1 Introduction AN ELECTRODEconstitutes the connection between a stimulator and excitable tissue or that between electrically active tissue and a recording instrument. In both cases, the connection usually includes an electrode/electrolyte interface. The term electrode was introduced by FARADAY (1834) while he was investigating electrolysis. He had been using the term 'pole' to identify a metal conductor in an electrolyte. He stated, 'In place of the term pole I propose using that of electrode'. A footnote in his paper states that odos means way. In other words, an electrode provides a way for current conduction into an electrolyte. Parenthetically, in the same paper, Faraday introduced the terms anode, cathode, anion, cation, electrolyte, electrolysis and the concept of a chemical equivalent. Although it has been known since the time of VOLTA (1793; 1800) that direct current passes through an electrode/electrolyte interface, the capacitive nature of the interface was first described by VARLEY (1871), who used a reflecting galvanometer ballistically to make measurements. He reported a value of 311/~F for a 1 in 2 platinum electrode in contact with sulphuric acid. WlEN (1896) stated that the interface included both capacitive and First received 21st June and in final form 9th September 1991
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538
resistive components. However, it remained for WARBURG (1899; 1901) to develop the concept that, for low current density, the interface can be represented by a series circuit consisting of resistance and capacitance, the values of which both depend inversely on frequency. GRAHAME (1952) introduced a special circuit symbol (W) to identify these two polarisation elements. However, such an eqivalent circuit predicts an infinite impedance for direct current, a situation that is not consistent with experimental evidence. Several models of the interface were proposed by GRAHAME (1952). In most models, there is provision for a direct-current path, created either by placing a resistive element across the Warburg capacitance or in parallel with the Warburg series capacitance and resistance. The resistive element that represents the ability of the electrode/electrolyte interface to pass direct current is known as a Faradic resistance. Like the Warburg components, the Faradic resistance is also current-density dependent. To date, it has been difficult to measure this important component accurately, and this paper describes a new method for measuring the Faradic resistance of a single electrode/electrolyte interface and provides values for several different metals in 0.9 per cent sodium chloride solution at room temperature over a range of current densities. The method employs the monopolar technique and a potential-sensing ring electrode, coaxial with the electrode being tested.
Medical & Biological Engineering & Computing
September 1992
2 Theory A single electrode/electrolyte interface can be modelled by three components: (a) the series Warburg resistance Rw and capacitance Cw (b) a parallel Faradic resistance R : (c) a half-cell potential E~/2, as shown in Fig. la. The Warburg components (Rw, Cw) are polarisation elements, the values of which depend on frequency and current density (ScITWANand MACZUK, 1965; SCHVCAN, 1968; JARON et al., 1969; GEDDES et at., 1971; GEDDES, 1975, RAGHEB and GEDDES, 1990). The Faradic resistance (R:), shown in Fig. lb, accounts for the direct-current properties of an electrode/electrolyte interface; R : also decreases with increasing frequency and current density (GEDDES, 1975). The half-cell potential (El/E) depends on o
electrode terminol Rw 9 t J
Cw El/2 etectrolyte II I" ---~--~-
Worburg impedonce Rf Rw t,
=
holf-cell potentiot
C
- r--1
/2
II--~-I,-
~-
:
Iqf
1"1 Rw
Cw
Fig. 1 (a) The Warburg components (R w, Cw) and half-cell potential (Ea/2) of an electrode/electrolyte interface. (b) To accommodate the ability of the interface to carry direct current, the Faradic resistance (R:) is placed in parallel with the Warburg components. For changing current, the half-cell potential is frequently omitted, as shown in (c )
the species of metal, the electrolyte and temperature. For all these reasons it is not possible to assign constant values to the components of an electrode/electrolyte interface. For changing current, it is convenient to neglect the halfcell potential (E1/2), and the electrode/electrolyte interface becomes that shown in Fig. lc. To measure the characteristics of a single electrode/ electrolyte interface, it is convenient to use the monopolar technique, in which the electrode under investigation is made small with respect to a large, distant reference electrode in a volume conductor. The potential of the electrode under test is measured with a coaxial potential-sensing electrode. Fig. 2a illustrates this method in which a constant-current source I is connected between the test (1) and reference (2) electrodes. The potential of the test electrode 1 is measured with a ring electrode 3 around its tip. Fig. 2b presents the equivalent circuit for the current source I, the reference (2) and test (1) electrodes and the electrolyte. Note that the potential-sensing electrode 3 measures a voltage Vt- 3 that appears across r, the resistance of the electrolyte between the potential-sensing electrode 3 and test electrode 1, as well as the potential across the impedance of the test electrode/electrolyte interface, consisting of R : in parallel with Rw and Cw in series. The resistor R e represents the resistance of the electrolyte from the potential-sensing electrode 3 to the reference electrode 2. When a constant-current pulse I of sufficient duration is applied to the circuit of Fig. 2, the measured voltage 1"1-3 exhibits a three-phase response (a, b, c), as shown in Fig. 3. Because the values of Rw, Cw and R : are different in the three phases, the subscripts a, b and c are used to make this distinction. In phase a, V~_ 3 rises instantly to V,, due to the voltage appearing across r, in series with Rw, and R : , in parallel. In point of fact = I[r + gwa gfa/(gw, + R:,)]
ol
it current I source
When Cw is fully charged, 1"1-3 exhibits the phase b plateau (Fb). Because Rw and Cw are current-density dependent, the waveform of the voltage rise in phase a will not be a simple exponential. When Cw is fully charged, V1- 3 = I(r + R:b ) = Fb. However, recall that R:b is current-density dependent, but r is not because it represents the resistance of the electrolyte between the test (1) and potential-sensing (3) electrodes. During the phase b, steady-state (DC) condition, the voltage on Cw is equal to IR:b. At the instant when the current pulse is terminated, I11_a drops immediately to Fc, which represents the voltage on the Warburg capacitance, i.e. IR:b, reduced by the voltage-divider action of R~c and R f t . The voltage
3
1 2
V~
IR:b[R:~/(R:c + Rw~)]
=
From Vc, the voltage decreases as the Warburg capacitance discharges through Rwc + R:c. No capacitorI
I~
V1-3
current
