Potential-Dependent Topological Modes in the Mercury Beating Heart

Article pubs.acs.org/JPCA

Potential-Dependent Topological Modes in the Mercury Beating Heart System Dinesh Kumar Verma,† A. Q. Contractor,‡ and P. Parmananda*,† †

Department of Physics, and ‡Department of Chemistry, Indian Institute of Technology, Bombay, Powai, Mumbai-400 076, India ABSTRACT: We study the dynamics of the mercury beating heart (MBH) system in an acidic solution in the absence of a strong oxidant. Furthermore, the system is subjected to an external square wave potential. It was observed that different shapes (circular, elliptical, triangular, and multilobed stars) of the mercury drop could be stabilized as the frequency of the external potential and the volume of the mercury were varied. The redox potential time series for this forced MBH system, corresponding to the different stabilized topological configurations, were also recorded, and their power spectra were analyzed. The obtained results, involving the different topological modes, were fairly reproducible and sustainable. A possible oxidation−reduction mechanism for these experimental observations is provided.

I. INTRODUCTION The mercury beating heart, or the MBH system, is an exquisite experimental illustration of the chemomechanical effect. Apart from being visually spectacular, it is a very simple experiment to perform. It consists of a mercury drop covered with an aqueous acid or basic solution placed in a concave vessel. An iron nail is employed to trigger the oscillations in the acid solution with a strong oxidant. If one touches the periphery of the Hg drop with this iron nail, the mercury drop begins to execute mechanical oscillations. Apart from these mechanical oscillations (observable), there are chemical oscillations that can be recorded if one monitors the redox potential between the mercury and a reference electrode. This system is chemomechanical in nature because the mechanical and the chemical oscillations are coupled to each other. In particular, the chemical reactions (redox reactions) occurring on the surface of the mercury drop in conjunction with the variations in the surface tension of the drop drives the system mechanically. Kühne was the first to observe these mechanical oscillations induced by chemical reactions. Later, Lippmann reported his experimental observations in 1873.1,2 After a latency period of nearly a century, this MBH system was revisited by Keizer et al. in 1979.3 They carried out a detailed analysis of the reactions and their underlying mechanisms for the MBH system in a glass tube configuration. Their two key observations were:3,4 (a) Mechanical oscillations can occur in both acidic and basic solutions. (b) For the acidic solution, formation and removal of mercury sulfate (Hg2SO4) film on the mercury drop takes place even in the absence of a strong oxidant due to the presence of the dissolved O2(aq). Furthermore, they proposed a mathematical model3,4 for their system and compared its functioning to that of an electrochemical cell. Subsequently, dynamics of the MBH system were studied experimentally5−11 both in the presence and in the absence of an applied (external) constant potential (potentiostatic). The mechanical excitations of the Hg drop have also been observed for linear and ring-shaped geometries by systematically varying © 2012 American Chemical Society

Figure 1. Schematic of the experimental setup: (A) function generator, (B) digital oscilloscope, (C) Fe, (D) Pt wire, (E) saturated calomel reference electrode, (F) watch glass, (G) computer, (H) Hg drop, and (I) H2SO4 solution. The dark circle in the center of the watch glass represents the Hg drop. The Hg is covered with the acidic solution. Furthermore, Fe wire and the reference electrode were submerged in the acidic solution.

the potential of the metal tip by Smolin et al.5 They observed standing waves in a linear geometry wherein the locations of the nodes were dependent on the potential of the metal tip while the solitary waves were circulating in the ring. In the works of Castillo-Rojas et al.,10,11 the authors found self-sustained oscillations for the MBH system in an acidic solution with [CeIV(SO4)3]2− being used as the strong oxidizing agent. They reported oscillations of period-1, period-3, and period-2 periodicities in the redox potential as well as different topological configurations of the mercury drop in a watch glass geometry. In this Article, we report the nonautonomous dynamics of MBH system for watch glass geometry in an acid aqueous solution without any strong oxidizing agent. In contrast to the previously performed experiments, there is no contact between the mercury drop and the Received: September 25, 2012 Revised: December 21, 2012 Published: December 31, 2012 267

dx.doi.org/10.1021/jp3095038 | J. Phys. Chem. A 2013, 117, 267−274

The Journal of Physical Chemistry A

Article

Figure 2. (a) Elliptical shape, (b) corresponding redox time series, (c) its power spectra at 3.0 Hz for 6 mL of Hg, and (d) isolated signal with a frequency of 3.0 Hz from the function generator.

analyzed. A set of possible reactions taking place for our system, on the basis of previous investigations,3,10,11 has been proposed.

