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Determination of the morphology of surface groups formed and PVDF-binder materials dispersed on graphite composite electrodes in terms of fractal geometry
Journal of Electroanalytical Chemistry 556 (2003) 75 /82 www.elsevier.com/locate/jelechem
Determination of the morphology of surface groups formed and PVDF-binder materials dispersed on graphite composite electrodes in terms of fractal geometry Seung-Bok Lee, Su-Il Pyun 1,* Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, 373-1 Guseong-Dong, Yuseong-Gu, Daejeon 305-701, Republic of Korea Received 14 December 2002; received in revised form 5 April 2003; accepted 25 April 2003
Abstract Morphological structures of surface groups formed and poly-vinylidene fluoride (PVDF)-binder materials dispersed on the PVDF-bonded graphite composite electrode were investigated in terms of fractal geometry using cyclic voltammetry combined with Kelvin probe force microscopy (KFM). When a fractal surface has single fractal geometry consisting of binder materials only, the overall fractal dimension was determined to be 1.82 from cyclic voltammetry based upon the peak current /scan rate relation, which is just the same in value as the individual fractal dimension of binder materials determined from KFM based upon the perimeter / area relation. By contrast, when a fractal surface has multifractal geometry composed of surface groups and binder materials, the overall fractal dimension was determined to be 1.77 from cyclic voltammetry. But the individual fractal dimensions were determined from KFM to distinguish the fractal dimension (1.70) of surface groups from that fractal dimension (1.82) of binder materials. The overall fractal dimension determined from cyclic voltammetry is just the average of the two individual fractal dimensions determined from KFM. # 2003 Elsevier B.V. All rights reserved. Keywords: Fractal dimension; Composite electrode; Surface groups; KFM; Perimeter /area relation
1. Introduction Poly-vinylidene fluoride (PVDF)-bonded graphite composite electrodes have been used as anode materials for secondary lithium batteries [1,2] because of the good safety and excellent lithium charge/discharge cycle life. The composite electrode is generally composed of graphite powder as the electrode material and PVDF as the binder material. Moreover, the surface of the graphite powder can be divided into an active graphite surface free of surface groups and an inactive graphite surface covered with surface groups. Therefore, the surface of the composite electrode can be classified into three types: active graphite surface, inactive gra-
* Corresponding author. Tel.: /82-42-869-3319; fax: /82-42-8693310. E-mail address: [email protected] (S.-I. Pyun). 1 ISE member. 0022-0728/03/$ - see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-0728(03)00331-0
phite surface, and dead graphite surface covered with binder materials. However, because the surface group layer usually extends at most to one or two monolayer thickness, and binder materials are non-uniformly distributed over the electrode surface, the surface morphology of the composite electrode has not been clearly established by conventional analytical methods such as atomic force microscopy (AFM) and scanning electron microscopy until now. One of the most powerful techniques for the analysis of the surface morphology of the electrodes is so-called Kelvin probe force microscopy (KFM) which is based upon the well-known Kelvin probe technique [3,4] and provides information on the lateral distribution of the surface potential on a microscopic scale. The surface potential corresponds to the potential difference between the sample specimen and a conducting probe that is positioned close to the sample surface. Since this value correlates with the difference in the work functions of
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the probe and the sample, the surface of the specimen in potential can be characterised using this technique. Fractal analysis has become a new and powerful tool to describe the geometric and structural properties of fractal surfaces, particle boundaries and pore structures, since their complex patterns are better described in terms of fractal geometry as long as the requirement of self-similarity is satisfied [5,6]. The latter term implies that the geometrical features of an object are independent of the magnification or observation scale. In the fractal description the most important parameter is the fractal dimension Df which is defined as the exponent that relates the mass M of an object to its size r M 8rDf
(1)
In this work, we analysed the morphology of surface groups formed and binder materials dispersed over the composite electrodes by employing the fractal concept. For this purpose, the cyclic voltammograms (CVs) were first measured to determine the overall fractal dimension of multifractal geometry composed of surface groups and binder materials by means of electrochemical methods. Then the 3D KFM images were obtained experimentally, and they were cross-sectioned by planes with constant surface potential in height into the 2D KFM images to visualise the morphology of surface groups and binder materials. Finally, the individual fractal dimensions of surface groups and binder materials were determined from the 2D KFM images based upon the perimeter /area relation to compare with that overall fractal dimension determined from the CV based upon the peak current /scan rate relation.
ified SLX50 graphite powder with 10 wt.% PVDF as a binder in n -methyl pyrrolidone solution, followed by pasting on Cu foil and drying in a vacuum oven at 110 8C for 8 h [8 /12]. 2.2. Electrochemical experiments including cyclic voltammetry A three-electrode electrochemical cell was employed for the electrochemical measurement. The PVDFbonded graphite composite electrode specimen was used as a working electrode. The Pt wire and saturated calomel electrode (SCE) were used as a counter electrode and a reference electrode, respectively. A solution containing 0.01 M K4[Fe(CN)6] and 0.1 M Na2SO4 was used as the electrolyte. The CVs were obtained from the electrode with various scan rates of 2 /104 mV s 1 in the potential range of /0.4 /0.6 VSCE using a potentiostat/ galvanostat (EG&G Model 263A). 2.3. KFM measurements KFM measurements were performed with an SPA 4000 STM/AFM system (Seiko Instruments) equipped with a KFM controller (Seiko Instruments) using commercial gold-coated silicon cantilevers. The resonance frequency f and spring constant C are given as 27 kHz and 1.6 N m 1, respectively. An a.c. bias voltage of 2 V at a frequency of 5 kHz was applied between the probe and sample. KFM images of the sample surface were acquired at a probe scan rate of 0.3 Hz. More detailed descriptions of the KFM technique can be found elsewhere [13,14].
