Extensive Study of Shape and Surface Structure Formation in the

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Extensive Study of Shape and Surface Structure Formation in the Mercury Beating Heart System E. Ramírez-Á lvarez,* J. L. Ocampo-Espindola, Fernando Montoya, F. Yousif, F. Vázquez, and M. Rivera Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Avenida Universidad 1001, Colonia Chamilpa 62209, Cuernavaca, Morelos, México S Supporting Information *

ABSTRACT: A phenomenological study of the mercury beating heart system in a three electrode electrochemical cell configuration forced with a harmonic perturbation is presented. The system is controlled via a potentiostat, where the mercury drop is electrically connected to a platinum wire and acts as the working electrode. This configuration exhibits geometrical shapes and complex surface structures when a harmonic signal is superimposed to the working electrode potential. This study involves a wide range of frequencies and amplitudes of the forcing signal. Differents levels of structure complexity are observed as a function of the parameters of the applied perturbation. At certain amplitudes and frequencies, rotational behavior is also observed.

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INTRODUCTION The Mercury Beating Heart (MBH) system is a classical chemo-mechanical oscillator that was first reported by Lippmann1 in the late 19th century. Until recently, it was generally accepted that capillarity and surface tension effects were responsible for the oscillations observed on the mercury. However, a hundred years passed until Keizer et al.2,3 brought this system back to the scientific community, describing it as a far from equilibrium system and developing a detailed study of different factors involved in the oscillation. The experimental setup designed by Keizer et al. consists of a glass tube containing mercury covered with an acid or basic solution. A piece of iron (acid condition) or aluminum (basic condition) was connected to a tungsten wire, which was kept in contact with the mercury surface. They concluded that the presence of oscillations depends on the tungsten wire position and the solution nature, namely, if the wire tip was positioned in the mercury drop center or in the perimeter, for iron-triggered or aluminum-triggered oscillations. Considering these conditions they proposed a chemical mechanism reaction for each configuration. The traditional MBH experiment is carried out in a watch glass covered with acid solution and K2Cr2O7 as oxidizing agent, where the mercury drop is in contact with an iron tip.4,5 Avnir6 studied this traditional configuration in acid solution, explaining the presence of oscillations as a consequence of mercury sulfate film forming and dissolving on the surface, changing the surface tension. Chang-Wook Kim et al. 7 studied iron-triggered and aluminum-triggered oscillations in basic and acid solution, respectively, and recorded the potential trace of the mercury electrode. Their proposed model was based on assuming that © XXXX American Chemical Society

the mercury potential becomes negative when it comes in contact with the negatively charged metals and that the addition of dichromate salt as oxidizing agent was not indispensable for oscillations to occur. A study of the MBH hydrodynamics modes in ring-shaped and linear groove geometries was carried out by Smolin and Imbihl.8 They showed evidence of standing waves, which periodically move for a wavelength fraction. Different modes of the standing wave were found in these configurations, and it was stated that the observed oscillations resulted from coupling between chemical and mechanical processes. Using γ-irradiation Castillo-Rojas et al.9 regenerated species of Hg2+ 2 in situ in the watch glass configuration and monitored the voltage on the mercury drop. Their findings include different modes such as circle, pentagon, hexagon, and 8- and 16- pointed stars, which appear when the chemical reaction produces a voltage difference between 770 mV and 760 mV/ SCE. In a more recent contribution, Verma et al. found additional shapes: circle, ellipse, triangle, square, and 5-, 6-, 7-, 8-, 9-, and 10- pointed stars, in the watch glass configuration applying a periodic square signal with a function generator via a platinum wire.10 In a study described by J. Olson et al.,11 the mercury drop hydrodynamic modes were explored employing a power supply. The experiment was conducted in a three electrode cell configuration controlling the voltage pulse sent to the mercury via a potentiostat. Olson and his co-workers also replaced the aluminum by an inert Pt counter electrode and investigated the Received: July 28, 2014 Revised: October 20, 2014

