- Email: [email protected]
Electrochemical nucleation
J- EfectmanaC Chem, 138 (1982) 241-254 Ekvier Squoia.SA. JIausa& e - P&ted
241 in The Netherlands
PART ti_.TpIE~EWcTR Oti&&TION .. ..: CARBON, : -_ .., GA&I @eparlmenl
(kzeiwd
ON V~OUS ~.
..I
GUNAWARDENi of
OF’SIL&Z
GRAHAM
HILLS &d IRENE MONTENEGRO
Chm.irrrY, The LTniwniy. Sourhampton SO9 5NH (England)
29th July 1980; in revised form 16th February 1982)
A study hxs been made of the electrochemical nucleation of silver on vitreous carbon from aqueous solutions of silver nitrate. The nucleation is shown to be progressive and maxs transferred controlled. The rzte of nucleation is somyhat better described by the aromistic theory than by clas.sical Theories. The addition of &?A r&&s the raie of nudleation as the result, it is _&ggested, of the.adsorpCon of EDTA by the graphite surface. The skasitivity of Lhe rate-of the nucleation to the condkion of the graphite surface is also shown by the effects of chaaging the salvation aa&ty.
INTRODUCTION
-This paper is concerned growth
with three-dimensional
of silver onto vitreous carbon.
on platinum
v&e
touched-on
electrochemical
The difficulties
previously
[I]
attending
nucleation
and here attention
is cxxrcentrated on
more suitable substrates. The seminal work m-this field is by Budevski studied
the mechanism
of the electrochemical
deposition
and
its electrodeposition et al. !2] who
of silver onto dislocation-
free sir@ cryst9.s of. silver itself, prepared by a special capillary technique. They found the depos?tron to occurby two-dimensional nucleation and growth of steps of monomofecular height. Astley~et aI. [3] studied the same reaction on vitreous carbon and~&so .concluded that. the~initial deposition occurs by two-dimensional, plate-byplate.g&wth, eventually leading however to thre+dimensi&~. nucleation_ Again, the
slow step,in the char& transfer. reaction was concluded tion OF-sib&. atoms, their surface concentration chemical
pre-equilibrium.
to~be the lattice incorpora-
being determined
by a fast electro
In more recent work, Morcos [4] investigated the under-
potent&l d&position of several metals, including silver, o&o “cleavage” graphite electrodes. It. followed &evious observations- that the electrodeposition of mercury o2to cle+age and edge graphite r&$+d only a small overpotential and in certain &.es no. overpotential :at a. He&, . a s+dy is reported of- ,the electrodeposition of &lye fr&‘aquqxs solutjon~&to_~+rfaces of. vi@z+s &bon. i. ~. .~ ~. CD1982 Etkevier Sequoia SA.
002&728/8~/OCiOO-O/X02.75
:
242
EXPERIMENTAL
The general experimental procedures were as in previous papers. A simple T-cell was used for recording voltammetric transients. The working electrodes were prepared from carbon cylinders, sealed by fusion under vacuum into glass tubing. The ends were cut flush and polished to a mirror finish on a slow turning, wet grinding wheel using finer and finer grades of alumina powder and ending with 0.05 pm powder on a Buechler microcloth. The circuhu surface area was 0.32 cm’. Fig. I(a) and (b) show scanning electron micrographs of unpolished and polished surfaces of vitreous carbon. The polishing procedure was continued until evident reproducibility of the surface was obtained Contact to the carbon electrode was made by a clean stainless steel rod sharply pointed at one end and resting on the dry, upper side of the carbon rod. RESULTS
AND
Linear sweep
DISCUSSION
valtammelty
The linear sweep voltammogram shown in Fig. 2 displays the characteristic features of nucleation, namely the large peak separation and the cross-over on the cathodic branch. The peak height is a linear function of the sweep rate and, using the usual formula for semi-infinite linear diffusion, leads to a diffusion coefficient only slightly higher than the correct value obtained from methods not affected by nucleation. Successive linear sweep voltammograms were not reproducible, the electrodeposition reaction taking place more readily in the second and successive sweeps. It seems likely that the deposited silver intercalates into the carbon, is not readily anoclically stripped and therefore promotes the nucleation and deposition of silver in the following cathodic cycle. In very dilute solutions of silver nitrate =GIO-* mol/cm3, a second anodic peak could be discerned and there is little doubt concerning the existence of two forms of electrodeposited silver on graphite. The cathodic/anodic charge ratio, QA/Qc, for the first sweep was determined directly using an electronic coulometer and was found to be 1.2. If the electrode potential was maintained at the anodic limit for increasingly long periods, then the irreproducibility decreased but even after 1 h there was evidence of pre-formed nuclei. It was a simple matter to monitor the small current attending the potentiostatic anodic dissolution of the supposedly intercalated silver. It was of small magnitude and a linear function of t-‘I’, indicative of slow diffusion of silver atoms out cf the graphite matrix. The silver could be removed immediately simply by mechanically polishing the electrode.
