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The mirage effect in electrochemistry
481
J. Electromd. Gem,, 228 (1987) 481-486 Ehvier Sequoia S.A., Lausanne - Printed in The Netherlands
Prelimii
note
THE MIRAGE EFFECT IN ELECTROCHEMISTRY
FRANC0
DECKER
**, REGIS T. NEUENSCHWANDER,
*
CARLOS L. CESAR and ANT6NIO
F.S.
PENNA Institute de FIsica, UNICAMP,
13081 Campimq
S. P. (Brazil)
(Received 24th April 1987)
Mirages are optical illusions due to the deflection of light beams travelling in a region close to a hot surface, where the density and the refraction index of air are less than elsewhere. An application of the mirage effect has been proposed recently by Boccara and co-workers [l], consisting in the detection of the heat wave generated by the absorption of modulated light in a solid via the measurement of the refractive index gradient in the fluid in contact with the absorbing sample. The refractive index gradient is measured by the periodical deflection of a He-Ne laser beam parallel to the sample surface. Such a technique, today calIed photothermal deflection spectroscopy (PDS), has been widely used since then to study the absorption spectra of solids. The fluid used in PDS experiments is sometimes an electrolyte [2,3], so care should be taken in the interpretation of the PDS signal since, in addition to the heat wave, a concentration wave may contribute as well to the gradient of the refractive index. In this note we discuss the mirage effect due exclusively to the concentration wave propagating in an electrolyte as a consequence of oxidation-reduction cycles at a dark electrode, with no intentional heating or illumination of the electrode. Our first aim is to analyze the sensitivity of this technique to concentration variations in the diffusion layer close to a planar electrode. The second aim is to discuss whether this technique is suitable to measure optically the diffusion properties of simple electrolytes. Double beam interferometry has been used in electrochemistry in order to observe refractive index fields during steady-state electrolysis [4,5]. This technique offers pictures of the diffusion layer that are intuitively understandable, but it requires high precision optical components and is not convenient for systems that undergo cyclic perturbations either in the electrode potential or in the cell current. The beam deflection technique that we propose in this work, on the contrary, is a
l Dedicated to Prof. H. Gerischer, one of the pioneers of time resolved methods in ekctrochemistry. ** To whom correspondence should be addressed.
0022-0728/87/$03.50
0 1987 Eltier
Sequoia S.A.
482
LOCK-IN
AMPLIFIER
GALVANOSTAT COII
in
0
Q
J
1
P
e
LENS
DETECTOR
Fig. 1. Experimental setup for beam deflection measurements in electrochemistry (for symbols see text).
typical modulation technique, requiring only a He-Ne laser and a position detector besides conventional electrochemical apparatus. The experimental setup used in this work (see Fig. 1) was analogous to that employed in PDS, where the modulating light beam is replaced by a sinusoidally modulated current driven through the electrochemical cell by means of a galvanostat (FAC Mod. 200) operating under external current control. The periodical deflection of the sampling He-Ne laser beam was measured by means of a position detector (Model SD-113-24-21-021 Bicell of Silicon Detector Corp.) coupled to a lock-in amplifier (EGG Mod. 124 A), which also supplied the modulation voltage input to the galvanostat. The electrochemical cell, with two opposite glass windows, was mounted on an optical stand in order to allow precise positioning of the sample.
