Journal of Colloid and Interface Science 382 (2012) 82–89
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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Adsorption of cationic surfactants on covered hanging mercury drop electrode surface of variable area Argyri Koniari, Antonis Avranas ⇑ Laboratory of Physical Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
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Article history: Received 13 March 2012 Accepted 27 May 2012 Available online 7 June 2012 Keywords: Capacitance current Condensed film Mercury droplet Fractal
a b s t r a c t Cetyldimethylbenzylammonium chloride (CDBACl) or cetyltrimethylammonium bromide (CTAB) is preadsorbed on mercury and used as substrate. The adsorptive stripping voltammetry with the two-step procedure is used. The mercury droplet with the preadsorbed surfactant is expanded in aqueous solutions of KCl, KBr, CTAB, CDBACl, or cetylethyldimethylammonium bromide (CEDAB). The surface area was increased from 0.0022 cm2 up to 0.0571 cm2. The surfactant molecules are maintained close to each other and in the vicinity of the electrode by the applied electric field. The expanding of the droplets resulted in a reorientation of the adsorbed molecules depending on the surfactant surface concentration. In some cases, condensed films were observed. Differences were noticed in the adsorption and desorption potential region. A linear increase in the capacitance current with the surface area was found in all cases up to a maximum increase in the surface area. Partly disorganized films were also observed. In some cases, defects were noticed during expansion. In one case, fractal structure was observed. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Mercury offers defect-free, atomically smooth, and highly reproducible surface for adsorption and self-assembly of various surfactants. The use of mercury as the electrode material in electron tunneling experiments has brought about several advantages. [1–5]. For example, mercury does not have a crystal lattice that might affect the structure of the self-assembled film; mercury could give denser films, has a remarkable affinity toward thiols, and there is no need to condition the electrode before use. Differential capacitance is linked to the understanding of systems such as adsorbed and spread films and of the fluctuations of several physical quantities [6–10], that is, voltage and electromagnetic field fluctuations, dipole moment, pH and charge, polarizibility, and dielectric dispersion of colloidal and polyelectrolyte systems. Herein, we describe the investigations on the formation and properties of these layers using electrochemical methods (capacitance measurements). In previous papers [11–13], we studied the adsorption of cetyldimethylbenzylammonium chloride (CDBACl) and cetyltrimethylammonium bromide (CTAB) on hanging mercury drop electrode (HMDE) using differential capacitance measurements at various electrolyte conditions and temperatures. In brief, both surfactants formed condensed films at potentials that were not connected with the potential of zero charge. The adsorption of CTAB results in the ⇑ Corresponding author. Fax: +30 2310997686. E-mail address:
[email protected] (A. Avranas). 0021-9797/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcis.2012.05.047
formation of a condensed film, a very close packing of the surfactant molecules adsorbed vertically at negative potentials and at room temperature, when KBr is used as a supporting electrolyte. The capacity time curves, C–t, at potentials where the film was formed show a nucleation and growth mechanism with induction time depending on the applied potential. The nucleation is due to both CTA+ and the specifically adsorbed Br. The most common approximation of the mechanism of nucleation and growth based on the Avrami equation [14] shows a linear dependence of lnhext (where hext is the extended interfacial coverage) vs. lnt, suggesting that the capacitance pit is due to two-dimensional condensation (the Avrami plot). The Avrami slope should be either 2 or 3 for instantaneous for progressive nucleation, respectively, but higher values have also been reported. Avrami analysis gives a slope close to 2, explained as a progressive one-dimensional nucleation with constant growth rate, which could be imagined as the formation of closed packed parallel stripes or hemicylinders [15]. The adsorption of CDBACl on HMDE studied shows the formation of condensed film at different potentials and conditions. The change of the capacitance with time is followed at the potentials where the film is formed. In some cases, a nucleation and growth mechanism with an induction time is observed. An observed increase in the capacitance with time is attributed to the formation of hemimicelles. In our previous paper [16], we studied the adsorption of CTAB and CDBACl on a hanging mercury electrode using a two-step procedure, that is, adsorptive transfer stripping voltammetry. The cadsorbed surfactants on the mercury drop were then transferred