"1
Fig. 2 Experimental apparatus for measuring the properties of a small-area test electrode (1). Current I is applied between the test electrode (1) and a large reference electrode (2). Potential is measured between the 0.1 cm 2 test electrode (1) and a 7ram diameter chlorided silver ring potentialsensing electrode (3). The resistor r represents the resistance of the electrolyte between the test electrode (1) and the potential-sensing electrode (3). R e represents the resistance of the electrolyte from the potential-sensing electrode (3) to the reference electrode (2) Medical & Biological Engineering & Computing
I t
C w chorging _
',
Vb
i t
V~ voltoge
vl-3
"
1
',a', I
(C w chQrged )
c
b I
,
Cw d i s c h o r g i n g
through Rw+R f
Fig. 3 The three phases (a, b, c) exhibited by V I _ constant-current pulse is initiated and arrested
September 1992
3
when a 539
discharge current flows through the constant-current source, because such a device has a very high output resistive impedance. The magnitude of Rw and R : depend on current density, which is changing as Cw discharges. Therefore the phase-c discharge waveform will not be a simple exponential. Although the foregoing equations identify three resistive quantities, r, Rw and R : , two of these ( R ~ , R : ) are currentdensity dependent and have different values during the three phases a, b, c. However, it is desired to measure R : and, during phase b, lib = I(r + R:b). Therefore by knowing r, the resistance of the electrolyte between the test (1) and potential-sensing (2) electrodes, and measuring lib, R:b can be calculated, i.e. R f b = Vb/I
-
-
Vb
V1-3 / va
/
I
currentI
3 M e t h o d s and m a t e r i a l s The measuring equipment was assembled as shown in Fig. 2. The current source consisted of an $44 Grass stimulator (Grass Instruments, Quincy, Massachusetts, USA) driving a model 2620 stimulus isolation unit (Tektronix, Beaverton, Oregon, USA). The 0.9 per cent saline (volume conductor) was contained in a 25 ml beaker, and the reference electrode was of brass shim stock, which covered the inner surface of the beaker. The area of the reference electrode was more than 100 times that of the test electrode. The coaxial, potentialsensing ring electrode 3 was 7 mm in diameter, and the test electrode 1 was placed in the centre of the ring. The potential-sensing electrode 3 was made of silver wire, chlorided to achieve the lowest impedance (GEDDES et al., 1969). The test electrodes were made of wire (typically 0.010 in diameter) of the metal studied. The exposed area in all cases was 0.1 cm 2. The potential between the test electrode (1) and the potential-sensing electrode (3) was measured with a unitygain preamplifier with an input impedance of 1012 Q. The input leakage current was set to zero by observing no change in output when a 100 Mf~ resistor was connected to the input and then short-circuited. The electrode potential 111-3 and the current pulse I were recorded on a twochannel strip-chart recorder (model 220, Gould, Cleveland, Ohio, USA). A negative current pulse was used to achieve a current density ranging from 0.1 to 100mAcm -2. This polarity was used because tissue stimulation requires the removal of positive charge from cell membranes. The duration of the current pulse was selected so that Cw became fully charged, i.e. phase b was revealed. After each trial at each current density, a period of 5-10 min was allowed for the electrode to re-establish equilibrium with the saline. All measurements were made at 25~ Data were obtained for electrodes of rhodium, stainless steel, platinum and platinum-iridium. The value of r, the resistance from the test electrode (1) to the coaxial potential-sensing ring electrode (3) was determined by obtaining the impedance-frequency relationship from 1 kHz to 100 kHz. Beyond 30 kHz, there was negligible reduction in impedance, and the impedance at this frequency was used to identify the magnitude of r, which was typically 45 ft.
~ ~
I i
r
The magnitude of r can be obtained by measuring the impedance between the test electrode 1 and the potentialsensing electrode 3 over a wide frequency range. As the frequency is increased, the impedance of the electrode/ electrolyte interfaces for electrodes 1 and 3 decreases, and the asymptotic, high-frequency impedance is r.
540
4 Results Fig. 4 is a typical example of the three-phase response of a 316 stainless-steel electrode to a negative-polarity, 1000ms, constant-current pulse that provided a current density of 1 0 m A c m -2. The Faradic resistance for this
I time
Fig. 4
Voltage (V1_3) between a O'l cm 2 stainless-steel test electrode and potential-sensing electrode in response to a 1000 ms constant-current pulse of 1 mA
30 000
24000 18000
12 ooo
6000
20
4'O
v
80
6'0
c u r r e n t d e n s i t y J , m A cm -2
Fig. 5 Faradic resistance Ry against current density (mA cm -2)
for a 0.1 cm 2 stainless-steel electrode in contact with a 0.9 per cent NaCl solution at 25~
0.4 A
~ 03 E _[&'o.2
0.1
1.o
2-0
31o
current density J,mA
4'.o
~'-o
cm -2
Fig. 6 Relationship between I / R f in millisiemens and current density J (mAcm - 2 ) for a 0"1 cm stainless-steel electrode in contact with 0.9 per cent saline. The zero-current density, Faradic resistance (R/o) is 345000f~. I / R : = 0.0029 + 0.0631J + O.O002J 2; R[o = 345 kf~
Medical & Biological Engineering & Computing
September 1992
electrode at the current density was Vb/I - r
= 1"7/1.0 x 10 -3 - 4 5 = 1655 f~
Fig. 5 is a plot of the Faradic resistance R f for the same electrode, for current density J ranging from 0.1 to 100mAcm -2. A similar relationship was obtained for rhodium, platinum and platinum-iridium. Because of the hyperbolic nature of the relationship between R I and J (Fig. 5), the reciprocal of R I was plotted against J, and a polynomial fit was obtained for the data. Fig. 6 illustrates the relationship for 1/R I and J for the same stainless-steel electrode. Note that, for zero-current density, the Faradic resistance (Rio) for the 0.1 cm 2 area electrode was 345 000 f]. Table 1 summarises the relationships between 1/R I and J for the four metal/saline interfaces investigated; the numbers in parentheses are the standard error of the estimate (SEE). The values for RIo, i.e. the Faradic resistance at zero-current density, are also shown in Table 1. Of the Table 1 Relationship between Faradic conductance Gy = 1/Ry in millisiemens and current density J in mAcm -2 for different electrode~saline interfaces for negative current pulses
Metal 316 SS Pt Rh Pt Ir
1/R s = A + BJ + (SEE)
Rio f~
CJ 2
0.0029 + 0.0631J + 0 " 0 0 0 2 J 2 (0-156) 0'033 + 0'071J + 0-00001J 2 (0.153) 0.009 + 0.074J + 0-0001,]2 (0.153) 0-021 + 0.094J - 0 - 0 0 0 1 J 2 (0.085)
345 000 30 300 111000 47 600
four metals tested, at zero-current density for the 0.1 c m 2 area electrode, platinum had the lowest Faradic resistance (30.3k~). Slightly higher was platinum-iridium (47.6kf~). Rhodium exhibited the next highest resistance (111 kf~), and stainless steel was the highest (345 kf~).