483
The working electrode was an optically flat platinum disk with an area of 0.28 cm2, while the counter electrode was a platinum wire. A SCE reference electrode was used in potentiostatic experiments. The cell electrolytes were prepared with analytical grade chemicals and triply distilled water, and were purged with nitrogen before each experiment. The calculation of the concentration distribution in an electrolyte when applying a sinusoidal alternating current was carried out long ago by Warburg [6] and Kruger [7]. According to Vetter [S], combining the equation for the current density I=&
sin ot
(1)
and Fick’s diffusion laws, with appropriate concentration c(x, t)
c(x, t)=c,+A
exp (-GX)
boundary
conditions,
we get for the
(2)
sir+/+$)
where x is the distance from the electrode, t is the time, D the diffusion coefficient and w the angular frequency. A is an amplitude factor which is linearly proportional to I0 [8]. The partial derivative of the concentration is
acg ‘) =-A/$
exp( -Ex)
sin(oi-
The beam deflection Ic,is proportional [41 ,_f?&ranac n ac ax
Ex)
(3)
to the first derivative of the concentration
(4)
where I is the distance that the beam travels in front of the electrode, n the refractive index, and &t/i3c the variation of n with concentration, which can be taken as constant [4]. The experimental results were obtained as follows. The position detector generates an ac voltage proportional to the beam deflection 4 due to the applied sinusoidal current. The amplitude S and the phase @ of such a voltage are measured with the lock-in amplifier as a function of the electrode-beam separation x, for different values of I,, and w. From the above equations, the plots of In S vs. x and of Cpvs. x should give straight lines with a slope equal to - ,/m, and S should be linearly proportional to I,. Our experimental results are shown in Figs. 2, 3 and 4. The data refer to the measurement of the mirage effect due to the concentration wave of copper ions generated by the reversible reaction cu2+ + 2 e- * cue
(5) Figure 2 shows that the logarithm of the beam deflection signal amplitude S approaches a straight line for an electrode-beam separation larger than 90 pm. This could be expected taking into account the finite size of the focal waist of the laser beam in front of the electrode. From gaussian beam optics [9], the focal waist diameter 2Wo of a perfectly collimated beam can be written as a function of the
484
‘0 1.5-
Oo OO
-4.53 - 0.0375 x 0 0
LOW z x
0.5-
: 5 a _J
_
1
o.o-
0.5-
-0.5-
-l.O0 DISTANCE / pm
Fig. 2. Beam deflection signal amplitude vs. electrode-beam C&O, +0.5 A4 H2S04.
DENSITY
/
200 / pm
separation. f = 0.5 Hz. Electrolyte 0.01 A4
Fig. 3. Phase shift of the beam deflection signal vs. electrode-beam 0.01 M CuSO, +0.5 M H2S04.
CURRENT
100 DISTANCE
separation. f = 0.5 Hz. Electrolyte
mAa?
Fig. 4. Beam deflection signal amplitude vs. current density amplitude. f =l Hz. Electrolyte 0.01 M Electrode-beam separation approximately 40 pm.
CuSO, +0.5 M H,SO,.
485
l/e2 laser beam diameter 2W and of the lens focal length
w, = Xf ‘/SW
f ‘: (6)
Thusin ourcase (f ’ = 80 mm and W = 0.4 mm), the focal waist is approximately 80 pm in diameter. If the focal waist is very close to the sample (W, 7 x Z 2 W,), part of the beam hits the electrode during the deflection experiment. Figure 3 shows that the phase difference ip approaches a straight line for x > 100 pm. The slopes of the two straight lines in Figs. 2 and 3 are the same, having a value of 0.0375 pm-‘. From this value and from the modulation frequency (f = 0.5 Hz) one can deduce D = 1.1 x 10e5 cm2 s-l, which is a reasonable value for the diffusion coefficient of Cu2+ in aqueous solution. The value of the thermal diffusion coefficient of such an electrolyte is orders of magnitude larger, so the measured effect is due unambiguously to concentration waves only. Figure 4 shows that the signal amplitude is linearly proportional to the current density amplitude, as expected from the theory. It is possible, in principle, to deduce D from the slope of such a straight line. In practice, however, for this calculation several physical and geometrical parameters have to be known precisely to avoid large errors in D. The results in Fig. 4 indicate that the sensitivity of our measurements was high, though we did not attempt to optimize the laser focus and the sample geometry. In fact, the lowest value of S was actually measured with an I, of 0.35 mA/cm2, for a modulation frequency of 1 Hz. The charge for depositing and dissolving a layer in each half cycle was then equal to jQ =
sin wt = J,T’210
IO - = 0.11 mC cmm2
rf
This charge is well below the charge required to deposit or remove a monolayer of copper [lo]. In conclusion, we have shown that the beam deflection technique based on the mirage effect is a promising technique for the study of diffusion phenomena in electrochemistry. Diffusion constants can be measured optically and compared to the results obtained with electrochemical techniques. The modulation technique allows high sensitivity, but low modulation frequencies have to be used due to the small value of the diffusion coefficients. Such high sensitivity should be very useful in the study of the under-potential deposition of metal monolayers, of the adsorption of hydrogen on noble metal electrodes, and of the formation of very thin oxide layers on metal and semiconductor electrodes. Work is in progress in our laboratory on this subject and further results will be published shortly.
