- Email: [email protected]
A study of the fractal dimensions of the electrodeposited poly-ortho-aminophenol films in presence of different anions
Synthetic Metals 108 Ž2000. 15–19 www.elsevier.comrlocatersynmet
A study of the fractal dimensions of the electrodeposited poly-ortho-aminophenol films in presence of different anions F. Gobal b
a,)
, K. Malek a , M.G. Mahjani b, M. Jafarian b, V. Safarnavadeh
b
a Department of Chemistry, Sharif UniÕersity of Technology, PO Box 11365-9516, Tehran, Iran Department of Chemistry, K.N. Toosi UniÕersity of Technology, PO Box 15875-4416, Tehran, Iran
Accepted 9 August 1999
Abstract Fractal dimensions of the electrodeposited poly-ortho-aminophenol ŽPOAP. films formed in the presence of Cly, SO42y, NOy 3 and ClO4y anions are investigated by the methods of electrochemical impedance spectroscopy and cyclic voltammetry. In the former, the extent of the ‘‘squashedness’’ of the semi-circle in the Nyquist plots and in the latter the slope of maxima of the diffusion current vs. the potential sweep rates in the logarithmic scale are used. The fractal dimensions in the 2.33–2.46 range are obtained and good agreement exists between the findings of the two methods. The length scale, the distances between two nearest points that the anions somehow sense ˚ range. q 2000 Elsevier Žby a yardstick of the size of their jump-lengths., were also derived and were found to be in the 1.4–11.7 A Science S.A. All rights reserved. Keywords: Fractal dimensions; Electrodeposited poly-ortho-aminophenol films; Anions
1. Introduction Conductive polymers can find applications ranging from electrochemical sensors w1x to solar cell w2x to usage in the electrochemical energy convertersw3x etc. Perhaps the most efficient method of the preparation of these materials is through the application of the electrochemical methods w4x. Under such conditions, the anions incorporated in the positively charged polymer for charge compensation, influence the growth rate, the morphology of the polymeric film, and the speed and extent of the electrochemical responses w5x. The surface morphology is one of the most important characteristics of these materials, and although its effect on the film’s conductivity have been studied w6x, the quantitative treatment of this problem can be further advanced by the availability of fractal theory and its methods w7x. Fractal structures have non-integer dimensions, and recently, many researchers have described the fractal nature of solid surfaces w8x. The fractal concepts have also been employed to describe the surface properties of polymeric films w9,10x. Electrochemical methods of cyclic voltammetry ŽCV. and impedance spectroscopy
)
Corresponding author. E-mail: [email protected]
ŽEIS. have been used to determine the fractal dimensions of the polymer surfaces formed by the electrochemical methods w11x. The fractal dimension of an electrochemically deposited polymeric film, Df , can be found by the analysis of the impedance–frequency Ž Z vs. v . dependence of the interface through Z Ž v . s R q B Ž jv . Df s Ž n q 1 . rn
yn
Ž 1. Ž 2.
where Eq. Ž1. is the electrical characteristic of a so called constant phase element ŽCPE. with j s Žy1.1r2 , n - 1 and B is a constant signifying the capacitive nature of the interface w12x. The relation between the fractal dimension and the exponent n ŽEq. Ž2.. has been found to be valid in some, but not all systems studied so far w13x. On the other hand, Stromme et al. w14x and others w15x have demonstrated that the exponent a , called fractal parameter that is the negative of the order of the current in a Riemann–Lioville transform w16x is related to fractal dimension through
a s Ž Df y 1 . r2
Ž 3.
where a can be obtained from the slope of the voltage sweep rate dependency of the peak current in a log–log scale w17x.
0379-6779r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 9 - 6 7 7 9 Ž 9 9 . 0 0 1 7 1 - X
16
F. Gobal et al.r Synthetic Metals 108 (2000) 15–19
The purpose of the present work is to determine the fractal dimensions of anions doped poly-ortho-aminophenol films by the methods of EIS and CV. Correlations are sought between the size of the anions, the length scales and the yardstick for scaling of the fractal surfaces and the fractal dimensions of the surfaces.