2. Experimental 2.1. Preparation of two types of PVDF-bonded SLX50 graphite electrode specimens It was reported [7] that the amount of surface groups formed on the graphite surface increases with heattreatment temperature and it reaches a maximum around 400 8C. At higher temperature, the surface group is oxidized into gaseous species (CO and CO2) and the amount of surface groups becomes nearly zero above 1500 8C. As-received SLX50 graphite powder obtained from Timcal Co., Switzerland, surely has almost no surface groups since it was synthesized above 2500 8C under a reduction atmosphere. The as-received SLX50 graphite powder was heat-treated at 300 8C for 3 h under an air atmosphere to give a large amount of surface groups, and we designated this heat-treated powder the surface-modified SLX50 graphite powder. The PVDF-bonded graphite composite electrode specimens were manufactured by mixing either the asreceived SLX50 graphite powder or the surface-mod-
3. Results and discussion Fig. 1 illustrates the CVs obtained from the PVDFbonded SLX50 graphite composite electrode at various potential scan rates in 0.01 M K4[Fe(CN)6]/0.1 M Na2SO4 solution. The CV clearly showed one set of welldefined current peaks. These current peaks are assigned to a redox couple as follows: [Fe(CN)6 ]3 e [Fe(CN)6 ]4
(2)
Fig. 2(a and b) give on a logarithmic scale the variations of peak currents of CVs obtained from the PVDF-bonded composite electrodes made from the asreceived SLX50 graphite and from the surface-modified SLX50 graphite, respectively, as a function of the potential scan rate. The peak currents of CVs in Fig. 2(a and b) were linearly proportional to the scan rate with slopes of 0.410 and 0.387, respectively, within the potential scan rate range no to ni mV s 1, but the relation between the peak currents and the scan rates
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Fig. 1. The CVs obtained from the PVDF-bonded SLX50 composite electrode at various scan rates in 0.01 M K4[Fe(CN)6]/0.1 M Na2SO4 solution.
deviates strongly from linearity outside the scan rate range. It is noted that when the recorded cyclic voltammetric current is limited by diffusion of the electroactive species to and away from the electrode surface, the fractal dimension Df of the reaction sites on the surface can be obtained by the following relation between the peak currents and the scan rates [15,16], Ipeak 8n(Df 1)=2
(3)
where, Ipeak is the peak current, n is the scan rate, and Df represents the fractal dimension. From Eq. (3) the fractal dimensions of the composite electrode made from the as-received SLX50 graphite and the surfacemodified SLX50 graphite were determined to be 1.82 and 1.77, respectively. The distribution of the sites where the electroactive species undergo reduction and oxidation carries extensive information about the surface geometry. A dimension of two would be obtained from the CVs measured on a perfectly flat and electrochemically active electrode, and a dimension of 1.585 would be obtained from an electrode whose surface was a Sierpinski gasket [17 /20]. The Sierpinski gasket is generated as follows: an initiator is a filled triangle. In each application of the generator, the generator eliminates a central triangle and the filled triangle is replaced by three triangles that have been scaled down by the factor of 1/2. An infinite
number of generations of the prefractals leave a fractal curve. Considering that surface groups and PVDF-binder materials on the surface of the composite electrodes can act as inactive sites or dead sites for electrochemical reactions, and at the same time the peak currents of CVs on a logarithmic scale were found to be linearly proportional to the scan rates with a slope lower than 0.5, it is reasonable to say that the lowered fractal dimension than 2.0 of the composite electrodes was evidence that surface groups are formed and PVDFbinder materials are simultaneously dispersed over the surface of the composite electrodes having self-similar properties. In other words, the morphology of surface groups formed and PVDF-binder materials dispersed gives the fractal dimension of the electrochemically active area. Moreover, when determining Df using diffusion-controlled electrochemistry, the diffusion layer length acts as a yardstick length, and it was derived as follows: Dx
zFADc Ipeak
(4)
where Dx is the diffusion layer length; z , the number of electrons transferred per electroactive species in the redox reaction (in our case z /1); F , Faraday constant; A , the exposed surface area of the working electrode; D ,
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materials. However, it was reported [18] that, if both active sites and inactive sites co-exist on the electrode, and both sites have truly isotropic and fractal properties, i.e. self-similar fractal properties, the individual fractal dimensions of the active site and inactive site are determined to be the same in value. Thus, the fractal dimension determined from the CVs can inherently represent the fractal dimension of surface groups and binder materials as well as the fractal dimension of the electrochemically active site. Fig. 3(a and b) present KFM images obtained from the PVDF-bonded composite made from the as-received SLX50 graphite and from the surface-modified SLX50 graphite, respectively. The surface potential profiles
Fig. 2. The variations of peak currents of CVs obtained from the PVDF-bonded composite electrodes made from (a) the as-received SLX50 graphite and from (b) the surface-modified SLX50 graphite as a function of the potential scan rate.
diffusivity of the electroactive species; c represents the bulk concentration of the electroactive species. Using Eq. (4) we can determine the inner cut-off range in Fig. 2(a and b) at the faster threshold scan of the scan rate ni as values of 4.5 and 2.3 mm, respectively, and outer cutoff range in Fig. 2(a and b) at the slower threshold scan rate no as values of 76 and 29 mm, respectively. Since the electrochemical reactions take place, as a matter of fact, only at electrochemically active sites on the composite electrode surface, at first sight it might seem that the fractal dimension determined from the CVs would not give the fractal dimension associated with surface groups and binder materials, but it would give only the fractal dimension for electrochemically active site which is free of surface groups and binder
Fig. 3. The KFM images obtained from the PVDF-bonded composite made from (a) the as-received SLX50 graphite and from (b) the surface-modified SLX50 graphite.