Potential step
e.rperimen1.r
The effects of nucleation are more clearly evident from the corresponding potentiostatic transients_ A set of these is shown in Fig. 3(a) from which it is clear
243
Elg
1. !kanning
polished
election
surface of vitrems
miaovlope carbon.
photographs
of:
(a) unpolished
surface
of
~~IECILLScarbon;
(b)
Fig. 2. Linear sweep voltammognm 0.01 M k&IO, in aqueous NaCIO,;
for the deposition of silver on10 a vitreous carbon elecuocle from electkde area=O.32 cm’; scan rate=O.l V/s.
that under the prevailing conditions a nucleation overpotential of at least 150 mV is required for any significant electrodeposition to take place. The nuclei resultii~g from these transients were easily observed under the microscope as the result of the grazing illumination and they could be counted and compared with the number
TABLE
1
Nuclear number densities, calculated from eqn. (I), concenLra!iori
as a function of overpotential and silver ion
IO%*,+ /mol cmp3 2.5
5
0.22 0.24 0.26 0.28
0.3 4.7 5.1 5.4 9.5 12.0 19.9 25.2 27.1
0.30
40.4
1.6 2.5 4.6 5.7 6.8 II.4 16.9 22.7 32.5 43.4
1.2
0.10
0.12 0.14 0.16 0.18 0.20
7.5
10
0.7 3.1 3.4 3.8 4.7 6.8 9.6 38.2 64.0 87.4 88.9
0.7 3.0 3.3 3.7 4.5 6.6 9.3 36.9 62.0 89.6 86.0
245
G 6 .. . r for .the dqiositiik of silver onto a vitreous cartion electrode E& 3. (a) Potcnti&tatic ckrent’&&ts fmm 0.05 M A&C’IOi in aquanrs -NoClO, +d at the overpotentials indiated (in mv); electrode ti=o.32 crn~. (b) I vs t ‘1’ plot_5of the rising-parw of th; transients in (a).
246 TABLE
2
Characteristics
--
rl
mV
I
-
cl-1.
s
of the potcntiostatic
103L. d cm-’
current maximum
10'12 mlL<~mal A’ cmPa s
IO-TIN, cm-l
10-6Nu, s-
’
clc2
IO-‘N cm-’
200
I .73
1.59
6.80
4.29
1.04
220
1.11
1.43
6.67
2.94
1.62
I.45
240
0.76
1.27
5.97
2.27
2.36
2.00 2.65
0.80
260
0.57
I.13
5.55
1.54
3.14
260
0.45
0.98
5.51
0.95
4.0.1
3.61
300
0.37
0.8 I
5.00
0.53
4.87
3.T7
320
O-33
0.68
5.11
0.25
5.54
4.85
340
0.27
0.55
5.23
0.10
6.69
5.53
evaluated from the corresponding cathodic current to give the nuclear number density. The currents corresponding to the rising parts of the potentiostatic transients are shown in Fig. 3(b). They are linear in I’/‘, indicative of the mass transfer controlled growth of hemispherical nucleation as required by the equation,
the quantities involved here being defined in Part L of this series. The corresponding values of D are readily obtained from high overpotential experiments (and found to be 1.0 X 1O-5 cm’s_‘) and used to evaluate N as a function of q and c. These values are given in Table 1. The concentration dependence of the slope d I/df ‘I’ is not systematically dependent on concentration, i.e. on c3i2, as predicted by eqn. (1) simply because the nucleation rate and hence IV itself is dependent on concentration_ As noted in Part I, the nuclear number density and thennature of the nucleation process can also be derived from the characteristics of the potentiostatic current maximum. For a single concentration. 5 X to-’ mol/cm3, these values of I,, and I,,, are shown as a function of over-potential in Table2. The theory set out in Part I requires that I’“1o.I c“13X be a constant and equal to 3.79 X IO-’ A’ cmp4 s for instantaneous or arrested nucleation or 6_04X IO-’ A’ cm-4 s for progressive nucleation, i.e. for continuous nucleation up to the overlap of the diffusion fields. The obserfcd values are also shown in Table 2; they are close to 6 and suggest that the nucleation process is progressive up to the overlap of the diffusion fields, i.e. progressive throughout and not instantaneous. On the assumption that this is so, it is possible to calculate the corresponding nuclear number density. Thus, for progressive nucleation it was shown that the time required to reach the potentiostatic current maximum, I,~~,,, is given by I mnn= (4.6733/&DAN,)“2. This allows the product AN,
(2)
to be calculated at each over-potential Fhich in turn
247
gives the saturation number density, Nut, i.e.N,, = ( AN,/2k’o)‘/z
(3)
where k; = ~(SmM/p)“2
(4)
This value of IV’, can be compared with the value of N calculated from eqn. (1) for instantaneous nucleation and these values are also shown in Table2. The agreement between the two sets of figures is good and suggests that they are effectively the same. It can be concluded that the period of rapid growth of new nuclei is short and that the nucleation rate rapidly attenuates to give an effectively constant nuclear number density over the greater part of the potentiostatic transient. This is the likely outcome of the progressive attenuation of the nucleation over-potential following the growth of the fist born nuclei and their diffusion zones. The resultant data therefore give values for N and N,A as a function of overpotential, in this case at a single concentration of 5 X 10m6mol/cn?. The classical theory of nucleation [5], which is based on macroscopic quantities, equates the free energy of the critical nucleus to the activation energy for the rate of nucleation, i.e. SG* = SG,,,, = 87;a’1%f~/3p~z~F~_r1~
(5)
In terms of this model log N-A should be a linear function of p-‘. A test of this relationship is shown in Fig. 4. The linearity is excellent but the value of the slope,
IO
Fig 4. A plot af In N,A
2a vs q-l
30
cm-responding
to the tmnsients
shown in Fig. 3.
m!!_
V
-xi
a2
Fig. 5. A
plot 01In N_A
vs q corresponding
to the traasienls
shown in Fig. 3.
0.23Vz, is 2 orders of magnitude lower than predicted 8aa’M2/3kTp’r’F2
by the classical model, namely
= 13V’.
Not r;urprisingly. the classical representation of hetc.ogeneous nucleation is a poor approximation and the linear dependence of the nucl.-ation rate on q-* is fortuitous. There is another model of nucleation, the so-calleo atomistic model [6], which also relates the rate of nucleation to that of the formatLt of the critical nucleus but in which the potential dependence is introduced in another way, i.e. by supposing that the electrochemical driving force is related to the product of the number of atoms in the critical nucleus and the overpotential; i.e. SG* = SC_
= (n + 1 - a)zFq
6)
This theory predicts a linear relation between In AN, and q_ The observed relation is shown in Fig 5. As is customary 161,it has been rsolved into ttio linear sections which allow n to be evaluated for an assumed value of a, in this case 0.5. The two values of n are 1.0 and 1.7 which are close to those found previously for other systems. The significance of these small values of n is hard to evaluate and they may simply be the result of the application of the high overpotential used in this work.