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into 0.1 M KBr or 0.1 M KCl under various conditions. Both surfactants are firmly adsorbed on the mercury after the transfer. The charge of the mercury droplets is turned positive by adsorption of the cationic surfactant but the droplets remain hydrophobic. On the other hand, the electrode, covered with a more or less dense monolayer, with surfactants pointing their tails toward the solutions is also probably hydrophobic. The repeated scan did not remove the adsorbed molecules. In the case of CTAB, the reorientation of the already adsorbed molecules could not lead to condensed film in the far negative potential region. The concentration of the adsorbed molecules is not enough for condensed-film formation. In the case of CDBACl, condensed films are observed when the transfer of the drop is performed at 5 °C or below. The pretreatment—the conditions the mercury droplet is formed, that is, at open or closed circuit, the initial potential, the time the droplet remained at a certain potential before the transfer, and the temperature—plays a role in the film formation. The reorientation of the molecules and the interaction of their hydrophobic chains result in a self-assembled condensed layer. In our following paper [17], the adsorbed CTAB or CDBACl were used as substrates. First, CTAB or CDBACl were adsorbed on mercury at 20 °C under various conditions (pretreatment). Then, mercury droplets covered with CTAB were transferred into CDBACl solutions, while those covered with CDBACl were transferred into CTAB solutions. Droplets covered with CTAB or CDBACl were also transferred into equimolar CTAB and CDBACl solutions. The adsorption of the second surfactant did not remove away the first one from the mercury, as evidenced by the capacitance measurements and the repeated scans. The surfactant molecules remain in the vicinity of the electrode. In all cases studied, there is a decrease in the capacitance in the potential range 0.8 to 1 V to very low capacitance values forming condensed film. Mixed films and synergy effects are observed. The already adsorbed CTAB on mercury does not permit the desorption–reorientation peaks of CDBACl. Shifts of the capacitance peaks are observed to more positive potentials and are attributed to the occurrence of a slow change in the organization of the monolayer. The electrical state of the preadsorbed surfactant would be of critical importance in the formation of the various structures. The results show the effect of the microenvironment on the adsorption and suggest that the ordering and arrangement of molecules could be controlled by appropriate selection of the preadsorbed molecules. In this paper, we extend our previous studies [16,17]. Droplets of two chosen sizes are formed in CTAB, CDBACl, or CEDAB solutions under various conditions. Droplets formed in the CTAB solution are then transferred into either KBr or CDBACl solutions (technically, the cells were swapped with no accompanying movement of the electrode). Droplets formed in the CDBACl solution are transferred either into KCl or CTAB solutions, while droplets formed in the CEDAB solution are transferred in CTAB solution. The droplet in the second solution is gradually expanded, and after each step, capacitance current–potential and capacitance current– time measurements are obtained. The capacitance current is measured, which is proportional to the capacitance. Mercury droplets are also expanded in both base electrolyte solutions alone and in CTAB in KBr, CDBACl in KCl, or CEDAB in KBr solutions, and the results are compared. In mercury drop expansion experiments, a large increase in the surface area and the concurrent monolayer expansion could easily generate pinhole defects that would allow a redox probe to move closer to the electrode surface than the average film thickness. Such an experiment for monolayers of n-octadecanethiol was first described by Janata et al. [3]. Slowinski et al. [1,5,18,19] had demonstrated that gradual expansion of a suspended Hg drop coated with an alkanethiolate monolayer resulted in a decrease in the monolayer thickness and that the volume of the film remained
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constant without generating pinhole defects. The decrease in the film thickness was inversely proportional to the increase in the surface area of the drop. This liquid-like character of these monolayers was explained by postulating that all alkanethiolate molecules adopted a gradually increasing average tilt as the film was expanded. Some authors studied the adsorption of surfactants on different mercury droplets of various sizes taking into consideration the fractal character of the adsorption and/or curvature effects [20,6,21,22]. There are numerous papers dealing with a fractal character of the electrode surface and adsorbate attached to it. Those studies are based on a much larger scaling factor using the applied perturbation frequency as a measure [23–25]. For example in [23], they analyzed the long-term behavior of growing uracil films at the mercury–electrolyte interface at various stages of film growth by means of time-resolved FFT impedance spectroscopy, while in [24] it was found that the nucleation process was not limited to the electrode surface, but was equally probable also on top of islands of a new phase. The fractional exponent has been shown to be directly related to the effective fractional dimension of the surface being thus the measure of irregularity [25]. Our experiments differ from those of other authors [20,26–31] who studied different sizes of mercury droplets formed in one solution and then transferred them into another solution. In our case, the droplet was formed in one solution and transferred and expanded in another solution or expanded in the same solution. Experiments investigate stepwise desorption or stepwise coadsorption of one or the other surfactant at the same mercury drop.
