m e r c u r y u n w e t t a b l e p o r o u s s o l i d s ( m e r c u r y porosimetry);
( 2 ) small a n g l e X-ray s c a t t e r i n g ; ( 3 ) e l e c t r o n and optical m i c r o s c o p y ; ( 4 )
centrifugal p o r o s i m e t r y ; ( 5 ) capillary displacement of w e t t i n g liquids by g a s ;
( 6 ) m e t h o d s based on g a s p e n e t r a t i o n ; (7) m e t h o d of s t a n d a r d porosimetry.
While in individual c o n c r e t e c a s e s each of these m e t h o d s can be u s e d , the
m e t h o d s of m e r c u r y and standard p o r o s i m e t r y are the most universal o n e s .
W h e n using the method of m e r c u r y porosimetry ( r e f . 128) the s i d e s u r f a c e of
p o r e s into w h i c h m e r c u r y is pressed can be o b t a i n e d d i r e c t l y by integration of
the Young-Dupr6 e q u a t i o n :
(14.2)
w h e r e B i s the contact a n g l e of m e r c u r y o n the solid b o u n d a r y , y the m e r c u r y
surface t e n s i o n , p the p r e s s u r e , V, the v o l u m e of m e r c u r y pressed into the
sample,
the p r e s s u r e a s the p o r e s are completely filled w i t h m e r c u r y .
T h e m e t h o d of standard p o r o s i m e t r y ( r e f . 129) i s based o n the m e a s u r e m e n t of
the e q u i l i b r i u m curve of r e l a t i v e m o i s t u r e c a p a c i t y , that is the r e l a t i o n s h i p
between the liquid c o n t e n t s of a test s a m p l e and of a standard o n e w i t h a
k n o w n pore d i s t r i b u t i o n . T h e m o i s t u r e capacity is the r a t i o of the v o l u m e of
the liquid content in a solid to the v o l u m e of the s o l i d . If the s a m p l e
c o n t a i n s h y d r o p h i l i c (metal. o x i d e , e t c ) and h y d r o p h o b i c ( p o l y m e r i c b i n d e r )
c o m p o n e n t s , w h e n u s i n g the method of s t a n d a r d p o r o s i m e t r y w i t h two different
w e t t i n g liquids (eg, w a t e r and liquid h y d r o c a r b o n s ) i t i s p o s s i b l e to identify
h y d r o p h i l i c , h y d r o p h o b i c and mixed pores. T h u s , the p o s s i b i l i t y a r i s e s of
c h a r c a t e r i z i n g the real s u r f a c e a r e a s w i t h the above-mentioned different types
of pores.
3.3.2. Limitations.
The main
difficulty
lies
in
the d e t e r m i n a t i o n of
m i c r o p o r e s w i t h radii ( 2 n m , i e of m o l e c u l a r s i z e s ( r e f . 130). S u c h p o r e s
could f o r m the m a i n part of the real s u r f a c e area v a l u e in s o m e materials. T h e
lower limit in pore d i a m e t e r m e a s u r a b l e by the H g p o r o s i m e t e r is set by the
highest p r e s s u r e at w h i c h the H g can be forced into the p o r e s of the s a m p l e .
In t h i s r e s p e c t , the t e c h n i q u e p r e s e n t s the difficulty that h i g h p r e s s u r e c a n
disrupt the p o r e s y s t e m to be m e a s u r e d .
A n o t h e r c o m p l i c a t i o n is related to the d i f f i c u l t y of c h o o s i n g the s h a p e f a c t o r
f o r real m a t e r i a l s . In the method of m e r c u r y porosimetry the v a l u e of A
730
COMMISSION ON ELECTROCHEMISTRY
depends on the 8 estimation. The latter depends on the nature of the material
and also whether during the measurements mercury is pressed into pores o r , on
leaves them (ref. 1 3 1 ) ,
and on the possibility of
the contrary, i t
amalgamation and contamination of mercury. The last two factors also change y .
The often observed hysteresis phenomena also complicate the measurements and
the interpretation of the results (ref. 1 3 2 ) .