It :is ‘known that metal deposition reactions are sensitive to the presence of additives, the normal purpose of which is to promote smooth and bright deposits_ In the absence of such tidditives, the deposit is often dendritic or granular and it seems reasonable to conclude that :the effect _of the .additive is_ to increase greatly the nucleation rate and the-nuclear number density. In the limit of very high number densities, the deposit is effectively smooth, planar and epitaxial. Common, inorganic additives are chloride and cyanide ions. Organic additives are often surface active materials. Here, a systematic_study.was attempted of the effect of. the common complexing agent .ethylene diamine tetra-acetic acid, EDTA. It was added in increasing concentrations to a standard 10 mM solution of A&IO, in aqueous 1 M HClO, and the effect on potentiostatic transients was noted of reactions of the type [EDTA]~-
+Ag+
[AgEDTA13-
*[AgEDTA]‘-
+Ag+
,
+[AgEDTA]‘-
Somewhat ‘surprisingly, the effect of the lowest concentration of EDTA was already marked. Even at a concentration of 0.002 M the nuclear number density was reduced by at least an .order of magnitude_ In every case a linear relation between 1 and t’/’ was observed from which N was evaluated and in each case the reference electrode
TABLE
3
densities for the deposition of silver onto virreous carbon from aqueous 0.01 .M A&IO, HClO,‘but in the presence of different concentrations of EDTA
Nuclear
-s/$J
IO?N/cm
-2
[EDTAJ/mM 0
~2
-. .
4
6
in 1 M
250
Fig. 6. Inrcrhcinl
[ension elemenls or a cap-shaped
nucleus.
was of silver immersed in the same complex-containing solution, so that the overpotential was not affected by the Nemst factor, i.e. by the change with the activity coefficient of the silver ions. The N values obtained at three successive concentrations of EDTA are shown in Table 3. The inhibiting effect seems to reach a limiting value at -0.004M and suggests that it cannot be interpreted simply in terms of complexation of the silver ions by the EDTA which is a continuous and progressive process. The fact that concentrations of EDTA less than 20 per cent of that of silver ions still affect the process, suggests a surface phenomenon arising from the adsorption of EDTA on the vitreous carbon surface. The effects of adsorption on nucleation have been considered elsewhere [7]. In general terms, impurity adsorption on the substrate is likely to decrease the binding energy of an adsorbed atom to the substrate and to decrease the rate of nucleation because, for a given overpotential, the population of adatoms would be lower. The presence of the adsorbed material is also likely to affect the value of SC,,, and hence the rate of nucleation, by changing the contact angle between the nucleus and the substrate. In all the equations used hitherto, a single surface tension term, CT,has be-en used to encompass the contributions from the three separate interfacial tensions, u,_~, that between the depositing metal and the substrate, (T,_~, that between the depositing metal and the solution and a,,, that between the substrate and the solution. At equilibrium, the interaction of these interfacial tensions defines the contact angle as shown in Fig. 6. This is the general depiction of a smooth cap shaped nucleus, the volume of which can be described as f~r’f,(O), the area by 2rrrz/,(8)
and the circumference by 25~ sin 0, where f,(B)=;(2-3cos6’+cos38)
(74
f,(e)=+(l
(7b)
-cos8)
25 l-
and the radius of the -base is r sin 8.’ The equilibrium~value of the interfacial SG, interfacial = 27rr’~(B)a,, Recalling
Young’s
:
_
free energy is therefore
+ rrz sin28(a,_, -
equation,
IJ~_~)
(8)
that
c2.3 = 01.2 + 01.3cos Q
(9)
eqn. (8) becopes SG, interfacial = sr’u,.,(2
-
3 cos 8 + co&?)
(10)
which simplifies to the term used previously when the nucleus is a hemisphere and 0 = 90”. However, in general, the corresponding bulk term, i.e. the corresponding supersaturation SG, bulk=
free energy is
$+,(e)
AG,,
(11)
where AG, is zF~ per mole. The total free energy of a cap shaped nucleus is therefore the sum of the interfacial
and bulk free energies. It is principally
radius and, if differentiated critical radius, corresponding
with respect to r and the differential
r,, to the maximum value of SG_
energy
of the
to zero, the
can be found.
The
is then
Q-
= (4rru;_,M2/3p2z2F2q2)(2-3
From
the definition
to nucleation
in the nuclear.free
a function
equated
MS
6 + cos%)
(12)
of the contact angle (eqn. (9)) it follows
exists only if uz, -u,
that a significant
barrier
z is less than u,.~. To put it another way, if the
is also zero and the formation of the one equilibrium contact angle is zero, SC_ phase upon the other will be instantaneous. IF B = 180°, which corresponds to zero wetting of the one phase by the other, then the bracketted term in eqn. (12) is unity and the equation reduces to that for homogeneous nucleation where the substrate plays no part in the formation The rate of heterogeneous
of the new phase. nucleation
can be restated as
J = wZN, exp( --GG,,,,/kT) where
w is the frequency
(13) with which
nucleus and thereby promotes non-equilibrium single
molecules
impingement
Zeldovitch or
atom
and N,
Although
and SC2
attaches
to a critically
nucleus or crystallite,
is the surface density of monomers, i.e. can occur either by direct of an adsorbed
that the latter is more rapid by a factor (l/kT)( are rspectively
sized
Z is the
this process
from the bulk [8] or by surface diffusion
Pound et al. [9] showed where SC:-
factor
adatoms.
