Electrochemical study of anomalous diffusion and fractal dimension in poly ortho aminophenol electroactive film: Comparative study

Journal of Electroanalytical Chemistry xxx (2013) xxx–xxx

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Electrochemical study of anomalous diffusion and fractal dimension in poly ortho aminophenol electroactive film: Comparative study A. Ehsani a,⇑, M.G. Mahjani b, M. Bordbar a, S. Adeli b a b

Department of Chemistry, Faculty of Science, University of Qom, P.O. Box 37185-359, Qom, Iran Department of Chemistry, Faculty of Science, K.N. Toosi University of Technology, P.O. Box 15875-4416, Tehran, Iran

a r t i c l e

i n f o

Article history: Available online xxxx Keywords: Conducting polymer Diffusion coefficients Fractal Impedance Anomalous

a b s t r a c t The poly ortho aminophenol (POAP) films were electropolymerised on graphite electrode using potentiostatic method. POAP films were also characterized by electrochemical impedance spectroscopy (EIS) in wide frequency range. The fractal dimension of poly ortho aminophenol (POAP) films in the presence of different counter ions was investigated. The effect of different anions on the electron conduction of POAP was explained in terms of their abilities to reduce repulsive interactions between redox sites and fractal dimension of the polymer. Diffusion coefficient of counter ions calculated from the slope of the Warburg line of impedance response of the film. A value of c that is the characteristic of anomalous diffusion is obtained by EIS method and then the relation between fractal dimension and anomalous diffusion has been investigated. The resulting Mott–Schottky plot of the polymer capacitance describes the reduced polymer as a p-type semiconductor. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Conducting polymers such as polypyrrole, polythiophenes or poly aniline represent a group of conjugated p-electron materials which process a combination of various electrical, optical and other semiconductor properties as a organic semiconductors that with respect to electronic energy levels hardly different from organic semiconductors [1]. Aminophenols are interesting members of the class of substituted anilines. The hydroxyl group in the phenyl ring can be oxidized to quinine and quinine can be reduced again. POAP gives a surface film of interesting electrochemical and electrochromic properties when it is electropolymerised in acidic solution [2,3]. The electropolymerisation reaction of OAP is initiated by oxidizing the respective monomer to a radical cation [4,5]. The variety of results for conductivity of the POAP film reported in the literature [6–9] show that the electrochemical response of POAP is strongly influenced by the experimental procedure used to produce the polymer film and the purity of starting monomer. It is well-known that without redox species in solution the charge-transport process of an electrode modified by an electroactive polymer film is affected by ionic transfer at the polymer|electrolyte interface, ionic and electronic charge carrier transport inside the polymer and an electronic transfer at the metal|polymer interface [10]. These processes would only be dependent on the degree of oxidation of the polymer. However, it has also been sug⇑ Corresponding author. Tel.: +98 251 2103038; fax: +98 251 2854973. E-mail address: [email protected] (A. Ehsani).

gested that the external supporting electrolyte contacting the polymer film could be incorporated into the polymer phase [11]. This internal electrolyte phase can play an important role in the charge-transport and charge transfer processes of the polymeric material. Electrochemical impedance spectroscopy (EIS) is one of the most universal and powerful electroanalytical techniques for fine characterization of chemical kinetics and transport process occurring in thin coated and ion insertion electrodes. Boundary conditions have a strong influence on the control of diffusion processes in electrochemical systems. For these systems, with mobile ions, diffusion fluxes implies a Warburg like impedance; this impedance is an x1/2 function

ZðixÞ / ðixÞ1=2

ð1Þ

However, in many cases impedance measurements of diffusive processes give rise to power laws in frequency which deviate more or less from the exact 1/2 exponent law [12]

ZðixÞ / ðixÞc=2

ð0 < c < 2Þ

ð2Þ

where x is the angular frequency of the external electric field. The Warburg-like impedance can be calculated from the Fick diffusion equation for process as with a vanishing relaxation time [1], or from a generalized diffusion equation for processes with a non-vanishing relaxation time [2]. The selective nature of borders and the diffusion length are very important to determine the Warburg impedance from Fick’s equation or from a generalized diffusion equation. Usually, the solutions of these problems are limited only to

