The fractal dimension of the surface, Ds, of thin columnar gold electrodeposits (surface roughness factor 50–100) grown on gold wire cathodes by electroreducing hydrous gold oxide layers has been determined by measuring the diffusion controlled current of the Fe(CN)4−6/Fe(CN)3−6 reaction. The diffusion current (I) vs. time (t) relationships obeyed a Iαt−α dependence with Ds = 2α + 1. The initial Ds, value is 2.5 ± 0.1, and decreases to 2.3 ± 0.1 by keeping the deposit in contact with the electrolyte solution at 298 K due to the smoothing of the rough metal surface by surface diffusion.Instituto de Investigaciones Fisicoquímicas Teóricas y AplicadasFacultad de Ciencias Exacta

Arvia, Alejandro Jorge

Herrasti, Pilar

Ocon, Pilar

Salvarezza, Roberto Carlos

Vara, J. M.

Vazquez, Luis

Journal of Electroanalytical Chemistry

English

SEDICI - Repositorio de la UNLP

101 
J. Electroanal. Chem., 319 (1991) 101-110 
Elsevier Sequoia S.A., Lausanne 
JEC 01755 
Fractal characterisation of electrodispersed gold electrodes 
P. Ocon a, P. Herrasti a, L. Vdzquez b, R.C. Salvarezza l+, J.M. Vara a 
and A.J. Arvia ’ 
a Departamento de Quimica Fisica Aplicada, C-II, Universidad Autbnoma de Madrid, 28049 Madrid 
(Spain) 
b Institute de Ciencias de Materiales, Sede B CSIC Departamento de Fisica Aplicada, C-XII, Consejo 
Superior de Investigaciones Cienti$cas, Universidad Authnoma de Madrid, 28049 Madrid (Spain) 
’ INIFTA, Universidad National de La Plats, Sucursal4, Casilla de Correo 16, 1900 La Plata (Argentina) 
(Received 14 June 1991) 
Abstract 
The fractal dimension of the surface, D,, of thin columnar gold electrodeposits (surface roughness 
factor 50-100) grown on gold wire cathodes by electroreducing hydrous gold oxide layers has been 
determined by measuring the diffusion controlled current of the Fe(CN)t- /Fe(CN)z- reaction. The 
diffusion current (II vs. time (t) relationships obeyed a I a t-” dependence with D, = 2a + 1. The 
initial D, value is 2.5 fO.l, and decreases to 2.3 rtO.1 by keeping the deposit in contact with the 
electrolyte solution at 298 K due to the smoothing of the rough metal surface by surface diffusion. 
INTRODUCTION 
Surface disorder and random roughness can play a determining role in many 
physical and chemical properties of surfaces and interfaces [l]. Highly dispersed 
metals used in heterogeneous catalysis and electrocatalysis exhibit extremely rough 
and irregular surfaces which can be characterised by using fractal geometry [2]. 
The demonstration of fractal geometry and the determination of the fractal 
dimension for real systems i difficult as the fractal behaviour does not extend over 
all lengths and the experimental methods are also limited to a certain range of 
scale lengths [2]. As the structure of thin metal films comprises nanometre-sized 
particles, a method based on scanning tunnelling microscopy @TM) has been 
recently developed to distinguish the fractal nature of solid materials in the 
’ Permanent address: INIFI’A, La Plata, Argentina. 
0022-0728/92/$05.00  1992 - Elsevier Sequoia S.A. All rights reserved 
102 
nanometre range [3]. This method was used to characterise the surface of thin 
columnar gold films grown from the electroreduction of oxide layers accumulated 
on gold wire cathodes [4] and to determine the fractal dimension of the specimen 
surface, 0, [5]. 
In this paper a macroscopic method was employed to estimate the fractal 
dimension of the gold electrodeposits based on the diffusion to a fractal surface 
[6]. The present method confirms the fractal nature of the deposit surface and the 