2. Experimental O-Aminophenol, hydrochloric, sulfuric, perchloric and nitric acids used in this work were all of Analar grade of Merck origin and were used without further purification. All solutions were prepared in doubly distilled water. Electropolymerization and subsequent electrochemical studies were carried out in a conventional three electrode cell with a glassy carbon electrode having an exposed circular area of 0.1 cm2 was employed as the working electrodeŽWE. and its potential monitored against a standard calomel electrode ŽSCE.. A large platinum plate formed the counter electrode. The cell was powered by an EG & G electrochemical system comprising of a 273 A potentiostatrgalvanostat and a SI 1255 Solartron frequency response analyzer with the entire system run by an IBM psrvaluepoint PC through M270 and M398 commercial softwares.
3. Results and discussion The poly-ortho-aminophenol ŽPOAP. film was deposited on a glassy carbon working electrode in the acidic media and in presence of different anions. POAP film was prepared through the anodic oxidation of a 0.1 M monomer solution in acidic media onto a glassy carbon electrode by cycling the potential between y0.2 to 0.90 VrSCE. The resultant film covered electrodes was subsequently washed and transferred to a monomer free solution for electrochemical studies. The film thickness as measured by the amount of charge passed through the process of the film formation was around 0.1 mm. A typical voltammogram presenting the influence of the incorporated anions is shown in Fig. 1, while the inset presents the typical voltammograms obtained at various potential sweep rates. A pair of peaks signifying polymer’s redox processes are present in all studies. Following the formalism developed by Stromme et al. w17x, the cathodic peak currents against the potential sweep rates in the log–log scale are presented in Fig. 2. Interestingly enough, the criteria is independent of the solution’s resistance compared to the use of peak’s separations for the evaluation of the film’s fractal dimension which is sensitive to the solution’s resistance w14x. Using the slopes, a ’s in the Eq. Ž3., the fractal dimensions of the polymeric films are obtained. In the presence of
Fig. 1. Cyclic voltammograms of POAP films in the presence of different anions. The inset presents the cyclic voltammograms recorded at the indicated sweep rates for a POAP film in the presence of NOy 3 anion.
F. Gobal et al.r Synthetic Metals 108 (2000) 15–19
Fig. 2. Log–log scale presentation of the plots of the peak currents vs. potential sweep rates for variously anion doped polymeric films; ŽI. 2 . y ClO4y, ŽII. SO4y , ŽIII. NOy 3 IV Cl .
y ClO4y, SO42y, NOy the fractal dimensions of the 3 and Cl films were obtained to be 2.46, 2.46, 2.46 and 2.32, respectively. The fractal dimension in the presence of Cly differs from the others. To shed light on the physical significance of the values of Df ’s, diffusion layer widths as a yardstick is employed to estimate the length scales traversed Ž‘‘seen’’. on the surface at the condition of the maximum current by the anions Žwhich are assumed to be involved in drawing currents.. According to the Fick’s first law, the diffusion-limited current is proportional to the magnitude of the concentration gradient of the electroactive species. Accordingly, the width of the diffusion layer, D X, is:
D X s zFADC bri peak
17
From the results summarized in Table 1, it can be concluded that the distances sensed in the presence of ˚ range and the different anions varies in the 11.7–2.98 A possible outer cutoff of the fractal region investigated by the peak current method occurs at the length scales larger ˚ than 11.7 A. The impedance spectroscopy of POAP films doped with Žprepared in presence of. different anions was studied in the frequency range of 100 KHz to 1 mHz and typical results are presented in Fig. 3 in the form of Nyquist plots. Plots consist of a small semicircle terminated to a large one at the low frequency end of the spectrum. The inset in Fig. 3 shows the equivalent circuit compatible with the results and the values of the circuit elements are obtained using Boukamp equivalent circuit software w19x. The parallel combination of charge transfer resistance R 1 and constant phase element CPE 1 accounts for the injection of electrons from the conductive polymer to the back metallic contact. R 2 and CPE 2 represent the injection of anions into the polymer matrix. In cases, a Warburge element have to be included into the circuit to account for the mass transfer effects which appears as a straight line in the low frequency end of the Nyquist plots and gives rise to a large magnitude for R 2 . However, when R 2 is finite, larger semicircle instead of a straight line, n can be obtained and using Eq. Ž2., the fractal dimensions can be derived and are 2.45, 2.43, 2.41 and 2.33 for ClO4y, SO42y, NOy 3 and Cly, respectively. These values correspond to the values of n being 0.70, 0.69, 0.71 and 0.76 for the corresponding anions, respectively. To determine the length scales used in the fractal scaling, Eq. Ž5. relating the electrode capacitance, Ce , film resistance, R and frequency of measurement, f to the length scale l is employed w20x.