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semi-infinite boundary conditions. With vanishing and non-vanishing relaxation time processes [12,13], and, moreover, for finite length diffusion conditions, reflective boundary [14] and transmissive boundary conditions, the latter two only for vanishing relaxation time processes. When anomalous diffusion is considered some properties will be different from the case of normal diffusion. When normal diffusion occurs, dimension of diffusion coefficient D is cm2/s. But in the case of anomalous diffusion the dimension of D will be cm2/sc, where c is the characteristic of anomalous diffusion. Anomaly behavior is related to the unusual dimension of surface geometry, i.e. fractal dimension. Fractal structures are arisen during specific condition of polymerization dynamic and have non-integer dimensions which could be easily calculated [15,16]. The fractal dimension is characteristic of complex structure which effects surface nature. The fractal dimension (Df) is a quantitative parameter for analyses of fractal objects, which is widely used for differentpurposes. In addition, it is one of the most important and useful parameters for analysis of structure of rough surfaces. Fractals have been characterized by several methods that can be classified as physical, chemical and electrochemical [17–19]. The aim of this paper is to present more insight into the processes appearing during oxidation and reduction of a POAP film electrode in different aqueous electrolytes, role of the electrosynthesis parameters (monomer concentration and electrolyte nature) on the kinetics and on the morphology of the POAP and relationship between the fractal dimension of POAP film and diffusion coefficients using electrochemical methods. 2. Experimental The chemicals used in this work were of Merck origin and used without further purification. All electrochemical measurements were carried out in a conventional three electrodes cell, powered by a potentiostat/galvanostat (EG&G 273A) and a frequency response analyzer (EG&G, 1025). The system was run by a PC through M270 and M398 software via a GPIB interface. The frequency range of 100 kHz to 10 mHz and modulation amplitude of 5 mV were employed for impedance studies. POAP films electrodeposited on a graphite rod of 0.2 cm2 area were employed as working electrode. Saturated calomel electrode (SCE) and a platinum wire were used as reference and counter electrodes respectively. The electropolymerization of POAP was performed potentiostatically using 0.1 M aqueous LiClO4 and LiCl solution and different monomer concentrations (1  103, 5  103, 1  102, 2  102, 5  102 and 7  102 M respectively). The electrochemical measurements were carried out in acidic solution (pH = 2) of HClO4, HCl and lithium salt (0.1 M) as supporting electrolyte. The thickness of the deposited film on graphite was estimated from the charge consumed in reducing the polymer (Q) and the molar concentration of electro-active sites in the film, which is obtained by faraday law [3]. For a given Q the molar concentration of electro-active sites in the film and then the mass of deposited polymer was estimated, considering a value of 2 for electron transfer and 109 for ortho aminophenol molecular weight. Assuming a value of 1.33 g cm3 for POAP films density at 25 °C and the geometric area of graphite as 0.2 cm2, the polymer film thickness can easily be calculated. The electrical impedance is calculated without subtracting the uncompensated resistance and the double layer capacitance. Fitting of experimental data to the proposed theoretical models was done by means of homemade and Z-view software. 3. Results and discussion Fig. 1 shows the cyclic voltammogram of POAP film that prepared as described in experimental section (0.01 M OAP) and

Fig. 1. Cyclic voltammograms of POAP films on graphite electrode in presence of (1)  ClO4 and (2) Cl anions.

presenting the influence of the incorporated anions, while voltammograms in Fig. 2 obtained at various potential sweep rates. A pair of peaks signifying polymer’s redox processes is present in all studies. In various scan rates by plotting ipeak vs scan rate in a log–log diagram, we obtain a from the slope of a linear fit to the data. The parameter a is related to the fractal dimension (Df) of the surface through [20].