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(Fig. 3(a)) of the composite electrode made from the asreceived SLX50 graphite showed a smooth surface with a small number of broad peaks, but the potential profiles (Fig. 3(b)) of the composite electrode made from the surface-modified SLX50 graphite revealed a rough surface which is composed of many sharp peaks with lower surface potential and some broad peaks with higher surface potential. It should be noted that the surface-modified SLX50 graphite contains a large amount of surface groups as well as PVDF-binder materials, but the as-received SLX50 graphite is considered to contain only PVDFbinder materials. Moreover, the surface potential of the surface covered with PVDF-binder materials is much higher than the potential of the surface covered with surface groups. Thus, we can assign the broad peaks with higher surface potential in the KFM images to PVDF-binder materials and the sharp peaks with lower surface potential to surface groups on the composite electrode. In order to visualise the real morphology of surface groups and PVDF-binder materials, we cross-sectioned the 3D KFM images of Fig. 3(a and b) by planes with constant surface potential in height into the 2D KFM images. Fig. 4(a) gives a 2D image obtained by crosssectioning the 3D KFM image of Fig. 3(a) by the plane with the value corresponding to 50% of the maximum height of the surface potential. Fig. 4(b and c) present the 2D images obtained by cross-sectioning the 3D KFM image of Fig. 3(b) by the planes with height values corresponding to 80 and 50% of the maximum surface potential, respectively. It should be noted that we have already borne out that the 2D image obtained by cross-sectioning the 3D KFM image of Fig. 3(a) with 50% of the maximum height value (Fig. 4(a)) was very similar to that 2D image obtained by cross-sectioning the 3D KFM image of Fig. 3(a) with 80% of the maximum height value. This showed that since surface groups were absent from the as-received SLX50 graphite, the morphology given by the 2D description did not change with the height of the cross-sectioning plane. Thus, in the case of the surface group-free as-received graphite composite electrode, the 2D image given in Fig. 4(a) represents the single morphology of PVDF-binder materials only dispersed over the composite electrode. By contrast, it was realised from Fig. 4(b and c) that the 2D image obtained by cross-sectioning Fig. 3(b) with 80% of the maximum height value was significantly different from the 2D image obtained by cross-sectioning Fig. 3(b) with 50% of the maximum height value. Considering the surface potential difference between the surface covered with surface groups and that covered with PVDF-binder materials, it is most probable that in the case of the surface-modified graphite composite electrode, the 2D image given in Fig. 4(b) represents the
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single morphology of PVDF-binder materials only dispersed over the composite electrode. However, the 2D image shown in Fig. 4(c) represents the multimorphology composed of surface groups formed and PVDF-binder materials dispersed over the composite electrode. Now we determined the fractal dimension from the cross-sectioned 2D image based upon the perimeter P and area A relation. It was reported that perimeter P and area A for self-similar shaped objects are related by [20] P aDf ADf =2
(5)
where a is a constant. Fig. 5(a /c) demonstrate the dependence of perimeter P on area A determined from Fig. 4(a /c), respectively. The P /A plots gave good linear relations above the threshold area AT :/1 /10 13 m2. It is noted that another linear relation below AT :/ 1 /10 13 m2 is physically meaningless due to the limitations of the KFM measurement. It should be stressed that the value of the slope (0.906) of the P /A plot in Fig. 5(a) determined from Fig. 4(a) coincides fairly well with that of the slope (0.916) of Fig. 5(b) determined from Fig. 4(b) which is considered to represent the single morphology of PVDF-binder materials only. This means that the fractal dimension (1.81) of PVDF-binder materials dispersed over the as-received SLX50 graphite composite electrode is in good agreement in value with that fractal dimension (1.83) of PVDF-binder materials dispersed over the surfacemodified SLX50 graphite composite electrode. This is caused by the same electrode preparation conditions, i.e. the same mixing speed, time and temperature, used in this work. Moreover, it was realised that the value of the fractal dimension (1.82) determined using cyclic voltammetry based upon the peak current /scan rate relation, from the surface group-free graphite composite electrode coincides fairly well with those values (1.81 and 1.83) determined using KFM based upon the perimeter / area relation, from the surface group-free graphite composite electrode. It is noted that the fractal dimension of 1.81 and 1.83 were determined by means of the image analysis of the 2D KFM images given in Fig. 4(a and b) which represent the single morphology of PVDF-binder materials only, and at the same time the fractal dimension of 1.82 is determined from the CVs measured on the composite electrode which contains PVDF-binder materials only. Therefore, in this work, we regarded the above three fractal dimensions as the fractal dimensions measured under single fractal geometry condition. From the coincidence among the fractal dimensions determined, it was realised that when a fractal surface has single fractal geometry containing binder materials only, the fractal dimension for binder materials determined
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Fig. 4. (a) Cross-sectional view of the 3D KFM image of Fig. 3(a) for the as-received SLX50 graphite by cross-sectioning by the plane with 50% of the maximum height of the surface potential; (b) cross-sectional view of the 3D KFM image of Fig. 3(b) for the surface-modified SLX50 graphite by cross-sectioning with 80% of the maximum height of the surface potential; (c) cross-sectional view of the 3D KFM image of Fig. 3(b) by crosssectioning with 50% of the maximum height of the surface potential.
from cyclic voltammetry is just the same in value as the fractal dimension determined from KFM. Now we discuss about the fractal dimension of surface groups formed on the composite electrode. In contrary to the case of PVDF-binder materials, surface groups can not be formed on the composite electrode alone, since binder materials are inevitable component for the composite electrode. Therefore, the composite electrode containing surface groups should always provide multi-morphology composed of surface groups and PVDF-binder materials.