3 . 3 . 3 . Evaluations. The method can be applied to materials with sufficiently
extended surface. The reliability of results depends largely on the choice of
the method of porogram measurement and of its conditions. For electrode
materials, especially multicomponent porous electrodes, the most promising is
the standard porosimetry method, which allows to distinguish the surface by
the hydrophobicity factor. Other advantages of this method are its relative
simplicity, the possibility of acheeving conditions of measurement resembling
most closely the real operating ones and of monitoring the surface area during
the measurements thanks to the nondestructive nature of this method.
3.4 Microscopy
Microscopy is one of the direct physical methods of determination of the real
surface area. The capacity of resolution goes from the macroscopic to the
atomic size depending on the technique. Thus, the order of magnitude of the
range of observation of the optical microscopy is the millimeter, that of the
scanning electron microscopy (SEM) the micrometer, and that of the scanning
tunneling microscopy (STM) the nanometer. The progress in the development of
STM is making its use in s i t u possible (ref. 1 3 3 ) .
3 . 4 . 1 Principles. The method is based on the determination of the particle
size of the material by optical or electron microscopes (refs. 7 , 1 3 4 ) . In its
simplest version the specific surface area is calculated according to the
equation :
Am = (Bd/p)(2nidi2/2nidi3)
(15.1)
where p is the real density of the material. and ni is the number of particles
with size di. The shape factor Bd amounts to 6 for strictly spheric and cubic
particles, while i t exceeds 6 for any other shape. Since the size of
individual particles can be determined with this technique, the results of the
microscope
can be
compared both with
data
from direct
surface area
measurements, giving values based on cis, and with those from the X-ray
analysis, giving values based on dv.
In the method of projections, the surface area is calculated via the Cauchy
expression:
A = (42a,/n)
(15.2)
A V = (4npNmZap/n)
(15.3)
or
where Pe, is the sum of the plane projected areas of n randomly
convex particles and N, is the number of particles per unit mass.
The modification of
the microscopic method based
phenomenon makes i t possible to determine the real
dispersion of material.
on the
surface
oriented
interference
area without
Electron microscopy can be used for surface roughness measurements with
lateral and vertical resolution of 1 nm. Transmission electron microscopy
(TEM) offers the possibility of providing direct imaging of individual metal
particles and is one of the most used and useful tool to characterize size,
135,136).
shape and
distribution
of
supported metal
particles
(refs.
Crystallites as small as 1 nm have been resolved and average crystallite
diameters of less than 2 nm have been obtained by TEM in its bright-field and
dark-field versions.
The fullest data on the surface profile of massive electrodes and in principle
on the A value can be obtained by means of the scanning tunneling microscopy
(STM) with a high resolving power (nanotopography). At ambient pressure,
lateral and vertical resolutions of 1 nm and better than 0 . 1 n m , respectively,
can be achieved (refs. 1 3 7 - 1 3 9 ) .
Real surface area measurements in electrochemistry
731
3 . 4 . 2 Limitations. Eqns.(l5.1) to ( 1 5 . 3 ) are statistical and their use gives
satisfactory results in cases where the size of a great number of particles
(at least hundreds)
is known, and especially when the particle size
distribution is sufficiently wide-ranging. The method is limited to materials
with
particles
of no
porosity
and
roughness.
The
reliability of
A
determination depends on the accuracy of the Bd estimation. When electron
microscopy is used, samples have to withstand high vacuum treatment without
showing structural changes. Electron bombardment should not affect the
material. In transmission electron microscopy the accelerating voltage may be
up to several hundred kV. The presence of contaminations (vacuum is rarely
better than 10-10 bar) and the heating due to the incident electron beam could
result in adsorbate-induced changes of the surface structure. In the STM
method, where the electron energy lies in the meV and eV range and is in
principle non-destructive. the accuracy of surface area determination depends
on the accuracy of the corresponding shape approximation of surface formation.
STM is a promising new tool for surface characterization (refs. 140-143). but
a s a technique for quantitative measurement of real surface areas i t has not
yet been unambiguously established.