5 Discussion Because the Faradic conductance represents the ease with which charge is transferred at an electrode/electrolyte interface, this quantity may be useful in selecting the metal species that will provide the lowest impedance communication with an electrolyte. It should be noted that the zero-current conductance will also depend on the type of electrolyte and its temperature. Apparently, the first to use a constant-current pulse to investigate the properties of an electrode/electrolyte interface were WEINMAN and MAHLER (1964) who demonstrated the nonlinearity of the interface for tungsten and platinum electrodes. The model that they used placed a resistive element across the Warburg capacitance to provide a direct-current path through the interface. The pulse durations that they used were too short to reveal the phase-b plateau, and no potential-sensing electrode was used. BLOCK (1968) used the Weinman-Mahler model and the constant-current method to estimate the resistance of the tip of a tungsten microelectrode carrying 10-9A. GREATBATCH (1967), GREATBATCH a n d C H A R D A C K (1968), G R E A T BATCH et al. (1969), MANSFIELD (1967) and JARON et al. (1969) used a constant-current pulse to investigate the properties of electrodes used for cardiac pacing. Mansfield et al. used a potential-sensing electrodes but did not correct for the voltage drop in the intervening electrolyte resistance. The durations of the current pulses used in the foregoing studies were typical of those used for cardiac Medical & Biological Engineering & Computing
pacing, i.e. fractional ms to ms in duration and no clear phase b was revealed, and Faradic resistance was not determined. DE BOER and VAN OOSTEROM (1978) studied the response of small-area (0.05 mm 2) platinum electrodes to current pulses in the fractional-to-millisecond range and found that a single time constant could not describe the electrode properties. N o phase-b plateau was revealed because of the short pulse durations used. Efforts have been made to estimate the Faradic resistance for direct current by measuring the Warburg components or the magnitude of their impedance to a lower and lower sinusoidal frequency. MURDOCK and ZIMMERMAN (1936) found that the Warburg model applied for platinum in contact with sulphuric acid down to 0.05 Hz. Their log-log plot of Rw and the reactance (1/2nfCw) of Cw were linear and parallel from 3500Hz down to 0.05 Hz, there being no hint of a zero-frequency extrapolated impedance value. GEDDES et al. (1971) measured the impedance/frequency characteristics of two circular 8.9 cm diameter, stainless-steel electrodes, separated by a bridge of electrode paste 1 cm thick, over a frequency range extending from 100kHz to 0.01Hz. Current densities ranging from 50pA to 10,000#A cm -2 (peak-to-peak) were investigated. Between 0.01 and 0-1Hz, the impedance/frequency curves for the higher current-density levels lay below those for the lower current densities. The lowest current-density curve exhibited a near-zero slope in the 0.1-0.01 Hz region, hinting at a finite zero-frequency (DC) impedance. ONARAL and SCHWAN (1982) investigated the impedance of a platinum electrode in contact with a NaCI solution from 1000 to 0.001 Hz. They found that the Warburg model applied in the audio-frequency range. Extrapolation of the impedance/frequency relationship hinted that there was a finite zero-frequency (DC) resistance value. They reported that the best model for the electrode/electrolyte interface consisted of a resistive element placed in parallel with the series Rw Cw Warburg model. It should be noted that the values of Rio obtained in this study use a 0.1 cm a electrode area and radial symmetry between the test and reference electrodes. In this study, current density was obtained by dividing the current by the geometric area. It is known that current density varies slightly over the surface of an electrode. Whether the relationship between 1~Rio, i.e. the Faradic conductance per cm 2, can be scaled to smaller or larger areas has not been investigated in this study. In addition, the particular values reported are for the metal/0.9 per cent saline interface at 25~ What they are in other electrolytes and temperatures awaits investigation. The practical importance of the DC Faradic resistance arises when direct current is passed through an electrode/ electrolyte, or when measuring the galvanic skin resistance. It will be important when long-duration pulses are applied to the electrodes in contact with an electrolyte. In conclusion, to the best of our knowledge, this is the first report to investigate the D C property of a single electrode/electrolyte interface using a potential-sensing electrode and correcting for the voltage drop in the electrolyte between the test and potential-sensing electrodes. By using a constant-current pulse of sufficient duration to reveal the phase-b plateau, detected by the coaxial potential-sensing electrode, it is possible to determine the Faradic resistance of a single electrode/electrolyte interface. Using this technique, we have found that, for all the metals tested, the Faradic resistance decreases dramatically with increasing current density. Stated differently, the Faradic conductance increases with increasing current density. By using a large-area, distant reference electrode
September 1992
541
and a potential-sensing electrode adjacent to the test electrode, the same m e t h o d can be applied to determine the Faradic resistance of an electrode on the h u m a n skin.
