Article pubs.acs.org/JPCB
Delayed Response of Interfacial Tension in Propagating Chemical Waves of the Belousov−Zhabotinsky Reaction without Stirring Ryo Tanaka,† Tomonori Nomoto,† Taro Toyota,‡ Hiroyuki Kitahata,§ and Masanori Fujinami*,† †
Department of Applied Chemistry and Biotechnology, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan § Department of Physics, Graduate School of Science, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan ‡
ABSTRACT: Time-resolved measurements of the interfacial tension of propagating chemical waves of the Belousov−Zhabotinsky reaction based on the iron complex catalysts were carried out without stirring by monitoring the frequency of capillary waves with the quasi-elastic laser scattering method. A delayed response of the interfacial tension with respect to absorption was found with the delay being ligand-dependent when the reaction was conducted at a liquid/liquid interface. This behavior is attributed to differences in adsorption activity of the hydrophobic metal catalyst. The delay time and the increase in interfacial tension were also reproduced by a model considering the rate constants of equilibrium adsorption.
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INTRODUCTION The Belousov−Zhabotinsky (BZ) reaction1,2 is one of the most well-known oscillatory chemical reactions. The concentration ratio of oxidized and reduced metal cations, such as Ce(IV)/ Ce(III) or Fe(III)/Fe(II), varies when organic molecules such as citric acid or malonic acid are brominated in aqueous acidic media catalyzed by the metal ions.3,4 This reaction is usually indicated by periodic color change of the solution under wellstirred conditions. The propagation of spontaneously generated chemical waves is also observed when the reagents are not stirred. In some BZ reaction systems, convective flow induced by chemical waves has been reported.5−7 Spontaneous motion of a droplet8,9 and unidirectional transport of a material object10 have also been introduced by applications of the BZ media in the conversion of chemical energy to mechanical work. Such flows or motions are based on the local changes in interfacial tension in the chemical waves of the BZ reaction. An increase in interfacial tension of 1 mN/m was observed in the BZ reaction under stirring with synchronous changes in the interfacial tension and potential when ferroin (tris(1,10-phenanthroline)iron(II)) was used as the metal catalyst at the air/liquid interface.11 A periodic increase in surface tension at the air/ water interface of chemical waves without stirring was also reported.12 The periodic changes in interfacial tension have been attributed to the differences in the surface activity of ferroin and ferriin (tris(1,10-phenanthroline)iron(III)). Most studies relating to the interfacial tension of the BZ reaction have been carried out at the air/liquid interface, although the flow also occurs at the liquid/liquid interface in the absence of stirring. © 2013 American Chemical Society
In the present study, the behavior of interfacial tension in chemical waves of the BZ reaction without stirring at both liquid/liquid and air/liquid interfaces is discussed. For measurement of the interfacial tension in the absence of stirring, methods which involve contact of a probe at the interface are not appropriate because the BZ reaction is often induced upon contact of the probe itself. Therefore, a noncontact interfacial tension measurement method is required for monitoring the interfacial tension with time. We adopted the quasi-elastic laser scattering (QELS) method for this purpose,13−15 which enabled detection without interference using a near-infrared laser by monitoring the frequency of capillary waves. Ligand dependences on the interfacial tension at the liquid/liquid interface and air/liquid interface are also discussed.