Ž 4.
where C b is the difference between bulk concentration of the anions inside the polymeric film and that of its surface at time t Žwhere the peak current is reached.. The value of D, diffusion coefficient, can be estimated, using the Randles–Sevcik equation w18x. Table 1 presents the width of the diffusion layer and diffusion coefficient of selected anions.
l s 1r Ž 2p fCe R .
Ž 5.
The results are presented in Table 2. In this equation, the capacitance, Ce at the frequency of f is obtained from the impedance studies where the software provides plots of C vs. log f. The choice of the frequency domains are made on the basis of the changes of the slopes in the
Table 1 Presentation of the diffusion coefficients and diffusion layer thickness for different anions a: Slow scan. b: Fast scan. Anion
a S0y2 4 ClO4y NOy 3 y Cl
˚. Diffusion layer thickness ŽA
D Žcm2 sy1 . b y13
2.4 = 10 6.5 = 10y13 6.8 = 10y13 5.8 = 10y13
y13
8.1 = 10 7.4 = 10y13 8.0 = 10y13 6.6 = 10y13
a
b
3.18 10.70 11.32 11.72
2.98 3.02 3.05 3.90
F. Gobal et al.r Synthetic Metals 108 (2000) 15–19
18
Fig. 3. Presentation of the Nyquist plots for POAP films doped with various anions. The inset presents the equivalent circuit compatible with the results.
˚ Bode-Z diagrams. The length scale in the 1.43–7.3 A range have been found. There is a partial overlap of the results obtained by these two vastly different methods. The results can be explained on the basis of distinction between outer and inner cutoffs in the polymer felt Žsensed. in the presence of different anions as signified by the fractal dimensions obtained by the methods of cyclic voltammetry and impedance spectroscopy. As seen from the data presented in Table 1, inner cutoff for anions y y decreases in the direction of SO42y- NOy 3 - ClO4 - Cl ; y hence, the scaling yardstick in presence of Cl is larger than the others. Obviously, the morphology of films are the same and the choice of the yardsticks and innerŽouter. cutoffs controlled by the choice of anions and effective diffusion coefficients set the observed Žapparent. morphology as signified by the fractal dimensions. For anions giving rise to larger fractal dimensions Žthus smaller yardstick. we have small outer cutoff limits and so in this case inner cutoff scale in two directions, perpendicular and along the surface of the film is the same or at least not very different and a self-similar fractal is concluded. In other words, in this case, we have no region at a distance from the working electrode Žpolymeric film surface. that is larger than the outer lateral cutoff. That is, in presence of Table 2 Length scales and cutoff frequency region for different anions Anion
˚. Length scale ŽA
Frequency cutoff region
SO4y2 ClO4y NOy 3 y
1.4–5.3 1.6–5.8 1.8–6.1 2.3–7.3
50 kHz–100 Hz 10 kHz–30 Hz 100 kHz–1 Hz 1 kHz–100 Hz
Cl
these anions the polymeric surface is sensed as bumpy in plane as perpendicular to the surface. On the other hand in presence of Cly with its smaller size the bumpiness of the film along the surface is sensed to be different from that perpendicular to the surface and the anion has different chances of moving along or perpendicular to the surface. Thus in presence of Cly a self-affine surface is detected. The fractal dimensions derived from the impedance measurements also depend on the measuring scale and as the length scales in the two methods of measurements overlap, the fractal dimensions come out almost the same.
4. Conclusion This work concludes that the electrodeposited POAP film is a fractal object. The fractal dimensions derived from the cyclic voltammetric and impedance spectroscopic measurements do indeed coincide. The smaller fractal dimension sensed in presence of Cly has origins in its smaller size and has the consequence of providing larger yardstick for scaling of the surface. Thus, the fractal surface is sensed self affine by Cly ion while it is felt self similar by ClO4y, SO42y and NOy 3 anions.