2. Experimental CTAB was from Fluka, puriss p.a. for ion-pair chromatography 99.8%. CDBACl was from Sigma 99.1% (dry basis). Cetylethyldimethylammonium bromide (CEDAB) 99.7% was from TCI Europe. The critical micelle concentration (cmc) of CTAB was found to be 9 104 M, of CDBACl 5 104 M, and of CEDAB 7.9 104 M in water, determined by surface tension measurements at 25 °C, in good agreement with the values reported previously at the same temperature [32,33]. No minimum in the surface tension–concentration curves for all surfactants was found, indicating their purity. CEDAB and CDBACl have larger headgroups compared to CTAB. The presence of the ethyl group of CEDAB and the benzyl group of CDBACl result in an increase in surface area A, compared to CTAB at the air/water interface. CTAB has also a somewhat higher cmc compared to the other two cationic surfactants. The previously reported data from surface tension measurements were 37.5 mN/m for 2 104 M CTAB in 0.1 M KBr, and 33.6 mN/m for 2 104 M CDBACl in 0.1 M KCl [17]. Thus, CDBACl is more surface active compared to CTAB. A synergy was also observed in the reduction in surface tension by both surfactants. KCl and KBr were from Merck KGaA (Germany), of suprapure quality, and were used as supporting electrolytes. Water was from a Millipore apparatus (USA). Two-step procedures were used before the measurements. The HMDE, from Bioanalytical Systems USA (BASi) (150 lm ID capillary), was immersed in the surfactant solutions (called ‘‘Solution I’’), which were 2 104 M CTAB in 0.1 M KBr or 2 104 M CDBACl in 0.1 M KCl, and 2 104 or 1 103 M CEDAB in 0.1 M KBr at 20 °C. A few mercury drops were formed and discarded in the solution. An Hg drop was created at the tip of the glass capillary. The initial surface area of the mercury drop was either 0.0265 or 0.0114 cm2 (size 2 or 8 on the BASi mercury electrode, respectively) and its reproducibility was found to be in the order 2 104 cm2. The mercury droplet remained in ‘‘Solution I’’ before
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transfer in all cases for 1 min in an open circuit, in order for the surfactant molecules to adsorb and accumulate at the interface. No significant difference in the differential capacitance curves was noted when longer equilibration periods were used before each experiment [16]. The surfactant remains attached to the droplet during transportation according to our previous results [16,17]. Then, the HMDE, coated with the adsorbed surfactant, was washed with water (in order to remove surfactant molecules that had not been adsorbed on mercury) and immediately dipped into the electrochemical cell containing the second solution (called ‘‘Solution II’’) that has 0.1 M KCl, 0.1 M KBr, and 2 104 M CTAB in 0.1 M KBr, or 2 104 M CDBACl in 0.1 M KCl, depending on the composition of ‘‘Solution I.’’ The volume of mercury extruded at the tip of the HDME capillary was controlled by pushing the knob at the front of the BASi controlled growth mercury electrode. All solutions were previously deaerated with nitrogen for 10 min, while a blanket of nitrogen was maintained above the fully deaerated solution during all experiments. The experiments were performed in a standard three-electrode cell that was temperature-controlled at 20 °C, using a Medinglab Model KT30 E 10 cryostat (Germany). An Ag/AgCl electrode in 3 M NaCl was used as a reference electrode. The reference electrode was connected to the cell via a liquid junction filled with the supporting electrolyte. A platinum bar served as the counter electrode located on the either side of the working BASi HMDE. Electrochemical measurements were conducted using PGSTAT302 Autolab. The measurements were carried out using 10 mV peakto-peak alternating signals of 740 Hz that was superimposed onto the polarization potential. At first, an ic–E curve was measured starting from 0.2 to 1.9 V with a scan rate of 16 mV s1 showing the potential regions of adsorption and desorption (this scan rate was used in all ic–E experiments). In addition, ic–t curves were obtained following potential jumps at various potentials. The size of the mercury droplets was increased in a stepwise manner up to a maximum, which was just before the detachment from the capillary tip, and after each mercury drop expansion step, ic–E and ic– t measurements were performed. The initial potential was 0.2 V in all scans. More experimental details can be found elsewhere [16,34–38]. In addition, in order to compare our results, we carried out capacitance current measurements following the increase in the droplet size in the base electrolyte solutions 0.1 M KCl and 0.1 M KBr and in all solutions called ‘‘Solution I’’ above. Many mercury droplets were formed and discarded from the capillary tip in water and weighed. From the known weight of the droplets, the volume of the mercury droplet was calculated, and finally the area of the mercury droplet. This process was repeated for mercury droplet of various sizes formed by continuously pushing the knob on the BASi electrode, which were then discarded from the capillary tip.