a single
it to a stable growing
the free energies of activation
monomer
[9],
SG$m- GGzf )). of desorption
and surface diffusion. When the surface diffusion term is predominant, the frequency w is-given by the product of two terms, namely the probability that an adatom is adjacent jumps
to a critical
nucleus
and
the frequency
with which
an adjacent
adatom
to join the nucleus, i.e.
o -‘27rrC siti8 o-N, .exp( dG,,.._/kT)~-
0 tixp( -Si$/kT)
(14
252
where u is the jump distance and o is defined in terms of the Einstein frequency v as 0 = (kT/h)[
1 - exp( --hv/kT)J
(19
h being Plan&s constant. In heterogeneous nucleation, the non-equilibrium Zeldovitch factor is given by Z = ( BG,,/3M’n,z)r’z
(16)
where nC is the number of monomers or atoms in the critical nucleus. The final expression for the rate of nucleation is therefore = X-‘c2 exp( [2 6Gi_ - 6G$, - GG,,,]/~T)
(17)
where k’=
k”(a sin 8rh+/857~mRT)[(2
+ cos 0)(1-
cos 8)2kT/12]“2
(18)
k” is a proportionality between c2 (c is bulk concentration of electrodepositing species) and the corresponding vapour pressure term in the original theory, 171is the adatom mass. Although eqn. (18) is still an approximation in that it neglects the statistical mechanical corrections introduced by Lothe and Pound [lo], it displays all the terms, 8, SC& and 6G$ which are likely to be sensitive to the presence of adsorbed surfactants. Thus, Fig. 7 shows three separate ways in which the adsorption of a surfactant might take place and thereby influence the rate olnucleation. The adsorption of a surfactant will by definition decrease u,_~ and uz,. On the other hand, the interfacial tension between nucleus and substrate is likely to be increased, although the process
(al
Fig. 7.
Schematic cross-sectional rcpresentarion of the way in which impurity can
hatching represents
impurity
adsorbale.
alfact nucleation. The
253
of nucleation may well be attended -by non-equilibrium factors such that CJ;.~is time : dependent; .. -. _~ .- In-the case of Fig. 7(a); the-presence of EDTA will cause uL3 to decrease and Q,,~ to increase~and-therefore cos 19and J-will decrease_ In the case of-Fig_ 7(b), both u,_~ Fd.q, Gill decrease while uI1 is likely to increase_ If the decrease in u,.~ is greater than the relative decrease in (u,~ - u,~) J will increase and vice versa. In the case of Fig. 7(c), u,,s and uz, decrease whilst u,,~ remains unchanged and as in (b), J may increase or decrease depending on the relative changes in u,.s and (ur3 - u,_~)_ However, the. decrease in ( uz, - u,~ ) will Abe less than in case (b) because u, z is unchanged..Accordingly~ case (c) should give rise to-higher values than case (b).’ To summa&e, in case (a) J should always be decreased by adsorption; in cases (b) and (c) the decrease in AG$,, will favour a decrease in J but the change in +,(0) may give rise to either a decrease or an increase in J. The evidence from the present work suggests that EDTA is readily adsorbed on vitre-ous carbon
and inhibits the nucleation
of silver effectively
by increasing
u,_~_
The iqflueti&z of the surface state of graphite on the nucleation of silver is also evident from m&surements of. the nuclear number density at different degrees of
acidity. The nuclear number density was determined from the rising parts of potentiostatic transients recorded as a function of over-potential and at increasing values of the hydrogen ion concentration. Figure 8 shows nuclear number densities as a function of overpotential for a solution of 4.6 mM AgClO,‘in 1 M KCIO,-HCIO,.
.
. . 6 .
om
IdN lx-t-3
.
/
006
073
.
a55
l
l
.
IO 9
.
I
V
.
.
2
cue
.
.
3
Fig. 8. Nuclear number density as a function of ova-potential and for different hydrogen ion concentrations incdicated in M.
254
iucreasti~
It is clear tbat the nucleation rate steadily increases with hjdrogen itin concentration. This is unlikely to be the result of consequential change in Silver ion activiky, i.e. other than those of the Nemst factor, and more likely. to b.e th$ result of the changing chemical composition and interfacial free energy of the &bon surface itself. ACKNOWLEDGEMJZNT
:
Grateful *&arks are offered to the British Council ior research~support For G.G. and to Instituto National de Investiga@o of Portugal for corresponding support of I.M. REFERENCES 1 G. Gunawardena. GJ. HiUs, I. Mootencgro. and Ei. Scharifker. J. Electroan& Ghan. 138,(1982) 225. Phys_ Status Solidi. 2 E Budcvski. W. EIoscanoff. T_ vitanoff. Z Scoinoff, A. KOQIXI and R. Kakhcv, 13 (1966) 577. F-J. Asdey. JA. Harrison and H.R Tbirsk, Trans. Faraday Sot., 64 (1968) 192. .. 1. Morcos. J. U auoanal. Chem.. 66 (1975).250. F_ Tbomfor and M. Volmer. AM. Physik.. 33 (1938) 109. A. Milchev and S. Stoyanov. 1. Eikctmanal. Ghan. 72 (1976) 33. J.P. Hirth and G.M. Pound, Condensation and Evaporation Nucleation and Growth Kinetics. Pcgamon F’ress. London, 1963. 8 J.H. Hollomon and D. Turnbull. in 8. Chalmas and R King (Eds.). Prop-c+ in Metal Physics. Vol. 4. Pcrgamon Press, London, 1953. 9 G-M. Pound, M-T_ Simnad and L. Yang, J. Chem. Phys.. 22 (1954) 1215. IO J. Lothe and G.M. Pound, J. Chem. Phys.. 36 (1962) 2080.
