1 Introduction
METAL ELECTRODES are used for recording bioelectric events and stimulating excitable tissue. The principal difference between recording and stimulating electrodes is the operating current density. Recording electrodes operate at a very low current density. Stimulating electrodes operate at a high current density. Despite the widespread use of electrodes, there is a paucity of quantitative information on their electrical properties. As long ago as 1932, FRICKE stated 'Our knowledge of the polarization produced by alternating currents at metallic electrodes is in a rather unsatisfactory state, experimentally as well as theoretically.' The same statement can be made today more than half a century later. The purpose of this study was to provide quantitative data on the electrical properties of typical electrode metals used for recording and stimulating over a broad range of frequency and current density. 2 Theory
As a result of WARBURG'S pioneering studies in 1899, it was discovered that a single electrode/electrolyte interface can be represented by a series capacitance C and resistance R as shown in Fig. la. However, C and R are unlike real capacitors and resistors because their values are frequency and current-density dependent. Often these components are called the polarisation capacitance and resistance. Warburg also found that, for low current density (range First received I st April and in final form 10th A u g u s t 1989
9 IFMBE: 1990 182
not specified), the reactance X of C (1/2ztfC) equals R; both varied almost inversely as the square root of frequency, i.e. R = X = k / v #f, where k is a constant. The consequence of this relationship is that the phase angle q~ is constant at re/4 for all frequencies. Only a limited number of studies have tested the accuracy of the Warburg model. When an electrode/electrolyte interface is operated with increasing sinusoidal current density, the resistance R decreases, the capacitance C increases, and the increase occurs at higher current densities as the frequency is increased. This behaviour has been investigated for a platinum electrode/electrolyte interface (SCHWAN, 1963; 1965; 1968; SCHWAN and MACZUK, 1965; JARON et al., 1969; a
electrode terminal 0
~
I(
R
electrolyte .............
C Rf
b
electrode terminal 0
[
~
I[ II \ t c
R
1
electrolyte ............
Rf
c
electrode _
terminal ~
R
Fig. 1
C
E
(a) Warbur9 equivalent for an electrode/electrolyte interface; (b) addition of the Faradic leakage resistance R I to account for the direct-current properties; (c) half-cell potential E of the electrode/electrolyte interface
Medical & Biological Engineering & Computing
March 1990
ONARAL and SCI-I'0r 1982) and for a stainless steel/saline electrode/electrolyte interface (GEDDESet al., 1971; 1972; 1973). WErNMAN and MAHLER (1963) studied electrode behaviour in response to the application of both constant current and constant voltage rectangular pulses. They stated that for platinum, tungsten and stainless steel in contact with saline, the electrode/electrolyte capacitance grew and the resistance declined with increasing current density. DVMOND (1970; 1976) reported that electrode/ electrolyte impedance properties measured with either square waves or sine waves were similar but not always equivalent. He stated that for either waveform the magnitude of the electrode/electrolyte impedance decreased as the frequency was increased (pulse duration was decreased). The difficulties involved in comparing the electrical properties of different metals, because of the highly nonlinear character of the electrode/electrolyte interface, were described by WEINMANand MAULER (1963). SCHWAN (1963) defined a 'limit current of linearity' as the current at which electrode/electrolyte resistance R and capacitance C deviated by 10 per cent from the values observed at low current density. Although the Warburg series R C equivalent is at the heart of the behaviour of an electrode/electrolyte interface, this equivalent does not account for the very-low-frequency behaviour of the interface. It is well known that such an interface can pass direct current. Therefore electrochemists place a resistance R I in parallel with the Warburg equivalent. Fig. lb shows this equivalent circuit in which R I represents the Faradic leakage resistance. The value of R I is high in the low-frequency region and is very dependent on current density, decreasing with an increase in current density. To complete the equivalent circuit of an electrode/ electrolyte interface, it is necessary to add the half-cell potential E. This is the potential developed at the electrode/electrolyte interface. The value of E depends on the species of metal and the electrolyte (species, concentration and temperature). Fig. lc illustrates the completed equivalent circuit of a single electrode/electrolyte interface. If one focuses attention on the nature of the electrode/ electrolyte impedence above 10Hz and is not concerned with electrode potentials, Fig. la provides a reasonably good representation and allows quantitative determination of R and C over a wide-frequency and current density range. The studies on the properties of different electrode/ electrolyte interfaces described herein employed this simplification. 