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EXPERIMENTAL SECTION Reagents and Solution Preparation. The reagents used were 150 mmol/L sodium bromate, 50 mmol/L malonic acid, 600 mmol/L sulfuric acid, 6 mmol/L ferroin, and 30 mmol/L sodium bromide. An aqueous solution of ferroin was prepared by mixing 1,10-phenanthroline and ferric sulfate solution in a 3:1 molar ratio. To clarify the effects of the ligand on the interfacial tension, 2,2′-bipyridine (bpy) was also used instead of 1,10-phenanthroline to produce the tris(2,2′-bipyridine)iron complex [Fe(bpy)3]2+/3+. All reagents were obtained from Kanto Chemical Co., Inc., Japan and dissolved in water Received: August 8, 2013 Revised: September 24, 2013 Published: October 9, 2013 13893
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oscillator. The time-resolved modulation frequency of the detected light intensity was spectrally resolved by a real-time spectrum analyzer (Tektronix RSA3303A). To calculate the interfacial tension from the detected frequency, the frequency at the air/water interface was used as a reference; 72 mN/m was taken as the surface tension of water. We assumed that the density of the aqueous reactant was the same as water and the densities of both phases are not changed during reaction. The interval of the time-resolved measurements was 5 s. Light Absorption of Chemical Waves in the Bulk Solution. To evaluate the concentration of reactants in bulk solution, absorption measurements for the propagation of the chemical wave pattern were carried out. The optical setup used to measure the time-resolved absorption profiles is shown in Figure 2. A halogen lamp (Hamamatsu L7893) was used as the
(Millipore, Milli-Q Integral 3). For sample preparation, we followed the methods of Miike and Müller.5 A quartz cell with 60 × 60 × 30 mm3 dimensions was used as a reactor, and the thickness of the mixture layer was approximately 1.3 mm. For interfacial tension measurements at the liquid/liquid interface, 30 mL of n-decane (Kanto Chemical Co. Ltd., Japan) was used as the organic phase. n-Decane was chosen because it is a nonvolatile solvent with a low activity of bromination. A plastic dish was placed on the n-decane layer to eliminate surface scattering from the air/decane interface. The resulting BZ solution was quiescent, and the chemical wave for the measurement was initiated by contacting a silver wire (Ø = 0.2 mm) to the fresh solution. The measurements were completed before bubbles rose to the surface to avoid any interference caused by the bubbles. All experiments were carried out at room temperature. Interfacial Tension Measurements. The experimental setup of the QELS method is shown in Figure 1. The system is
Figure 2. Experimental setup for the time-resolved absorption measurements of the BZ chemical waves.
Figure 1. Optical setup of the QELS method using an infrared laser for the interfacial tension measurement of the BZ chemical waves.
light source, and the white light output from an optical fiber was collimated and transmitted to the sample solutions vertically from the bottom to the top. The transmitted light was introduced into an optical fiber (Ø = 50 μm) and detected by a spectrometer (Ocean Optics, USB2000+). The diameter of the detection area in the transmitted light spot was 0.3 mm. The spectra of the transmitted light were recorded in 1 s intervals and were converted into absorbance values. Because it was not possible to measure the interfacial tension and absorption simultaneously, these measurements were performed separately, and the first wave from the initiation of the silver wire was compared by normalization of the propagation speed of the chemical wave, which was monitored by a BW CMOS camera (Artray, ARTCAM-130MI-BW).
based on the angle- and frequency-resolved detection of interfacial quasi-elastic light scattering derived from capillary waves.13−18 This scattering process is also a kind of Brillouin scattering by ripplons, which is analogous to Brillouin scattering by acoustic modes in the bulk media. There is a dispersion relation in the capillary wave also known as Lamb’s equation: 1/2 1 ⎛ γ ⎞ 3/2 ⎜ ⎟ f= ⎜ ⎟ k 2π ⎝ ρ1 + ρ2 ⎠
(1)