The P /A plot of Fig. 5(c) clearly gives two straight lines with different slopes above the threshold area AT :/10 13 m2, which means that the multi-morphology gives multifractal geometry satisfying the self-similar condition. The slopes of the two straight lines are determined to be 0.912 and 0.852, which correspond to the fractal dimensions of 1.82 and 1.70, respectively. Surprisingly, one of the fractal dimensions, the higher value of 1.82, coincides exactly with the fractal dimension of PVDF-binder materials. Then, it is most probable that the other of the fractal dimensions, the lower
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This means that when a fractal surface has multifractal geometry composed of surface groups and PVDF-binder materials, it is possible to make a distinction between the multifractal islands composed of surface groups and binder materials with the help of KFM image analysis. The individual fractal dimensions of surface groups and binder materials were readily determined from the ratio of perimeter to area of their respective islands which can be estimated from the number of corresponding pixels in the 2D KFM images. In contrast, when a fractal surface has multifractal geometry, the diffusing electroactive ions do not sense distinctively from each other, surface groups and binder materials, but they sense the overall fractal geometry of the inactive site as well as the active site in cyclic voltammetry. Fig. 2(b) measured on the surface-modified graphite specimen showed that the peak current / scan rate relation gives a single straight line with a slope of 0.387, indicating an overall fractal dimension of 1.77. When a fractal surface has multifractal geometry, the overall fractal dimension determined from cyclic voltammetry correlates to the individual fractal dimensions of Df,1 and Df,2 determined from KFM by the following summation rule [18] P B1 ADf;1 =2 B2 ADf;2 =2
(6)
In this equation the total perimeter length is expressed as the sum of two terms, in which B1 and B2 are constants. Using Eq. (6), the overall fractal dimension was calculated as a value of 1.76, which is just the average of the two individual fractal dimensions (1.70 and 1.82). It is interesting to note that the overall fractal dimension determined from the CVs (1.77) coincides fairly well in value with the averaged fractal dimension (1.76) calculated from the KFM images.
4. Conclusions
Fig. 5. The dependence of perimeters on areas (a) obtained from the 2D image of Fig. 4(a); (b) obtained from the 2D image of Fig. 4(b); (c) obtained from the 2D image of Fig. 4(c).
value of 1.70, reveals the fractal dimension of surface groups formed on the surface-modified SLX50 graphite composite electrode.
In the present work, the morphological structures of surface groups and PVDF-binder materials have been investigated in terms of fractal geometry. The following conclusions can be drawn from the experimental results and theoretical consideration. (1) The overall fractal dimension was determined from cyclic voltammetry based upon the peak current /scan rate relation to be 1.829/0.006 in the presence of single fractal geometry made of PVDF-binder materials only, and 1.779/0.006 in the presence of multifractal geometry composed of surface groups and binder materials. (2) The individual fractal dimensions of surface groups and binder materials were quantitatively determined to be 1.709/0.02 and 1.829/0.012, respectively, from KFM based upon the perimeter /area relation,
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regardless of the presence of the single fractal geometry or the presence of multifractal geometry. (3) When a fractal surface has single fractal geometry, the overall fractal dimension determined from cyclic voltammetry is just the same in value as the individual fractal dimension for binder materials determined from KFM. By contrast, when a fractal surface has multifractal geometry, the overall fractal dimension was determined from cyclic voltammetry to be just the average of the two individual fractal dimensions determined from KFM.
Acknowledgements The receipt of a research grant under the programme ‘National R&D Project for Nano Science and Technology’ funded from MOST, Republic of Korea and of a research grant under the internal research programme ‘Technological Development of High Performance Lithium Battery’ from Korea Advanced Institute of Science and Technology (KAIST) 2000/2002 is gratefully acknowledged. Incidentally, this work was partly supported by the Brain Korea 21 project.