3.4.3 Evaluations. In the simplest version, the method is applicable for
estimating the surface of some types of nonporous powder-like electrode
materials. I t gives reliable results i f the particle size exceeds (by one
order of magnitude or more) the distance resolved by the microscope ( 1 pm for
optical and I nm for electron microscopes). The best results are obtained for
solid samples with a narrow distribution of particles and shape close to
spherical. The sample observed in the microscope must be representative of the
original material. Therefore, several samples should be examined.
3.5 Other methods
This group includes methods, that are relatively seldom used in surface area
estimations or are limited to special cases (refs. 86,126,144-146), such a s
( 1 ) weighing of saturated vapour adsorbed on a solid, ( 2 ) thermodesorption
methods, ( 3 ) determining the surface area by measurement of the wetting heat
(absolute Harkins-Jura method), ( 4 ) gravimetric and volumetric methods, ( 5 )
methods
based
on
liquid
or
gas
permeability
and
displacement,
(6)
radioisotopic methods, (7) methods of surface potential measurement of pure
metal thin films, ( 8 ) methods based on the measurement of metal dissolution
rate, (9) methods based on the hysteresis of adsorption isotherms, (10)
methods for one-dimensional roughness (profile) determination (profilometer,
stereoscan, etc.), ( 1 1 ) optical techniques affected by surface roughness
(scattering or diffuse reflectance of light). (19) measurements based on NMR
spin-lattice relaxation.
4.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
REFERENCES
Pure Appl. Chem. 58, 437 (1986).
Quantities, Units and Symbols in Physical Chemistry, Blackwell, Oxford (1987)
Pure Appl. Chem. 31, 579 (1972); 46, 71 (1976).
Pure Appl. Chem. 37. 499 (1974).
Pure Appl. Chem. 58, 967 (1986).
B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco (1982).
C. R. Adams, H. A. Benesi. R. M. Curtis and R. G. Meisenheimer, J. Catal. 1 , 336 (1962).
D. C. Graharne. J. Am. Chem. SOC. 79, 701 (1957).
V. I. Melik-Gaikasian, V. V. Voronchikhina and E. A. Zakharova, Elektrokhimiya 12, 1420
(1968).
J. Broadhead. G. J. Hills and D. R. Kinnibrugh, J. Appl. Electrochem. 1 , 147 (1971).
E. M. L. Valeriote and R. G. Barradas, Chem. lnstr. 1 . 153 (1968).
G. H. Nancollas and C. A. Vincent, Electrochim. Acta 1 0 , 97 (1965).
G. S. Smith, Trans. Fareday SOC. 47, 63 (1951).
R. G. Barradas and F. M. Kimnerle. Can. J. Chem. 45, (1967).
M. Carla, G. Papeschi and R. Guidelli, J. Electroanal. Chem. 127. 267 (1981).
J. Campbell, J. Phys. D 3, 1499 (1970).
J. W. Perrarn, J. B. Hayter and R. J. Hunter, J. Electroanal. Chem. 42, 291 (1973).
R. R. Salem, Zh. Fiz. Khim. 50, 2667 (1976).
V. S. Boitzov, 1. V. Osipov, E. V. Stenina, N. V. Fedorovich and B. B. Damaskin.
Elektrokhimiya 13, 1588 (1977).
D. M. Mohilner, J. C. Kreuser, H. Nakadornari and P. R. Mohilner, J. Electrochem. SOC.
123. 359 (1976).
M. Breiter, J. Electroanal. Chem. 81, 275 (1977).
732
COMMISSION ON ELECTROCHEMISTRY
I . M. Novoselkii, N. I . Konevskikh. L. Ya. Egorov and E. P. Sidorov, Elektrokhimiye 7,
893 (1971).
23. E. Robert, Oberf1.-Surf. 22, 261 (1981).
24. T. Ohmori. J. Electroanel. Chem. 157. 159 (1983).
25. R. Parsons and F. R. G. Zobel, J. Electroanel. Chem. 9, 333 (1965).
26. G. Valette and A. Hamelin. J. Electroanal. Chem. 45. 301 (1973).
27. D. 1 . Leikis. K. V. Rybalka and E. S. Sevastiyanov in Adsorbtziys i Dvonoi
Elektricheskii Sloi v Elektrokhimiyi, M. "Nauka" (1972). p. 5.