where f, γ, k, ρ1, and ρ2 are the frequency, interfacial tension, wavenumber of the capillary wave, and densities of two interfacial phases, respectively. The scattered light frequency is blue- or red-shifted by the frequency of the capillary wave. By optical heterodyne detection using a local oscillator with the original light frequency, the frequency shift is converted into a time-dependent intensity modulation with the capillary wave frequency. In our detection setup, a near-infrared diode laser (980 nm, 200 mW, Thorlabs PL980P330J) was used as the light source. The near-infrared laser was used because the input laser itself affected the BZ reaction when the reagents absorb laser light at wavelengths in the UV and visible regions.19 The scattered light from the interface was detected at a certain angle from the transmitted light beam using an avalanche photodiode (Hamamatsu C5331-11). The first-order Fraunhofer diffracted light from a slit below the sample cell was used as a local
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RESULTS AND DISCUSSION Delayed Response of the Liquid/Liquid Interfacial Tension with Respect to the Bulk Redox Reaction. The time-resolved absorbance profile of a ferroin-based BZ solution at 510 nm measured at the liquid/liquid interface without stirring is shown in Figure 3. A repeated sharp decrease and gradual recovery due to the BZ chemical waves was observed. Because ferroin has a maximum light absorption at 510 nm and the absorption coefficient of the oxidized ferriin form is lower, the rapid decrease and gradual increase in absorption correspond to a rapid increase in the concentration of ferriin 13894
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Interfacial Tension and Bulk Absorption in Using 2,2′Bipyridines. Under stirring, the reaction products and all reagents are rapidly moved to the interfacial region. However, this is not the case in the absence of stirring where the different adsorption and kinetic properties of reagents and products contribute to their significantly different concentration−time profiles at the interface. Therefore, we carried out a similar BZ reaction to that described above using 2,2′-bipyridine (bpy) as a ligand, which has a different hydrophobicity from 1,10phenanthroline. This was chosen because the hydrophobicity of the ligand has been shown to influence its adsorption activity.11 The chemical waves of the BZ reaction using [Fe(bpy)3]2+/3+ were observed, but the reaction reagents were paler in color compared with the case using ferroin and ferriin. The resulting time-resolved interfacial tension and bulk absorption profiles of the first chemical wave in the BZ solution of [Fe(bpy)3]2+/3+ at 522 nm are shown in Figure 5a and b,
Figure 3. Time-resolved absorption profile of BZ chemical waves at 510 nm based on the ferroin/ferriin redox couple at the liquid/liquid interface.
through oxidation and a gradual decrease through reduction back to the ferroin form in the bulk solution, respectively. To examine the relationship between the interfacial tension and bulk absorption, the time-resolved interfacial tension and absorbance are shown in Figure 4. In the present study, in order
Figure 5. Time profiles of (a) interfacial tension and (b) absorption at 522 nm for the first wave of the BZ reaction based on the [Fe(bpy)3]2+/3+ redox couple at the liquid/liquid interface after initiation by the silver wire.
Figure 4. Time profiles of (a) interfacial tension and (b) absorption at 510 nm for the first wave of the BZ reaction based on the ferroin/ ferriin redox couple at the liquid/liquid interface after initiation by the silver wire.
respectively. The increase in interfacial tension during the propagation of the chemical waves was also observed in this case, and the peak position of the interfacial tension was at 30 s, which was shorter than in the case of ferroin. Conversely, the relaxation time of the interfacial tension was 140−160 s, which was about 3 times longer than in the case of ferroin. These results suggest that the interfacial tension is affected by the adsorption behavior of the iron complex catalysts and their hydrophobicity. Relationship between the Dynamics of Bulk Concentration and Interfacial Tension. We considered that the delay in the change in interfacial tension with respect to bulk absorption may be due to the adsorption−desorption rate of the catalyst at the interface. Since the heat value produced by BZ reaction is very small (T ∼ 0.1 K) as reported by Epstein et al.,20 the temperature gradient effect can be negligible in the current study. When the chemical wave reached the detection point, the catalyst complex in the bulk and at the interface became oxidized, resulting in a change in absorbance. However, the rate of adsorption and desorption was slower than the rate of the redox reaction. As a result, during the time when the interfacial tension increased after the bulk absorption minimum, the iron catalysts gradually desorbed from the