expanding it in a solution containing either the base electrolyte or the surfactant solution. Variation of the monolayer thickness was accomplished by careful expansion of the mercury drop. The continuous expansion of the drop that previously had adsorbed a surfactant in a base electrolyte solution would be expected to give, after many expanding steps, capacitance current values close to those of capacitance current of droplets in the base electrolyte solutions. Also, the continuous expanding of a droplet containing a surfactant from ‘‘Solution I’’ in ‘‘Solution II’’ would be expected to give values close to the ones containing only the surfactant from ‘‘Solution II.’’ 3.1. Capacitance current measurements in 0.1 M KBr or 2 104 M CTAB in 0.1 M KBr (‘‘Solution II’’) a. Mercury droplet formed in 2 104 M CTAB in 0.1 M KBr (‘‘Solution I’’), transferred and expanded into 0.1 M KBr (‘‘Solution II). The capacitance current–potential curves are given in Fig. 1. The droplet with an initial area of 0.0114 cm2 was formed in 2 104 M CTAB in 0.1 M KBr (‘‘Solution I’’) and then transferred into 0.1 M KBr (‘‘Solution II’’). The droplet area increased to 0.0214, 0.0299, 0.0381, and 0.0444 cm2. Condensed films are not observed in the far negative potential range (more negative to approximately 1.6 V). Adsorption minima are observed at 0.7 and 1.0 V. The expanding of the droplet results in a shift of these two adsorption minima as well as desorption peaks at approximately 1.7 V to slightly more positive potentials. This is attributed to a slow change in the organization of the monolayer. The minimum at 0.7 V is more pronounced compared to this at 1.0 V. Similar results, but with shifting of the capacity minimum negatively by 0.07 V, had also been observed for thinning of the membrane by the drop expansion for the phospholipid monolayers at the mercury/water interface [31]. The origin of that effect is not clear. b. Mercury droplet formed in 2 104 M CDBACl in 0.1 M KCl (‘‘Solution I’’), transferred and expanded into 2 104 M CTAB in 0.1 M KBr (‘‘Solution II’’). Some results of capacitance current measurements in 2 104 M CTAB in 0.1 M KBr (‘‘Solution I’’) are given in Fig. 2. In all measurements, condensed film at potentials more negative to 1.5 V and the adsorption minima at 0.7 and 1 V are observed. The potentials of the minimum and desorption peaks remain the same. Potential jump from 0.2 V to 1.8 V is shown in Fig. 2b.
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3. Results and discussion We mainly focused our experiments of the capacitance current time measurements at four potentials, 0.7, 1.0, 1.6, and 1.8 V where maximum adsorption–minimum capacitance current was observed in the ic–E curves. One potential (0.7 V) was quite close to the potential of zero charge (pzc) while the other three were at the more negative potential region. At potentials positive to the pzc, the surfactants were very slightly adsorbed (so we did not measure the change of the capacitance current with time) [29]. The time required for the adsorbed structure to reach an equilibrium state is very important in order to understand the nature of the various phenomena that take place at the interface [39]. In our studies, we measured the adsorption on the same droplet after
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Fig. 3. ic–E curves. The droplet was formed in 2 104 M CDBACl in 0.1 M KCl (‘‘Solution I’’) and then transferred into 2 104 M CTAB in 0.1 M KBr (‘‘Solution II’’). The initial droplet area was 0.0114 cm2 (1) and the expansion was similar to Fig. 1.