28. A. N. Frumkin, Potenzialny Nulevogo Zariada, M. "Nsuka" (1979), p. 122.
29. W. Schmickler and D. Henderson, Progr. Surf. Sci. 22, 323 (1986).
30. L. Blum, D. Henderson and R. Parsons, J. Electroanal. Chem. 161, 389 (1984).
31. I. A. Bagotskaya, B. B. Damaskin and M. D. Levi, J. Electroanal. Chem. 115, 189 (1980).
32. G. Valette, J. Electroanal. Chem. 138 37 (1982); 224, 285 (1987).
33. P. Siviglia, A. Daghetti and S. Trasatti. Coll. Surf. 7, 15 (1983).
34. S. Ardizzone and S. Trasatti, J. Electroenal. Chem. 251. 409 (1988).
35. F. G. Will and C. A. Knorr, 2. Elektrochem. 64, 258 (1960).
36. A. N. Frumkin in P. Delahay and C. W. Tobias (Eds.), Advances in Electrochemistry and
Eletrochemicel Engineering, Vol. 3, Wiley-Interscience. New York. 1963, p. 287.
37. S . Gilrnan. J. Phys. Chem. 67. 78 (1963); J. Electroanel. Chem. 7. 382 (1964).
38. S . Gilman, J. Phys. Chem. 71. 4339 (1967).
39. R. Woods, J. Electroenal. Chem. 49, 217 (1974).
40. D. V. Sokolskii, B. Yu. Nogerbekov, N. N. Gudeleva and R. G. Mustafina, Elektrokhimiya
22, 1185 (1986).
41. A. G. Pshenichnikov, Mat. Chem. Phys. 22, 121 (1989).
42. S. Motoo and N. Furuya, J. Electroanal. Chem. 167, 309 (1984).
43. M. Hayes and A. 7. Kuhn, Appl. Surf. Sci. 6. 1 (1980).
44. T. Biegler, D. A. J. Rand and R. Woods, J. Electroanel. Chem. 29, 269 (1971).
45. J. Bett. K. Kinoshita, K. Routsis and P. Stonehart. J. Catal. 29, 160 (1973).
46. G. G. Barna, S. N. Frank and T. H. Teherani, J. Electrochem. SOC. 129, 746 (1982).
47. T. Kessler, A. M. Castro Lura. W. E. Triaca and A. J. Arvia, J. Appl. Electrochem. 16,
693 (1986).
48. M. R. Tarasewich. K. A. Radushkina and R. Kh. Burstein. Elektrokhimiya 3, 455 (1967).
49. B. Love, K. Seto and J. Lipkowski. J. Electroanal. Chem. 199, 219 (1986).
50. D. Armand and J. Claviliver, J. Electroanal. Chem. 263, 109 (1989).
51. M. Breiter. K. Hoffmann and C. Knorr, Z. Elektrochem. 61, 1168 (1957).
52. A, A. Michri, A. G. Pshchenichnikov and R. Kh. Burshtein, Elektrokhimiya 8, 364 (1972).
53. R. K. Burshtein, Elektrokhimiya 3, 349 (1967).
54. H. Angerstein-Kozlowska, B. E. Conway, A. Hamelin and L. Stoicoviciu. Electrochim. Act8
31, 1051 (1986).
55. S. B. Brumner and A. C. Makrides. J. Electrochem. SOC.111, 1122 (1964).
56. V. A. Vicente and S. Bruckenstein, J. Electroanel. Chem. 82, 187 (1977).
57. A. Vashkyalis and 0. Demontaite. Elektrokhimiya 1 4 . 1213 (1978).
58. H. Siegenthaler and K. Jiittner. J. Electroanel. Chem. 163. 327 (1984).
59. M. A. Quiroz. Y. Meas. E. Lamy-Pitara and J. Barbier, J. Electroenal. Chem. 157. 165
(1983).