to avoid the influence of the accumulated reaction products on the interfacial tension, we focused on the time profile of the first wave of BZ reaction after initiation of silver wire. Time zero was set to the time at which the chemical wavefront reached the detection point in both profiles by observation of the CMOS camera. An increase in interfacial tension during propagation of the chemical wave was observed (Figure 4a); however, the peak position of the interfacial tension (67 s) was delayed with respect to the minimum value of absorption (Figure 4b). The interfacial tension recovered after 40 s, whereas the absorbance continued to decrease until 250 s. Thus, there is a significant difference between the time profiles of absorption and interfacial tension. In the case of the BZ reaction under stirring, the change in surface tension and redox reaction have been reported to be synchronized.11 However, the above results indicate that the redox reaction in the bulk solution and the interfacial tension are not synchronized when the solution is not stirred with decane as the organic phase. 13895
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interface because of the low bulk concentration of reduced catalyst, and the catalysts adsorbed again when the concentration of reduced catalyst increased. To evaluate the difference between the interfacial and bulk behavior and to examine if the delay is characterized by adsorption equilibrium, we approximated the time constant of adsorption−desorption from the time profiles of bulk absorption. The adsorption rate of the oxidized and reduced catalyst can be written as
B B (0)) − gox κoxcox (0) γ(0) = γ0 − grd κ rd(c init − cox g κ rd − gox κox = γ0 − grd κ rdc init + rd αrdc init αrd − αox g κ rd − gox κox Abs(0) − rd αrd − αox
Equation 7 can be finally transformed to g κ rd − gox κox d γ (t ) 1⎛ = ⎜γ(t ) − γ(0) + rd dt αrd − αox τ⎝
dcrdI
1 = − (crdI(t ) − κ rd·crdB(t )) dt τ
I dcox 1 I B = − (cox (t ) − κox ·cox (t )) dt τ
(2a)
⎞ (Abs(t ) − Abs(0))⎟ ⎠
(9)
Using the measured interval of the time-resolved absorption, Δt, and the absorbance at each time step, the derivative of interfacial tension, Δγ(t)/Δt, is calculable at each time step of absorption measurement. By summation of the calculated derivatives from t = 0, the time profile of interfacial tension that corresponds to the integral of eq 9 was numerically calculated. The calculated time profile of the interfacial tension is shown in Figure 6. We deduced that the calculated time profile affords
(2b)
where cIrd, cIox, cBrd, and cBox are the amount of adsorbed reduced catalyst, the amount of adsorbed oxidized catalyst, the bulk concentration of reduced catalyst, and the bulk concentration of oxidized catalyst, respectively. The equations explicitly include the amount of adsorbed catalyst in the equilibrium state, and κrd and κox are the adsorption coefficients for equilibrium adsorption. τ is the time constant of equilibrium adsorption and desorption. The time constant corresponds to the recovery time to the equilibrium state when the amount of the adsorbed catalyst is deviated from the equilibrium amount. The initial amount of catalyst, cinit, can be written as B c init = crdB(t ) + cox (t )
(8)
(3)
when we consider that the amount of catalyst at the interface is much smaller than that in the bulk. The time-resolved absorption, Abs(t), can be written using the bulk concentration as B Abs(t ) = αrd·crdB(t ) + αox ·cox (t )
(4)
where αrd and αox are absorption coefficients. Here, we assumed that the decrease in interfacial tension is proportional to the amount of adsorbed catalyst: I γ(t ) = γ0 − (grd ·crdI(t ) + gox ·cox (t ))
Figure 6. (a) Absorption−time profile at 510 nm and (b) the numerically calculated difference in interfacial tension of the BZ chemical wave based on the ferroin/ferriin redox couple with decane as the organic phase. (c) Absorption−time profile at 522 nm and (d) the numerically calculated difference in interfacial tension based on the [Fe(bpy)3]2+/3+ redox couple with decane as the organic phase.