References w1x M.D. Imiside, R. John, P.J. Riley, G.G. Wallace, J. Electroanal. Chem. 300 Ž1991. 879. w2x N. Arsalanti, K.E. Geckeler, J. Pract. Chem. 337 Ž1995. 1. w3x Electrochim. Acta, Special issue, 40, 1995. w4x M.G. Mahjani, F. Gobal, M. Jafarian, Indian J. Chem. 36A Ž1997. 177.
F. Gobal et al.r Synthetic Metals 108 (2000) 15–19 w5x M.M. Musiani, Electrochim. Acta 35 Ž1990. 1665. w6x M.L. Marcos, I. Rodriguez, J. Gonzalez-Velasco, Electrochim. Acta 32 Ž1987. 1435. w7x B.B. Mandelbrot, in: Fractal Geometry of Nature, Freeman, San Francisco, 1983. w8x L.A. Zooke, J. Leddy, J. Phys. Chem. B, 1998, 10013. w9x K. Aoki, J. Phys. Chem. 95 Ž1991. 9037. w10x K. Aoki, J. Theor. Biol. 141 Ž1989. 11. w11x R.W. Murray, A.G. Ewing, R.D. Durst, Anal. Chem. 59 Ž1987. 379A, and references cited therein. w12x R. de Levie, Electrochim. Acta 10 Ž1965. 113. w13x T. Pajkossy, J. Electroanal. Chem. 300 Ž1991. 1.
19
w14x M. Stromme, G.A. Niklasson, C.G. Granqvist, Solid State Commun. 96 Ž1995. 151. w15x T. Pajkossy, L. Nyikos, Electrochim. Acta 34 Ž1989. 181. w16x K.B. Oldham, J. Spanier, in: Fractional Calculus, Academic Press, New York, 1974. w17x M. Stromme, G.A. Niklasson, C.G. Granqvist, Phys. Rev. B 52 Ž1995. 14192. w18x A.J. Bard, L.R. Faulkner, in: Electrochemical Methods; Fundamentals and Applications, Wiley, New York, 1980. w19x B.A. Boukamp, in: Equivalent Circuit User Manual, TH Twente, 1989. w20x T. Pajkossy, J. Electroanal. Chem. 364 Ž1994. 111.
A study of the fractal dimensions of the electrodeposited poly-ortho-aminophenol films in presence of different anions F. Gobal b
a,)
, K. Malek a , M.G. Mahjani b, M. Jafarian b, V. Safarnavadeh
b
a Department of Chemistry, Sharif UniÕersity of Technology, PO Box 11365-9516, Tehran, Iran Department of Chemistry, K.N. Toosi UniÕersity of Technology, PO Box 15875-4416, Tehran, Iran
Accepted 9 August 1999
Abstract Fractal dimensions of the electrodeposited poly-ortho-aminophenol ŽPOAP. films formed in the presence of Cly, SO42y, NOy 3 and ClO4y anions are investigated by the methods of electrochemical impedance spectroscopy and cyclic voltammetry. In the former, the extent of the ‘‘squashedness’’ of the semi-circle in the Nyquist plots and in the latter the slope of maxima of the diffusion current vs. the potential sweep rates in the logarithmic scale are used. The fractal dimensions in the 2.33–2.46 range are obtained and good agreement exists between the findings of the two methods. The length scale, the distances between two nearest points that the anions somehow sense ˚ range. q 2000 Elsevier Žby a yardstick of the size of their jump-lengths., were also derived and were found to be in the 1.4–11.7 A Science S.A. All rights reserved. Keywords: Fractal dimensions; Electrodeposited poly-ortho-aminophenol films; Anions
1. Introduction Conductive polymers can find applications ranging from electrochemical sensors w1x to solar cell w2x to usage in the electrochemical energy convertersw3x etc. Perhaps the most efficient method of the preparation of these materials is through the application of the electrochemical methods w4x. Under such conditions, the anions incorporated in the positively charged polymer for charge compensation, influence the growth rate, the morphology of the polymeric film, and the speed and extent of the electrochemical responses w5x. The surface morphology is one of the most important characteristics of these materials, and although its effect on the film’s conductivity have been studied w6x, the quantitative treatment of this problem can be further advanced by the availability of fractal theory and its methods w7x. Fractal structures have non-integer dimensions, and recently, many researchers have described the fractal nature of solid surfaces w8x. The fractal concepts have also been employed to describe the surface properties of polymeric films w9,10x. Electrochemical methods of cyclic voltammetry ŽCV. and impedance spectroscopy
)
Corresponding author. E-mail: [email protected]
ŽEIS. have been used to determine the fractal dimensions of the polymer surfaces formed by the electrochemical methods w11x. The fractal dimension of an electrochemically deposited polymeric film, Df , can be found by the analysis of the impedance–frequency Ž Z vs. v . dependence of the interface through Z Ž v . s R q B Ž jv . Df s Ž n q 1 . rn
yn
Ž 1. Ž 2.