241 in The Netherlands
PART ti_.TpIE~EWcTR Oti&&TION .. ..: CARBON, : -_ .., GA&I @eparlmenl
(kzeiwd
ON V~OUS ~.
..I
GUNAWARDENi of
OF’SIL&Z
GRAHAM
HILLS &d IRENE MONTENEGRO
Chm.irrrY, The LTniwniy. Sourhampton SO9 5NH (England)
29th July 1980; in revised form 16th February 1982)
A study hxs been made of the electrochemical nucleation of silver on vitreous carbon from aqueous solutions of silver nitrate. The nucleation is shown to be progressive and maxs transferred controlled. The rzte of nucleation is somyhat better described by the aromistic theory than by clas.sical Theories. The addition of &?A r&&s the raie of nudleation as the result, it is _&ggested, of the.adsorpCon of EDTA by the graphite surface. The skasitivity of Lhe rate-of the nucleation to the condkion of the graphite surface is also shown by the effects of chaaging the salvation aa&ty.
INTRODUCTION
-This paper is concerned growth
with three-dimensional
of silver onto vitreous carbon.
on platinum
v&e
touched-on
electrochemical
The difficulties
previously
[I]
attending
nucleation
and here attention
is cxxrcentrated on
more suitable substrates. The seminal work m-this field is by Budevski studied
the mechanism
of the electrochemical
deposition
and
its electrodeposition et al. !2] who
of silver onto dislocation-
free sir@ cryst9.s of. silver itself, prepared by a special capillary technique. They found the depos?tron to occurby two-dimensional nucleation and growth of steps of monomofecular height. Astley~et aI. [3] studied the same reaction on vitreous carbon and~&so .concluded that. the~initial deposition occurs by two-dimensional, plate-byplate.g&wth, eventually leading however to thre+dimensi&~. nucleation_ Again, the
slow step,in the char& transfer. reaction was concluded tion OF-sib&. atoms, their surface concentration chemical
pre-equilibrium.
to~be the lattice incorpora-
being determined
by a fast electro
In more recent work, Morcos [4] investigated the under-
potent&l d&position of several metals, including silver, o&o “cleavage” graphite electrodes. It. followed &evious observations- that the electrodeposition of mercury o2to cle+age and edge graphite r&$+d only a small overpotential and in certain &.es no. overpotential :at a. He&, . a s+dy is reported of- ,the electrodeposition of &lye fr&‘aquqxs solutjon~&to_~+rfaces of. vi@z+s &bon. i. ~. .~ ~. CD1982 Etkevier Sequoia SA.
002&728/8~/OCiOO-O/X02.75
:
242
EXPERIMENTAL
The general experimental procedures were as in previous papers. A simple T-cell was used for recording voltammetric transients. The working electrodes were prepared from carbon cylinders, sealed by fusion under vacuum into glass tubing. The ends were cut flush and polished to a mirror finish on a slow turning, wet grinding wheel using finer and finer grades of alumina powder and ending with 0.05 pm powder on a Buechler microcloth. The circuhu surface area was 0.32 cm’. Fig. I(a) and (b) show scanning electron micrographs of unpolished and polished surfaces of vitreous carbon. The polishing procedure was continued until evident reproducibility of the surface was obtained Contact to the carbon electrode was made by a clean stainless steel rod sharply pointed at one end and resting on the dry, upper side of the carbon rod. RESULTS
AND
Linear sweep
DISCUSSION
valtammelty
The linear sweep voltammogram shown in Fig. 2 displays the characteristic features of nucleation, namely the large peak separation and the cross-over on the cathodic branch. The peak height is a linear function of the sweep rate and, using the usual formula for semi-infinite linear diffusion, leads to a diffusion coefficient only slightly higher than the correct value obtained from methods not affected by nucleation. Successive linear sweep voltammograms were not reproducible, the electrodeposition reaction taking place more readily in the second and successive sweeps. It seems likely that the deposited silver intercalates into the carbon, is not readily anoclically stripped and therefore promotes the nucleation and deposition of silver in the following cathodic cycle. In very dilute solutions of silver nitrate =GIO-* mol/cm3, a second anodic peak could be discerned and there is little doubt concerning the existence of two forms of electrodeposited silver on graphite. The cathodic/anodic charge ratio, QA/Qc, for the first sweep was determined directly using an electronic coulometer and was found to be 1.2. If the electrode potential was maintained at the anodic limit for increasingly long periods, then the irreproducibility decreased but even after 1 h there was evidence of pre-formed nuclei. It was a simple matter to monitor the small current attending the potentiostatic anodic dissolution of the supposedly intercalated silver. It was of small magnitude and a linear function of t-‘I’, indicative of slow diffusion of silver atoms out cf the graphite matrix. The silver could be removed immediately simply by mechanically polishing the electrode.
Potential step
e.rperimen1.r
The effects of nucleation are more clearly evident from the corresponding potentiostatic transients_ A set of these is shown in Fig. 3(a) from which it is clear
243
Elg
1. !kanning
polished
election
surface of vitrems
miaovlope carbon.
photographs
of:
(a) unpolished
surface
of
~~IECILLScarbon;
(b)
Fig. 2. Linear sweep voltammognm 0.01 M k&IO, in aqueous NaCIO,;
for the deposition of silver on10 a vitreous carbon elecuocle from electkde area=O.32 cm’; scan rate=O.l V/s.