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dx.doi.org/10.1021/jp507596b | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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amplitudes from 1 to 5 Vpp. Current intensity and voltage time series for each sinusoidal signal are recorded using a data acquisition DAQ from Measurement Computing model USB1608-HS. Every experiment was developed using clean mercury. Mercury was cleaned from the sulfates produced by the reaction by repeated cleansing with distilled water after being stirred in acid solution for 24 h. All security recommendations on the handling of mercury were met. Sequential photographs of the mercury drop capturing the changes in the geometrical structures were taken for each harmonic potential applied, using an 18 megapixel Canon camera with a macro lens EF-S of 60 mm. Chemical Reactions. According to Keizer et al.,2,3 surface tension changes result from the formation and removal of a mercury sulfate film on the mercury surface in acid solution. The most complete chemical mechanism was proposed by Castillo-Rojas et al.;9 in their work they study the MBH system in acid solution with Pt as WE, iron as CE, and saturated calomel electrode as RE. Their proposed mechanisms consider different oxidizing agents for Hg0 depending to their oxidizing strength. In our configuration the proposed chemical reactions based on the dissolved O2 in solution as the oxidizing agent are as follows. The chemical processes occurring at the working electrode are

system in the absence of oxygen in basic or neutral solution. They found different mercury drop oscillation modes from a concentric circle to 2, 3, and 4 folds, each of which alternates between two superimposed shapes of the same kind. Voltage control by a potentiostat implies a continued connection between the tungsten wire and the mercury; for this reason, the tungsten position was not important in this case. Each oscillation mode was affected by the mercury mass, the voltage applied between tungsten and aluminum electrodes, and the distance between the tungsten and the mercury when a power supply is used. The chemical mechanism proposed until now explains the origin of the oscillations as a consequence of changes in the surface tension on the mercury drop. To the best of our knowledge, the variety of structures generated on the mercury drop surface when a harmonic potential is applied has not been reported for our experimental configuration. Here, an extensive study of the mercury shapes and surface structures in a three electrode electrochemical cell glass watch configuration in acid media when a harmonic voltage signal is applied via a potentiostat is presented. In this configuration, inert Pt is electrically connected to the mercury drop, a copper rod is used as counter electrode, and a calomel reference electrode permits the applied potential (V(t)) to be controlled with the use of a potentiostat. A wide range of amplitudes and frequencies of the harmonic wave potential are applied systematically, looking at the shapes and surface structures observed as a result of the chemo-mechanical processes and hydrodynamics of the system.

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EXPERIMENTAL SETUP The system studied consisted of a three electrode electrochemical cell, where a mercury drop of 23 g contained in a watch glass is used as a working electrode (WE). The drop is connected to a platinum wire, 0.33 mm diameter, placed in its center and always in contact with it. The Pt wire provides the electrical connection necessary to control the potential between the WE and a saturated calomel reference electrode (RE). As counter electrode (CE), a copper rod of 6.35 mm diameter was used. CE and RE were placed equidistant from the mercury drop as shown in Figure 1. An acid solution of 1 M H2SO4 was

2H+ + 2e− → H2(g)

(1)

O2 + 2Hg 0 + 4H+ ⇌ 2Hg 2 + + 2H 2O

(2)

Hg 2 + + Hg 0 ⇌ Hg 22 +

(3)

Hg 22 + + SO24 − ⇌ Hg 2SO4 (film)

(4)

Hg 2SO4 (film) ⇌ Hg 2SO4 (sol)

(5)

For the copper oxidation in the counter electrode: Cu → Cu 2 + + 2e−

(6)

The metallic mercury general regeneration reaction is the following: Cu 0 + Hg 22 + ⇌ Cu 2 + + 2Hg 0

(7)

In other words, the mercury(I) reduction takes place via the Hg2SO4 dissolution: Cu 0 + Hg 2SO4 (film) ⇌ Cu 2 + + 2Hg 0 + SO24 −

(8)

Cu 0 + Hg 2SO4 (sol) ⇌ Cu 2 + + 2Hg 0 + SO24 −

(9)

Through reaction 1, H2 bubbles are released into the gas phase. The presence of atmospheric oxygen dissolved in the solution makes the addition of another oxidizing agent unnecessary, and the corresponding oxidation reaction takes place, reaction 2. The Hg(I) ions are in equilibrium with the Hg(II) ions, reaction 3. The Hg(I) ions in the presence of the sulfate ions form an insoluble mercury sulfate thin film on the drop surface by reaction 4. At the same time, the formed salt is in equilibrium with the soluble specie in solution, reaction 5. The Hg(I) reduction is taking place through reactions 8 and 9, regenerating the Hg0 and completing one cycle.