Acknowledoment---This work was supported by the Hillenbrand Biomedical Engineering Center, Purdue University.
References BLOCK, M. T. (1968) The electrical and biological properties of tungsten microelectrodes. Med. & Biol. & Eng., 6, 517-525. DE BOER, R. W. and VAN OOS~ROM, A. (1978) Electrical properties of platinum electrodes: impedance measurements and time-domain analysis. Med. & Biol. Eng. & Comput., 16, 1-10. FARADAY, M. (1834) Experimental researches in electricity. Phil. Trans. R. Soc. London, 124, 77-122, GEDDES, L. A., BAKER, L. E. and MOORE, A. G. (1969) Optimum electrolytic chloriding of silver electrodes. Med. & Biol. Eng., 7, 49-56. GEDDES, L. A., DA COSTA, C. P. and WtSE, G. (1971) The impedance of stainless-steel electrodes. Ibid., 9, 511-521. GEDDES, L. A. (1975) Characteristics of defibrillating electrodes and living tissue. Proc. Cardioc Defib. Conf., Purdue University, West Lafayette, Indiania, USA, lst-3rd Oct., 49-53. GRAHAME, D. C. (1952) Mathematical theory of the Faradic admittance. J. Electrochem. Soc., 99, (12) 370C 385C. GREATBATCH, W. (1967) Electrochemical polarization of physiological electrodes. Med. Res. Eng., 6, (2), 13-17. GREATBATCH,W. and CHARDACK,W. M. (1968) Myocardial and endocardial electrodes for chronic implantation. Ann. N Y Acad. Sci., 148, 234-251. GREATBACH,W., PEIRSMA,B., SHANNON,F. D. and CALHOON,S. W. (1969) Polarization phenomena relating to physiological electrodes. Ibid., 149, 722-744. JARON, D., BRILLER,S. A., SCHWAS, H. P. and GESELOWITZ,D. B. (1969) Nonlinearity of cardiac pacemaker electrodes. 1EEE Trans. BME-16, 132-138. MASSFmLD, P. B. (1967) Myocardial stimulation. Am. J. Physiol., 212, 1475-1488. MURDOCK, C. G. and ZIMMERMAN, E. T. (1936) Polarization impedance at low frequencies. Physics, 7, 211-219. ONARAL, B. and SCHWAS, H. P. (1982) Linear and nonlinear properties of platinum electrode polarisation. Part 1. Frequency dependence at very low frequencies. Med. & Biol. Eno. & Comput., 20, 299-306. RAGrmB, T. and GEDD~S, L. A. (1990) The electrical properties of metallic electrodes. Ibid., 28, 182-186. SCHWAS, H. P. and MACZUK, J. G. (1965) Electrode polarization impedance: limits of linearity. Proc. 18th Ann. Conf. Eng. in Med. & Biol., Paper 5.1, 24. SCHWAS, H. P. (1968) Electrode polarization impedance and measurements in biological materials. Ann. N Y Acad. Sci., 148, 191-209. VARLEV, C. F. (1871) Polarization of metallic surfaces in aqueous solutions. Phil. Trans. R. Soc. London, 161, 129-136. VOLTA, A. (1793) Account of some discoveries made by Mr Galvani of Bologna with experiments and observations on them. In two letters from Mr Alexander Volta, FRS, Professor of Natural Philosophy in the University of Pavia, to Mr Tiberius Cavallo, FRS, Phil. Trans. R. Soc. London, 83, 285291. VOLTA, A. (1800) On the electricity excited by the mere contact of conducting substances of different kinds. In a letter from Mr
542
Alexander Volta, FRS, Professor of Natural Philosophy in the University of Pavia, to the Rt. Hon. Sir Joseph Banks, Bart. KBFRS, Ibid., 90, 744-746. WARBURG, E. (1899) Uber das Verhalten sorgenannter unpolarisbarer Electroden gegen Wechselstrom. Ann. Phys. Chem. 67, 493-499. WARBURG, E. (1901) tJber die Polarisationscapacitat des Platins. Ann. Phys. 6, 125-135. WEINMAN, J. and MAHLER, J. (1964) An analysis of electrical properties of metal electrodes. Med. & Biol. Eng., 2, 299-310 WlEN, M. (1896) tJber die Polarization bei Wechselstrom. Ibid., 58, 37-72.
Authors' biographies Susan Mayer was born in Green Bay, Wisconsin, USA. She recived a BS in Medical Technology in 1981 and worked in this area until 1989 when she enrolled in the MSEE program at Purdue University, West Lafayette, Indiana, receiving the degree in 1991. She is presently employed in industry developing a bloodglucose sensor.
Dr Leslie A. Geddes is the Emeritus Showalter Distinguished Professor of Bioengineering at Purdue University. Born in Scotland and educated in Canada, he holds the Bachelor's and Master's degrees in Electrical Engineering from McGill University and the Ph.D. degree in Physiology from Baylor University College of Medicine. He was awarded a D.Sc. Honoris Causa by McGill in 1971. Dr. Geddes has conducted research in electrocardiography, electroencephalography, electromyography, cardiac output, cardiac pacing, ventricular defibrillation, blood pressure and recording and simulating electrodes. He is a registered professional engineer in the state of Texas and has published over 600 scientific papers and 12 books. Dr Joe D. Bourland received a BA, in Science/ Engineering and a BS in Electrical Engineering from Rice University and the Ph.D. in Physiology from Baylor College of Medicine in Houston, Texas, USA. He is Co-ordinator for Engineering at the Hillenbrand Biomedical Engineering Center, Purdue University. His research interests are ventricular fibrillation/ defibrillation, electrophysiology and biomedical instrumentation. He is author of more than 100 publications in these areas and holds several patents. Lawrence L. Ogborn is Associate Professor and Director of Laboratory Programmes in the Electrical Engineering Department at Purdue University. He earned the BSEE at Rose Hulman Institute and the MSEE and Ph.D. from Purdue. Professor Ogborn has performed experimental research in the areas of general electronic circuits, measurements, instrumentation and power electronics. His current research interests include modelling, simulation and analysis of power electronic circuits, optimal design techniques, and general instrumentation and measurement problems. He is a Registered Professional Engineer in Indiana.
