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Demodulation polarography with triangularly modulated polarizing voltage
ELECTROANALYTICALCHEMISTRYAND INTERFACIALELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
App. 1
PRELIMINARY NOTE D e m o d u l a t i o n p o l a r o g r a p h y w i t h triangularly m o d u l a t e d polarizing voltage
WENNEMAR A. BROCKE
Zentrallabor fiir ChemischeAnalyse, KernforschungsanlageJi~lich {KFA) GmbH, Jiilich {FederalRepublic Germany) (Received 8th October 1971)
Recently the sensitivity of the new second-order technique "demodulation polarography''1 has been demonstrated to be higher by one order of magnitude than that of conventional a.c. polarography at almost equal complexity of apparatus. This advantage results from the higher ratio of faradaic to capacitive current as an inherent property of some polarographic methods based on the non-linearity of the faradaic impedance. Considering that the undesired capacitive current rather than random noise contributed by the cell or the amplifying device connected to it determines the sensitivity of demodulation polarography, a suitable method able to suppress coherent noise should be adapted for sensitivity improvement. In a recent paper 2 a new a.c. polarographic technique has been proposed. By applying a triangular a.c. voltage across the electrode interface the capacitive current can be transformed into a d.c. signal by a special measuring device which also separates it from the alternating faradaic current. This elimination method needs no phase alignment* so that there is no complication of measurement. In this note it is proposed to adapt the capacitive current suppressing method 2 to demodulation polarographyt . For this purpose the polarizing voltage Uc is modulated by a triangular signal rather than by a sinusoidal one corresponding to the triangular voltage superimposed on the d.c. potential in the mentioned type of a.c. polarography2 . If the waveforms of the faradaic demodulation current iFD and the capacitive demodulation current iCD then coincide with those of the faradaic current i F and the capacitive current iC respectively the elimination method can successfully be combined with demodulation polarography. E.g. for the reversible electrode process the computation of the waveforms proceeds as follows (Notation is taken from ref. 1). Equation (6) in ref. 1 has to be replaced by the triangularly modulated wave UD = t~D [1 + (8m/Tr2) (sin Wmt -- 3 - 2 sin 3~Omt + 5 -2 sin 5Wrnt - . . . )
sin wot ] (1)
Then eqns. (21) and (22) in ref. 1 become *Compare the a.c. polarographictechnique using an ampfitude-modulatedsinusoidal voltage3. J. ElectroanaL Chem., 33 (1971) App.1-3
App.2
PRELIMINARY NOTE
iFD ~ Wm% [sin(Wm t + ¼7r) -- 3-3/2 sin(3w m t + ¼1r) + 5-3/2 sin(5COmt + ¼rt) - - . . . ]
(2)
Comparing eqn. (2) with eqn. (20) in ref. 2 one realizes that eqn. (2) contains the sine series expansion of the curved saw-tooth waveform depicted in Fig. 2c, II in ref. 2. The cosine terms of eqn. (20) in ref. 2 are the result of the cosine series expansion of the polarizing triangular voltage according to eqn. (15) in ref. 2 whereas in eqn. (1) of this note the sine series expansion has been used for the modulating triangular voltage. With eqns. (23) and (24) in ref. 1 one obtains for the capacitive demodulation current iCD = corn [cos Wmt - 1/3 cos 3corot + 1/5 cos 5win t - . . . ] (3) Equation (3) contains the cosine series expansion of the square-wave function as shown in Fig. 2a, II in ref. 2 for the capacitive current. With eqns. (2) and (3) the waveforms of the demodulation signals iFD and iCD have been demonstrated to be the same as those obtained for the a.c. polarographic signals in ref. 2. This result holds for any'modulating voltage and polarizing voltage waveform respectively, and it is assumed without proof to be relevant for the irreversible case, too.
[FD
ICD
Fig. 1. The triangularly modulated polarizing voltage uD causes the faradaic demodulation current iFD and the capacitivedemodulation current iCD.