ACKNOWLEDGEMENTS
The authors thank CNPq for financial support. F.D. is grateful to H. Vargas for stimulating discussions.
486 REFERENCES 1 A.C. Boccara, D. Foumier and J. Badoz, Appl. Phys. Lett., 36 (1980) 180. 2 A.M. DortheMerle, J.P. Morand and E. Maurin, 4th Int. Meeting on Photoacoustic, Thermal and Related Sciences: Technical Digest, Ville d’Esttre1 (Canada), Aug. 1985, Abstract MD 5.1. 3 J.P. Roger, D. Foumier, A.C. Boccara, R. Nouf and D. Cahen in ref. 2, , Abstract MD 6.1. 4 R.H. MuIler in P. Delahay and C.W. Tobias (Eds.), Advances in Electrochemistry and Electrochemical Engineering, Vol. 9, Wiley, New York, 1973, p. 281. 5 K.S.V. Santhanam and R.N. O’Brien, J. Electroanal. Chem., 160 (1984) 377. 6 E. Warburg, Ann. Phys. Chem. (Leipzig) N.F., 67 (1899) 493. 7 F. Kruger, Z. Phys. Chem., 45 (1903) 1. 8 K.J. Vetter, Electrochemical Kinetics, Academic Press, New York, 1967, p. 200. 9 A. Yariv, Quantum Electronics, 2nd ed., Wiley, New York, 1975, pp. 110-113. 10 D.M. Kolb in H. Gerischer and C.W. Tobias (Eds.), Advances in Electrochemistry and Electrochemical Engineering, Vol. 11, Wiley, New York, 1978, p. 125.
J. Electromd. Gem,, 228 (1987) 481-486 Ehvier Sequoia S.A., Lausanne - Printed in The Netherlands
Prelimii
note
THE MIRAGE EFFECT IN ELECTROCHEMISTRY
FRANC0
DECKER
**, REGIS T. NEUENSCHWANDER,
*
CARLOS L. CESAR and ANT6NIO
F.S.
PENNA Institute de FIsica, UNICAMP,
13081 Campimq
S. P. (Brazil)
(Received 24th April 1987)
Mirages are optical illusions due to the deflection of light beams travelling in a region close to a hot surface, where the density and the refraction index of air are less than elsewhere. An application of the mirage effect has been proposed recently by Boccara and co-workers [l], consisting in the detection of the heat wave generated by the absorption of modulated light in a solid via the measurement of the refractive index gradient in the fluid in contact with the absorbing sample. The refractive index gradient is measured by the periodical deflection of a He-Ne laser beam parallel to the sample surface. Such a technique, today calIed photothermal deflection spectroscopy (PDS), has been widely used since then to study the absorption spectra of solids. The fluid used in PDS experiments is sometimes an electrolyte [2,3], so care should be taken in the interpretation of the PDS signal since, in addition to the heat wave, a concentration wave may contribute as well to the gradient of the refractive index. In this note we discuss the mirage effect due exclusively to the concentration wave propagating in an electrolyte as a consequence of oxidation-reduction cycles at a dark electrode, with no intentional heating or illumination of the electrode. Our first aim is to analyze the sensitivity of this technique to concentration variations in the diffusion layer close to a planar electrode. The second aim is to discuss whether this technique is suitable to measure optically the diffusion properties of simple electrolytes. Double beam interferometry has been used in electrochemistry in order to observe refractive index fields during steady-state electrolysis [4,5]. This technique offers pictures of the diffusion layer that are intuitively understandable, but it requires high precision optical components and is not convenient for systems that undergo cyclic perturbations either in the electrode potential or in the cell current. The beam deflection technique that we propose in this work, on the contrary, is a
l Dedicated to Prof. H. Gerischer, one of the pioneers of time resolved methods in ekctrochemistry. ** To whom correspondence should be addressed.