where Eq. Ž1. is the electrical characteristic of a so called constant phase element ŽCPE. with j s Žy1.1r2 , n - 1 and B is a constant signifying the capacitive nature of the interface w12x. The relation between the fractal dimension and the exponent n ŽEq. Ž2.. has been found to be valid in some, but not all systems studied so far w13x. On the other hand, Stromme et al. w14x and others w15x have demonstrated that the exponent a , called fractal parameter that is the negative of the order of the current in a Riemann–Lioville transform w16x is related to fractal dimension through
a s Ž Df y 1 . r2
Ž 3.
where a can be obtained from the slope of the voltage sweep rate dependency of the peak current in a log–log scale w17x.
0379-6779r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 9 - 6 7 7 9 Ž 9 9 . 0 0 1 7 1 - X
16
F. Gobal et al.r Synthetic Metals 108 (2000) 15–19
The purpose of the present work is to determine the fractal dimensions of anions doped poly-ortho-aminophenol films by the methods of EIS and CV. Correlations are sought between the size of the anions, the length scales and the yardstick for scaling of the fractal surfaces and the fractal dimensions of the surfaces.
2. Experimental O-Aminophenol, hydrochloric, sulfuric, perchloric and nitric acids used in this work were all of Analar grade of Merck origin and were used without further purification. All solutions were prepared in doubly distilled water. Electropolymerization and subsequent electrochemical studies were carried out in a conventional three electrode cell with a glassy carbon electrode having an exposed circular area of 0.1 cm2 was employed as the working electrodeŽWE. and its potential monitored against a standard calomel electrode ŽSCE.. A large platinum plate formed the counter electrode. The cell was powered by an EG & G electrochemical system comprising of a 273 A potentiostatrgalvanostat and a SI 1255 Solartron frequency response analyzer with the entire system run by an IBM psrvaluepoint PC through M270 and M398 commercial softwares.
3. Results and discussion The poly-ortho-aminophenol ŽPOAP. film was deposited on a glassy carbon working electrode in the acidic media and in presence of different anions. POAP film was prepared through the anodic oxidation of a 0.1 M monomer solution in acidic media onto a glassy carbon electrode by cycling the potential between y0.2 to 0.90 VrSCE. The resultant film covered electrodes was subsequently washed and transferred to a monomer free solution for electrochemical studies. The film thickness as measured by the amount of charge passed through the process of the film formation was around 0.1 mm. A typical voltammogram presenting the influence of the incorporated anions is shown in Fig. 1, while the inset presents the typical voltammograms obtained at various potential sweep rates. A pair of peaks signifying polymer’s redox processes are present in all studies. Following the formalism developed by Stromme et al. w17x, the cathodic peak currents against the potential sweep rates in the log–log scale are presented in Fig. 2. Interestingly enough, the criteria is independent of the solution’s resistance compared to the use of peak’s separations for the evaluation of the film’s fractal dimension which is sensitive to the solution’s resistance w14x. Using the slopes, a ’s in the Eq. Ž3., the fractal dimensions of the polymeric films are obtained. In the presence of
Fig. 1. Cyclic voltammograms of POAP films in the presence of different anions. The inset presents the cyclic voltammograms recorded at the indicated sweep rates for a POAP film in the presence of NOy 3 anion.