3 M e t h o d s and materials Using the circuit shown in Fig. 2, the series-equivalent (Warburg) resistance R and capacitance C characteristics of a 0.5 mm 2 area metal/saline interface were measured at 22~ for several electrode metals. The active or test electrode (1) consisted of a length of wire which was well insulated except for the 0.5 mm 2 tip which constituted the interface. The electrode was prepared by cleaning the wire in acetone and insulated by dipping in lacquer. A large passive electrode (of negligible impedance compared with that of the 0.5 mm 2 area electrode) was used to complete the circuit. The passive electrode (2) was a strip of metal 12mm wide and bent into a U-shape as shown. The area of this electrode in contact with the electrolyte (0.9 per cent saline) was about 1400mm 2. The passive electrode metal was chosen to minimise the DC potential measured between it and the active or test electrode. Theoretically, this requires using a metal which is identical to the test electrode. The DC potential between test electrodes made Medical & Biological Engineering & Computing
of 316 stainless-steel, silver, rhodium, palladium, platinum and MP35N (an alloy consisting of 35 per cent cobalt, 35 per cent nickel, 20 per cent chromium, and 10 per cent molybdenum) and a passive electrode made of stainlesssteel was measured and found to be less than 100mV in each case. Thus, a large stainless-steel passive electrode was used for measuring the equivalent resistance, R and capacitance C of each of these metals. For a copper active electrode, a copper passive electrode was used. Similarly, an aluminium active electrode and an aluminium passive electrode were used. iRr
Rr=detector :
Fig. 2 Comparison bridge used to measure the resistive R and capacitive C components of an electrode~electrolyte interface
To measure the resistive and capacitive components of the interface, a comparison bridge was operated in the constant-current mode, i.e. the values of the resistors R, used in the ratio arms were equal and high with respect to the impedance of the small area electrode/electrolyte interface. A sine wave generator (Model 166, Wavetek, San Diego, California) was used to select the desired current. The current density was calculated by dividing the peakto-peak value of the sinusoidal current by the 0.5mm 2 area of the test electrode. In the study, eight frequencies ranging from 100 to 20000 Hz were chosen and the seriesequivalent resistance R and the capacitance C were measured for sinusoidal current densities of 0.25, 1.0, 2.5, 7.5, 25, 75, 250 and 1000Am -2. The magnitudes of the resistance and capacitance were plotted against current density for each of the eight frequencies for each type of electrode/ electrolyte interface. 4 Results Fig. 3a illustrates the series equivalent resistance R and capacitance C of 316 stainless-steel against peak-to-peak alternating current density for 100, 200, 500, 1000, 2000, 5000, 10000, and 20000Hz. Fig. 3b shows the results for platinum (Pt). The results for silver (Ag), MP35N, palladium (Pd), aluminium (Al), rhodium (Rh), and copper (Cu) are shown in Figs. 4-6. For each frequency, the resistance R decreased and capacitance C increased at current density levels above some critical value (linearity limit). Notable exceptions were the behaviour of silver (Ag) and MP35N at frequencies above 1 kHz. For silver at frequencies above 1 kHz, R began to increase and C began to decrease slightly at current densities beyond the linearity limit. Similarly, for MP35N at frequencies above l kHz, R began to increase slightly at current densities beyond the linearity limit. Aluminium also exhibited anomalous behaviour at 100, 200 a n d 500Hz with R first increasing and then decreasing as the current density was increased. The current density linearity limit was identified as the current density at which the values of R or C deviate from those observed at low current densities by 10 p e r cent (ScHNVAN, 1963). The linearity limit marks the current density below which R and C are nearly constant at a particular frequency, and thus the current density below
March 1990
183
which linear system theory can be used to model the electrode/electrolyte interface. With the exception of copper, the current density linearity limit increased with increasing frequency. To emphasise this fact, the linearity limits at each frequency are connected by a broken line identified as the locus on each illustration. In most cases, the 10 per cent increase in capacitance occurred at a lower current density than the 10 per cent decrease in resistance, i.e. in most cases the locus for C lies to the left of the locus for R. 20
For easier comparison of the current-carrying capabilities of the various electrode materials, Fig. 7 is presented and shows the current density linearity limit (using the 10 per cent criterion) against frequency for each of the eight electrode metals. In Fig. 7a, the current density for a 10 per cent decrease in resistance R is plotted against frequency, and in Fig. 7b the current density for a 10 per cent increase in capacitance C is plotted against frequency. In both cases the current desnity linearity limit for Cu is quite s t a i n l e s s - steel
s t a i n l e s s - steel 100m
e
J o c u s ~, ~ -
I00 200 100
Hz
~ lO G
0 -20k 0-1
1.0
10
,o[ 0 0"1
1000
I00