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44, 36, 26, and 16s, when the droplet area is 0.0114, 0.0214, 0.0299, or 0.0381 cm2, respectively. The capacitance current–potential curves are given in Fig. 3. The initial droplet having an area of 0.0114 cm2 was formed in 2 104 M CDBACl in 0.1 M KCl (‘‘Solution I’’) and then transferred into 2 104 M CTAB in 0.1 M KBr (‘‘Solution II’’). The adsorbed CDBACl cannot inhibit the formation of the CTAB condensed film at potentials more negative than 1.5 V. The broad desorption area
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The capacitance current immediately decreases to approximately 1.5 108 A, where a condensed film is formed in less than 50s. The increase in the droplet area, while the potential remains constant at 1.8 V, results in an increase in the value to 3.5 107 A, due to the destruction of the condensed film. However, the CTAB ions in the bulk are adsorbed on the mercury droplet and the capacitance current after a few second decreases. A higher steady value of 3 108 A is obtained (compared to 1.5 108 A before), resulting again in formation of a condensed film. The increase in the droplet size results again in an increase in the capacitance value followed by its decrease. The increase in the droplet size results in a momentary ‘‘dilution’’ of the surfactants ions on mercury, a reorganization of the adsorbed molecules and an increase in the capacitance current. This increase is due to the presence of ions from the base electrolyte and more probable of the K+ at this far negative potential, which are more comparable to the surface-active CTAB ions. An intercalation of water molecules, resulting in an increase in the dielectric constant of the film, is also possible. After a few seconds, the more surface-active CTAB is adsorbed and the capacitance current decreases. There is a decrease in the first value after drop expansion. This is due to the fact that it is more difficult to destroy the condensed film remove the already adsorbed ions from the interface. The kinetics of the film formation is different after the expansion. The successive expanding of the droplet results in a faster kinetics for the reorientation of CTAB to form the condensed film. The equilibrium capacitance current values are 0.16 107, 0.3 107, 0.4 107, and 0.52 107 A and are obtained in approximately
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Fig. 2. Measurements in 2 104 M CTAB in 0.1 M KBr. (a) ic–E curves. (b) Capacitance current transients at 1.8 V. The initial mercury drop was formed at 0.2 V. When steady capacitance current values were obtained at 1.8 V, the droplet was expanded. The initial droplet area for both figures was 0.0114 cm2 (1) and the expansion was similar to Fig. 1.
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t (s) Fig. 4. (a) ic–E curves in 1 103 M CEDAB in 0.1 M KBr. The initial mercury drop area was 0.0114 cm2, formed at 0.2 V, and the expansion was similar to Fig. 1. Line: ic–E curve of 2 104 M CTAB in 0.1 M KBr. (b) Capacitance current transients in 2 104 M CEDAB in 0.1 M KBr. The mercury drop was formed at 0.2 V. When steady capacitance current values were obtained at 1.8 V, the droplet was expanded. The initial droplet area was (1) 0.0022 cm2 and increased to (2) 0.0059, (3) 0.0096, (4) 0.0113, (5) 0.0143, (6) 0.0161, and (7) 0.0200 cm2.
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(approximately 1.2 to 1.45 V) observed in Fig. 2a when only CTAB is present changes to the desorption peak at approximately 1.3 V. Due to the presence of both surfactants that are coadsorbed in the potential range 0.6 to 1.0 V, the two adsorption minima attributed to CTAB are not so clear in Fig. 3 and they do not have identical values. c. Mercury droplet formed in 2 104 or 1 103 M CEDAB in 0.1 M KBr (‘‘Solution I’’), transferred and expanded into 2 104 M CTAB in 0.1 M KBr (‘‘Solution II). At first, in Fig. 4 are given the results of the capacitance current measurements in 1 103 M CEDAB in 0.1 M KBr without any transfer. Similar curves are obtained (not shown) for 2 104 M CEDAB. CEDAB differs from CTAB in that on the quaternary nitrogen atom the methyl group has been replaced by the ethyl group. This small change results in remarkable differences in the potential region negative to 1.5 V where CEDAD not only does not form a condensed film, but is practically almost desorbed from the interface at that potential range. However, the adsorption behavior of CEDAB is similar to that of CTAB, in the potential region 0.6 to 1.0 V. CEDAB does not form a condensed film in the far negative potential region even after prolonged stay of the mercury droplet in a negative potential. This is shown in Fig. 4b, where the initial stay of a droplet of 0.0022 cm2 for 300 s at 1.8 V results in steady values. The increase in the droplet area results in an increase in the capacitance current values to remarkably steady values of the current with time, without formation of a condensed film. This is due to the presence of the ethyl group that increase the available surface area, sterically hindering the close approach and interaction of the alkyl groups in order to form the condensed film.