influence of the slow reorganisation processes at the surface of the deposit 
immersed in the electrolyte solution on the value of 0,. A good correlation 
between the present results and those recently reported by using the STM method 
is obtained. 
EXPERIMENTAL 
Columnar structured gold deposits were prepared by electroreducing hydrous 
gold oxide (hereafter denoted as gold oxide) grown on polycrystalline gold wire 
electrodes (length = 0.2 cm, radius = 0.05 cm> placed in a conventional three-com- 
partment electrochemical cell containing 0.5 M H,SO, at 298 K [4]. The gold 
oxide layer was accumulated by anodising the gold electrode at 2.6 V vs. the 
standard hydrogen electrode (SHE) for a time 1,. By changing t,, the amount of 
the gold oxide can be varied conveniently so that films with average thicknesses 
ranging between 10 and 1000 nm can be produced. Subsequently, the gold oxide 
layer was electroreduced by applying a potential scan from 1.64 V to 0.34 V at 0.02 
V s-l. Under these experimental conditions, a columnar-type gold electrodeposit 
is grown on the gold substrate [7]. The surface area and the roughness factor, R, of 
these deposits was evaluated through voltammetry by using the O-electrodesorp- 
tion charge and taking the 0-electrodesorption monolayer charge density equal to 
0.420 mC cmm2 for a polycrystalline gold electrode [8]. 
Slow reorganisation processes at the rough columnar gold films were detected 
by keeping them during lo5 s at open circuit in 0.5 M H,SO, solution at 298 K. 
For these specimens, a decrease in the electrodeposit area can be observed, i.e. the 
value of the surface area changed from 8 cm2 to 1 cm2 after lo4 s [7,9]. This effect 
is due to the increase in grain size in order to decrease the surface Gibbs energy of 
the entire system [91. 
Conventional voltammetry and potentiostatic urrent transient measurements in 
the diffusion-controlled regime were performed in a three-compartment electro- 
chemical cell. The electrolyte solution was 5 mM K,[Fe(CN),] + 5 mM K,[Fe(CN),] 
in 0.5 M NaNO, [lo]. Occasionally 10 mM NaCN was also added to the electrolyte 
solution to check the influence of the CN- ion, but in this concentration range the 
latter did not cause any effect on the current transients. The latter were run by 
stepping the potential from 0.5 V to 1.1 V (SHE) and recording the current with a 
Tektronix digital oscilloscope. 
STM measurements were made using a piezo tube STM microscope operating 
in air. Pt tips cut from a 0.2 mm diameter wire were used. STM measurements 
103 
were run at 1-2 nA con$tant tunnel current, and 0.1 V tunnel voltage (tip positive). 
The STM data were acquired with a fully automated workstation and stored as 
binary files with, typically, 256 X 2.56 pixels. STM imaging was complemented with 
conventional scanning electron microscope (SEMI observations. 
RESUL,TS 
Let us first consider the structure of gold electrodeposits resulting from STM 
and SEM imaging. The STM gray scale topographies of recently prepared gold 
electrodeposits obtained at different magnifications are shown in Fig. 1. Small 
rounded grains with sizes ranging between 10 and 20 nm are clearly observed at 
Fig. 1. STM images of a gold electrodeposit (R = 50); (a) 0.3x0.3 ~ttt; (b) 1 xl ,um. Cc) SEM 
micrograph of the same gold electrodeposit. The bar indicates 1 pm. 
Fig. 2. SEM micrograph of the cross-section of a gold electrodeposit (R = 80). The bar indicates 1 pm. 
the higher resolutions (Fig. la). These grains, which correspond to the top of the 