B Fig. 2. Schematic diagram of the demodulation polarograph with elimination of the capacitive demodulation current. (Go) generator for the polarizingvoltage, (Gm) generator for the triangular modulating voltage, (Mod) modulator and power amplifier, (R) ramp generator, (C) cell, (CC) coupling circuit, (LP) low pass filter, (A1) broad-band amplifier, (R1) full-waverectifier, (A2)narrow-band amplifier, (R2) rectifier, (TB) time base. £ Electroanal. Chem., 33 (1971) App.l-3
PRELIMINARY NOTE
App.3
Consequently theoretical consideration promises a successful elimination of the capacitive demodulation current iCD in the case of triangular modulation of the polarizing voltage UD. Figure 1 shows this signal causing the faradaic demodulation current iFD (for the reversible electrode process) and the capacitive demodulation current iCD. Figure 2 shows the schematic diagram of the new mode of a demodulation polarograph with triangularly modulated polarizing voltage which is assumed to be able to improve the sensitivity up to three orders of magnitude in comparison with the conventional a.c. polarography. A proper design of the electronic circuitry involved is necessary for the development of the measurement device working as close as possible to the theory outlined in this note. The development of a corresponding instrument is in progress at our laboratory. REFERENCES 1 W.A. Brocke,J. Electroanal, Chem., 30 (1971) 237. 2 J.H. Sluyters, J.S.M.C. Breukeland M. Sluyters-Rehbach,J. Electroanal. Chem., 31 (1971) 201. 3 A.V. Zheleztsov,Zh. Anal, Khim., 26 (1971) 644. J. Electroanal. Chem., 33 (1971) App.1-3
App. 1
PRELIMINARY NOTE D e m o d u l a t i o n p o l a r o g r a p h y w i t h triangularly m o d u l a t e d polarizing voltage
WENNEMAR A. BROCKE
Zentrallabor fiir ChemischeAnalyse, KernforschungsanlageJi~lich {KFA) GmbH, Jiilich {FederalRepublic Germany) (Received 8th October 1971)
Recently the sensitivity of the new second-order technique "demodulation polarography''1 has been demonstrated to be higher by one order of magnitude than that of conventional a.c. polarography at almost equal complexity of apparatus. This advantage results from the higher ratio of faradaic to capacitive current as an inherent property of some polarographic methods based on the non-linearity of the faradaic impedance. Considering that the undesired capacitive current rather than random noise contributed by the cell or the amplifying device connected to it determines the sensitivity of demodulation polarography, a suitable method able to suppress coherent noise should be adapted for sensitivity improvement. In a recent paper 2 a new a.c. polarographic technique has been proposed. By applying a triangular a.c. voltage across the electrode interface the capacitive current can be transformed into a d.c. signal by a special measuring device which also separates it from the alternating faradaic current. This elimination method needs no phase alignment* so that there is no complication of measurement. In this note it is proposed to adapt the capacitive current suppressing method 2 to demodulation polarographyt . For this purpose the polarizing voltage Uc is modulated by a triangular signal rather than by a sinusoidal one corresponding to the triangular voltage superimposed on the d.c. potential in the mentioned type of a.c. polarography2 . If the waveforms of the faradaic demodulation current iFD and the capacitive demodulation current iCD then coincide with those of the faradaic current i F and the capacitive current iC respectively the elimination method can successfully be combined with demodulation polarography. E.g. for the reversible electrode process the computation of the waveforms proceeds as follows (Notation is taken from ref. 1). Equation (6) in ref. 1 has to be replaced by the triangularly modulated wave UD = t~D [1 + (8m/Tr2) (sin Wmt -- 3 - 2 sin 3~Omt + 5 -2 sin 5Wrnt - . . . )
sin wot ] (1)
Then eqns. (21) and (22) in ref. 1 become *Compare the a.c. polarographictechnique using an ampfitude-modulatedsinusoidal voltage3. J. ElectroanaL Chem., 33 (1971) App.1-3
App.2
PRELIMINARY NOTE
iFD ~ Wm% [sin(Wm t + ¼7r) -- 3-3/2 sin(3w m t + ¼1r) + 5-3/2 sin(5COmt + ¼rt) - - . . . ]
(2)
Comparing eqn. (2) with eqn. (20) in ref. 2 one realizes that eqn. (2) contains the sine series expansion of the curved saw-tooth waveform depicted in Fig. 2c, II in ref. 2. The cosine terms of eqn. (20) in ref. 2 are the result of the cosine series expansion of the polarizing triangular voltage according to eqn. (15) in ref. 2 whereas in eqn. (1) of this note the sine series expansion has been used for the modulating triangular voltage. With eqns. (23) and (24) in ref. 1 one obtains for the capacitive demodulation current iCD = corn [cos Wmt - 1/3 cos 3corot + 1/5 cos 5win t - . . . ] (3) Equation (3) contains the cosine series expansion of the square-wave function as shown in Fig. 2a, II in ref. 2 for the capacitive current. With eqns. (2) and (3) the waveforms of the demodulation signals iFD and iCD have been demonstrated to be the same as those obtained for the a.c. polarographic signals in ref. 2. This result holds for any'modulating voltage and polarizing voltage waveform respectively, and it is assumed without proof to be relevant for the irreversible case, too.
[FD
ICD
Fig. 1. The triangularly modulated polarizing voltage uD causes the faradaic demodulation current iFD and the capacitivedemodulation current iCD.
B Fig. 2. Schematic diagram of the demodulation polarograph with elimination of the capacitive demodulation current. (Go) generator for the polarizingvoltage, (Gm) generator for the triangular modulating voltage, (Mod) modulator and power amplifier, (R) ramp generator, (C) cell, (CC) coupling circuit, (LP) low pass filter, (A1) broad-band amplifier, (R1) full-waverectifier, (A2)narrow-band amplifier, (R2) rectifier, (TB) time base. £ Electroanal. Chem., 33 (1971) App.l-3
PRELIMINARY NOTE
App.3
Consequently theoretical consideration promises a successful elimination of the capacitive demodulation current iCD in the case of triangular modulation of the polarizing voltage UD. Figure 1 shows this signal causing the faradaic demodulation current iFD (for the reversible electrode process) and the capacitive demodulation current iCD. Figure 2 shows the schematic diagram of the new mode of a demodulation polarograph with triangularly modulated polarizing voltage which is assumed to be able to improve the sensitivity up to three orders of magnitude in comparison with the conventional a.c. polarography. A proper design of the electronic circuitry involved is necessary for the development of the measurement device working as close as possible to the theory outlined in this note. The development of a corresponding instrument is in progress at our laboratory. REFERENCES 1 W.A. Brocke,J. Electroanal, Chem., 30 (1971) 237. 2 J.H. Sluyters, J.S.M.C. Breukeland M. Sluyters-Rehbach,J. Electroanal. Chem., 31 (1971) 201. 3 A.V. Zheleztsov,Zh. Anal, Khim., 26 (1971) 644. J. Electroanal. Chem., 33 (1971) App.1-3