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In Fig. 5 are given ic–E curves of mercury droplets formed at two different CEDAB concentrations of 2 104 M and 1 103 M, and then transferred and expanded into 2 104 M CTAB (the effect of the initial concentration of surfactant in ‘‘Solution I’’). These ic–E curves differ, although the ic–E curves for 2 104 and 1 103 M CEDAB alone are almost the same. In both figures, the capacitance current in the potential region 0.2 V to 1.2 V is almost identical. At more negative potentials, there are differences. The desorption region in Fig. 5a is 1.2 V to 1.4 V and increases to 1.2 V to 1.6 V with the increase in the CEDAB concentration. At more negative potentials, there is an evidence of a condensedfilm formation [13]. The increase in CEDAB concentration results in the inhibition of the condensed-film formation by CTAB, present in Fig. 5b. The expanding of the droplet shown in Fig. 5b results in a reorientation of the adsorbed CEDAB and the incoming CTAB, but this reorientation does not permit the CTAB molecules to closely approach and form a film, and mixtures of CEDAB and CTAB molecules coexist on mercury, evidenced by the higher capacitance current values compared to those for CTAB alone. The amount of adsorbed CEDAB increases with the increase in the concentration, clearly shown in Fig. 6. The first potential jump is from 0.2 V to 1.8 V. The capacitance current decreases, but very slowly, toward an almost steady value. Then, while the potential remains at 1.8 V the mercury drop is expanded, the capacitance current increases and then again decreases. The kinetics of this decrease depends on the CEDAB concentration. These figures show that the preadsorbed CEDAB inhibits the approach of CTAB at the interface and this inhibition is related to the CEDAB concentration. However, CTAB ions finally manage to reach the interface, but cannot form the condensed film the measuring time studied.
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E (V) Fig. 5. ic–E curves. The droplet was formed in (a) 2 104 M CEDAB in 0.1 M KBr or (b) 1 103 M CEDAB in 0.1 M KBr (‘‘Solution I’’) and then transferred and expanded into 2 104 M CTAB in 0.1 M KBr (‘‘Solution II’’). The initial droplet area was 0.0114 cm2 (1) and the expansion was similar to Fig. 1. In both curves, the line is the ic–E curve for a 2 104 M CTAB in 0.1 M KBr.
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t (s) Fig. 6. Capacitance current transients. The mercury droplet is formed in (a) 2 104 M CEDAB in 0.1 M KBr or (b) 1 103 M CEDAB in 0.1 M KBr (‘‘Solution I’’) and then transferred and expanded into 2 104 M CTAB in 0.1 M KBr (‘‘Solution II’’). The initial droplet area was 0.0022 cm2 (1) and then expanded to 0.0059 (2), 0.0096 (3), 0.0113 (4), and 0.0143 (5) cm2.
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The CEDAB ions remain close to the interface and this is evidenced by the following expanding of the droplet. The capacitance current increases and again slowly decreases, much more slowly compared to when only CTAB is present (Fig. 2b), without obtaining steady values after higher times, indicating that even after 400 s, formation of a condensed film by CTAB molecules is not observed. The expanding of the mercury droplets results in a reorientation of both CEDAB and CTAB. The continuous expanding in the CTAB solution results in an increase in the amount of CTAB that is adsorbed on the mercury droplet, which is not enough to form the condensed film due to CEDAB (that has a constant concentration) although at this potential range it is less adsorbed compared to CTAB (Fig. 4), inhibiting finally the formation of the condensed film. In Fig. 6a, the lower capacitance current values obtained before expanding the drop are 0.18 107, 0.35 107, and 0.4 107 A, much higher than the equilibrium capacitance current values in CTAB (‘‘Solution I’’), which are obtained faster and are 0.055 107, 0.1 107, 0.157 107, and 0.17 107 A, when the droplet area increases from 0.0022 to 0.0059, 0.0096 and 0.0113 cm2 respectively. The values in Fig. 6b are 0.38 107, 0.69 107, 0.87 107, and 0.76 107 A, again much higher compared to the values obtained in the absence of CEDAB. It is interesting to note that in Fig. 6 the first initial capacitance current values obtained after expanding the mercury drop are almost the same in both figures, that is, do not depend on the CEDAB concentration. In some ic–t curves (not shown), a sudden decrease was observed and afterward an increase and then a decrease (like oscillations). This could be attributed to the insertion of CTAB ions somewhere in the double layer, leading instantly to lower capacitance current values; however, these molecules were then rearranged at the interface, a situation looking like an opening and closing of the CEDAB molecules from the interface by the CTAB molecules. Figs. 3 and 5a differ in the substrate of the adsorbed molecules used in the formation of the mercury drop in ‘‘Solution I.’’ These figures differ especially in the desorption potential range around 1.3 V, as well as at the far negative potential region, where the capacitance current values in the presence of CDBACl are lower, compared to those in the presence of CEDAB. These differences also exist after the expanding of the mercury drop. There is a different interaction between CEDAB–CTAB and CDBACl–CTAB.