60. T. D. Gladisheva, B. I . Podlovchenko and Z. A. Zikrina. Elektrokhimiya 23, 1446 (1987).
61. B. I. Podlovchenko and E. A. Kolyadko, J. Electroanel. Chem. 224, 225 (1987)
62. A. T. Hubbard et a l . , J. Electroanal. Chem. 168, 43 (1984).
63. C. L. Scortichini and C. N. Reilley, J. Eletroanal. Chem. 139, 233 (1982).
64. C. L. Scortichini, F. E. Woodward and C. N. Reilley, J. Electroanal. Chem. 139, 265
( 1982).
65. P. C. Andricacos and P. N. Ross, J. Electroanal. Chem. 167. 301 (1984).
66. G. Singh, M.H. Miles and S . Srinivasan in A.D. Franklin (Ed.), Electrocatalysis on Nonmetallic Surfaces, NBS Spec. Publ. N. 455 (1976) p. 289.
67. J. O'M. Bockris and T. Otagawa, J. Electrochem. SOC. 131, 290 (1984).
68. L. D. Burke and 0. J. Murphy, J. Electroanal. Chem. 96, 19 (1979).
69. B. V. Tilak, C. G. Rader and S . K. Rangarajan, J. Electrochem. SOC.124, 1879 (1977).
70. K. Micka and I . Rouser, Electrochim. Acta 32, 1387 (1987).
71. R. Boggio, A. Carugati and S . Trasatti, J. Appl. Electrochem. 17, 828 (1987).
72. A. Daghetti, G. Lodi and S . Trasatti. Mat. Chem. Phys. 8, 1 (1983).
73. R. K. Schofield. Nature 160, 480 (1974).
74. H. J. Van de Hull and J. Lyklema, J. Colloid Interface Sci. 23, 500 (1967).
75. J. Lyklema and H. J. Van den Hull, Proc. Int. Symp. IUPAC, Surface Area Determination,
Butterworths, London, 1970, p. 341.
76. J. Lyklema in J. O'M. Bockris, D. A. J. Rand and B. J. Welch (Eds.), Trends in
Electrochemistry, Plenum, New York, 1977. p. 159.
77. H. J. Van den Hull, J. Colloid Interface Sci. 86, 173 (1982).
78. M. C. H. Mouat. Coll. Surf. 24, 51 (1987).
79. A. Kozawa, J. Electrochem. SOC. 106. 552 (1959).
80. A. Kozawa, J. lnorg. Nucl. Chem. 21, 315 (1961).
81. A. Kozawa, S. C. Paterniti and T. A. Reilly in R. S. Alwitt (Ed.). Oxide-Electrolyte
Interfaces, The Electrochemical Society, Pennington, N.J.. 1973, p. 72.
82. A. Kozawa and T. Takai in T. Takamurs and A. Kozawa (Eds.), Surface Electrochemistry,
22
Real surface area measurements in electrochemistry
83.
84.
85.
86.
87.
88.
89.
733
Jpn. SOC. Sci. Press. Tokyo, 1978. p. 56.
T. Arikado, C. lwakura and H. Tamura, Electrochim. Acta 22, 513 ( 1 9 7 7 ) .
C. H. Giles, A. P. D‘Silva and A. S. Tuvedi in Proc. lnt. Symp. “Surface Area
determination”. Butterworths, London, 1969, p. 317.
C. H. Giles and A. P. D’Silva. Trans. Faraday SOC.65. 1943,2516 ( 1 9 6 9 ) .
A. W. Adamson. Physical Chemistry of Surfeces, 4th Ed., J. Wiley and Sons, New YorkLondon, 1982.
A. KellomYki, J. Colloid Interface Sci. 105. 270 ( 1985) .
R. Brina and A. De Battisti, J. Cbem. Educ. 64, 175 ( 1 9 8 7 ) . .
P. N. Ross. K. Kinoshita, A . J. Scarpellino and P. Stonehart, J. Electroanal. Chem. 59.
177 ( 1975) .
106.
107.
108.
109.