Ip / ma

a¼

Df  1 2

ð3Þ ð4Þ

Fig. 2b shows ipeak vs scan rate as obtained for the POAP film from cyclic voltammograms given in Fig. 2a. The data points lie on a straight line in the log–log diagram, and the slope gives a of the straight line. Substituting a value in the Eq. (4) we obtain the  fractal dimension of POAP film in the presence of ClO4 and Cl, 2.48 and 2.32 respectively. This results show that the films electrodeposited in the presence of Cl are more compact and present less  surface defects than those deposited in presence of ClO4 . On the other hand, the POAP thin films deposited in the presence of  ClO4 are very thick and present a rough surface compared to the others, that poly (o-toluidine) thin films showed similar counter ions influence [21]. This difference in thickness is in good agreement with the values of the anodic peaks currents in the cyclic voltammograms of Fig. 2. According the Otero and Sansi~nena works [22] we have evaluated the role of the electrosynthesis parameters (monomer concentration and electrolyte nature) on the kinetics and on the morphology of the POAP. For this evaluation, the electrochemical synthesis of POAP was performed potentio statically using 0.1 M aqueous LiClO4 and LiCl solution and different monomer concentrations. The empirical kinetics of the electrosynthesis of the conducting polymer samples, as obtained from electrical parameters, can be written as:

Rp ¼

dQ ¼ k½monomera ½electrolyteb dt

ð5Þ

where Rp is the polymerization rate (the electrical charge consumed during the polymerization per unit of polymerization time), a and b the reactions orders and k is the kinetic constant. From the chronoamperogram obtained during each electropolymerization,

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Fig. 2. (a) Cyclic voltammograms recorded at the sweep rates of 100, 200, 300, 400 and 500 mV/s for a POAP film in the presence of ClO4 anion. (b) Presents the log–log scale  presentation of the peak current vs potential sweep rates for ClO4 doped polymeric films.

the related charges consumed can be obtained. Taking the logarithms of Eq. (5), we have:

log Rp ¼ log

dQ ¼ log k þ a log½monomer þ b log½electrolyte dt

ð6Þ

This equation shows that a plot of log dQ/dt against log [monomer] or log [electrolyte] gives a straight line, the slope of which represents the order of reaction related to the monomer (a) or electrolyte (b) concentration. Indeed, this is the case since the double logarithmic plot of the experimental data (Fig. 3) gives a straight line. This plot allows to obtain the kinetic order a according to Eq. (6):

log Rp ¼ log dQ ¼ 2:42 þ 0:39 ½monomer dt Rp / ½monomer0:39 Fig. 4 shows a plot of log dQ/dt against log [electrolyte]. From the slope of this curve the order of reaction for this electrode can be evaluated (b = 0.56) for POAP–Cl and (b = 0.64) for POAP–ClO4. The difference seems to be related to the nature of the electrode/ electrolyte interfaces. Electrochemical impedance spectroscopy can access relaxation phenomena over many orders of magnitude and has been em-

ployed for the study of the kinetics of the charge-transfer process into and across the electroreactive films [23–25]. The processes occurred in the course of redox transition of film are a combination of electron transfer at the film/solution interface, slow diffusion of interstitial ions in the solid lattice of film, flipping-flopping of ion across the film/solution interface and fast ion transport in the bulk of solution [26,27]. Accordingly, the Faradic current which passes through the film/solution interface is a function of counter ions concentration and the potential at this interface and two potential steps of dE1: through the film and dE2: at the film/solution interface dominate. The electrochemical impedance Zf is calculated as the ratio of potential to current under a small perturbation of potential. Therefore, the Faradaic impedance is:

Zf ¼

dE1 dE2 þ dIf dIf

ð7Þ

and the flux of charged species at the film/solution interface (using the Taylor’s series expansion and Laplace transformation) is [27]:

dJ ion nion ¼ dE2 1 þ fion ½coth½dðjx=Dion Þ0:5 =ðjxDion Þ0:5 

ð8Þ

in this equation:

Fig. 3. Charge vs polarization time for a POAP–ClO4 electrode at different monomer concentration (a) and related double logarithm plot (b). Synthesis solution: 0.1 M LiClO4.

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A. Ehsani et al. / Journal of Electroanalytical Chemistry xxx (2013) xxx–xxx



Fig. 4. Double logarithm plot for a POAP modified electrode at different concentration (0.05, 0.1, 0.25, 0.5 and 0.8 M) of ClO4 anions (a) and Cl anions (b). 1

1

nion ¼ bion ; K 1ion ðC ion  C ion; min Þ  C ion;so ln bion K 1 ð9Þ ion ðC ion; max  C ion Þ h i h i 1 1 0 fion ¼ K 1ion exp bion ðE  E0 Þ K 1 ion exp bion ðE  E Þ C ion;so ln