Medical & Biological Engineering & Computing
September 1992
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538
resistive components. However, it remained for WARBURG (1899; 1901) to develop the concept that, for low current density, the interface can be represented by a series circuit consisting of resistance and capacitance, the values of which both depend inversely on frequency. GRAHAME (1952) introduced a special circuit symbol (W) to identify these two polarisation elements. However, such an eqivalent circuit predicts an infinite impedance for direct current, a situation that is not consistent with experimental evidence. Several models of the interface were proposed by GRAHAME (1952). In most models, there is provision for a direct-current path, created either by placing a resistive element across the Warburg capacitance or in parallel with the Warburg series capacitance and resistance. The resistive element that represents the ability of the electrode/electrolyte interface to pass direct current is known as a Faradic resistance. Like the Warburg components, the Faradic resistance is also current-density dependent. To date, it has been difficult to measure this important component accurately, and this paper describes a new method for measuring the Faradic resistance of a single electrode/electrolyte interface and provides values for several different metals in 0.9 per cent sodium chloride solution at room temperature over a range of current densities. The method employs the monopolar technique and a potential-sensing ring electrode, coaxial with the electrode being tested.
Medical & Biological Engineering & Computing
September 1992
2 Theory A single electrode/electrolyte interface can be modelled by three components: (a) the series Warburg resistance Rw and capacitance Cw (b) a parallel Faradic resistance R : (c) a half-cell potential E~/2, as shown in Fig. la. The Warburg components (Rw, Cw) are polarisation elements, the values of which depend on frequency and current density (ScITWANand MACZUK, 1965; SCHVCAN, 1968; JARON et al., 1969; GEDDES et at., 1971; GEDDES, 1975, RAGHEB and GEDDES, 1990). The Faradic resistance (R:), shown in Fig. lb, accounts for the direct-current properties of an electrode/electrolyte interface; R : also decreases with increasing frequency and current density (GEDDES, 1975). The half-cell potential (El/E) depends on o
electrode terminol Rw 9 t J
Cw El/2 etectrolyte II I" ---~--~-
Worburg impedonce Rf Rw t,
=
holf-cell potentiot
C
- r--1
/2
II--~-I,-
~-
:
Iqf
1"1 Rw
Cw
Fig. 1 (a) The Warburg components (R w, Cw) and half-cell potential (Ea/2) of an electrode/electrolyte interface. (b) To accommodate the ability of the interface to carry direct current, the Faradic resistance (R:) is placed in parallel with the Warburg components. For changing current, the half-cell potential is frequently omitted, as shown in (c )
the species of metal, the electrolyte and temperature. For all these reasons it is not possible to assign constant values to the components of an electrode/electrolyte interface. For changing current, it is convenient to neglect the halfcell potential (E1/2), and the electrode/electrolyte interface becomes that shown in Fig. lc. To measure the characteristics of a single electrode/ electrolyte interface, it is convenient to use the monopolar technique, in which the electrode under investigation is made small with respect to a large, distant reference electrode in a volume conductor. The potential of the electrode under test is measured with a coaxial potential-sensing electrode. Fig. 2a illustrates this method in which a constant-current source I is connected between the test (1) and reference (2) electrodes. The potential of the test electrode 1 is measured with a ring electrode 3 around its tip. Fig. 2b presents the equivalent circuit for the current source I, the reference (2) and test (1) electrodes and the electrolyte. Note that the potential-sensing electrode 3 measures a voltage Vt- 3 that appears across r, the resistance of the electrolyte between the potential-sensing electrode 3 and test electrode 1, as well as the potential across the impedance of the test electrode/electrolyte interface, consisting of R : in parallel with Rw and Cw in series. The resistor R e represents the resistance of the electrolyte from the potential-sensing electrode 3 to the reference electrode 2. When a constant-current pulse I of sufficient duration is applied to the circuit of Fig. 2, the measured voltage 1"1-3 exhibits a three-phase response (a, b, c), as shown in Fig. 3. Because the values of Rw, Cw and R : are different in the three phases, the subscripts a, b and c are used to make this distinction. In phase a, V~_ 3 rises instantly to V,, due to the voltage appearing across r, in series with Rw, and R : , in parallel. In point of fact = I[r + gwa gfa/(gw, + R:,)]
ol
it current I source
When Cw is fully charged, 1"1-3 exhibits the phase b plateau (Fb). Because Rw and Cw are current-density dependent, the waveform of the voltage rise in phase a will not be a simple exponential. When Cw is fully charged, V1- 3 = I(r + R:b ) = Fb. However, recall that R:b is current-density dependent, but r is not because it represents the resistance of the electrolyte between the test (1) and potential-sensing (3) electrodes. During the phase b, steady-state (DC) condition, the voltage on Cw is equal to IR:b. At the instant when the current pulse is terminated, I11_a drops immediately to Fc, which represents the voltage on the Warburg capacitance, i.e. IR:b, reduced by the voltage-divider action of R~c and R f t . The voltage
3
1 2
V~
IR:b[R:~/(R:c + Rw~)]
=
From Vc, the voltage decreases as the Warburg capacitance discharges through Rwc + R:c. No capacitorI
I~
V1-3
current
"1
Fig. 2 Experimental apparatus for measuring the properties of a small-area test electrode (1). Current I is applied between the test electrode (1) and a large reference electrode (2). Potential is measured between the 0.1 cm 2 test electrode (1) and a 7ram diameter chlorided silver ring potentialsensing electrode (3). The resistor r represents the resistance of the electrolyte between the test electrode (1) and the potential-sensing electrode (3). R e represents the resistance of the electrolyte from the potential-sensing electrode (3) to the reference electrode (2) Medical & Biological Engineering & Computing
I t