F. Gobal et al.r Synthetic Metals 108 (2000) 15–19
Fig. 2. Log–log scale presentation of the plots of the peak currents vs. potential sweep rates for variously anion doped polymeric films; ŽI. 2 . y ClO4y, ŽII. SO4y , ŽIII. NOy 3 IV Cl .
y ClO4y, SO42y, NOy the fractal dimensions of the 3 and Cl films were obtained to be 2.46, 2.46, 2.46 and 2.32, respectively. The fractal dimension in the presence of Cly differs from the others. To shed light on the physical significance of the values of Df ’s, diffusion layer widths as a yardstick is employed to estimate the length scales traversed Ž‘‘seen’’. on the surface at the condition of the maximum current by the anions Žwhich are assumed to be involved in drawing currents.. According to the Fick’s first law, the diffusion-limited current is proportional to the magnitude of the concentration gradient of the electroactive species. Accordingly, the width of the diffusion layer, D X, is:
D X s zFADC bri peak
17
From the results summarized in Table 1, it can be concluded that the distances sensed in the presence of ˚ range and the different anions varies in the 11.7–2.98 A possible outer cutoff of the fractal region investigated by the peak current method occurs at the length scales larger ˚ than 11.7 A. The impedance spectroscopy of POAP films doped with Žprepared in presence of. different anions was studied in the frequency range of 100 KHz to 1 mHz and typical results are presented in Fig. 3 in the form of Nyquist plots. Plots consist of a small semicircle terminated to a large one at the low frequency end of the spectrum. The inset in Fig. 3 shows the equivalent circuit compatible with the results and the values of the circuit elements are obtained using Boukamp equivalent circuit software w19x. The parallel combination of charge transfer resistance R 1 and constant phase element CPE 1 accounts for the injection of electrons from the conductive polymer to the back metallic contact. R 2 and CPE 2 represent the injection of anions into the polymer matrix. In cases, a Warburge element have to be included into the circuit to account for the mass transfer effects which appears as a straight line in the low frequency end of the Nyquist plots and gives rise to a large magnitude for R 2 . However, when R 2 is finite, larger semicircle instead of a straight line, n can be obtained and using Eq. Ž2., the fractal dimensions can be derived and are 2.45, 2.43, 2.41 and 2.33 for ClO4y, SO42y, NOy 3 and Cly, respectively. These values correspond to the values of n being 0.70, 0.69, 0.71 and 0.76 for the corresponding anions, respectively. To determine the length scales used in the fractal scaling, Eq. Ž5. relating the electrode capacitance, Ce , film resistance, R and frequency of measurement, f to the length scale l is employed w20x.
Ž 4.
where C b is the difference between bulk concentration of the anions inside the polymeric film and that of its surface at time t Žwhere the peak current is reached.. The value of D, diffusion coefficient, can be estimated, using the Randles–Sevcik equation w18x. Table 1 presents the width of the diffusion layer and diffusion coefficient of selected anions.
l s 1r Ž 2p fCe R .
Ž 5.
The results are presented in Table 2. In this equation, the capacitance, Ce at the frequency of f is obtained from the impedance studies where the software provides plots of C vs. log f. The choice of the frequency domains are made on the basis of the changes of the slopes in the
Table 1 Presentation of the diffusion coefficients and diffusion layer thickness for different anions a: Slow scan. b: Fast scan. Anion
a S0y2 4 ClO4y NOy 3 y Cl
˚. Diffusion layer thickness ŽA
D Žcm2 sy1 . b y13
2.4 = 10 6.5 = 10y13 6.8 = 10y13 5.8 = 10y13
y13
8.1 = 10 7.4 = 10y13 8.0 = 10y13 6.6 = 10y13
a
b
3.18 10.70 11.32 11.72
2.98 3.02 3.05 3.90
F. Gobal et al.r Synthetic Metals 108 (2000) 15–19
18
Fig. 3. Presentation of the Nyquist plots for POAP films doped with various anions. The inset presents the equivalent circuit compatible with the results.