surface area. The capacitance of the film follows the constant volume model. However, the slopes of these lines differ, depending on the system studied. In Fig. 7 are given plots of capacitive current vs. the mercury droplet area. In both cases, there is an increase in the capacitance current. The line 2 illustrates an almost linear increase in the capacitance current, with R2 = 0.9985. However, line 1 illustrates an almost linear increase in the capacitance current from 0.011 cm2 up to approximately 0.03 cm2, that is, an increase in the surface area up to approximately 300%. For higher values of surface areas up to approximately 0.05 cm2, that is, an increase up to 450% studied, since the mercury droplet is afterward detached from the electrode, there is a lower increase in the capacitance current, that is, experimental values are lower than those predicted by the model. In [19], the authors focused on experiments in which the monolayer of alkanethiol was first self-assembled on an Hg drop, then the electrode was immersed in a thiol-free solution of an electrolyte, and the Hg drop was expanded stepwise by small increments. Capacitance and tunneling measurements were performed after each expansion step. The formation of defect- and pinhole-free monolayers on the sessile drop by changing the drop surface area was investigated. Two opposite scenarios might be envisioned upon the monolayer expansion. At first, an expansion of an alkanethiolate monolayer coating the Hg drop resulted in a progressively larger average tilt of the alkane chains without generating pinhole defects. Later, pinhole defects allowed a redox probe closer access to the electrode surface. An increase up to approximately 130% of the droplet area resulted in a linear increase in the capacitance. The continuous expansion would lead to capacitance value identical with the values obtained for systems containing only the second surfactant in Solution II. Thus, the transfer of a mercury drop formed in a surfactant solution where no condensed film is generated, like CEDAB, and then continuous expansion in a CTAB solution at 1.8 V shows the formation of a condensed film depending on the initial CEDAB concentration. Thus, pinholes are observed leading to partly disorganized films. Many systems, such as biological and adsorbed and spread films, are either fractal structures or exhibit fractal behavior and can, therefore, be described with effective fractal dimension D [6,26–30]. The approach is based on the possibility to describe quantitatively complex objects that are statistically scale-invariant, physical realizations of mathematical fractals that appear the
3.2. Capacitance current measurements in 2 104 M CDBACl in 0.1 M KCl (‘‘Solution II’’) The results are given in the Supplementary file. -7
5.0x10
4. Comparison of the results
1
-7
According to the Helmholtz model of the double electric layer, the capacitance C is expressed by the equation
C ¼ ee0 A=d
i c (Α)
4.0x10
-7
3.0x10
2
-7
where e is the dielectric constant of the monolayer and d is the thickness of the film. Assuming that the monolayer volume V remains constant [1,5,18,19] and equal to A d, then the capacitance is expected to increase linearly with A, as long as the dielectric constant of the film remains the same. The adsorption of surfactant results in a decrease in the capacitance of the adsorbed layer in respect to that of the pure electrolyte. The adsorbed organic molecules have a lower dielectric constant than electrolyte. The monolayer thickness changes by the expansion of the mercury droplet. There is an increase in the surface area from 0.0022 cm2 up to 0.0571 cm2. In all cases studied, there is an initial linear increase in the capacitive current (that is related to the capacitance), with
2.0x10
-7
1.0x10
0.0 0.01
0.02
0.03
0.04
0.05
2
A (cm ) Fig. 7. Plots of ic vs. surface area of mercury droplet. The droplet was formed in (1) 2 104 M CDBACl in 0.1 M KCl (‘‘Solution I’’), transferred and expanded in 2 104 M CTAB in 0.1 M KBr (‘‘Solution II’’) or (2) in 2 104 M CTAB in 0.1 M KBr (‘‘Solution I’’) transferred and expanded into 2 104 M CDBACl in 0.1 M KCl (‘‘Solution II’’). Both measurements are at 0.7 V. R2 = 0.9985 for the line (2).