ð10Þ

where the subscript ion represents the solid-state diffusing ion. d is the mean diffusion length, Dion is the diffusion coefficient of ion through the film, x is the angular frequency of ac the imposed sinup soidal signal, j = 1 and E0 is the formal potential. Also, Cion,min and Cion,max are minimum concentration of the sites occupied by the species in the host film and maximum concentration of the sites available for insertion of ion in the film structure, respectively, Cion,soln is the ion concentration in the bulk of solution, and Cion is the concentration of occupied sites in the film and K 1ion and K 1 ion are the kinetic rate constants of transfers, which are potential dependent. In these equations, n is negative/positive for the insertion/deinsertion of ion. Film of polymer have very thin thickness and therefore, oE1 is negligible in comparison with oE2. So, the equation of Faradaic impedance (Eq. (3)) is reduced to:

dE2 1 Zf ¼ ¼ Fnion dIf

( ) 1 þ ðfion sion cothðjxsion ÞÞ0:5

film. These behaviors were modeled by the dominance of different components in electrical equivalent circuits. The Nyquist diagrams will be better interpreted if constant phase elements (CPEs) were replaced with the pure capacitances in inhomogeneous surface. The impedance of this element is [30]:

Z CPE ¼

1 T 0 ðjxÞn

ð16Þ

which T0 is constant phase element coefficient and n is constant phase element exponent. n is equal to unity for perfect capacitance. Nyquist plot recorded at the dc-potential of 0.15 V in Fig. 5 shows formation of double layer capacitance with charge transfer resistance of anion in the working electrode surface. The slope of the linear tail is higher than a pure Warburg line and lower than a pure capacitance. However, based on Eq. (12), the theoretical impedance response should be a line with a slope of unity followed

ð11Þ

dðjxsion Þ0:5

where sion = d2/Dion is the time constant of the diffusion process. One another approach which can be used to interpret the impedance response is the model of the wave transmission in a finitelength RC transmission line [28] which was used for a porous electrode or an electroreactive film [29]. In this expression, the Faradaic impedance is:

( Z f ¼ Rct þ Z FLW ¼ Rct þ RFLW ctnhð

ðjxRFLW C FLW Þ0:5 ðjxRFLW C FLW Þ

Þ 0:5

) ð12Þ

where Rct is the charge-transfer resistance, RFLW analogizes the resistance of the diffusion of a species through a finite length and CFLW describes the capacitance of the finite space. By comparing Eqs. (11) and (12), it can be deduced that:

sion ¼ RFLW C FLW ¼ d Rct ¼ fion sion RFLW nion ¼

1 FRct

d2 Dion

ð13Þ

ð14Þ

ð15Þ

As the bias of the system is systematically varied, different signatures were observed in the Nyquist diagrams and different processes dominated the electrochemical characteristics of the



Fig. 5. Presentation of the Nyquist plots for POAP films doped with (1) ClO4 and (2) Cl anions, inset; equivalent circuit for the Nyquist plots.

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A. Ehsani et al. / Journal of Electroanalytical Chemistry xxx (2013) xxx–xxx

by a vertical line; open circuit terminus Warburg impedance. Therefore, both parts of impedance curves in Fig. 5 are deviated from the ideal ones. This behavior can be explained in terms of anomalous diffusion [17]: higher slope than unity observed for semi-infinite diffusion when the diffusing species wait after each jump for a period drown from a broad power-law distribution. The effect is that some diffusing species stick for a long time in diffusion path and diffusion becomes slower. The electrical equivalent circuit compatible with the Nyquist diagrams shown in inset Fig. 5. In this circuit, R1, CPE1 and R2 are the solution resistance, a constant phase element describes the double layer capacitance, charge-transfer process of redox couple. Also, Wo is the open circuit terminus Warburg element. Using Eqs. (12) and (13) and the values of the circuit elements, the values of the diffusion coefficient of ions in the film, Dion, were obtained 2.82  1010 cm2 s1 and  1.65  1010 for ClO4 and Cl respectively. As can be seen in Nyquist complex plots for films with different thickness (Fig. 6), higher electron and ion transport rates are obtained for the thicker film (50 nm) as compared with the thinner one (28 nm). This fact can be explained by considering an increase in the degree of porosity of a POAP film with the increase of its thickness, as was demonstrated in [31]. In this regard, while thick POAP films exhibit enough open structures that should allow the incorporation of large amounts of electrolyte, the less porous structure of a thin POAP film should incorporate a lesser amount of solution as compared with that of a thick film. Thus, a higher fraction of charge would be transported by the inner electrolyte incorporated in the tick film as compared with that transported by the inner electrolyte contained in the thin film. Thus, higher amounts of electrolyte incorporated into a thick film as compared with a thin one, would cause a decrease in the resistance of charge transport through it or an increase in the diffusion coefficient values. Then, it could be suggested that the low quantity of electrolyte contained