that under the prevailing conditions a nucleation overpotential of at least 150 mV is required for any significant electrodeposition to take place. The nuclei resultii~g from these transients were easily observed under the microscope as the result of the grazing illumination and they could be counted and compared with the number
TABLE
1
Nuclear number densities, calculated from eqn. (I), concenLra!iori
as a function of overpotential and silver ion
IO%*,+ /mol cmp3 2.5
5
0.22 0.24 0.26 0.28
0.3 4.7 5.1 5.4 9.5 12.0 19.9 25.2 27.1
0.30
40.4
1.6 2.5 4.6 5.7 6.8 II.4 16.9 22.7 32.5 43.4
1.2
0.10
0.12 0.14 0.16 0.18 0.20
7.5
10
0.7 3.1 3.4 3.8 4.7 6.8 9.6 38.2 64.0 87.4 88.9
0.7 3.0 3.3 3.7 4.5 6.6 9.3 36.9 62.0 89.6 86.0
245
G 6 .. . r for .the dqiositiik of silver onto a vitreous cartion electrode E& 3. (a) Potcnti&tatic ckrent’&&ts fmm 0.05 M A&C’IOi in aquanrs -NoClO, +d at the overpotentials indiated (in mv); electrode ti=o.32 crn~. (b) I vs t ‘1’ plot_5of the rising-parw of th; transients in (a).
246 TABLE
2
Characteristics
--
rl
mV
I
-
cl-1.
s
of the potcntiostatic
103L. d cm-’
current maximum
10'12 mlL<~mal A’ cmPa s
IO-TIN, cm-l
10-6Nu, s-
’
clc2
IO-‘N cm-’
200
I .73
1.59
6.80
4.29
1.04
220
1.11
1.43
6.67
2.94
1.62
I.45
240
0.76
1.27
5.97
2.27
2.36
2.00 2.65
0.80
260
0.57
I.13
5.55
1.54
3.14
260
0.45
0.98
5.51
0.95
4.0.1
3.61
300
0.37
0.8 I
5.00
0.53
4.87
3.T7
320
O-33
0.68
5.11
0.25
5.54
4.85
340
0.27
0.55
5.23
0.10
6.69
5.53
evaluated from the corresponding cathodic current to give the nuclear number density. The currents corresponding to the rising parts of the potentiostatic transients are shown in Fig. 3(b). They are linear in I’/‘, indicative of the mass transfer controlled growth of hemispherical nucleation as required by the equation,
the quantities involved here being defined in Part L of this series. The corresponding values of D are readily obtained from high overpotential experiments (and found to be 1.0 X 1O-5 cm’s_‘) and used to evaluate N as a function of q and c. These values are given in Table 1. The concentration dependence of the slope d I/df ‘I’ is not systematically dependent on concentration, i.e. on c3i2, as predicted by eqn. (1) simply because the nucleation rate and hence IV itself is dependent on concentration_ As noted in Part I, the nuclear number density and thennature of the nucleation process can also be derived from the characteristics of the potentiostatic current maximum. For a single concentration. 5 X to-’ mol/cm3, these values of I,, and I,,, are shown as a function of over-potential in Table2. The theory set out in Part I requires that I’“1o.I c“13X be a constant and equal to 3.79 X IO-’ A’ cmp4 s for instantaneous or arrested nucleation or 6_04X IO-’ A’ cm-4 s for progressive nucleation, i.e. for continuous nucleation up to the overlap of the diffusion fields. The obserfcd values are also shown in Table 2; they are close to 6 and suggest that the nucleation process is progressive up to the overlap of the diffusion fields, i.e. progressive throughout and not instantaneous. On the assumption that this is so, it is possible to calculate the corresponding nuclear number density. Thus, for progressive nucleation it was shown that the time required to reach the potentiostatic current maximum, I,~~,,, is given by I mnn= (4.6733/&DAN,)“2. This allows the product AN,
(2)
to be calculated at each over-potential Fhich in turn
247
gives the saturation number density, Nut, i.e.N,, = ( AN,/2k’o)‘/z
(3)
where k; = ~(SmM/p)“2
(4)
This value of IV’, can be compared with the value of N calculated from eqn. (1) for instantaneous nucleation and these values are also shown in Table2. The agreement between the two sets of figures is good and suggests that they are effectively the same. It can be concluded that the period of rapid growth of new nuclei is short and that the nucleation rate rapidly attenuates to give an effectively constant nuclear number density over the greater part of the potentiostatic transient. This is the likely outcome of the progressive attenuation of the nucleation over-potential following the growth of the fist born nuclei and their diffusion zones. The resultant data therefore give values for N and N,A as a function of overpotential, in this case at a single concentration of 5 X 10m6mol/cn?. The classical theory of nucleation [5], which is based on macroscopic quantities, equates the free energy of the critical nucleus to the activation energy for the rate of nucleation, i.e. SG* = SG,,,, = 87;a’1%f~/3p~z~F~_r1~
(5)
In terms of this model log N-A should be a linear function of p-‘. A test of this relationship is shown in Fig. 4. The linearity is excellent but the value of the slope,
IO
Fig 4. A plot af In N,A
2a vs q-l
30
cm-responding
to the tmnsients
shown in Fig. 3.
m!!_
V
-xi
a2
Fig. 5. A
plot 01In N_A
vs q corresponding
to the traasienls
shown in Fig. 3.
0.23Vz, is 2 orders of magnitude lower than predicted 8aa’M2/3kTp’r’F2
by the classical model, namely
= 13V’.
Not r;urprisingly. the classical representation of hetc.ogeneous nucleation is a poor approximation and the linear dependence of the nucl.-ation rate on q-* is fortuitous. There is another model of nucleation, the so-calleo atomistic model [6], which also relates the rate of nucleation to that of the formatLt of the critical nucleus but in which the potential dependence is introduced in another way, i.e. by supposing that the electrochemical driving force is related to the product of the number of atoms in the critical nucleus and the overpotential; i.e. SG* = SC_
= (n + 1 - a)zFq
6)
This theory predicts a linear relation between In AN, and q_ The observed relation is shown in Fig 5. As is customary 161,it has been rsolved into ttio linear sections which allow n to be evaluated for an assumed value of a, in this case 0.5. The two values of n are 1.0 and 1.7 which are close to those found previously for other systems. The significance of these small values of n is hard to evaluate and they may simply be the result of the application of the high overpotential used in this work.