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5. Conclusions
log i c
-6.5
-7.0
D=2.05 -1.0 V -7.5
D=2.4 -0.7 V -8.0 -1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
log r Fig. 8. Plots of log ic (A) vs. log r (cm) for mercury droplet formed in 2 104 M CDBACl in 0.1 M KCl (‘‘Solution I’’), transferred and expanded into 2 104 M CTAB in 0.1 M KBr (‘‘Solution II’’) at 0.7 and 1.0 V. R2 = 0.958 and 0.993 and for 0.7 V and 1.0 V, respectively.
same on all length scales [6]. The basic property of fractal objects is expressed by a relation of the form ‘‘feature’’-‘‘scale’’D, where ‘‘feature’’ should be considered in the broadest sense (e.g., the current density of an electrochemical process, surface area, etc) and the ‘‘scale’’ could be particle size, cross-sectional area of an adsorbate, or layer thickness. In the capacitance measurements, the layer adsorbed on the surface of the mercury droplet is considered the fractal structure. The size of the electrode surface determines the size of the adsorbed structure. The exponent D may represent the topological dimension of a Euclidian space or the fractal dimension of a fractal space. In our HMDE experiments, the mercury surface is almost perfectly spherical and it remains spherical regardless of its size. The fractal dimension D was determined from the size scaling of the HMDE. D is related to the capacitive current that is proportional to the electrode surface A that is described by the electrode radius r through the relation, capacitive current ic A rD. D can be obtained from the slope of log ic log r. In the absence of adsorbed layer, D = 2, while in the presence of a fractal layer values of D greater than 2 are obtained. In all the systems studied, we made the log ic log r plots and from the slope we found D. These systems included capacitance measurements in ‘‘Solution I’’ and in ‘‘Solution II.’’ The plots were made at the potentials given above. In all the cases studied except from one system at one potential, the calculated slope resulted in values of D lower to 2 (up to 1.8 in some cases), showing absence of fractals. In Fig. 8 are given plots of log ic log r for two cases studied: one with D close to 2 (2.05) and one quite above 2, that is, a higher fractal dimension. The system is for a mercury droplet formed in 2 104 M CDBACl in 0.1 M KCl (‘‘Solution I’’), transferred and expanded into 2 104 M CTAB in 0.1 M KBr (‘‘Solution II’’). The capacitance measurements were made at two potentials: 0.7 V and 1.0 V. At 0.7 V, the electrode is supposed to be very much like a nonpolar electrode. At 0.7 V, D has a value above 2 and is close to 2.4. According to [17], the ratio of the final to initial capacitance for the same system and potential was found 2.8, well above the one for the formation of hemispherical or hemicylindrical micelles. This high ratio connected with the high D value indicates that fractal structures are present in this system and this potential. This potential is where maximum adsorption of CTAB and CDBACl on mercury is observed, and this potential is quite close to the potential of zero charge. It could be considered that high final to initial capacitance values are indications of fractal structures.
Our methodology combines two parameters: the expanding electrode area and the applied potential. After expanding, the first adsorbed surfactant remains on the mercury drop or close to the interface, and since it is not removed, it contributes to capacitance. The selected surfactants show the influence of molecular geometry (substituent position) on the mixed layer structure. Capacitance current measurements provide evidence for the decreasing film thickness as a function of the degree to which the mercury drop is expanded. The exact composition of the film as a function of the Hg drop expansion remains unknown, since both thickness of the film and the dielectric constant influence the measured capacitance current values [19], that is, some conclusions could be considered as speculative. The surfactants maintain their defect-free characteristics even when the surface area of a drop is increased. In some cases, the defects were reported during the expansion. The shape and conformation of the adsorbed molecules depends on electrostatic factors including the substrate’s surface charge (electrode potential) [40]. The fractal structure observed could be related to the ratio of final to initial capacitance. Future studies on the adsorption of polymers on mercury as substrates that inhibit or do not permit the introduction of the second surfactant and connection with the critical aggregation concentration (cac) are intended.
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jcis.2012.05.047.
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