Figure 1. Schematic of the experimental setup. It consists of an arbitrary function generator, a potentiostat, and a three electrode electrochemical cell: A mercury drop connected to a Pt wire (WE), a copper rod (CE), and a saturated calomel electrode (RE).

used as electrolyte. The solution covers the watch glass and is 2 cm in depth. A sinusoidal wave potential A sin(2πft) is created using a signal generator Rigol DG4162 and is superimposed to the anodic potential, V0 = 0, applied to the WE by a potentiostat Pine AFRDE5. The total signal, V(t) = V0 + A sin(2πf t), controls the redox voltage between the WE and RE in the electrochemical cell. The wide spectrum of sinusoidal waves studied includes frequencies from 1 to 100 Hz and

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RESULTS AND DISCUSSIONS First, the platinum wire was covered with glass capillary tubing and sealed with parafilm in such a way that approximately 2 B



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MBH configurations. The mercury drop is exhibited at two specific sinusoidal wave potentials, 25 Hz and 51 Hz, a pentagon structure that rotates. Such apparent rotation, observed also in the absence of forcing as will be reported in future work, could be the result of a resonance phenomena. Another explanation can be drawn from the work by Smolin and Imbihl,8 who studied the MBH in linear grooves and observed a standing wave mode where the wavelength was determined by the applied potential. They also reported the presence of slow additional modes superimposed on the standing wave that periodically move the wavelength within a fraction. The combination of these two superimposed modes could be responsible of the apparent rotation in our configuration experiment. Current intensity time series during the oscillatory formation of structures in the mercury drop were acquired. Figure 3 shows the oscillations in current intensity for the mercury drop structures during sinusoidal wave potential of 14 Hz and amplitudes of 1 V, 2 V, 3 V, and 4 V peak to peak. Oscillations in current intensity result from the reaction occurring on the mercury surface, Hg0 → Hg2+ 2 , show a fast increase and a lower decrease during which a structure is formed with its transients (for instance, one five-peak star and its transients: a pentagon and a circular structure showed in Figure 2). Current time series at 14 Hz and amplitude of 1 Vpp exhibits two peaks at the top of one oscillation and one smaller peak between oscillations possibly related with the three figures observed (five-peak star, pentagon, and circle). Time series at higher amplitudes and frequencies, not presented here, do not exhibit these additional peaks possibly caused by a fast sampling rate. Figure 4 shows the time series for the anodic current at 40 Hz and amplitudes of 2 Vpp and 4 Vpp. According to Table 2, at these conditions an 11-peak structure is observed, also used as footprint to assess reproducibility of the structures reported here. The structures observed in the system are very sensitive to the platinum wire position. For this reason, an 11 peak shaped structure, observed at a potential sinusoidal signal of 41 Hz and 2 Vpp amplitude, is chosen as reference to guarantee reproducibility. Once a specific sinusoidal wave potential is set, a transient that last about 30 s occurs, exhibiting simple beatings in circular shape or, in some cases, transitions between different geometric structures (squares, circle, pentagons). In our observations, as frequency increases the number of peaks and lobes increases, shapes increasing in geometrical complexity are observed every time. Surface structure increases also with frequency. An increase in amplitude, at a fixed frequency, in most cases results in smoothing of the peaks tending to more rounded shapes. However, in some cases an increase in amplitude can also result in more complex structure formation. Table 2 shows some of the most characteristic structures observed in our study of harmonic potentials. In order to build Table 2 as simplified as possible, the frequency at which a structure shows up for the first time is chosen, for increasing frequencies. In this way it is assumed that from 2 to 6 Hz all the structures observed are ellipses or beating circles. See Supporting Information for the complete Table 2 with pictures of the experimental mercury structures. There are some noteworthy similarities between surface structures reported here and those reported by J. Rajchenbach et al.12 in which a fluid layer of 1 cm deep silicon oil (with Newtonian rheological behavior) exhibits alternatively a star and a polygon shape by vertically vibrating the container. In

mm of the wire tip was inside of the mercury drop to prevent any contact with the solution. The surface structures and border shapes of the mercury drop seem to be the same compared with those obtained with the uncovered platinum wire. Since the structures are better appreciated without this cover, we show only the pictures using the bare wire. For a fixed amplitude and frequency of the sinusoidal potential, transitions between a pair of shapes that pass throught the circular shape appear in the mercury drop, as described in Figure 2. In this case, using an amplitude of 2 Vpp