iron (Fe) nail (1.0 mm diameter) for our experimental configuration. The Fe electrode was placed vertically in the solution at a distance of approximately 2.5 cm from the periphery of the mercury drop. A 6 Vpp square wave potential (shown in Figure 2d) is supplied between the Fe nail and the mercury drop. This implies that the system is forced periodically (nonpotentiostatic), and consequently the observed dynamics are nonautonomous. To the best of our knowledge, this is the first time that such an experimental configuration for the MBH system, in an acidic solution, has been

II. EXPERIMENTAL SETUP The experimental setup consists of a watch glass (15 cm diameter) containing a fixed (4.5, 6, and 8 mL) volume of the mercury metal (Hg) covered with a 6 M H2SO4 acid solution. It is a three electrode system wherein the mercury drop and the iron nail act as the anode (working electrode) and the cathode (counter 268



Article

Table 1. Topology of the 4.5 mL Hg Drop as a Function of the Forcing Frequency While the Amplitude Is Maintained Fixed at 6 Vpp no.

mercury shape

no. of lobes

frequency range (Hz)

1 2 3 4 5 6 7 8

ellipse triangle (heart) square 5-pointed star 6-pointed star 7-pointed star 8-pointed star 9-pointed star

2 3 4 5 6 7 8 9

2.7−3.2 3.4−4.4 4.5−5.1 6.4−6.8 6.9−8.4 9.9−10.5 10.6−11.9 13.5−14.0

Table 2. Topology of the 6.0 mL Hg Drop as a Function of the Forcing Frequency While the Amplitude Is Maintained Fixed at 6 Vpp no.

mercury shape

no. of lobes

frequency range (Hz)

1 2 3 4 5 6 7 8 9

ellipse triangle (heart) square 5-pointed star 6-pointed star 7-pointed star 8-pointed star 9-pointed star 10-pointed star

2 3 4 5 6 7 8 9 10

3.0−3.7 3.8−4.5 5.1−5.2 6.3−7.4 7.5−8.6 9.4−10.1 10.2−11.0 13.1−13.4 13.5−14.5

electrode) alternatingly, and the saturated calomel electrode (SCE, Hg/Hg2Cl2, saturated KCl) is employed as the reference electrode. A platinum (Pt) wire, with a fine tip, is used to superimpose the external voltage signal on the Hg drop. This Pt wire is covered with Parafilm only leaving the small tip exposed. This small tip is subsequently submerged in the center of the mercury drop, and it is ensured that there is no contact of this tip with the acidic solution. An iron nail of 1.0 mm diameter (Sigma Aldrich) of 99.99% purity is used for the experiments. The redox voltage time series of the mercury drop is recorded using a digital oscilloscope (Tektronix, TDS 1002 B). A square wave potential (6 Vpp), generated by a function generator (Tektronix, AF 3021B), is superimposed between the Hg drop and the Fe nail. For safety purposes, the experiments were carried out in a ventilated place. A schematic of experimental setup is presented in Figure 1. To reiterate, the Fe nail was placed vertically in the acid solution approximately 2.5 cm away from the periphery of the mercury drop. This was done to avoid any contact between the nail and the mercury while the Hg drop is executing its mechanical oscillations. A square wave potential was supplied between the iron nail and the Hg drop via the platinum wire. The potential of Hg drop was measured with respect to the calomel reference electrode and recorded using a digital oscilloscope. These recorded data were simultaneously transferred to the computer, using commercial data acquisition software (NI LabView SignalExpress), for detailed analysis.

Figure 3. (a) Triangular shape, (b) corresponding redox time series, and (c) its power spectra at 4.3 Hz for 6 mL of Hg.

formation of the film leads to a decrease in the surface tension. This alternating increase and decrease in the surface tension leads to the inception of the observed mechanical oscillations. The formation and removal of the (Hg2SO4) film, in the presence of dissolved O2, can also be achieved through a superimposed voltage difference across the Hg−Fe electrodes. Therefore, the MBH can exhibit mechanical oscillations even in the absence of a strong oxidant provided there is an external voltage difference superimposed.

III. UNDERLYING CHEMICAL REACTIONS Since the pioneering work of Keizer et al.,3 it is known that for the MBH system in an acidic solution, in the presence of a strong oxidant, the formation and removal of a surface film (Hg2SO4) takes place. This cyclic removal and formation of the surface film modifies the surface tension of the Hg drop. The surface tension is increased when the removal of the film takes place, whereas the 269



Article

Figure 5. (a) The 5-pointed star and (b) corresponding redox time series for 6 mL of Hg.

pulse train, the Fe electrode behaves as the anode and the Hg electrode as the cathode. Therefore, in this case, oxidation takes places at the Fe nail and reduction takes place at the Hg drop. We can divide these possible reactions into two parts. (i) The first is oxidation of mercury (corresponding to the positive cycle). At anode (Hg): 2Hg 0 → Hg 22 + + 2e−

(1)

and at cathode (Fe): O2 + 2H+ + 2e− → H 2O

(2)

Hg2+ 2

is the free ion liberated in the solution. This free ion partially combines with the sulfate ion (SO42−(aq)) and forms an insoluble Hg2SO4 film on the surface of the mercury drop.