It :is ‘known that metal deposition reactions are sensitive to the presence of additives, the normal purpose of which is to promote smooth and bright deposits_ In the absence of such tidditives, the deposit is often dendritic or granular and it seems reasonable to conclude that :the effect _of the .additive is_ to increase greatly the nucleation rate and the-nuclear number density. In the limit of very high number densities, the deposit is effectively smooth, planar and epitaxial. Common, inorganic additives are chloride and cyanide ions. Organic additives are often surface active materials. Here, a systematic_study.was attempted of the effect of. the common complexing agent .ethylene diamine tetra-acetic acid, EDTA. It was added in increasing concentrations to a standard 10 mM solution of A&IO, in aqueous 1 M HClO, and the effect on potentiostatic transients was noted of reactions of the type [EDTA]~-
+Ag+
[AgEDTA13-
*[AgEDTA]‘-
+Ag+
,
+[AgEDTA]‘-
Somewhat ‘surprisingly, the effect of the lowest concentration of EDTA was already marked. Even at a concentration of 0.002 M the nuclear number density was reduced by at least an .order of magnitude_ In every case a linear relation between 1 and t’/’ was observed from which N was evaluated and in each case the reference electrode
TABLE
3
densities for the deposition of silver onto virreous carbon from aqueous 0.01 .M A&IO, HClO,‘but in the presence of different concentrations of EDTA
Nuclear
-s/$J
IO?N/cm
-2
[EDTAJ/mM 0
~2
-. .
4
6
in 1 M
250
Fig. 6. Inrcrhcinl
[ension elemenls or a cap-shaped
nucleus.
was of silver immersed in the same complex-containing solution, so that the overpotential was not affected by the Nemst factor, i.e. by the change with the activity coefficient of the silver ions. The N values obtained at three successive concentrations of EDTA are shown in Table 3. The inhibiting effect seems to reach a limiting value at -0.004M and suggests that it cannot be interpreted simply in terms of complexation of the silver ions by the EDTA which is a continuous and progressive process. The fact that concentrations of EDTA less than 20 per cent of that of silver ions still affect the process, suggests a surface phenomenon arising from the adsorption of EDTA on the vitreous carbon surface. The effects of adsorption on nucleation have been considered elsewhere [7]. In general terms, impurity adsorption on the substrate is likely to decrease the binding energy of an adsorbed atom to the substrate and to decrease the rate of nucleation because, for a given overpotential, the population of adatoms would be lower. The presence of the adsorbed material is also likely to affect the value of SC,,, and hence the rate of nucleation, by changing the contact angle between the nucleus and the substrate. In all the equations used hitherto, a single surface tension term, CT,has be-en used to encompass the contributions from the three separate interfacial tensions, u,_~, that between the depositing metal and the substrate, (T,_~, that between the depositing metal and the solution and a,,, that between the substrate and the solution. At equilibrium, the interaction of these interfacial tensions defines the contact angle as shown in Fig. 6. This is the general depiction of a smooth cap shaped nucleus, the volume of which can be described as f~r’f,(O), the area by 2rrrz/,(8)
and the circumference by 25~ sin 0, where f,(B)=;(2-3cos6’+cos38)
(74
f,(e)=+(l
(7b)
-cos8)
25 l-
and the radius of the -base is r sin 8.’ The equilibrium~value of the interfacial SG, interfacial = 27rr’~(B)a,, Recalling
Young’s
:
_
free energy is therefore
+ rrz sin28(a,_, -
equation,
IJ~_~)
(8)
that
c2.3 = 01.2 + 01.3cos Q
(9)
eqn. (8) becopes SG, interfacial = sr’u,.,(2
-
3 cos 8 + co&?)
(10)
which simplifies to the term used previously when the nucleus is a hemisphere and 0 = 90”. However, in general, the corresponding bulk term, i.e. the corresponding supersaturation SG, bulk=
free energy is
$+,(e)
AG,,
(11)
where AG, is zF~ per mole. The total free energy of a cap shaped nucleus is therefore the sum of the interfacial
and bulk free energies. It is principally
radius and, if differentiated critical radius, corresponding
with respect to r and the differential
r,, to the maximum value of SG_
energy
of the
to zero, the
can be found.
The
is then
Q-
= (4rru;_,M2/3p2z2F2q2)(2-3
From
the definition
to nucleation
in the nuclear.free
a function
equated
MS
6 + cos%)
(12)
of the contact angle (eqn. (9)) it follows
exists only if uz, -u,
that a significant
barrier
z is less than u,.~. To put it another way, if the
is also zero and the formation of the one equilibrium contact angle is zero, SC_ phase upon the other will be instantaneous. IF B = 180°, which corresponds to zero wetting of the one phase by the other, then the bracketted term in eqn. (12) is unity and the equation reduces to that for homogeneous nucleation where the substrate plays no part in the formation The rate of heterogeneous
of the new phase. nucleation
can be restated as
J = wZN, exp( --GG,,,,/kT) where
w is the frequency
(13) with which
nucleus and thereby promotes non-equilibrium single
molecules
impingement
Zeldovitch or
atom
and N,
Although
and SC2
attaches
to a critically
nucleus or crystallite,
is the surface density of monomers, i.e. can occur either by direct of an adsorbed
that the latter is more rapid by a factor (l/kT)( are rspectively
sized
Z is the
this process
from the bulk [8] or by surface diffusion
Pound et al. [9] showed where SC:-
factor
adatoms.