K. Kinoshita and P. N. Ross, J. Electroanel. Chem. 78, 313 ( 1 9 7 7 ) .
J. F. Rodriguez, T. Mebrahtu and M. P. Soriaga, J. Electroanel. Chem. 233, 283 ( 1 9 8 7 ) .
G. N. Salaita, L. Laguren-Davidson, F. Lu, N. Walton, E. Wellner, D. A. Stern, N.
Batina, D. G. Frank, C.-H. Lin, C. S. Benton and A. T. Hubbard, J. Electroanel. Chem.
245, 253 ( 1 9 8 8 ) .
R. S . Hanscn, Y. Fu and F. E. Bartell. J. Phys. Cbem. 53, 769 ( 1 9 4 9 ) .
T. Gu, J. Colloid Interface Sci. 85. 601 ( 1 9 8 2 ) .
J. C1. Puippe, Oberf1.-Surf. 26, nr. 6 ( 1 9 8 5 ) .
P. J. Lingane. Anel. Chem. 36. 1723 ( 1 9 6 4 ) .
L. Meites, Polarographic Techniques, 2nd Ed., Wiley, New York, 1965.
J. E. B. Randles, Trans. Faraday SOC.44, 327 ( 1 9 4 8 ) .
A. J. Bard, Anal. Chem. 33, 11 (1 9 6 1 ).
R. J. Lutz, A. Menawat and J. I . Peterson, AIChE J. 28. 1027 ( 1 9 8 2 ) .
S . Brunauer, P. H. Ermnett and E. Teller, J. Am. Chem. SOC.60. 309 ( 1 9 3 8 ) .
D. Dollimore, P. Spooner and A. Turner, Surf. Technol. 4, 121 ( 1 9 7 6 ) .
P. T. John, R. K. Aggarwal and K. V. Chetty, J. Sci. lnd. Res. 36. 415 ( 1 9 7 7 ) .
N. E. Buyanova, R. V. Zagrafskaya, A. P. Karnaukhov, and A. S. Shepelina,
Kinet.
Katal. 24, 1187 ( 1 9 8 3 ) .
Ma. M. Martin, J. M. D. Tascon, J. L. Garcia Fierro. J. A. Pajares and L. Gonzalez
Tejuca, J. Catsl. 71, 201 ( 1 9 8 1 ) .
S . J. Rotheberg et al.. J. Colloid Interface Sci. 116, 541 ( 1 9 8 7 ) .
M. A. F. Pyman and A. M. Posner, J. Colloid Interface Sci. 66. 85 ( 1 9 7 8 ) .
A. Nag, B. Sadhukhan and D. K. Chattoraj, Coll. Surf. 23, 83 ( 1 9 8 7 ) .
S. Lowell, J. Shields, G. Charalambous and J. Manzione, J. Colloid lnterface Sci. 86,
110.
R. Kh. Burshtein, V. S. Vilinskaya, N. G. Bulavina and V. Ya. Shepelev, Elektrokhimiya
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
101.
102.
103.
104.
105.
191 ( 1 9 8 2 ) .
13, 1550 ( 1977).
Y. L. Sandler. J. Electrochem. Sac. 121, 764 ( 1 9 7 4 ) .
A. P. Karnaukhov, J. Colloid Interface Sci. 103. 311 ( 1 9 8 5 ) .
J. L. Stickney, S. D. Rosasco, D. Song, M. P. Soriaga and A. T. Hubbard. Surf. Sci.
130, 326 ( 1 9 8 3 ) .
114. J. L. Lemaitre, P. G. Menon and F. Delannay in F. Delannay (Ed.), Charecterizetion of
Heterogeneous Catalysts, Dekker, New York, 1984.
115. J. R. Anderson, Structure of Metallic Catalysts, Academic Press, London, 1975.
116. W. Fischer and P. Wissmann, Appl. Surf. Sci. 1 1 / 1 2 , 109 ( 1 9 8 2 ) .
117. A. Renouprez in D. H. Everett and R. H. Ottewill (Eds.), Surface Area Determination,
Butterworths, London, 1970, p. 3 6 1 .