Figure 4. (a) Square shape, (b) corresponding redox time series, and (c) its power spectra at 5.1 Hz for 6 mL of Hg.

Hg 22 + + SO24 −(aq) ⇌ Hg 2SO4 (insoluble)

(3)

(ii) The second is reduction of mercury (corresponding to the negative cycle). At anode (Fe):

In our experimental configuration, a square wave potential (6 Vpp) is applied between the electrodes (Hg and Fe). During the positive cycle of this pulse train, the Hg electrode works as the anode and the Fe electrode works as the cathode. Consequently, oxidation takes places at the Hg drop and reduction takes place at the Fe nail. On the contrary, during the negative cycle of the

Fe → Fe2 + + 2e−

(4)

and at cathode (Hg): Hg 22 + + 2e− → 2Hg 0 270

(5)



Article

Figure 6. (a) The 6-pointed star and (b) corresponding redox time series for 6 mL of Hg. Figure 7. (a) The 7-pointed star and (b) corresponding redox time series for 6 mL of Hg.

Because of the formation of Hg0, during the reduction at the cathode, removal of the insoluble film takes place. Hence, the superimposed periodic square potential provokes the cyclic formation and removal of Hg2SO4 film on the Hg drop. Because these redox reactions are coupled to the surface tension of the mercury drop, the drop starts to exhibit mechanical oscillations that continue up until all of the H+ ions are converted to H2O.

The amplitude of the forcing function was set at 6 Vpp (shown in Figure 2d). Subsequently, the forcing frequency was increased between the 1−15 Hz range in steps of 0.1 Hz. The frequency was maintained constant for approximately a minute at each step to eliminate transients in the mechanical oscillations. Different topological modes were found to be stable for a particular frequency interval. The observed results for 4.5 mL of Hg are presented in Table 1. Apart from the topologies reported in the Table 1, circles and circles with changing radii were also recorded. These two shapes were seen, most of the time, as the drop changed from one stable topology to another. Therefore, they were repeatedly encountered between the boundaries of the frequency intervals separating two stable topologies. Although the experiments were carried out carefully, some errors in the presented frequency intervals are inevitable, more so in the lower and the upper limits of the reported ranges. However, the frequency ranges reported seem to persist (qualitatively) when the experiments were repeated. Table 2 presents the results obtained for the 6 mL volume of mercury. Figures 2−10 show the topological configuration of the mercury drop, redox time series, and, in some cases, the corresponding power spectra. Furthermore, the characteristic

IV. RESULTS We analyzed the topological modes of the mercury drops and their corresponding redox potential time series as a function of the frequency of the applied potential and volume of the mercury drop. Maintaining the amplitude of the superimposed potential pulse train constant, its frequency was systematically varied (bifurcation/ control parameter), and the different topological modes observed were recorded in conjunction with the corresponding oscillation profiles of the redox potential time series. These experiments were carried for three different volumes of the Hg drop. Tabulated results for two such volumes (4.5 and 6 mL) are presented later. For each volume of the Hg drop, the experiments were repeated about 20 times to evaluate the reproducibility and robustness of the different topological modes. For the purposes of consistency, the topological modes and the corresponding time series of the redox potential are shown when the volume of the Hg drop was chosen to be 6 mL. 271



Article

Figure 9. (a) The 9-pointed star and (b) corresponding redox time series for 6 mL of Hg.

of Hg drop. Subsequently, the frequency domain for the different topological modes was mapped out (results not shown). The only new feature for the experiments with 8 mL of Hg drop was the appearance of an 11-pointed star at higher forcing frequencies. Our experimental observations can be summarized as follows: • As the forcing frequency increases, the complexity of the structures augments. Starting with simple structures like ellipse, triangle, and square, one can encounter up to an 11-pointed star. • This enhanced complexity is reflected in the redox potential time series. By visual inspection or by comparing the power spectra of simple structures to that of the 8pointed star and 10-pointed star, it is evident that the dynamical behavior is rendered more complex with an increase in the forcing frequency. • Furthermore, it was observed that higher volumes of the Hg drop were able to stabilize more complex topological modes. For example, the 11-pointed star was seen only for

Figure 8. (a) The 8-pointed star, (b) corresponding redox time series, and (c) its power spectra at 11.0 Hz for 6 mL of Hg.