0022-0728/87/$03.50
0 1987 Eltier
Sequoia S.A.
482
LOCK-IN
AMPLIFIER
GALVANOSTAT COII
in
0
Q
J
1
P
e
LENS
DETECTOR
Fig. 1. Experimental setup for beam deflection measurements in electrochemistry (for symbols see text).
typical modulation technique, requiring only a He-Ne laser and a position detector besides conventional electrochemical apparatus. The experimental setup used in this work (see Fig. 1) was analogous to that employed in PDS, where the modulating light beam is replaced by a sinusoidally modulated current driven through the electrochemical cell by means of a galvanostat (FAC Mod. 200) operating under external current control. The periodical deflection of the sampling He-Ne laser beam was measured by means of a position detector (Model SD-113-24-21-021 Bicell of Silicon Detector Corp.) coupled to a lock-in amplifier (EGG Mod. 124 A), which also supplied the modulation voltage input to the galvanostat. The electrochemical cell, with two opposite glass windows, was mounted on an optical stand in order to allow precise positioning of the sample.
483
The working electrode was an optically flat platinum disk with an area of 0.28 cm2, while the counter electrode was a platinum wire. A SCE reference electrode was used in potentiostatic experiments. The cell electrolytes were prepared with analytical grade chemicals and triply distilled water, and were purged with nitrogen before each experiment. The calculation of the concentration distribution in an electrolyte when applying a sinusoidal alternating current was carried out long ago by Warburg [6] and Kruger [7]. According to Vetter [S], combining the equation for the current density I=&
sin ot
(1)
and Fick’s diffusion laws, with appropriate concentration c(x, t)
c(x, t)=c,+A
exp (-GX)
boundary
conditions,
we get for the
(2)
sir+/+$)
where x is the distance from the electrode, t is the time, D the diffusion coefficient and w the angular frequency. A is an amplitude factor which is linearly proportional to I0 [8]. The partial derivative of the concentration is
acg ‘) =-A/$
exp( -Ex)
sin(oi-
The beam deflection Ic,is proportional [41 ,_f?&ranac n ac ax
Ex)
(3)
to the first derivative of the concentration
(4)
where I is the distance that the beam travels in front of the electrode, n the refractive index, and &t/i3c the variation of n with concentration, which can be taken as constant [4]. The experimental results were obtained as follows. The position detector generates an ac voltage proportional to the beam deflection 4 due to the applied sinusoidal current. The amplitude S and the phase @ of such a voltage are measured with the lock-in amplifier as a function of the electrode-beam separation x, for different values of I,, and w. From the above equations, the plots of In S vs. x and of Cpvs. x should give straight lines with a slope equal to - ,/m, and S should be linearly proportional to I,. Our experimental results are shown in Figs. 2, 3 and 4. The data refer to the measurement of the mirage effect due to the concentration wave of copper ions generated by the reversible reaction cu2+ + 2 e- * cue
(5) Figure 2 shows that the logarithm of the beam deflection signal amplitude S approaches a straight line for an electrode-beam separation larger than 90 pm. This could be expected taking into account the finite size of the focal waist of the laser beam in front of the electrode. From gaussian beam optics [9], the focal waist diameter 2Wo of a perfectly collimated beam can be written as a function of the
484
‘0 1.5-
Oo OO
-4.53 - 0.0375 x 0 0
LOW z x
0.5-
: 5 a _J
_
1
o.o-
0.5-
-0.5-
-l.O0 DISTANCE / pm
Fig. 2. Beam deflection signal amplitude vs. electrode-beam C&O, +0.5 A4 H2S04.
DENSITY
/
200 / pm
separation. f = 0.5 Hz. Electrolyte 0.01 A4
Fig. 3. Phase shift of the beam deflection signal vs. electrode-beam 0.01 M CuSO, +0.5 M H2S04.
CURRENT
100 DISTANCE
separation. f = 0.5 Hz. Electrolyte
mAa?