118. B. E. Warren and B.L. Averbach. J. Appl. Phys. 21, 595 ( 1 9 5 0 ) .
119. P. Schemer, Gttinger Nachr. 2, 98 ( 1 9 1 8 ) .
120. R. J. Farrauto, AlChE Symp. Ser. 70, 9 ( 1 9 7 4 ) .
121. B. Moraweck, Ph. de Montgolfier and A. J. Renouprez. J. Appl. Cryst. 10, 191 ( 1 9 7 7 ) .
122. V. D. Allred, S. R. Buxtonb and J. P. McBride, J. Phys. Cbem. 61, 117 ( 1 9 5 7 ) .
123. W. S. Brey Jr. and B. H. Davis, J. Colloid Interface Sci. 70, 10 ( 1 9 7 9 ) .
124. A. M. Skundin. Elektrokhimiya 20, 713 ( 1 9 8 4 ) .
125. L. H e r n h , J. Morales and J. L. Tirado, J. Colloid lnterface Sci. 115, 109 ( 1 9 8 7 ) .
126. T. A. Dorling and R. L. Moss, J. Catal. 7, 378 ( 1 9 6 7 ) .
127. S . J. Gregs and K. S. W. Sing, Adsorption, Surface Area and Porosity, Acad. Press.
Ins., London-N.Y., 1982.
128. H. L. Ritter and L. C. Drake, lnd. Eng. Chem. 17, 782 ( 1 9 4 5 ) .
129. Yu. M. Volfkovich, V. S. Bagobky, V. E. Sosenkin and E. I . Shcolnikov, Elektrokhimiya
16, 1620 ( 1 9 8 0 ) .
130. B. H. Davis, Appl. Catal. 10, 185 (1 9 8 4 ).
131. A. Lane, N. Shah and Wm. C. Conner, J. Colloid lnterface Sci. 109. 235 ( 1 9 8 6 ) .
132. Wm. C. Conner, A. M. Lane and A. J. Hoffman, J. Colloid Interface Sci. 100, 185 ( 1 9 8 4 ) .
133. P. Lustenberger, H. Rohrer, R. Cristoph and H. Siegenthaler. J. Electroanal. Chem. 243,
111.
112.
113.
225 ( 1 9 8 8 ) .
134.
135.
136.
137.
138.
K.
of
D.
D.
G.
J.
Kinoshita and P. Stonehart in J. O’M. Bockris and B. E. Conway (Eds.),Modern Aspects
Electrochemistry, Vol. 1 2 , Plenum, New York. 1977, p. 183.
W. Butler, Micron 4, 410 ( 1 9 7 3 ) .
E. Fornwalt and K. Kinoshita, Micron 4, 99 ( 1973) .
Binnig and H. Rohrer, Sci. Am. 40 (August 1985) .
A. Golovchenko, Science 232. 48 ( 1 9 8 6 ) .
734
COMMISSION ON ELECTROCHEMISTRY
J. A. Garcia, A. M. Bard. R. Miranda, H. Rohrer, Ch. Gerber, R. Garcia Canth and J. L.
Pena, Metrol. 21, 135 (1985).
140. L. Vazques. J. Gomez. A. M. Baro, N. Garcia, M. L. Marcos, J. Velasco Gonzales, J. M.
Vara, A. J. Arvia, J. Press. A. Garcia and M. Aguilar, J. h e r . Chem. SOC. 109, 1730
(1987).
141. H.-L. Liu, F.-R. F. Fan, C. W. Lin et al. J. h e r . Chem. SOC. 108, 3838 (1986).
142. R. Miranda e t el., Appl. Phys. Lett. 47, 367 (1985).
143. L. Vasquez et el., J. Am. Chem. SOC. 109, 1730 (1987).
144. J. M. Thomas and W. J. Thomas, Introduction to the Principles of Heterogeneous
Catalysis, Acad. Press, London-New York, 1967.
145. A. J. Salkind in E. Yeager and A. J. Salkind. Techniques of Electrochemistry, Vol. 1 ,
J. Wiley and Sons, New York-London, 1972.
146. C. L. Glaves. P. J. Davis and D. M. Smith, Powder Technol. 5 4 , 261 (1988).
139.