(5)
where grd and gox are the coefficients of decrease of interfacial tension and γ0 is the initial interfacial tension in the absence of adsorbates. Because the oxidized catalyst desorbs more readily, the relationship between grd and gox is grd > gox > 0. By derivation of eq 5, the rate of interfacial tension becomes d c I (t ) d c I (t ) d γ (t ) = −grd · rd − gox · ox dt dt dt
the peak position at 67 s and a 5 mN/m increase in surface tension by using a time constant of τ = 64 s and coefficient of (grdκrd − goxκox)/(αrd − αox) = 25. This compares well with the experimentally determined peak position at 67 s and about 5 mN/m increase in surface tension in the case of the ferroin catalyst. In the case of the [Fe(bpy)3]2+/3+ catalyst, the time constant was 15 s and the coefficient (grdκrd − goxκox)/(αrd − αox) was 8, resulting in a 30 s delay and a 3 mN/m increase in surface tension. The 3-fold difference in the time constant is attributed to the difference in adsorption activity of the ligands and the oxidized/reduced catalyst, although it is difficult to separate the effect of the adsorption coefficients and the reduced interfacial tension. In the numerical analysis, the time constants of adsorption and desorption were assumed to be the same. A decrease in interfacial tension was also assumed to be proportional to the amount of adsorbed catalyst. These assumptions might have influenced the interpretation of the relationship with interfacial
(6)
and by substitution of the above equations, g κ rd − gox κox d γ (t ) 1⎛ = ⎜γ0 − γ(t ) − grd κ rdc init + rd αrdc init dt αrd − αox τ⎝ −
grd κ rd − gox κox αrd − αox
⎞ Abs(t )⎟ ⎠
(7)
was introduced. Here, because the interfacial tension at t = 0 was 13896
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tension. Clarification of the time scales of absorption and desorption and the relationship between interfacial tension and adsorption remains to be made in future studies. Effects of the First Wave on Subsequent Waves. An increase in interfacial tension was not always observed in the second or subsequent waves after initiation by the silver wire, whereas an increase was always observed in the first waves, as described above. We suggest that this is because the modulation of the interfacial tension in the subsequent waves is not only influenced by the composition of the bulk but is also affected by the adsorption−desorption behavior of the previous wave. Further investigation is required to unveil the effect on interfacial tension of the chemical waves following the first wave. Surface Tension and Bulk Concentration at the Air/ Liquid Interface. Surface tension measurements at the air/ liquid interface of the BZ chemical wave were also carried out for comparison with the results at the liquid/liquid interface. In the case of the air/liquid interface, we waited at least 5 min after extraction of the reactants in the cell to ensure that the surface tension and adsorption of bromomalonic acid had reached equilibrium12 before the BZ chemical waves were initiated. The resulting time-dependent surface tension of the first chemical wave in ferroin solution is shown in Figure 7a. Figure 7b is the
Figure 8. Time profiles of (a) interfacial tension and (b) absorption at 522 nm for the first wave of the BZ reaction based on [Fe(bpy)3]2+/3+ at the air/liquid interface after initiation by the silver wire.
Under stirred conditions,21 the rate of the surface tension change in [Fe(bpy)3]2+/3+ was reported to be about 0.6 mN/m· s. The most probable reason why this was not observed in the present study is that the surface tension was below the detection limit of our system.
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CONCLUSIONS The differences in interfacial tension in the BZ reaction under stirred and nonstirred conditions were unveiled. For the same composition of bulk reagents, there was a considerable difference in the response time of the interfacial tension between the air/water and liquid/liquid interfaces. The delay was explained in terms of the hydrophobicity of the metal catalyst and the time constants of adsorption equilibrium by measuring the ligand dependence and performing numerical calculations. The results of this study are important, as they represent the first experimental and numerical results for the time constants of adsorption in relation to the interfacial tension in the BZ reaction under nonstirred conditions.
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Figure 7. Time profiles of (a) interfacial tension and (b) absorption at 510 nm for the first wave of the BZ reaction based on the ferroin/ ferriin redox couple at the air/liquid interface after initiation by the silver wire.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
corresponding time profile of absorbance. The propagation speed of the chemical wave was 0.75 mm/s, which was about half of that at the liquid/liquid interface. The difference between the time of absorption minimum and surface tension maximum was 3 s. The increase in surface tension of 1.5 mN/m was repeatedly observed when the chemical wave reached the detection point. The time constant of adsorption equilibrium was calculated to be 2 s and the coefficient became (grdκrd − goxκox)/(αrd − αox) = 2, although the delay was within the interval of the surface tension measurement. The time constant of adsorption equilibrium differs by a factor of 30 between the air/liquid and liquid/liquid interfaces. In the case of the [Fe(bpy)3]2+/3+ solution, a change in surface tension in the chemical wave was not observed, as shown in Figure 8a. The presence of chemical waves and observation of a time-dependent absorption time profile (Figure 8b) indicate that oxidation and reduction occurred.
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REFERENCES
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