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[2] S. Megahed, B. Scrosati, J. Power Sources 51 (1994) 79. [3] L. Kelvin, Philos. Mag. 46 (1898) 82, cited in Ref. [4]. [4] O.A. Semenikhin, L. Jiang, T. Iyoda, K. Hashimoto, A. Fujishima, Electrochim. Acta 42 (1997) 3321. [5] S. Miller, R. Reifenberger, J. Vac. Sci. Tech. B 10 (1992) 1203. [6] D. Vanderputten, J.T. Moonen, H.B. Brom, J.C.M. Brokkenzijp, M.A.I. Michels Maj, Phys. Rev. Lett. 69 (1992) 494. [7] K. Kinoshita, Carbon: Electrochemical and Physicochemical Properties (Chapter 3), Wiley, New York, 1988, pp. 86 /173 (Chapter 3). [8] S.-B. Lee, S.-I. Pyun, Carbon 40 (2002) 2333. [9] S.-I. Pyun, S.-B. Lee, W.-Y. Chang, J. New Mater. Electrochem. System 5 (2002) 281. [10] S.-B. Lee, S.-I. Pyun, Electrochim. Acta 48 (2002) 419. [11] W.-Y. Chang, S.-I. Pyun, S.-B. Lee, J. Solid State Electrochem. (2003), in press. [12] S.-B. Lee, S.-I. Pyun, J. Solid State Electrochem. (2003), in press. [13] H.O. Jacobs, H.F. Knapp, A. Stemmer, Rev. Sci. Instrum. 70 (1999) 1756. [14] J. Lu¨, L. Eng, R. Bennewitz, E. Meyer, H.-J. Gu¨ntherodt, E. Delamarche, L. Scandella, Surf. Interface Anal. 27 (1999) 368. [15] M. Strømme, G.A. Niklasson, C.G. Granqvist, Phys. Rev. B 52 (1995) 14192. [16] M. Strømme, G.A. Niklasson, C.G. Granqvist, Solid State Commun. 96 (1995) 151. [17] T. Pajkossy, L. Nyikos, Electrochim. Acta 34 (1989) 181. [18] J.C. Russ, Fractal Surfaces, Plenum Press, New York, 1994, pp. 59 /81 and 191 /225 (Chapter 3 and 7). [19] M.S. Mattsson, G.A. Niklasson, C.G. Granqvist, Phys. Rev. B 54 (1996) 17884. [20] J. Feder, Fractals (Chapter 12), Plenum Press, New York, 1988, pp. 200 /211 (Chapter 12).
Determination of the morphology of surface groups formed and PVDF-binder materials dispersed on graphite composite electrodes in terms of fractal geometry Seung-Bok Lee, Su-Il Pyun 1,* Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, 373-1 Guseong-Dong, Yuseong-Gu, Daejeon 305-701, Republic of Korea Received 14 December 2002; received in revised form 5 April 2003; accepted 25 April 2003
Abstract Morphological structures of surface groups formed and poly-vinylidene fluoride (PVDF)-binder materials dispersed on the PVDF-bonded graphite composite electrode were investigated in terms of fractal geometry using cyclic voltammetry combined with Kelvin probe force microscopy (KFM). When a fractal surface has single fractal geometry consisting of binder materials only, the overall fractal dimension was determined to be 1.82 from cyclic voltammetry based upon the peak current /scan rate relation, which is just the same in value as the individual fractal dimension of binder materials determined from KFM based upon the perimeter / area relation. By contrast, when a fractal surface has multifractal geometry composed of surface groups and binder materials, the overall fractal dimension was determined to be 1.77 from cyclic voltammetry. But the individual fractal dimensions were determined from KFM to distinguish the fractal dimension (1.70) of surface groups from that fractal dimension (1.82) of binder materials. The overall fractal dimension determined from cyclic voltammetry is just the average of the two individual fractal dimensions determined from KFM. # 2003 Elsevier B.V. All rights reserved. Keywords: Fractal dimension; Composite electrode; Surface groups; KFM; Perimeter /area relation
1. Introduction Poly-vinylidene fluoride (PVDF)-bonded graphite composite electrodes have been used as anode materials for secondary lithium batteries [1,2] because of the good safety and excellent lithium charge/discharge cycle life. The composite electrode is generally composed of graphite powder as the electrode material and PVDF as the binder material. Moreover, the surface of the graphite powder can be divided into an active graphite surface free of surface groups and an inactive graphite surface covered with surface groups. Therefore, the surface of the composite electrode can be classified into three types: active graphite surface, inactive gra-
* Corresponding author. Tel.: /82-42-869-3319; fax: /82-42-8693310. E-mail address: [email protected] (S.-I. Pyun). 1 ISE member. 0022-0728/03/$ - see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-0728(03)00331-0
phite surface, and dead graphite surface covered with binder materials. However, because the surface group layer usually extends at most to one or two monolayer thickness, and binder materials are non-uniformly distributed over the electrode surface, the surface morphology of the composite electrode has not been clearly established by conventional analytical methods such as atomic force microscopy (AFM) and scanning electron microscopy until now. One of the most powerful techniques for the analysis of the surface morphology of the electrodes is so-called Kelvin probe force microscopy (KFM) which is based upon the well-known Kelvin probe technique [3,4] and provides information on the lateral distribution of the surface potential on a microscopic scale. The surface potential corresponds to the potential difference between the sample specimen and a conducting probe that is positioned close to the sample surface. Since this value correlates with the difference in the work functions of
76
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the probe and the sample, the surface of the specimen in potential can be characterised using this technique. Fractal analysis has become a new and powerful tool to describe the geometric and structural properties of fractal surfaces, particle boundaries and pore structures, since their complex patterns are better described in terms of fractal geometry as long as the requirement of self-similarity is satisfied [5,6]. The latter term implies that the geometrical features of an object are independent of the magnification or observation scale. In the fractal description the most important parameter is the fractal dimension Df which is defined as the exponent that relates the mass M of an object to its size r M 8rDf
(1)
In this work, we analysed the morphology of surface groups formed and binder materials dispersed over the composite electrodes by employing the fractal concept. For this purpose, the cyclic voltammograms (CVs) were first measured to determine the overall fractal dimension of multifractal geometry composed of surface groups and binder materials by means of electrochemical methods. Then the 3D KFM images were obtained experimentally, and they were cross-sectioned by planes with constant surface potential in height into the 2D KFM images to visualise the morphology of surface groups and binder materials. Finally, the individual fractal dimensions of surface groups and binder materials were determined from the 2D KFM images based upon the perimeter /area relation to compare with that overall fractal dimension determined from the CV based upon the peak current /scan rate relation.