Fig. 4. Beam deflection signal amplitude vs. current density amplitude. f =l Hz. Electrolyte 0.01 M Electrode-beam separation approximately 40 pm.
CuSO, +0.5 M H,SO,.
485
l/e2 laser beam diameter 2W and of the lens focal length
w, = Xf ‘/SW
f ‘: (6)
Thusin ourcase (f ’ = 80 mm and W = 0.4 mm), the focal waist is approximately 80 pm in diameter. If the focal waist is very close to the sample (W, 7 x Z 2 W,), part of the beam hits the electrode during the deflection experiment. Figure 3 shows that the phase difference ip approaches a straight line for x > 100 pm. The slopes of the two straight lines in Figs. 2 and 3 are the same, having a value of 0.0375 pm-‘. From this value and from the modulation frequency (f = 0.5 Hz) one can deduce D = 1.1 x 10e5 cm2 s-l, which is a reasonable value for the diffusion coefficient of Cu2+ in aqueous solution. The value of the thermal diffusion coefficient of such an electrolyte is orders of magnitude larger, so the measured effect is due unambiguously to concentration waves only. Figure 4 shows that the signal amplitude is linearly proportional to the current density amplitude, as expected from the theory. It is possible, in principle, to deduce D from the slope of such a straight line. In practice, however, for this calculation several physical and geometrical parameters have to be known precisely to avoid large errors in D. The results in Fig. 4 indicate that the sensitivity of our measurements was high, though we did not attempt to optimize the laser focus and the sample geometry. In fact, the lowest value of S was actually measured with an I, of 0.35 mA/cm2, for a modulation frequency of 1 Hz. The charge for depositing and dissolving a layer in each half cycle was then equal to jQ =
sin wt = J,T’210
IO - = 0.11 mC cmm2
rf
This charge is well below the charge required to deposit or remove a monolayer of copper [lo]. In conclusion, we have shown that the beam deflection technique based on the mirage effect is a promising technique for the study of diffusion phenomena in electrochemistry. Diffusion constants can be measured optically and compared to the results obtained with electrochemical techniques. The modulation technique allows high sensitivity, but low modulation frequencies have to be used due to the small value of the diffusion coefficients. Such high sensitivity should be very useful in the study of the under-potential deposition of metal monolayers, of the adsorption of hydrogen on noble metal electrodes, and of the formation of very thin oxide layers on metal and semiconductor electrodes. Work is in progress in our laboratory on this subject and further results will be published shortly.
ACKNOWLEDGEMENTS
The authors thank CNPq for financial support. F.D. is grateful to H. Vargas for stimulating discussions.
486 REFERENCES 1 A.C. Boccara, D. Foumier and J. Badoz, Appl. Phys. Lett., 36 (1980) 180. 2 A.M. DortheMerle, J.P. Morand and E. Maurin, 4th Int. Meeting on Photoacoustic, Thermal and Related Sciences: Technical Digest, Ville d’Esttre1 (Canada), Aug. 1985, Abstract MD 5.1. 3 J.P. Roger, D. Foumier, A.C. Boccara, R. Nouf and D. Cahen in ref. 2, , Abstract MD 6.1. 4 R.H. MuIler in P. Delahay and C.W. Tobias (Eds.), Advances in Electrochemistry and Electrochemical Engineering, Vol. 9, Wiley, New York, 1973, p. 281. 5 K.S.V. Santhanam and R.N. O’Brien, J. Electroanal. Chem., 160 (1984) 377. 6 E. Warburg, Ann. Phys. Chem. (Leipzig) N.F., 67 (1899) 493. 7 F. Kruger, Z. Phys. Chem., 45 (1903) 1. 8 K.J. Vetter, Electrochemical Kinetics, Academic Press, New York, 1967, p. 200. 9 A. Yariv, Quantum Electronics, 2nd ed., Wiley, New York, 1975, pp. 110-113. 10 D.M. Kolb in H. Gerischer and C.W. Tobias (Eds.), Advances in Electrochemistry and Electrochemical Engineering, Vol. 11, Wiley, New York, 1978, p. 125.