The electrical characteristics of carbon fibre microelectrodes

Journal of Neuroscience Methods, 3 (1980) 37--48 © Elsevier/North-Holland Biomedical Press 37 THE ELECTRICAL CHARACTERISTICS OF CARBON FIBRE MICROELECTRODES K. FOX, M. ARMSTRONG-JAMES and J. MILLAR Department of Physiology, The London Hospital Medical College, Turner Street, London E1 2AD (U.K.) (Received March 17th, 1980} (Accepted May 19th, 1980) Key words: recording microelectrodes -- carbon fibre microelectrodes -- iontophoresis The impedance of carbon fibre-containing microelectrodes was measured at a range of frequencies. From this and other data an equivalent circuit model for the microelectrodes was constructed. Various parameters of the model that contribute to the overall noise performance of the microelectrodes when recording extracellular nerve action potentials were discussed. INTRODUCTION A r e c e n t p a p e r ( A r m s t r o n g - J a m e s a n d Millar, 1 9 7 9 ) d e s c r i b e d t h e cons t r u c t i o n o f m i c r o e l e c t r o d e s c o n t a i n i n g a single c a r b o n fibre ( d i a m e t e r 7--8 p m ) in t h e r e c o r d i n g barrel. T h e s e m i c r o e l e c t r o d e s a p p e a r t o h a v e similar r e c o r d i n g qualities in t h e c e n t r a l n e r v o u s s y s t e m t o t u n g s t e n m i c r o e l e c t r o d e s ( G e s t e l a n d et al., 1 9 5 9 ; F r a n k a n d B e c k e r , 1 9 6 4 ; Merrill a n d A i n s w o r t h , 1 9 7 2 ) b u t are easier t o c o n s t r u c t , a n d can b e used in m u l t i b a r r e l m i c r o e l e c t r o d e s in i o n t o p h o r e t i c studies (Curtis, 1 9 6 4 ) . I n t h e p r e s e n t p a p e r , we describe s o m e o f t h e electrical c h a r a c t e r i s t i c s o f t h e s e m i c r o e l e c t r o d e s . METHODS R e s i s t a n c e o f carbon fibres Single c a r b o n fibres w e r e r e m o v e d f r o m large b u n d l e s using fine j e w e l l e r ' s f o r c e p s a n d laid across a piece o f clean w a x - c o a t e d l a b o r a t o r y p a p e r w i t h t h e i r ends d i p p i n g i n t o t w o small m e r c u r y puddles. ( T h e fibres m a y b e obt a i n e d f r o m C o u r t a u l d s , C a r b o n Fibres Division, P.O. B o x 16, C o v e n t r y , C V 6 5AE, U.K.). A DC signal o f a f e w millivolts was a p p l i e d across silver wires d i p p i n g i n t o t h e m e r c u r y a n d t h e resulting c u r r e n t r e a d o f f w i t h an accurate ammeter (Solartron 7040). The distance between the mercury p u d d l e s was m e a s u r e d a n d h e n c e r e s i s t a n c e per u n i t length o f t h e fibres obtained. 38 impedance o f carbon fibre microelectrodes Single-barrel carbon fibre microelectrodes were prepared as described earlier (Armstrong-James and Millar, 1979). After the carbon tips had been cut off with forceps, they were further etched to the desired final length in a bead of dilute (~0.1 M) chromic acid with a current of about 500 pA AC (50 Hz). The impedance was measured by using a potential divider system as shown in Fig. 1. A 100 mV sine wave was applied to a precision (-+1%) 1 M resistor in series with the electrode, and the voltage drop monitored with an FET voltage follower (input resistance >1012 ~ ) . Alternatively, the 100 mV was applied to the indifferent electrode (silver--silver chloride) and the precision resistor grounded. Peak-to-peak voltages were measured on an oscilloscope. In later experiments the voltage across the microelectrode was held constant at 5 mV and the source voltage altered. The results obtained from both techniques gave similar results. The impedance measured in this way is, of course, the impedance for the complete system of microelectrode--saline bath--indifferent electrode. However, the impedance of the saline and indifferent electrode is low compared to that of the microelectrode, and can be ignored for most purposes. Noise levels A 'Neurolog' NL100-NL103 AC coupled differential voltage follower probe was used in these experiments. The peak-to-peak noise voltage was estimated visually after suitable gain and filtering from an oscilloscope display at low sweep speeds. In differential mode, the peak total system noise with both channels A and B connected to the probe ground was found to be ~ 1 0 gV at a bandwidth of 10 Hz to 10 kHz. Microelectrode noise was estimated by connecting channel A to a carbon fibre microelectrode in a saline Mercury or S a l i n e ~ 1M~ | Silver C h l o r i d e d ~__ silver wire Glass p i p e t t e - C a r b o n fiber . - - = o CRO Insulation --- .