columnar elements of the film, cannot be resolved clearly by SEM (Fig. 1~). 
However, ramified self-similar voids are observed at all length scales, indicating 
the fractal nature of the gold electrodeposit surfaces. The cross-section of the 
electrodeposits (Fig. 2) shows that the film itself is constituted by elongated grains 
with sizes ranging between 500 and 3000 mrr. These features are consistent with a 
columnar-like structure [71. The latter are better described as a self-affine rather 
than a self-similar fractal [11,12]. It should be noted that the intersection of a 
plane with a self-affine surface generates elf-similar lakes or islands [5,13]. 
Typical voltammograms run at 0.01 V s- ’ for a smooth gold wire (R = 1.1) and 
for a gold electrodeposit (t, = 2 min, R = 50) exhibit the pair of conjugated current 
peaks and the diffusional limiting currents related to the [Fe(CN)J4-/[Fe(CN),]3- 
redox couple (Fig. 3). The diffusional current is similar at both the smooth and the 
rough electrode surfaces, indicating that the microscopic structure of the rough 
electrode is not seen by the electroactive species. For the rough electrode the 
voltammogram becomes broader El41 as the scan rate increases from 0.01 V s-l to 
OS v s-l. 
Diffusion-controlled current transients for the IFe(CNI,14-* [Fe(CN),13-+ e- 
reaction (Fig. 4a) were obtained by employing a smooth gold wire (R = 1.11, a gold 
electrodeposit grown on the gold wire (R = 501, and the same electrodeposit after 
105 
Q 
E 
-c!O4_ 
O- 
-QO4- 
-#3_ 
I t 
0.2 a4 06 08 1.0 12 
E/V 
Fig. 3. Voltammograms of the [Fe(CN),14-/[Fe(CN),13- redox couple on gold electrodes in the base 
solution at 0.01 V s-l. Dashed line, R = 1.1, and full line R = 50. 
it has been “aged” at open circuit in 0.5 M H,SO, for 2 X lo5 s (R = 3). These 
results which are displayed as log I vs. log t plots (Fig. 4a) exhibit for the smooth 
gold wire a linear response within the time scale of the experiments with a slope 
cy = + 0.50 rlr 0.05. On the other hand, the same plots for the recently prepared and 
for the “aged” gold electrodeposits how a linear behaviour with (Y = 0.72 f 0.05 
and 0.61 rt: 0.05, respectively, extending from t = 4 x 10V3 s to fC = 0.04 s. The 
value of t, is the time from which the experimental points deviate from the slope 
(Y. 
Similar experiments made using a gold electrodeposit with R = 100 (t, = 5 min) 
and after keeping the same electrodeposit in the electrolyte for t = 8 x lo4 s 
(R = 20) and for t = 2 X 10’ s (R = 20) yield LY = 0.76 + 0.05, a = 0.62 + 0.05 and 
(Y = 0.66 rt 0.05, respectively (Fig. 4b). This means that LY remains constant for 
t > 1 x lo5 s. Besides, for these rough electrodeposits, the deviations observed in 
the linear log I vs. log t plots move towards large t values. 
DISCUSSION 
For a non-stationa~ electrochemical reaction under diffusion control the diffu- 
sion layer thickness increases with time and the concentration gradient for the 
diffusing species decreases. When the process involves a soluble reacting species in 
solution diffusing under semi-infinite linear conditions towards a planar electrode, 
106 
T 
-l 
c "4o - - 
- 
1.00 - 
z 
-I 
0.60 - 
0.20 - 
-0.20 - 
-0.60 
a 
-1.00 I / I I , I I / , I I I , 
-3.00 -2.20 -1.40 -0.60 
m (t/s) 
107 
the non-stationary diffusion-controlled current is given by the Cottrell equation 
[lo]: 
z = nFc( D/?rsrt)0.5 (1) 
where c and D are the bulk concentration and the diffusion coefficient of the 
electroactive species, and it and F have the usual meaning. 