(isolated) pulse profile of the superimposed voltage signal is shown in Figure 2d. Figure 11 shows the plot for the number of the lobes versus the midpoints of the frequency intervals of Table 2. It clearly indicates that the number of lobes observed in the mercury drop are directly propotional to the frequency of the superimposed voltage signal. All of the reported figures are for the 6 mL of Hg drop system. As mentioned before, these frequency scan experiments were also conducted for an 8 mL 272



Article

Figure 11. The dark circles correspond to the number of lobes observed for the mercury drop versus the midpoints of the frequency ranges in the 6 mL of Hg experimental configuration. The solid line represents the corresponding linear fit.

• The reported structures persist for different amplitudes of the square wave potential. It was observed that the amplitude of the mechanical oscillations is proportional to the forcing amplitude. • The observed topological modes also seem to persist for different concentrations of H2SO4.

V. CONCLUSIONS AND DISCUSSION We have studied experimentally the MBH system wherein chemically induced mechanical oscillations of the mercury drop can be observed. The novelty of our experiments is that an external square wave potential was employed to drive the redox reactions. These reactions are responsible for the emergence of mechanical oscillations of the Hg drop by virtue of the variations they provoke in the surface tension of the drop. The possible oxidation−reduction reactions have been discussed in section III. Castillo-Rojas et al. had reported10,11 that the MBH system exhibits nonlinear dynamics. The redox time series in their work shows both aperiodic and periodic oscillations. In our experiments, the system behavior is entrained to the frequency of the superimposed potential pulse train. Consequently, most of the observed redox time series for lower forcing frequencies show period-1 dynamics. This is also reflected in their corresponding power spectra. However, although the redox time series shows period-1 behavior, they correspond to different topological modes of the Hg drop such as circles, ellipse, triangle, square, and stars with few lobes. As the complexity of the stabilized structures increases, so does the aperiodicity of the recorded time series. For example, the time series for the 8- and 10-pointed stars show aperiodic behavior. Consequently, their power spectra are more diffused. Finally, because the observed topological modes and the redox time series are robust and reproducible, this system could be used as a playground to test numerous concepts of nonlinear dynamics. We plan to study different types of synchronization phenomena using coupled MBH oscillators in the near future. Furthermore, an array of MBH oscillators could be used to study spatiotemporal dynamics and pattern formation in coupled discrete oscillators. Finally, a population of such oscillators could be configured to verify the existence of quorum sensing behavior.

Figure 10. (a) The 10-pointed star, (b) corresponding redox time series, and (c) its power spectra at 14.0 Hz for 6 mL of Hg.

8 mL of Hg, whereas the 10-pointed star was found only for 6 and 8 mL of mercury volumes. • From Figure 11, it can be concluded that the number of lobes in the topological modes of the mercury drop is proportional to the frequency of the applied signal. 273



■

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We would like to thank Mr. Sajid Sarif and Mr. Vikash Kumar for their valuable suggestions and useful discussions. Financial support from DST (India) and IIT Bombay is acknowledged.

■

REFERENCES

(1) Lippmann, G. Ann. Phys. (Berlin, Ger.) 1873, 149, 565. (2) Hoff, H. E.; Geddes, L. A.; Valentinuzzi, M. E.; Powell, T. Cardiovasc. Res. Cent. Bull. 1971, IX, 117. (3) Keizer, J.; Rock, P. A.; Lin, S. W. J. Am. Chem. Soc. 1979, 101, 5637−5649. (4) Lin, S. W.; Keizer, J.; Rock, P. A.; Stenschke, H. Proc. Natl. Acad. Sci. U.S.A. 1974, 71, 4477−4481. (5) Smolin, S.; Imbihl, R. J. J. Phys. Chem. 1996, 100, 19055−19058. (6) Smithwick, R. W., III; Hembree, D. M., Jr. J. Colloid Interface Sci. 1990, 140, 57−65. (7) Ealy, J. L., Jr. J. Chem. Educ. 1993, 70, 491−492. (8) Sanchez, M. M.; Sanchez, M. T. M. J. Chem. Educ. 1993, 70, 1042− 1042. (9) Olson, J.; Ursenbach, C.; Birss, V. I.; Laidlaw, W. G. J. Phys. Chem. 1989, 93, 8258−8263. (10) Castillo-Rojas, S.; Gonzalez-Chavez, J. L.; Vicente, L.; Burillo, G. J. Phys. Chem. A 2001, 105, 8038−8045. (11) Castillo-Rojas, S.; Burillo, G.; Vicente, L. Chem. Educ. 2002, 7, 159−166.

274


Potential-Dependent Topological Modes in the Mercury Beating Heart

Recommend Documents