ified SLX50 graphite powder with 10 wt.% PVDF as a binder in n -methyl pyrrolidone solution, followed by pasting on Cu foil and drying in a vacuum oven at 110 8C for 8 h [8 /12]. 2.2. Electrochemical experiments including cyclic voltammetry A three-electrode electrochemical cell was employed for the electrochemical measurement. The PVDFbonded graphite composite electrode specimen was used as a working electrode. The Pt wire and saturated calomel electrode (SCE) were used as a counter electrode and a reference electrode, respectively. A solution containing 0.01 M K4[Fe(CN)6] and 0.1 M Na2SO4 was used as the electrolyte. The CVs were obtained from the electrode with various scan rates of 2 /104 mV s 1 in the potential range of /0.4 /0.6 VSCE using a potentiostat/ galvanostat (EG&G Model 263A). 2.3. KFM measurements KFM measurements were performed with an SPA 4000 STM/AFM system (Seiko Instruments) equipped with a KFM controller (Seiko Instruments) using commercial gold-coated silicon cantilevers. The resonance frequency f and spring constant C are given as 27 kHz and 1.6 N m 1, respectively. An a.c. bias voltage of 2 V at a frequency of 5 kHz was applied between the probe and sample. KFM images of the sample surface were acquired at a probe scan rate of 0.3 Hz. More detailed descriptions of the KFM technique can be found elsewhere [13,14].
2. Experimental 2.1. Preparation of two types of PVDF-bonded SLX50 graphite electrode specimens It was reported [7] that the amount of surface groups formed on the graphite surface increases with heattreatment temperature and it reaches a maximum around 400 8C. At higher temperature, the surface group is oxidized into gaseous species (CO and CO2) and the amount of surface groups becomes nearly zero above 1500 8C. As-received SLX50 graphite powder obtained from Timcal Co., Switzerland, surely has almost no surface groups since it was synthesized above 2500 8C under a reduction atmosphere. The as-received SLX50 graphite powder was heat-treated at 300 8C for 3 h under an air atmosphere to give a large amount of surface groups, and we designated this heat-treated powder the surface-modified SLX50 graphite powder. The PVDF-bonded graphite composite electrode specimens were manufactured by mixing either the asreceived SLX50 graphite powder or the surface-mod-
3. Results and discussion Fig. 1 illustrates the CVs obtained from the PVDFbonded SLX50 graphite composite electrode at various potential scan rates in 0.01 M K4[Fe(CN)6]/0.1 M Na2SO4 solution. The CV clearly showed one set of welldefined current peaks. These current peaks are assigned to a redox couple as follows: [Fe(CN)6 ]3 e [Fe(CN)6 ]4
(2)
Fig. 2(a and b) give on a logarithmic scale the variations of peak currents of CVs obtained from the PVDF-bonded composite electrodes made from the asreceived SLX50 graphite and from the surface-modified SLX50 graphite, respectively, as a function of the potential scan rate. The peak currents of CVs in Fig. 2(a and b) were linearly proportional to the scan rate with slopes of 0.410 and 0.387, respectively, within the potential scan rate range no to ni mV s 1, but the relation between the peak currents and the scan rates
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Fig. 1. The CVs obtained from the PVDF-bonded SLX50 composite electrode at various scan rates in 0.01 M K4[Fe(CN)6]/0.1 M Na2SO4 solution.
deviates strongly from linearity outside the scan rate range. It is noted that when the recorded cyclic voltammetric current is limited by diffusion of the electroactive species to and away from the electrode surface, the fractal dimension Df of the reaction sites on the surface can be obtained by the following relation between the peak currents and the scan rates [15,16], Ipeak 8n(Df 1)=2
(3)
where, Ipeak is the peak current, n is the scan rate, and Df represents the fractal dimension. From Eq. (3) the fractal dimensions of the composite electrode made from the as-received SLX50 graphite and the surfacemodified SLX50 graphite were determined to be 1.82 and 1.77, respectively. The distribution of the sites where the electroactive species undergo reduction and oxidation carries extensive information about the surface geometry. A dimension of two would be obtained from the CVs measured on a perfectly flat and electrochemically active electrode, and a dimension of 1.585 would be obtained from an electrode whose surface was a Sierpinski gasket [17 /20]. The Sierpinski gasket is generated as follows: an initiator is a filled triangle. In each application of the generator, the generator eliminates a central triangle and the filled triangle is replaced by three triangles that have been scaled down by the factor of 1/2. An infinite
number of generations of the prefractals leave a fractal curve. Considering that surface groups and PVDF-binder materials on the surface of the composite electrodes can act as inactive sites or dead sites for electrochemical reactions, and at the same time the peak currents of CVs on a logarithmic scale were found to be linearly proportional to the scan rates with a slope lower than 0.5, it is reasonable to say that the lowered fractal dimension than 2.0 of the composite electrodes was evidence that surface groups are formed and PVDFbinder materials are simultaneously dispersed over the surface of the composite electrodes having self-similar properties. In other words, the morphology of surface groups formed and PVDF-binder materials dispersed gives the fractal dimension of the electrochemically active area. Moreover, when determining Df using diffusion-controlled electrochemistry, the diffusion layer length acts as a yardstick length, and it was derived as follows: Dx
zFADc Ipeak
(4)
where Dx is the diffusion layer length; z , the number of electrons transferred per electroactive species in the redox reaction (in our case z /1); F , Faraday constant; A , the exposed surface area of the working electrode; D ,
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materials. However, it was reported [18] that, if both active sites and inactive sites co-exist on the electrode, and both sites have truly isotropic and fractal properties, i.e. self-similar fractal properties, the individual fractal dimensions of the active site and inactive site are determined to be the same in value. Thus, the fractal dimension determined from the CVs can inherently represent the fractal dimension of surface groups and binder materials as well as the fractal dimension of the electrochemically active site. Fig. 3(a and b) present KFM images obtained from the PVDF-bonded composite made from the as-received SLX50 graphite and from the surface-modified SLX50 graphite, respectively. The surface potential profiles
Fig. 2. The variations of peak currents of CVs obtained from the PVDF-bonded composite electrodes made from (a) the as-received SLX50 graphite and from (b) the surface-modified SLX50 graphite as a function of the potential scan rate.