C w chorging _
',
Vb
i t
V~ voltoge
vl-3
"
1
',a', I
(C w chQrged )
c
b I
,
Cw d i s c h o r g i n g
through Rw+R f
Fig. 3 The three phases (a, b, c) exhibited by V I _ constant-current pulse is initiated and arrested
September 1992
3
when a 539
discharge current flows through the constant-current source, because such a device has a very high output resistive impedance. The magnitude of Rw and R : depend on current density, which is changing as Cw discharges. Therefore the phase-c discharge waveform will not be a simple exponential. Although the foregoing equations identify three resistive quantities, r, Rw and R : , two of these ( R ~ , R : ) are currentdensity dependent and have different values during the three phases a, b, c. However, it is desired to measure R : and, during phase b, lib = I(r + R:b). Therefore by knowing r, the resistance of the electrolyte between the test (1) and potential-sensing (2) electrodes, and measuring lib, R:b can be calculated, i.e. R f b = Vb/I
-
-
Vb
V1-3 / va
/
I
currentI
3 M e t h o d s and m a t e r i a l s The measuring equipment was assembled as shown in Fig. 2. The current source consisted of an $44 Grass stimulator (Grass Instruments, Quincy, Massachusetts, USA) driving a model 2620 stimulus isolation unit (Tektronix, Beaverton, Oregon, USA). The 0.9 per cent saline (volume conductor) was contained in a 25 ml beaker, and the reference electrode was of brass shim stock, which covered the inner surface of the beaker. The area of the reference electrode was more than 100 times that of the test electrode. The coaxial, potentialsensing ring electrode 3 was 7 mm in diameter, and the test electrode 1 was placed in the centre of the ring. The potential-sensing electrode 3 was made of silver wire, chlorided to achieve the lowest impedance (GEDDES et al., 1969). The test electrodes were made of wire (typically 0.010 in diameter) of the metal studied. The exposed area in all cases was 0.1 cm 2. The potential between the test electrode (1) and the potential-sensing electrode (3) was measured with a unitygain preamplifier with an input impedance of 1012 Q. The input leakage current was set to zero by observing no change in output when a 100 Mf~ resistor was connected to the input and then short-circuited. The electrode potential 111-3 and the current pulse I were recorded on a twochannel strip-chart recorder (model 220, Gould, Cleveland, Ohio, USA). A negative current pulse was used to achieve a current density ranging from 0.1 to 100mAcm -2. This polarity was used because tissue stimulation requires the removal of positive charge from cell membranes. The duration of the current pulse was selected so that Cw became fully charged, i.e. phase b was revealed. After each trial at each current density, a period of 5-10 min was allowed for the electrode to re-establish equilibrium with the saline. All measurements were made at 25~ Data were obtained for electrodes of rhodium, stainless steel, platinum and platinum-iridium. The value of r, the resistance from the test electrode (1) to the coaxial potential-sensing ring electrode (3) was determined by obtaining the impedance-frequency relationship from 1 kHz to 100 kHz. Beyond 30 kHz, there was negligible reduction in impedance, and the impedance at this frequency was used to identify the magnitude of r, which was typically 45 ft.
~ ~
I i
r
The magnitude of r can be obtained by measuring the impedance between the test electrode 1 and the potentialsensing electrode 3 over a wide frequency range. As the frequency is increased, the impedance of the electrode/ electrolyte interfaces for electrodes 1 and 3 decreases, and the asymptotic, high-frequency impedance is r.
540
4 Results Fig. 4 is a typical example of the three-phase response of a 316 stainless-steel electrode to a negative-polarity, 1000ms, constant-current pulse that provided a current density of 1 0 m A c m -2. The Faradic resistance for this
I time
Fig. 4
Voltage (V1_3) between a O'l cm 2 stainless-steel test electrode and potential-sensing electrode in response to a 1000 ms constant-current pulse of 1 mA
30 000
24000 18000
12 ooo
6000
20
4'O
v
80
6'0
c u r r e n t d e n s i t y J , m A cm -2
Fig. 5 Faradic resistance Ry against current density (mA cm -2)
for a 0.1 cm 2 stainless-steel electrode in contact with a 0.9 per cent NaCl solution at 25~
0.4 A
~ 03 E _[&'o.2
0.1
1.o
2-0
31o
current density J,mA
4'.o
~'-o
cm -2
Fig. 6 Relationship between I / R f in millisiemens and current density J (mAcm - 2 ) for a 0"1 cm stainless-steel electrode in contact with 0.9 per cent saline. The zero-current density, Faradic resistance (R/o) is 345000f~. I / R : = 0.0029 + 0.0631J + O.O002J 2; R[o = 345 kf~
Medical & Biological Engineering & Computing
September 1992
electrode at the current density was Vb/I - r
= 1"7/1.0 x 10 -3 - 4 5 = 1655 f~
Fig. 5 is a plot of the Faradic resistance R f for the same electrode, for current density J ranging from 0.1 to 100mAcm -2. A similar relationship was obtained for rhodium, platinum and platinum-iridium. Because of the hyperbolic nature of the relationship between R I and J (Fig. 5), the reciprocal of R I was plotted against J, and a polynomial fit was obtained for the data. Fig. 6 illustrates the relationship for 1/R I and J for the same stainless-steel electrode. Note that, for zero-current density, the Faradic resistance (Rio) for the 0.1 cm 2 area electrode was 345 000 f]. Table 1 summarises the relationships between 1/R I and J for the four metal/saline interfaces investigated; the numbers in parentheses are the standard error of the estimate (SEE). The values for RIo, i.e. the Faradic resistance at zero-current density, are also shown in Table 1. Of the Table 1 Relationship between Faradic conductance Gy = 1/Ry in millisiemens and current density J in mAcm -2 for different electrode~saline interfaces for negative current pulses
Metal 316 SS Pt Rh Pt Ir
1/R s = A + BJ + (SEE)
Rio f~
CJ 2
0.0029 + 0.0631J + 0 " 0 0 0 2 J 2 (0-156) 0'033 + 0'071J + 0-00001J 2 (0.153) 0.009 + 0.074J + 0-0001,]2 (0.153) 0-021 + 0.094J - 0 - 0 0 0 1 J 2 (0.085)
345 000 30 300 111000 47 600
four metals tested, at zero-current density for the 0.1 c m 2 area electrode, platinum had the lowest Faradic resistance (30.3k~). Slightly higher was platinum-iridium (47.6kf~). Rhodium exhibited the next highest resistance (111 kf~), and stainless steel was the highest (345 kf~).