A different situation arises for the case of diffusion towards fractal surfaces. 
This problem has been studied extensively from both theoretical and experimental 
viewpoints [6,15]. In this case, the time dependence of the diffusion current 
becomes more complex, involving a Z a tP relationship for t < t, and the fulfil- 
ment of eqn. (l), i.e. la t-0.5, for t > t,. The value of t, is related to the size of 
the largest irregularities, A, at rough surfaces by [El: 
A2 = Dt, (2) 
where D is the diffusion coefficient of the electroactive species. From eqn. (2), 
taking D = 5 x 10m6 cm2 s- ’ (estimated from the slope of a Z vs. t- ‘I2 linear plot 
for the smooth gold wire), and A z 3 X 10m4 cm (Fig. 2) the Z vs. tpu behaviour is 
expected for t < 0.03 s. The relation between LY and the fractal dimension of the 
electrode surface, D,, is given by [10,15]: 
D,=2a+l (3) 
From eqn. (3) and the (Y values shown in Fig. 4 one obtains D, = 2.0 + 0.1 for the 
smooth gold wire, D, = 2.5 k 0.1 for the gold electrodeposits and D, = 2.3 f 0.1 for 
electrodeposits which have been “aged” in contact with the electrolyte. The values 
of D, are practically independent of R within t-0.1, at least when R is changed 
between 50 and 100. The difference between the values of D, of recently prepared 
electrodeposits and those obtained for the same electrodes after “ageing” in the 
electrolyte is related to the slow reorganisation phenomena occurring at the metal 
surface [7,9]. In the present case the slow reorganisation process can be followed 
through the decrease in the D, value up to about lo5 s. For t > lo5 s, the D, value 
remains close to 2.3 f 0.1. It should be noted that for a cauliflower platinum 
electrode the diffusion-controlled current measurements give D, = 2.46 [lo] in 
good agreement with the D, value obtained in the present work for recently 
prepared gold electrodes. For platinum electrodeposits D, is practically time 
independent [3] as its surface diffusion coefficient in the electrolyte at 25°C is 
lower than that reported for gold 191. 
Fig. 4. (a) Log I vs. log t for different gold electrodes: (*) smooth gold wire (R = 1.11, a = OSOkO.05; 
(a) gold electrodeposit (R = 501, a= 0.72kO.05; (0) gold electrodeposit after “ageing” in 0.5 M 
H,SO, for t = 10’ s (R = 31, (Y = 0.61 rtO.05. (b) Log I vs. log t for different gold electrodes: (A) gold 
electrodeposit (R = NO), a = 0.76 f 0.05; (01 gold electrodeposit after “ageing” in 0.5 M H,SO, for 
t = 8x lo4 s (R = 201, a = 0.62f0.05; (x) gold electrodeposit after “ageing” in 0.5 M H,SO, for 
t=2x105 s(R=20), a=0.66+0.05. 
108 
TABLE 1 
Values of D, for different electrodeposits 
Diffusion-controlled reaction 
measurements 
DS 
Gold eiectrodeposits 
At=50 2.4 
R=80 
R=lOO 2.5 
“Aged” gold electrodeposits 
R-3 2.2 
R = 10 
R = 20 2.2-2.0 
Platinum electrodeposits 
R=? 2.46 (ref. 10) 
R=80 
“Aged” platinum electrodeposits 
R=68 
STM method 
(ref. 3) 
4 
2.5 
2.3 
2.5 
2.5 
The values of 0, derived for gold electrodeposits from the diffusion-controlled 
current transients agree with those recently determined by the ex-situ STM 
technique [3] (Table 1). This coincidence is particularly significant in justifying 
some assumptions implied in the STM method used to obtain the fractal dimen- 
sion of rough surfaces. In this method Q is estimated from I),, the fractal 
dimension of the perimeter of either lakes or islands generated by the intersection 
(b) 
@ 
3.5 - 
2.0 I , 1 2.5 3.0 35 4.0 45 5.0 5 
log,* [area /nm'l 
Fig. 5. (a) Pattern of lakes generated by STM image processing for a gold electrodeposit (R = 80). (b) 