diffusivity of the electroactive species; c represents the bulk concentration of the electroactive species. Using Eq. (4) we can determine the inner cut-off range in Fig. 2(a and b) at the faster threshold scan of the scan rate ni as values of 4.5 and 2.3 mm, respectively, and outer cutoff range in Fig. 2(a and b) at the slower threshold scan rate no as values of 76 and 29 mm, respectively. Since the electrochemical reactions take place, as a matter of fact, only at electrochemically active sites on the composite electrode surface, at first sight it might seem that the fractal dimension determined from the CVs would not give the fractal dimension associated with surface groups and binder materials, but it would give only the fractal dimension for electrochemically active site which is free of surface groups and binder
Fig. 3. The KFM images obtained from the PVDF-bonded composite made from (a) the as-received SLX50 graphite and from (b) the surface-modified SLX50 graphite.
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(Fig. 3(a)) of the composite electrode made from the asreceived SLX50 graphite showed a smooth surface with a small number of broad peaks, but the potential profiles (Fig. 3(b)) of the composite electrode made from the surface-modified SLX50 graphite revealed a rough surface which is composed of many sharp peaks with lower surface potential and some broad peaks with higher surface potential. It should be noted that the surface-modified SLX50 graphite contains a large amount of surface groups as well as PVDF-binder materials, but the as-received SLX50 graphite is considered to contain only PVDFbinder materials. Moreover, the surface potential of the surface covered with PVDF-binder materials is much higher than the potential of the surface covered with surface groups. Thus, we can assign the broad peaks with higher surface potential in the KFM images to PVDF-binder materials and the sharp peaks with lower surface potential to surface groups on the composite electrode. In order to visualise the real morphology of surface groups and PVDF-binder materials, we cross-sectioned the 3D KFM images of Fig. 3(a and b) by planes with constant surface potential in height into the 2D KFM images. Fig. 4(a) gives a 2D image obtained by crosssectioning the 3D KFM image of Fig. 3(a) by the plane with the value corresponding to 50% of the maximum height of the surface potential. Fig. 4(b and c) present the 2D images obtained by cross-sectioning the 3D KFM image of Fig. 3(b) by the planes with height values corresponding to 80 and 50% of the maximum surface potential, respectively. It should be noted that we have already borne out that the 2D image obtained by cross-sectioning the 3D KFM image of Fig. 3(a) with 50% of the maximum height value (Fig. 4(a)) was very similar to that 2D image obtained by cross-sectioning the 3D KFM image of Fig. 3(a) with 80% of the maximum height value. This showed that since surface groups were absent from the as-received SLX50 graphite, the morphology given by the 2D description did not change with the height of the cross-sectioning plane. Thus, in the case of the surface group-free as-received graphite composite electrode, the 2D image given in Fig. 4(a) represents the single morphology of PVDF-binder materials only dispersed over the composite electrode. By contrast, it was realised from Fig. 4(b and c) that the 2D image obtained by cross-sectioning Fig. 3(b) with 80% of the maximum height value was significantly different from the 2D image obtained by cross-sectioning Fig. 3(b) with 50% of the maximum height value. Considering the surface potential difference between the surface covered with surface groups and that covered with PVDF-binder materials, it is most probable that in the case of the surface-modified graphite composite electrode, the 2D image given in Fig. 4(b) represents the
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single morphology of PVDF-binder materials only dispersed over the composite electrode. However, the 2D image shown in Fig. 4(c) represents the multimorphology composed of surface groups formed and PVDF-binder materials dispersed over the composite electrode. Now we determined the fractal dimension from the cross-sectioned 2D image based upon the perimeter P and area A relation. It was reported that perimeter P and area A for self-similar shaped objects are related by [20] P aDf ADf =2
(5)
where a is a constant. Fig. 5(a /c) demonstrate the dependence of perimeter P on area A determined from Fig. 4(a /c), respectively. The P /A plots gave good linear relations above the threshold area AT :/1 /10 13 m2. It is noted that another linear relation below AT :/ 1 /10 13 m2 is physically meaningless due to the limitations of the KFM measurement. It should be stressed that the value of the slope (0.906) of the P /A plot in Fig. 5(a) determined from Fig. 4(a) coincides fairly well with that of the slope (0.916) of Fig. 5(b) determined from Fig. 4(b) which is considered to represent the single morphology of PVDF-binder materials only. This means that the fractal dimension (1.81) of PVDF-binder materials dispersed over the as-received SLX50 graphite composite electrode is in good agreement in value with that fractal dimension (1.83) of PVDF-binder materials dispersed over the surfacemodified SLX50 graphite composite electrode. This is caused by the same electrode preparation conditions, i.e. the same mixing speed, time and temperature, used in this work. Moreover, it was realised that the value of the fractal dimension (1.82) determined using cyclic voltammetry based upon the peak current /scan rate relation, from the surface group-free graphite composite electrode coincides fairly well with those values (1.81 and 1.83) determined using KFM based upon the perimeter / area relation, from the surface group-free graphite composite electrode. It is noted that the fractal dimension of 1.81 and 1.83 were determined by means of the image analysis of the 2D KFM images given in Fig. 4(a and b) which represent the single morphology of PVDF-binder materials only, and at the same time the fractal dimension of 1.82 is determined from the CVs measured on the composite electrode which contains PVDF-binder materials only. Therefore, in this work, we regarded the above three fractal dimensions as the fractal dimensions measured under single fractal geometry condition. From the coincidence among the fractal dimensions determined, it was realised that when a fractal surface has single fractal geometry containing binder materials only, the fractal dimension for binder materials determined
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Fig. 4. (a) Cross-sectional view of the 3D KFM image of Fig. 3(a) for the as-received SLX50 graphite by cross-sectioning by the plane with 50% of the maximum height of the surface potential; (b) cross-sectional view of the 3D KFM image of Fig. 3(b) for the surface-modified SLX50 graphite by cross-sectioning with 80% of the maximum height of the surface potential; (c) cross-sectional view of the 3D KFM image of Fig. 3(b) by crosssectioning with 50% of the maximum height of the surface potential.