5 Discussion Because the Faradic conductance represents the ease with which charge is transferred at an electrode/electrolyte interface, this quantity may be useful in selecting the metal species that will provide the lowest impedance communication with an electrolyte. It should be noted that the zero-current conductance will also depend on the type of electrolyte and its temperature. Apparently, the first to use a constant-current pulse to investigate the properties of an electrode/electrolyte interface were WEINMAN and MAHLER (1964) who demonstrated the nonlinearity of the interface for tungsten and platinum electrodes. The model that they used placed a resistive element across the Warburg capacitance to provide a direct-current path through the interface. The pulse durations that they used were too short to reveal the phase-b plateau, and no potential-sensing electrode was used. BLOCK (1968) used the Weinman-Mahler model and the constant-current method to estimate the resistance of the tip of a tungsten microelectrode carrying 10-9A. GREATBATCH (1967), GREATBATCH a n d C H A R D A C K (1968), G R E A T BATCH et al. (1969), MANSFIELD (1967) and JARON et al. (1969) used a constant-current pulse to investigate the properties of electrodes used for cardiac pacing. Mansfield et al. used a potential-sensing electrodes but did not correct for the voltage drop in the intervening electrolyte resistance. The durations of the current pulses used in the foregoing studies were typical of those used for cardiac Medical & Biological Engineering & Computing
pacing, i.e. fractional ms to ms in duration and no clear phase b was revealed, and Faradic resistance was not determined. DE BOER and VAN OOSTEROM (1978) studied the response of small-area (0.05 mm 2) platinum electrodes to current pulses in the fractional-to-millisecond range and found that a single time constant could not describe the electrode properties. N o phase-b plateau was revealed because of the short pulse durations used. Efforts have been made to estimate the Faradic resistance for direct current by measuring the Warburg components or the magnitude of their impedance to a lower and lower sinusoidal frequency. MURDOCK and ZIMMERMAN (1936) found that the Warburg model applied for platinum in contact with sulphuric acid down to 0.05 Hz. Their log-log plot of Rw and the reactance (1/2nfCw) of Cw were linear and parallel from 3500Hz down to 0.05 Hz, there being no hint of a zero-frequency extrapolated impedance value. GEDDES et al. (1971) measured the impedance/frequency characteristics of two circular 8.9 cm diameter, stainless-steel electrodes, separated by a bridge of electrode paste 1 cm thick, over a frequency range extending from 100kHz to 0.01Hz. Current densities ranging from 50pA to 10,000#A cm -2 (peak-to-peak) were investigated. Between 0.01 and 0-1Hz, the impedance/frequency curves for the higher current-density levels lay below those for the lower current densities. The lowest current-density curve exhibited a near-zero slope in the 0.1-0.01 Hz region, hinting at a finite zero-frequency (DC) impedance. ONARAL and SCHWAN (1982) investigated the impedance of a platinum electrode in contact with a NaCI solution from 1000 to 0.001 Hz. They found that the Warburg model applied in the audio-frequency range. Extrapolation of the impedance/frequency relationship hinted that there was a finite zero-frequency (DC) resistance value. They reported that the best model for the electrode/electrolyte interface consisted of a resistive element placed in parallel with the series Rw Cw Warburg model. It should be noted that the values of Rio obtained in this study use a 0.1 cm a electrode area and radial symmetry between the test and reference electrodes. In this study, current density was obtained by dividing the current by the geometric area. It is known that current density varies slightly over the surface of an electrode. Whether the relationship between 1~Rio, i.e. the Faradic conductance per cm 2, can be scaled to smaller or larger areas has not been investigated in this study. In addition, the particular values reported are for the metal/0.9 per cent saline interface at 25~ What they are in other electrolytes and temperatures awaits investigation. The practical importance of the DC Faradic resistance arises when direct current is passed through an electrode/ electrolyte, or when measuring the galvanic skin resistance. It will be important when long-duration pulses are applied to the electrodes in contact with an electrolyte. In conclusion, to the best of our knowledge, this is the first report to investigate the D C property of a single electrode/electrolyte interface using a potential-sensing electrode and correcting for the voltage drop in the electrolyte between the test and potential-sensing electrodes. By using a constant-current pulse of sufficient duration to reveal the phase-b plateau, detected by the coaxial potential-sensing electrode, it is possible to determine the Faradic resistance of a single electrode/electrolyte interface. Using this technique, we have found that, for all the metals tested, the Faradic resistance decreases dramatically with increasing current density. Stated differently, the Faradic conductance increases with increasing current density. By using a large-area, distant reference electrode
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541
and a potential-sensing electrode adjacent to the test electrode, the same m e t h o d can be applied to determine the Faradic resistance of an electrode on the h u m a n skin.
Acknowledoment---This work was supported by the Hillenbrand Biomedical Engineering Center, Purdue University.