Log P vs. log A plot for the pattern depicted in (a). The value of L)p resulting from (b) is 1.5. From ref. 
3. 
109 
of a plane with the fractal surface. A plot of log P (perimeter) vs. log A (area) for 
the lakes or islands is made to obtain the value of D, [5,13] (Fig. 5). The latter is 
related to 4 by the following equation: 
4=Llp+ 1 C-3 
although there are exceptions to eqn. (4) [Sl. Besides, as the STM provides 
information at the nanometre scale, a large number of STM images has to be 
processed to obtain a representative Q value. Tberefore, the present results allow 
us to conclude that both methods are equally efficient for the determination of the 
fractal dimension of electrodeposited metal surfaces such as gold and platinum 
(Table 1). 
Finally, it should be noted that Q = 2.5 would be consistent with a random 
columnar growth process controlled by electric or ~ncentration fields 121. 
CONCLUSIONS 
The fractal dimension of the surface of gold eIectrode~sits has been deter- 
mined from diffusion~controlled current transient measurements of the 
[Fe(CN),14-/[Fe(CN),13- reaction. The results confirm the fractai nature of the 
surface of gold electrodeposits grown far from the equilibrium conditions. The 
influence of the surface diffusion of metal atoms producing a smoothing of the 
surface reflects in the decrease of the value of the fractal dimension of the surfaces 
in contact with the electrolyte solution. The present results also demonstrate the 
validity of the assumption made in the determination of the fractal dimension of 
rough metal surfaces by STM image processing. 
A fellowship from the Comision Interministerial de Ciencia y Tecnologia 
(Spain) and the Consejo National de Investigaciones Cientificas y TCcnicas 
(Argentina) to R.C.S. is gratefully acknowledged. Financial support for this work 
was obtained from project ~TS9-02~ CICYT (Spain). 
REFERENCES 
G.A. Somotjai, Chemistry in Two Dimensions: Surfaces, Cornell University Press, Ithaca, NY, 1981, 
P. Meakin in D. Avnir (Ed.), The Fractai Approach to Heterogeneous Chemistry, John Wiley & 
Sons, New York, 1989. 
J.M. Gomez-Rodriguez, L. V&quez, A.M. Barb, C. Alonso, R.C. Salvarezza, J.M. Vara and A.J. 
Arvia, J. Phys. Chem., in press. 
A. Chialvo, W.E. Triaca and A.J. Arvia, J. Electroanal Chem., 171 (1988 303. 
B.B. Mandelb~t, The Fractal Geometry of Nature, Freeman, San Francisco, CA, 1977. 
S. Havhn in D. Avnir (Ed.), The Fractal Approach to Heterogeneous Chemistry, John Wiley 6t 
Sons, New York, 1989. 
110 
7 L. Vbzquez, A. Bartolome, A.M. Barb, C. Alonso, R.C. Salvarezza and A.J. Arvia, Surf. Sci., 215 
(1989) 171. 
8 S. Trasatti and O.A. Petrii, Real Surface Area Measurements in Electrochemistry, J. Pure Appl. 
Chem., 67 (1991) 711. 
9 C. Alonso, R.C. Salvarezza, J.M. Vara, A.J. Arvia, L. Vazquez, A. Bartolome and A.M. Barb, J. 
Electrochem. Sot., 137 (1990) 2161. 
10 T. Pajkossy, J. Electroanal. Chem., 30 (1991) 1. 
11 P. Meakin, J. Phys. A, 20 (1987) L1113. 
12 A. Family and T. Vicsek, J. Phys. A, 18 (1985) L75. 
13 J. Feder, Fractals, Plenum Press, New York, 1988. 
14 T. Pajkossy and L. Nyikos, Electrochim. Acta, 34 (1989) 181. 
15 T. Pajkossy and L. Nyikos, Electrochim. Acta, 34 (1989) 171. 


Fractal characterisation of electrodispersed gold electrodes

http://sedici.unlp.edu.ar/bitstream/handle/10915/87026/Documento_completo.pdf?sequence=1

Fractal characterisation of electrodispersed gold electrodes

Abstract

Similar works

Full text

Available Versions

SEDICI - Repositorio de la UNLP