Figure 2. Outer shapes and internal surface structures sequence (from left to right, top to bottom) for a sinusoidal voltage signal of 14 Hz and 2 Vpp, showing a five-peak star and transient pentagon shapes observed between the star formations.

with a frequency of 14 Hz, a rotated five peaks-stars structure is observed. These outer shapes and internal surface structures are not stationary; therefore, a sequence of intermediate states between the two main formations can be captured with the camera. These four images correspond to two sequential oscillations in potential after the transient period elapsed. For the range of amplitudes and frequencies of the harmonic perturbation studied in this work, the mercury drop exhibits different levels of complexity in the shape and structure. We observed that the structure complexity grows monotonically as the frequency is increased. Table 1 shows pictures of complex structures at some characteristic sinusoidal wave potentials. Structures with 3, 5, 7, and 9 lobes have been observed, all of them with an internal geometrical surface structure with the same number of sides. Pictures of transient structures of lobe and flower figures with good quality were not captured due to very short life spans. Structures like the 13 peak shape in Table 1 were observed for different numbers of peaks, going from 3 peaks at 7 Hz to 20 at 100 Hz. In these cases the internal surface structure is even more elaborate than the simple outer several sides reported in other MBH configurations. The structure of 13 peaks shown in Table 2 at 53 Hz and 1 Vpp exhibits a circular heart surrounded by a 13-lobe structure and a smaller innermost 13-peak structure. Several of these surface complex structures have not been previously reported for other C



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Table 1. Pictures of Some Characteristic and Complex Mercury Beating Heart Structures Observed for Harmonic Wave Potential with Frequencies (f) of 12, 48, 55, 70, and 100 Hz and Amplitudes (A) of 1 to 4 Vppa

a

In each case the structure oscillates between two rotated shapes.

Table 2. Mercury Beating Heart Structures Observed for Harmonic Wave Potential Applied with Different Frequencies (f) and Amplitudes (A)a A (V)

a

f (Hz)

1

2

3

4

5

2 7 11 12 18 32 33 38 40 42 44 45 47 50 51 52

circle 2 concentric circles circle 4 sides 6 sides 3 lobes 4 lobes 5 sides circle ellipse rectangule 12 peak star 12 peak star 7 lobes 3 sides 5 sides with 13 peaks

2 concentric circles 3 sides 4 sides oscillations between shapes 6 sides 3 lobes 10 sides 5 sides 11 peak star 6 lobes circle 12 peak star 7 lobes 13 peak star 5 sides with 13 peaks 8 lobes

ellipse 3 sides 4 sides 5 peak star 6 sides 9 sides 10 sides circle 11 peak star 6 lobes 12 peak star 12 peak star 7 lobes 13 peak star not defined different shapes

ellipse 3 sides 4 sides 5 sides 2 concentric circles 3 concentric circles 10 sides 11 peak star 11 peak star 3 sides with 12 peaks 12 peak star squared with 11 peaks 13 peak star 8 sides not defined 5 petal flower

ellipse sides 4 sides 5 sides 2 concentric circles 3 concentric circles  circle 11 peak star 3 sides with 3 peaks 12 peak star 4 sides with 12 peaks 13 peak star 8 sides 3 sides 5 petal flower

In each case the structure is oscillating between two rotated shapes.

such case, the shapes observed are the result of resonant coupling of three parametrically forced gravity waves. In the

case of our MBH configuration, even though a chemical reaction takes place, the surface structures are better explained D



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Figure 3. Time series for the anodic current (I) for sinusoidal voltages of 14 Hz frequency and amplitudes of (a) 1 Vpp, (b) 2 Vpp, (c) 3 Vpp, and (d) 4 Vpp. Subsections (e) and (f) show the power spectra for time series (a) and (b), respectively. Both PS plots exhibit peaks at the main frequency ω0 = 14 Hz, and its harmonics 2ω0, 3ω0, 4ω0, etc.

as traveling mechanical waves. In this sense traveling waves coupling, originated by the electrochemical process and shaped by the mercury hydrodynamics, may explain the observed complex surface structures.