in a thin polymer film is unable to reduce the electrostatic repulsion between charged redox sites. However, large quantity of electrolyte incorporated into a thick film can shield the redox centers from interaction between them and so the existence of a more compact distribution of these centers, as compared with that present in thin films, thereby increasing the rate of the charge-transport process by intrinsic electron hopping. In this regard, it is  possible that ClO4 anions were more effective than Cl anions to shield the redox centers from interaction between them. In the x vs h Bode plots, there is one peak in the maximum phase angle, i.e. one relaxation process is taking place at the polymer electrolyte interface at different potential values. This process  may be due to diffusion of dopant anions (ClO4 and Cl) in the polymer matrix. The x vs Z Bode plot (Fig. 7) shows that the impedance decreases with increasing the size of dopant anions in the POAP film. This behavior can be explained by the strong bond ing of ClO4 , might be that its size corresponds exactly to the distance between two aminophenol units. On the other hand, the hard and soft acid base concept developed by Pearson [32] appears to be an interesting way for the interpretation of the polymer doping interactions. The large conjugated polymeric chain with highly delocalized positive charges can be considered as a soft acid. The best-fitted dopant should be a soft base, in which a charge delocalization can occur. The geometry and softness of this anion, when compared to Cl have been put forward to interpret this result.  The radius of ClO4 anions are larger than the other anion carrying a highly delocalized charge [33]. More than by the size of the anion the electrochemical behavior and the charge transport within the polymer is thus determined by the shape and by the electronic characteristics of the dopant anion [32]. It may be concluded that polarons, which are involved in the electronic conduction, are the  most localized by ClO4 anion and are consequently the less mobile here. From the fractal model of the polymer/electrolyte interface, the fractal dimension (Df) can be calculated from the following equation [3].

Df ¼

1 þ1 n

ð17Þ

where (n) value derived from Eq. (16). Df calculatedwith impedance data is good agreement with CV results and shown in Table 1. The Fractal dimension Df is related to surface roughness and when Df = 2 the surface is completely smooth, but when Df = 3 the surface is completely rough and amorphous. So with increasing



Fig. 6. Presentation of the Nyquist plots for POAP films doped with ClO4 anions in different film thickness, 28 nm and 50 nm.



Fig. 7. Bode plot for POAP films polarized in 0.1 M aqueous solution of (a) ClO4 and (b) Cl at 0.15 V.

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Table 1 presentation of the diffusion coefficients, charge carrier density, flat band potential, c and fractal dimensions for different anions in POAP films modified graphite electrodes. Anion  ClO4 

Cl

Efb (mV) 227 220

N (cm3) 19

4.54  10 2.32  1019

Df (CV)

Df (EIS)

c

Di (cm2/s)

2.35 2.23

2.39 2.26

0.68 0.74

2.82  1010 1.65  1010

Df from 2 to 3 the roughness of surface increases. Film roughness shows a surface pattern which is characterized by Df. On the other hand surface dimensions deviates from Euclidean pattern and particles diffuse through fractal object by abnormal transport, i.e. anomalous diffusion. Consequently it can be concluded that there exist a relation between fractal dimension and anomalous diffusion coefficient. According to presented discussion, occurrence of anomalous diffusion is determined by parameter c which is the characteristic of anomalous diffusion. The values of c for diffusing the particles through the polymer film can be found with fitting of EIS data at low frequencies (which is related to diffusion process) with following equation [34,35]:

ZðsÞ ¼ Rwxdc1 ðxd=sÞ1c=2 coth½ðs=xd Þc=2 

ð18Þ

In which Rw is a constant and s = ix and x is frequency. In impedance plots xd is a frequency at which an impedance pattern change is observed, that between the Warburg-like response at high frequencies and the capacitive behavior at lower ones. In terms of diffusive transport, this characteristic frequency signals the time needed to charge completely the whole film. To fitting data using MATLAB software, the real and imaginary part of Eq. (12) must be derived according to Euler’s formula (eix = cos x + i sin x) and Taylor expansion of coth(x):

Z Re ¼ Rw xc1 cos

p 2

ðc  1Þ



Z im e ¼ Rw xcd x1 þ 1=3Rw xc1 sin

ð19Þ p 2

ðc  1Þ



ð20Þ

The values of c in presence of different anions obtained from fitting of EIS data with Eqs. (19) and (20) are presented in Table 1. When c = 1 the Nyquist diagram at low frequencies is a straight line parallel to the vertical axis (the slope is infinity). In this case, diffusion is normal. When c < 1 the slope of the Nyquist diagram at low frequencies will be lower than infinity (lower than 90°) and the straight line tends to right side and in this state anomalous diffusion occurs. With decreasing c from 1 to 0.5 the slope of the Nyquist diagram at low frequencies will decrease and so anomalous diffusion will increase. According to values of c found in Table 1 with decreasing of Df, the value of c tends to 1 and diffusion process tends to normal diffusion. Increment of Df shows increment of surface roughness. That means with increment of roughness, trapping of diffusing particles in the holes increases and they spend more time than usual to diffuse through the film and so anomalous diffusion increases. According to the our previous works [3,19,36], the behavior of space charge capacitance vs E (potential) dependence and the observed capacitance values were typical of a thin film semiconductor electrode and suggest the formation of space charge or depletion region within the polymer film. This conclusion is consistent with numerous result of other author who demonstrated the formation of a space charge region (SCR) on conducting polymer modified electrodes. At the negative potentials, the space charge region extends over whole film. As the potential drops across the SCR decrease, its thickness becomes smaller than the film thick-

Fig. 8. Dependence of C 2 sc on dc applied potential, for POAP films polarized in 0.1 M  aqueous solution of (a) ClO4 , (b) Cl.

ness, and a quasi-neutral region is formed and the electrode capacitance increases. The dependence of the electrode capacitance on the potential in the simplest case is given by the Mott–Schottky equation [35]:

C 2 ¼

  KT E  Efb  e ee0 eNA 2

2

ð21Þ

where C is the space charge capacitance, e is the dielectric constant of the polymer, e0 is the permittivity of free space, e is the elementary charge, k is Boltzmann’s constant, T is the absolute temperature, N is the carrier density that set up the space charge, (E  Efb) is the absolute value of the potential drop across the SCR. The flat band potential Efb is the potential at which the thickness of the SCR is zero. From Eq. (18) it follow that C2 vs E line are known as Mott–Schottky plots. Fig. 8 presents the C2 vs E dependences for the POAP film in the presence of different counter ions, that obtained from Nyquist plots of films in different offset potential. One can see that each curve has a linear portion that can be described by the Mott–Schottky law to a first approximation. Extrapolating these linear portions, we can estimate the values of the flat band potential of film in presence of different anions. The values of the carrier density in two cases can be also obtained and presented in Table 1. Furthermore, the negative slopes of Mott–Schottky plots of them show that we can categorize them as p-type semiconductors that space charge is established by counter anions. In this case, polarons or bipolarons act as holes in ordinary semiconductors.

4. Conclusions This work concludes that the electrodeposited POAP film by using potentiostatic method in a graphite electrode is fractal object with semiconductor properties. The fractal dimension derived from the cyclic voltammetry and impedance spectroscopy. Fractal dimension and anomalous diffusion parameter c are thoroughly interconnected. The effect of different anions on the electron conduction of POAP was explained in terms of their abilities to reduce repulsive interactions between redox sites and fractal dimension of the polymer. It was found that diffusion constants depend not only on the type of anion present in the electrolyte but also on the film thickness, fractal dimension and electrolyte concentration. With regard to the type of anion, at fixed film thickness and electrolyte concentration ionic diffusion coefficients are lower in the presence  of Cl anions as compared with those in the presence of ClO4 anions.

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Acknowledgements We gratefully acknowledge the support of this work by Qom University and K.N. Toosi University of Technology Research Council.

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