Hz
~oo /
METAL ELECTRODES are used for recording bioelectric events and stimulating excitable tissue. The principal difference between recording and stimulating electrodes is the operating current density. Recording electrodes operate at a very low current density. Stimulating electrodes operate at a high current density. Despite the widespread use of electrodes, there is a paucity of quantitative information on their electrical properties. As long ago as 1932, FRICKE stated 'Our knowledge of the polarization produced by alternating currents at metallic electrodes is in a rather unsatisfactory state, experimentally as well as theoretically.' The same statement can be made today more than half a century later. The purpose of this study was to provide quantitative data on the electrical properties of typical electrode metals used for recording and stimulating over a broad range of frequency and current density. 2 Theory
As a result of WARBURG'S pioneering studies in 1899, it was discovered that a single electrode/electrolyte interface can be represented by a series capacitance C and resistance R as shown in Fig. la. However, C and R are unlike real capacitors and resistors because their values are frequency and current-density dependent. Often these components are called the polarisation capacitance and resistance. Warburg also found that, for low current density (range First received I st April and in final form 10th A u g u s t 1989
9 IFMBE: 1990 182
not specified), the reactance X of C (1/2ztfC) equals R; both varied almost inversely as the square root of frequency, i.e. R = X = k / v #f, where k is a constant. The consequence of this relationship is that the phase angle q~ is constant at re/4 for all frequencies. Only a limited number of studies have tested the accuracy of the Warburg model. When an electrode/electrolyte interface is operated with increasing sinusoidal current density, the resistance R decreases, the capacitance C increases, and the increase occurs at higher current densities as the frequency is increased. This behaviour has been investigated for a platinum electrode/electrolyte interface (SCHWAN, 1963; 1965; 1968; SCHWAN and MACZUK, 1965; JARON et al., 1969; a
electrode terminal 0
~
I(
R
electrolyte .............
C Rf
b
electrode terminal 0
[
~
I[ II \ t c
R
1
electrolyte ............
Rf
c
electrode _
terminal ~
R
Fig. 1
C
E
(a) Warbur9 equivalent for an electrode/electrolyte interface; (b) addition of the Faradic leakage resistance R I to account for the direct-current properties; (c) half-cell potential E of the electrode/electrolyte interface
Medical & Biological Engineering & Computing
March 1990
ONARAL and SCI-I'0r 1982) and for a stainless steel/saline electrode/electrolyte interface (GEDDESet al., 1971; 1972; 1973). WErNMAN and MAHLER (1963) studied electrode behaviour in response to the application of both constant current and constant voltage rectangular pulses. They stated that for platinum, tungsten and stainless steel in contact with saline, the electrode/electrolyte capacitance grew and the resistance declined with increasing current density. DVMOND (1970; 1976) reported that electrode/ electrolyte impedance properties measured with either square waves or sine waves were similar but not always equivalent. He stated that for either waveform the magnitude of the electrode/electrolyte impedance decreased as the frequency was increased (pulse duration was decreased). The difficulties involved in comparing the electrical properties of different metals, because of the highly nonlinear character of the electrode/electrolyte interface, were described by WEINMANand MAULER (1963). SCHWAN (1963) defined a 'limit current of linearity' as the current at which electrode/electrolyte resistance R and capacitance C deviated by 10 per cent from the values observed at low current density. Although the Warburg series R C equivalent is at the heart of the behaviour of an electrode/electrolyte interface, this equivalent does not account for the very-low-frequency behaviour of the interface. It is well known that such an interface can pass direct current. Therefore electrochemists place a resistance R I in parallel with the Warburg equivalent. Fig. lb shows this equivalent circuit in which R I represents the Faradic leakage resistance. The value of R I is high in the low-frequency region and is very dependent on current density, decreasing with an increase in current density. To complete the equivalent circuit of an electrode/ electrolyte interface, it is necessary to add the half-cell potential E. This is the potential developed at the electrode/electrolyte interface. The value of E depends on the species of metal and the electrolyte (species, concentration and temperature). Fig. lc illustrates the completed equivalent circuit of a single electrode/electrolyte interface. If one focuses attention on the nature of the electrode/ electrolyte impedence above 10Hz and is not concerned with electrode potentials, Fig. la provides a reasonably good representation and allows quantitative determination of R and C over a wide-frequency and current density range. The studies on the properties of different electrode/ electrolyte interfaces described herein employed this simplification. 