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CONCLUSIONS For the MBH experiment described here, the electrochemical process gives the energy necessary to maintain the oscillations; however, structures observed are governed by mercury hydrodynamics as in the silicon oil case,12 surface tension changes, and charge distribution. In the MBH experimental configuration reported here, Pt wire position is an important parameter for a specific structure to show up, suggesting symmetry breaking of the chemomechanical structures. The mercury drop structure observed depends on the frequency and amplitude of the vibration applied. As frequency increases, shapes with higher number of peaks and more complex surface structures appear. The outcome of an increase in amplitude results, for the majority of voltage values used, in the same general structure but with more or less defined peaks or sides. This is observed in sinusoidal wave potentials of 1 to 11 Hz and 35 to 37 Hz. In other cases, an increase in amplitude leads to complete structure changes, for example, for frequencies of 12, 18, 25, 32 to 34, 42 to 44, 51, 52, and 60 Hz in Table 1 (and also in the Supporting Information). As the reaction advances on the mercury drop surface, an increase in the drop mass has an important effect on the mode and surface structure of the mercury. Apparent rotation of the mercury drop that takes place at some specific sinusoidal wave potential (25 Hz and 51 Hz probably resonant frequencies)

Figure 4. Time series for the anodic current (I) for sinusoidal voltages of (a) 40 Hz and 2 Vpp, (b) 40 Hz and 4 Vpp, and (c) Fourier transform (FT) of the current time series (b) with ω0 = 40 Hz and the harmonics 2ω0, 3ω0, 4ω0, etc. E



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suggests the presence of mode combination or traveling and standing wave interaction that will be explored in future work.

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ASSOCIATED CONTENT

* Supporting Information S

A complete Table 1 is supplied. It includes pictures of the observed mercury structures, after a 30 s transient is discarded, at sinusoidal wave potential signals with frequencies ranging from 1 to 100 Hz and amplitudes from 1 to 5 Vpp, in PDF format. This material is available free of charge via the Internet at http://pubs.acs.org

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by CONACYT, SEP-PROMEP, and SI-UAEM. REFERENCES

(1) Lippmann, G. The Relation Between Capillary and Electrical Phenomena. G. Ann. Phys. 1873, 149, 546−561. (2) Keizer, J.; Rock, P. A.; Lin, S.-W. Analysis of the Oscillations in “Beating Mercury Heart” System. J. Am. Chem. Soc. 1979, 101, 5637− 5649. (3) Lin, S.-W.; Keizer, J.; Rock, P. A.; Stenschke, H. On the Mechanism of Oscillations in the Beating Mercury Heart. Proc. Natl. Acad. Sci. U. S. A. 1974, 71, 4477−4481. (4) Demiri, S.; Najdoski, M.; Mirceski, V.; Petrusevski, V. M.; Rosenberg, D. Mercury Beating Heart: Modifications to the Classical Demonstration. J. Chem. Educ. 2007, 84, 1292. (5) Marqués, M. I.; Zhao, Y.-W.; García, N. Revisiting the Beating Mercury Heart Systems: Steps in the Voltage Figures Due to Nanocontacts. J. Phys. Chem. B 1997, 101, 2333−2338. (6) Avnir, D. Chemically induced pulsations of interfaces: The mercury beating heart. J. Chem. Educ. 1989, 66, 211. (7) Kim, C. W.; Yeo, I.-H.; Paik, W.-K. Mechanism of the mercury beating heart: An experimental study of the electrochemicalmechanical oscillator. Electrochim. Acta 1996, 41, 2829−2836. (8) Smolin, S.; Imbihl, R. Hydrodynamic Modes of the Beating Mercury Heart in Varying Geometries. J. Phys. Chem. 1996, 100, 19055−19058. (9) Castillo-Rojas, S.; González-Chávez, J. L.; Vicente, L.; Burillo, G. Study of the Extinction Dynamics of the Mercury Beating Heart Reaction in Acid Solution and in the Presence of γ-Radiation. J. Phys. Chem. A 2001, 105, 8038−8045. (10) Verma, D. K.; Contractor, A. Q.; Parmananda, P. PotentialDependent Topological Modes in the Mercury Beating Heart System. J. Phys. Chem. A 2013, 117, 267−274. (11) Olson, J.; Ursenbach, C.; Birss, V. I.; Laidlaw, W. G. Hydrodynamic mode selection due to the electrocapillary effect: the mercury beating heart in neutral and basic solutions. J. Phys. Chem. 1989, 93, 8258−8263. (12) Rajchenbach, J.; Clamond, D.; Leroux, A. Observation of StarShaped Surface Gravity Waves. Phys. Rev. Lett. 2013, 110, 094502.

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Extensive Study of Shape and Surface Structure Formation in the

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