References BLOCK, M. T. (1968) The electrical and biological properties of tungsten microelectrodes. Med. & Biol. & Eng., 6, 517-525. DE BOER, R. W. and VAN OOS~ROM, A. (1978) Electrical properties of platinum electrodes: impedance measurements and time-domain analysis. Med. & Biol. Eng. & Comput., 16, 1-10. FARADAY, M. (1834) Experimental researches in electricity. Phil. Trans. R. Soc. London, 124, 77-122, GEDDES, L. A., BAKER, L. E. and MOORE, A. G. (1969) Optimum electrolytic chloriding of silver electrodes. Med. & Biol. Eng., 7, 49-56. GEDDES, L. A., DA COSTA, C. P. and WtSE, G. (1971) The impedance of stainless-steel electrodes. Ibid., 9, 511-521. GEDDES, L. A. (1975) Characteristics of defibrillating electrodes and living tissue. Proc. Cardioc Defib. Conf., Purdue University, West Lafayette, Indiania, USA, lst-3rd Oct., 49-53. GRAHAME, D. C. (1952) Mathematical theory of the Faradic admittance. J. Electrochem. Soc., 99, (12) 370C 385C. GREATBATCH, W. (1967) Electrochemical polarization of physiological electrodes. Med. Res. Eng., 6, (2), 13-17. GREATBATCH,W. and CHARDACK,W. M. (1968) Myocardial and endocardial electrodes for chronic implantation. Ann. N Y Acad. Sci., 148, 234-251. GREATBACH,W., PEIRSMA,B., SHANNON,F. D. and CALHOON,S. W. (1969) Polarization phenomena relating to physiological electrodes. Ibid., 149, 722-744. JARON, D., BRILLER,S. A., SCHWAS, H. P. and GESELOWITZ,D. B. (1969) Nonlinearity of cardiac pacemaker electrodes. 1EEE Trans. BME-16, 132-138. MASSFmLD, P. B. (1967) Myocardial stimulation. Am. J. Physiol., 212, 1475-1488. MURDOCK, C. G. and ZIMMERMAN, E. T. (1936) Polarization impedance at low frequencies. Physics, 7, 211-219. ONARAL, B. and SCHWAS, H. P. (1982) Linear and nonlinear properties of platinum electrode polarisation. Part 1. Frequency dependence at very low frequencies. Med. & Biol. Eno. & Comput., 20, 299-306. RAGrmB, T. and GEDD~S, L. A. (1990) The electrical properties of metallic electrodes. Ibid., 28, 182-186. SCHWAS, H. P. and MACZUK, J. G. (1965) Electrode polarization impedance: limits of linearity. Proc. 18th Ann. Conf. Eng. in Med. & Biol., Paper 5.1, 24. SCHWAS, H. P. (1968) Electrode polarization impedance and measurements in biological materials. Ann. N Y Acad. Sci., 148, 191-209. VARLEV, C. F. (1871) Polarization of metallic surfaces in aqueous solutions. Phil. Trans. R. Soc. London, 161, 129-136. VOLTA, A. (1793) Account of some discoveries made by Mr Galvani of Bologna with experiments and observations on them. In two letters from Mr Alexander Volta, FRS, Professor of Natural Philosophy in the University of Pavia, to Mr Tiberius Cavallo, FRS, Phil. Trans. R. Soc. London, 83, 285291. VOLTA, A. (1800) On the electricity excited by the mere contact of conducting substances of different kinds. In a letter from Mr
542
Alexander Volta, FRS, Professor of Natural Philosophy in the University of Pavia, to the Rt. Hon. Sir Joseph Banks, Bart. KBFRS, Ibid., 90, 744-746. WARBURG, E. (1899) Uber das Verhalten sorgenannter unpolarisbarer Electroden gegen Wechselstrom. Ann. Phys. Chem. 67, 493-499. WARBURG, E. (1901) tJber die Polarisationscapacitat des Platins. Ann. Phys. 6, 125-135. WEINMAN, J. and MAHLER, J. (1964) An analysis of electrical properties of metal electrodes. Med. & Biol. Eng., 2, 299-310 WlEN, M. (1896) tJber die Polarization bei Wechselstrom. Ibid., 58, 37-72.
Authors' biographies Susan Mayer was born in Green Bay, Wisconsin, USA. She recived a BS in Medical Technology in 1981 and worked in this area until 1989 when she enrolled in the MSEE program at Purdue University, West Lafayette, Indiana, receiving the degree in 1991. She is presently employed in industry developing a bloodglucose sensor.
Dr Leslie A. Geddes is the Emeritus Showalter Distinguished Professor of Bioengineering at Purdue University. Born in Scotland and educated in Canada, he holds the Bachelor's and Master's degrees in Electrical Engineering from McGill University and the Ph.D. degree in Physiology from Baylor University College of Medicine. He was awarded a D.Sc. Honoris Causa by McGill in 1971. Dr. Geddes has conducted research in electrocardiography, electroencephalography, electromyography, cardiac output, cardiac pacing, ventricular defibrillation, blood pressure and recording and simulating electrodes. He is a registered professional engineer in the state of Texas and has published over 600 scientific papers and 12 books. Dr Joe D. Bourland received a BA, in Science/ Engineering and a BS in Electrical Engineering from Rice University and the Ph.D. in Physiology from Baylor College of Medicine in Houston, Texas, USA. He is Co-ordinator for Engineering at the Hillenbrand Biomedical Engineering Center, Purdue University. His research interests are ventricular fibrillation/ defibrillation, electrophysiology and biomedical instrumentation. He is author of more than 100 publications in these areas and holds several patents. Lawrence L. Ogborn is Associate Professor and Director of Laboratory Programmes in the Electrical Engineering Department at Purdue University. He earned the BSEE at Rose Hulman Institute and the MSEE and Ph.D. from Purdue. Professor Ogborn has performed experimental research in the areas of general electronic circuits, measurements, instrumentation and power electronics. His current research interests include modelling, simulation and analysis of power electronic circuits, optimal design techniques, and general instrumentation and measurement problems. He is a Registered Professional Engineer in Indiana.
Medical & Biological Engineering & Computing
September 1992