˚ Bode-Z diagrams. The length scale in the 1.43–7.3 A range have been found. There is a partial overlap of the results obtained by these two vastly different methods. The results can be explained on the basis of distinction between outer and inner cutoffs in the polymer felt Žsensed. in the presence of different anions as signified by the fractal dimensions obtained by the methods of cyclic voltammetry and impedance spectroscopy. As seen from the data presented in Table 1, inner cutoff for anions y y decreases in the direction of SO42y- NOy 3 - ClO4 - Cl ; y hence, the scaling yardstick in presence of Cl is larger than the others. Obviously, the morphology of films are the same and the choice of the yardsticks and innerŽouter. cutoffs controlled by the choice of anions and effective diffusion coefficients set the observed Žapparent. morphology as signified by the fractal dimensions. For anions giving rise to larger fractal dimensions Žthus smaller yardstick. we have small outer cutoff limits and so in this case inner cutoff scale in two directions, perpendicular and along the surface of the film is the same or at least not very different and a self-similar fractal is concluded. In other words, in this case, we have no region at a distance from the working electrode Žpolymeric film surface. that is larger than the outer lateral cutoff. That is, in presence of Table 2 Length scales and cutoff frequency region for different anions Anion
˚. Length scale ŽA
Frequency cutoff region
SO4y2 ClO4y NOy 3 y
1.4–5.3 1.6–5.8 1.8–6.1 2.3–7.3
50 kHz–100 Hz 10 kHz–30 Hz 100 kHz–1 Hz 1 kHz–100 Hz
Cl
these anions the polymeric surface is sensed as bumpy in plane as perpendicular to the surface. On the other hand in presence of Cly with its smaller size the bumpiness of the film along the surface is sensed to be different from that perpendicular to the surface and the anion has different chances of moving along or perpendicular to the surface. Thus in presence of Cly a self-affine surface is detected. The fractal dimensions derived from the impedance measurements also depend on the measuring scale and as the length scales in the two methods of measurements overlap, the fractal dimensions come out almost the same.
4. Conclusion This work concludes that the electrodeposited POAP film is a fractal object. The fractal dimensions derived from the cyclic voltammetric and impedance spectroscopic measurements do indeed coincide. The smaller fractal dimension sensed in presence of Cly has origins in its smaller size and has the consequence of providing larger yardstick for scaling of the surface. Thus, the fractal surface is sensed self affine by Cly ion while it is felt self similar by ClO4y, SO42y and NOy 3 anions.
References w1x M.D. Imiside, R. John, P.J. Riley, G.G. Wallace, J. Electroanal. Chem. 300 Ž1991. 879. w2x N. Arsalanti, K.E. Geckeler, J. Pract. Chem. 337 Ž1995. 1. w3x Electrochim. Acta, Special issue, 40, 1995. w4x M.G. Mahjani, F. Gobal, M. Jafarian, Indian J. Chem. 36A Ž1997. 177.
F. Gobal et al.r Synthetic Metals 108 (2000) 15–19 w5x M.M. Musiani, Electrochim. Acta 35 Ž1990. 1665. w6x M.L. Marcos, I. Rodriguez, J. Gonzalez-Velasco, Electrochim. Acta 32 Ž1987. 1435. w7x B.B. Mandelbrot, in: Fractal Geometry of Nature, Freeman, San Francisco, 1983. w8x L.A. Zooke, J. Leddy, J. Phys. Chem. B, 1998, 10013. w9x K. Aoki, J. Phys. Chem. 95 Ž1991. 9037. w10x K. Aoki, J. Theor. Biol. 141 Ž1989. 11. w11x R.W. Murray, A.G. Ewing, R.D. Durst, Anal. Chem. 59 Ž1987. 379A, and references cited therein. w12x R. de Levie, Electrochim. Acta 10 Ž1965. 113. w13x T. Pajkossy, J. Electroanal. Chem. 300 Ž1991. 1.
19
w14x M. Stromme, G.A. Niklasson, C.G. Granqvist, Solid State Commun. 96 Ž1995. 151. w15x T. Pajkossy, L. Nyikos, Electrochim. Acta 34 Ž1989. 181. w16x K.B. Oldham, J. Spanier, in: Fractional Calculus, Academic Press, New York, 1974. w17x M. Stromme, G.A. Niklasson, C.G. Granqvist, Phys. Rev. B 52 Ž1995. 14192. w18x A.J. Bard, L.R. Faulkner, in: Electrochemical Methods; Fundamentals and Applications, Wiley, New York, 1980. w19x B.A. Boukamp, in: Equivalent Circuit User Manual, TH Twente, 1989. w20x T. Pajkossy, J. Electroanal. Chem. 364 Ž1994. 111.