3 M e t h o d s and materials Using the circuit shown in Fig. 2, the series-equivalent (Warburg) resistance R and capacitance C characteristics of a 0.5 mm 2 area metal/saline interface were measured at 22~ for several electrode metals. The active or test electrode (1) consisted of a length of wire which was well insulated except for the 0.5 mm 2 tip which constituted the interface. The electrode was prepared by cleaning the wire in acetone and insulated by dipping in lacquer. A large passive electrode (of negligible impedance compared with that of the 0.5 mm 2 area electrode) was used to complete the circuit. The passive electrode (2) was a strip of metal 12mm wide and bent into a U-shape as shown. The area of this electrode in contact with the electrolyte (0.9 per cent saline) was about 1400mm 2. The passive electrode metal was chosen to minimise the DC potential measured between it and the active or test electrode. Theoretically, this requires using a metal which is identical to the test electrode. The DC potential between test electrodes made Medical & Biological Engineering & Computing
of 316 stainless-steel, silver, rhodium, palladium, platinum and MP35N (an alloy consisting of 35 per cent cobalt, 35 per cent nickel, 20 per cent chromium, and 10 per cent molybdenum) and a passive electrode made of stainlesssteel was measured and found to be less than 100mV in each case. Thus, a large stainless-steel passive electrode was used for measuring the equivalent resistance, R and capacitance C of each of these metals. For a copper active electrode, a copper passive electrode was used. Similarly, an aluminium active electrode and an aluminium passive electrode were used. iRr
Rr=detector :
Fig. 2 Comparison bridge used to measure the resistive R and capacitive C components of an electrode~electrolyte interface
To measure the resistive and capacitive components of the interface, a comparison bridge was operated in the constant-current mode, i.e. the values of the resistors R, used in the ratio arms were equal and high with respect to the impedance of the small area electrode/electrolyte interface. A sine wave generator (Model 166, Wavetek, San Diego, California) was used to select the desired current. The current density was calculated by dividing the peakto-peak value of the sinusoidal current by the 0.5mm 2 area of the test electrode. In the study, eight frequencies ranging from 100 to 20000 Hz were chosen and the seriesequivalent resistance R and the capacitance C were measured for sinusoidal current densities of 0.25, 1.0, 2.5, 7.5, 25, 75, 250 and 1000Am -2. The magnitudes of the resistance and capacitance were plotted against current density for each of the eight frequencies for each type of electrode/ electrolyte interface. 4 Results Fig. 3a illustrates the series equivalent resistance R and capacitance C of 316 stainless-steel against peak-to-peak alternating current density for 100, 200, 500, 1000, 2000, 5000, 10000, and 20000Hz. Fig. 3b shows the results for platinum (Pt). The results for silver (Ag), MP35N, palladium (Pd), aluminium (Al), rhodium (Rh), and copper (Cu) are shown in Figs. 4-6. For each frequency, the resistance R decreased and capacitance C increased at current density levels above some critical value (linearity limit). Notable exceptions were the behaviour of silver (Ag) and MP35N at frequencies above 1 kHz. For silver at frequencies above 1 kHz, R began to increase and C began to decrease slightly at current densities beyond the linearity limit. Similarly, for MP35N at frequencies above l kHz, R began to increase slightly at current densities beyond the linearity limit. Aluminium also exhibited anomalous behaviour at 100, 200 a n d 500Hz with R first increasing and then decreasing as the current density was increased. The current density linearity limit was identified as the current density at which the values of R or C deviate from those observed at low current densities by 10 p e r cent (ScHNVAN, 1963). The linearity limit marks the current density below which R and C are nearly constant at a particular frequency, and thus the current density below
March 1990
183
which linear system theory can be used to model the electrode/electrolyte interface. With the exception of copper, the current density linearity limit increased with increasing frequency. To emphasise this fact, the linearity limits at each frequency are connected by a broken line identified as the locus on each illustration. In most cases, the 10 per cent increase in capacitance occurred at a lower current density than the 10 per cent decrease in resistance, i.e. in most cases the locus for C lies to the left of the locus for R. 20
For easier comparison of the current-carrying capabilities of the various electrode materials, Fig. 7 is presented and shows the current density linearity limit (using the 10 per cent criterion) against frequency for each of the eight electrode metals. In Fig. 7a, the current density for a 10 per cent decrease in resistance R is plotted against frequency, and in Fig. 7b the current density for a 10 per cent increase in capacitance C is plotted against frequency. In both cases the current desnity linearity limit for Cu is quite s t a i n l e s s - steel
s t a i n l e s s - steel 100m
e
J o c u s ~, ~ -
I00 200 100
Hz
~ lO G
0 -20k 0-1
1.0
10
,o[ 0 0"1
1000
I00
Hz
~oo /