from cyclic voltammetry is just the same in value as the fractal dimension determined from KFM. Now we discuss about the fractal dimension of surface groups formed on the composite electrode. In contrary to the case of PVDF-binder materials, surface groups can not be formed on the composite electrode alone, since binder materials are inevitable component for the composite electrode. Therefore, the composite electrode containing surface groups should always provide multi-morphology composed of surface groups and PVDF-binder materials.
The P /A plot of Fig. 5(c) clearly gives two straight lines with different slopes above the threshold area AT :/10 13 m2, which means that the multi-morphology gives multifractal geometry satisfying the self-similar condition. The slopes of the two straight lines are determined to be 0.912 and 0.852, which correspond to the fractal dimensions of 1.82 and 1.70, respectively. Surprisingly, one of the fractal dimensions, the higher value of 1.82, coincides exactly with the fractal dimension of PVDF-binder materials. Then, it is most probable that the other of the fractal dimensions, the lower
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This means that when a fractal surface has multifractal geometry composed of surface groups and PVDF-binder materials, it is possible to make a distinction between the multifractal islands composed of surface groups and binder materials with the help of KFM image analysis. The individual fractal dimensions of surface groups and binder materials were readily determined from the ratio of perimeter to area of their respective islands which can be estimated from the number of corresponding pixels in the 2D KFM images. In contrast, when a fractal surface has multifractal geometry, the diffusing electroactive ions do not sense distinctively from each other, surface groups and binder materials, but they sense the overall fractal geometry of the inactive site as well as the active site in cyclic voltammetry. Fig. 2(b) measured on the surface-modified graphite specimen showed that the peak current / scan rate relation gives a single straight line with a slope of 0.387, indicating an overall fractal dimension of 1.77. When a fractal surface has multifractal geometry, the overall fractal dimension determined from cyclic voltammetry correlates to the individual fractal dimensions of Df,1 and Df,2 determined from KFM by the following summation rule [18] P B1 ADf;1 =2 B2 ADf;2 =2
(6)
In this equation the total perimeter length is expressed as the sum of two terms, in which B1 and B2 are constants. Using Eq. (6), the overall fractal dimension was calculated as a value of 1.76, which is just the average of the two individual fractal dimensions (1.70 and 1.82). It is interesting to note that the overall fractal dimension determined from the CVs (1.77) coincides fairly well in value with the averaged fractal dimension (1.76) calculated from the KFM images.
4. Conclusions
Fig. 5. The dependence of perimeters on areas (a) obtained from the 2D image of Fig. 4(a); (b) obtained from the 2D image of Fig. 4(b); (c) obtained from the 2D image of Fig. 4(c).
value of 1.70, reveals the fractal dimension of surface groups formed on the surface-modified SLX50 graphite composite electrode.
In the present work, the morphological structures of surface groups and PVDF-binder materials have been investigated in terms of fractal geometry. The following conclusions can be drawn from the experimental results and theoretical consideration. (1) The overall fractal dimension was determined from cyclic voltammetry based upon the peak current /scan rate relation to be 1.829/0.006 in the presence of single fractal geometry made of PVDF-binder materials only, and 1.779/0.006 in the presence of multifractal geometry composed of surface groups and binder materials. (2) The individual fractal dimensions of surface groups and binder materials were quantitatively determined to be 1.709/0.02 and 1.829/0.012, respectively, from KFM based upon the perimeter /area relation,
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regardless of the presence of the single fractal geometry or the presence of multifractal geometry. (3) When a fractal surface has single fractal geometry, the overall fractal dimension determined from cyclic voltammetry is just the same in value as the individual fractal dimension for binder materials determined from KFM. By contrast, when a fractal surface has multifractal geometry, the overall fractal dimension was determined from cyclic voltammetry to be just the average of the two individual fractal dimensions determined from KFM.
Acknowledgements The receipt of a research grant under the programme ‘National R&D Project for Nano Science and Technology’ funded from MOST, Republic of Korea and of a research grant under the internal research programme ‘Technological Development of High Performance Lithium Battery’ from Korea Advanced Institute of Science and Technology (KAIST) 2000/2002 is gratefully acknowledged. Incidentally, this work was partly supported by the Brain Korea 21 project.
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