a single
it to a stable growing
the free energies of activation
monomer
[9],
SG$m- GGzf )). of desorption
and surface diffusion. When the surface diffusion term is predominant, the frequency w is-given by the product of two terms, namely the probability that an adatom is adjacent jumps
to a critical
nucleus
and
the frequency
with which
an adjacent
adatom
to join the nucleus, i.e.
o -‘27rrC siti8 o-N, .exp( dG,,.._/kT)~-
0 tixp( -Si$/kT)
(14
252
where u is the jump distance and o is defined in terms of the Einstein frequency v as 0 = (kT/h)[
1 - exp( --hv/kT)J
(19
h being Plan&s constant. In heterogeneous nucleation, the non-equilibrium Zeldovitch factor is given by Z = ( BG,,/3M’n,z)r’z
(16)
where nC is the number of monomers or atoms in the critical nucleus. The final expression for the rate of nucleation is therefore = X-‘c2 exp( [2 6Gi_ - 6G$, - GG,,,]/~T)
(17)
where k’=
k”(a sin 8rh+/857~mRT)[(2
+ cos 0)(1-
cos 8)2kT/12]“2
(18)
k” is a proportionality between c2 (c is bulk concentration of electrodepositing species) and the corresponding vapour pressure term in the original theory, 171is the adatom mass. Although eqn. (18) is still an approximation in that it neglects the statistical mechanical corrections introduced by Lothe and Pound [lo], it displays all the terms, 8, SC& and 6G$ which are likely to be sensitive to the presence of adsorbed surfactants. Thus, Fig. 7 shows three separate ways in which the adsorption of a surfactant might take place and thereby influence the rate olnucleation. The adsorption of a surfactant will by definition decrease u,_~ and uz,. On the other hand, the interfacial tension between nucleus and substrate is likely to be increased, although the process
(al
Fig. 7.
Schematic cross-sectional rcpresentarion of the way in which impurity can
hatching represents
impurity
adsorbale.
alfact nucleation. The
253
of nucleation may well be attended -by non-equilibrium factors such that CJ;.~is time : dependent; .. -. _~ .- In-the case of Fig. 7(a); the-presence of EDTA will cause uL3 to decrease and Q,,~ to increase~and-therefore cos 19and J-will decrease_ In the case of-Fig_ 7(b), both u,_~ Fd.q, Gill decrease while uI1 is likely to increase_ If the decrease in u,.~ is greater than the relative decrease in (u,~ - u,~) J will increase and vice versa. In the case of Fig. 7(c), u,,s and uz, decrease whilst u,,~ remains unchanged and as in (b), J may increase or decrease depending on the relative changes in u,.s and (ur3 - u,_~)_ However, the. decrease in ( uz, - u,~ ) will Abe less than in case (b) because u, z is unchanged..Accordingly~ case (c) should give rise to-higher values than case (b).’ To summa&e, in case (a) J should always be decreased by adsorption; in cases (b) and (c) the decrease in AG$,, will favour a decrease in J but the change in +,(0) may give rise to either a decrease or an increase in J. The evidence from the present work suggests that EDTA is readily adsorbed on vitre-ous carbon
and inhibits the nucleation
of silver effectively
by increasing
u,_~_
The iqflueti&z of the surface state of graphite on the nucleation of silver is also evident from m&surements of. the nuclear number density at different degrees of
acidity. The nuclear number density was determined from the rising parts of potentiostatic transients recorded as a function of over-potential and at increasing values of the hydrogen ion concentration. Figure 8 shows nuclear number densities as a function of overpotential for a solution of 4.6 mM AgClO,‘in 1 M KCIO,-HCIO,.
.
. . 6 .
om
IdN lx-t-3
.
/
006
073
.
a55
l
l
.
IO 9
.
I
V
.
.
2
cue
.
.
3
Fig. 8. Nuclear number density as a function of ova-potential and for different hydrogen ion concentrations incdicated in M.
254
iucreasti~
It is clear tbat the nucleation rate steadily increases with hjdrogen itin concentration. This is unlikely to be the result of consequential change in Silver ion activiky, i.e. other than those of the Nemst factor, and more likely. to b.e th$ result of the changing chemical composition and interfacial free energy of the &bon surface itself. ACKNOWLEDGEMJZNT
:
Grateful *&arks are offered to the British Council ior research~support For G.G. and to Instituto National de Investiga@o of Portugal for corresponding support of I.M. REFERENCES 1 G. Gunawardena. GJ. HiUs, I. Mootencgro. and Ei. Scharifker. J. Electroan& Ghan. 138,(1982) 225. Phys_ Status Solidi. 2 E Budcvski. W. EIoscanoff. T_ vitanoff. Z Scoinoff, A. KOQIXI and R. Kakhcv, 13 (1966) 577. F-J. Asdey. JA. Harrison and H.R Tbirsk, Trans. Faraday Sot., 64 (1968) 192. .. 1. Morcos. J. U auoanal. Chem.. 66 (1975).250. F_ Tbomfor and M. Volmer. AM. Physik.. 33 (1938) 109. A. Milchev and S. Stoyanov. 1. Eikctmanal. Ghan. 72 (1976) 33. J.P. Hirth and G.M. Pound, Condensation and Evaporation Nucleation and Growth Kinetics. Pcgamon F’ress. London, 1963. 8 J.H. Hollomon and D. Turnbull. in 8. Chalmas and R King (Eds.). Prop-c+ in Metal Physics. Vol. 4. Pcrgamon Press, London, 1953. 9 G-M. Pound, M-T_ Simnad and L. Yang, J. Chem. Phys.. 22 (1954) 1215. IO J. Lothe and G.M. Pound, J. Chem. Phys.. 36 (1962) 2080.