- Sintered A g . A g C I d i s k - - - // j/ / 0.9%Saline Fig. 1. A p p a r a t u s used t o measure mJcroeleetrode impedance. A sine wave is a p p ] i e d via a reversing switch to a 1 M ~ resistor in series with the microelectrode and a saline bath. T h e voltage drop across the m i c r o e l e c t r o d e is m o n i t o r e d with an F E T (Field E f f e c t Transistor) headstage. 39 bath (as in Fig. 1), with a silver--silver chloride indifferent electrode connected to the probe ground. Channel B was left grounded and A-B recording mode used. RESULTS Resistance of carbon fibres The DC current--voltage curves for carbon fibres were straight lines with a slope resistance of 250 Ft/mm +10% up to +1.0 V. The resistivity of graphite is quoted (Weast, 1977) as 1375 p~2/cm. Thus, for a cylindrical fibre with a diameter between 7 and 8 pm, the resistance should be between 357 ~2/mm and 273 ~2/mm. The experimental value is close to the predicted value, indicating that carbon fibres are a low resistance form of graphite. The resistance of the fibres was, however, very small compared to the total impedance of the complete microelectrodes (see below). Impedance of single-barrel carbon fibre microelectrodes Single-barrel carbon fibre microelectrodes were prepared and the stem filled with mercury. The impedance was tested, as described in Methods, at a range of frequencies. The results for 5 electrodes with exposed tip lengths of 25--30 pm are shown in Fig. 2. It can be seen that all electrodes produced an S-shaped curve on log--log co-ordinates, with a slope near to --1 in the region 100 Hz to 1 kHz. A further two sets of microelectrodes (not illustrated) were prepared with the stems filled with: (a) saturated (~3 M) sodium chloride solution; and (b) dilute (0.9%) sodium chloride solution. The impedance--frequency plots for these electrodes at high frequencies (>100 Hz) were in a similar range to those of the mercury-filled electrodes. At low frequencies (<100 Hz) the dilute saline electrodes occasionally had a higher impedance (>100 M~2 at 5 Hz). Impedance of electrodes with different tip lengths Electrodes were prepared with exposed tip lengths of 60 pm. Their impedance was plotted, and then the tips were etched back to 7--10 pm. The electrode was washed and the impedance replotted. Fig. 3 shows a result for an electrode that gave a comparatively large impedance change with length. It can be seen that a reduction from 60 pm to 7 pm nearly doubled the impedance at 10 kHz, had no effect at 10 Hz, and varied proportionately at intermediate frequencies. Other electrodes showed similar or smaller changes. One electrode was prepared with an initial length of 60 pm and then etched until the fibre ended flush with the glass insulation. It was then further etched until the fibre was recessed 65 pm back into the glass. An abbreviated impedance plot (10 Hz, 100 Hz, 1 kHz and 10 kHz points) was lOOM IOM U C t~ "0 Q. E 1M lOOK 1OK 1Hz t 10Hz J 100Hz J 1KHz l IOKHz Frequency (Hz) Fig. 2. Impedance--frequency plots for single-barrel carbon fibre microelectrodes, 25--30 /zm exposed carbon fibre tip. "lOOM ~ IOM 4) U "0 O. _E tip 1M 60 pm tip lOOK 1OK 1Hz I I I I I 10Hz IOOHz 1K Hz 1OK Fiz Frequency (Hz) Fig. 3. Impedance--frequency plots for a single-barrel carbon fibre microelectrode with tip etched to two different lengths, 60/~m and 7/lm. 41 100M ........ 6 4 p m tip e x p o s e d .... 0 p m tip e x p o s e d - - 6 4 }Jm tip r e c e s s e d inside glass 10M ",. x C 1M r, E D Q \ lOOK ""'...... 1OK 1Hz I 10Hz IOOHz I I 1KHz 1OKHz Frequency (Hz) Fig. 4. Impedance--frequency plots for a single-barrel carbon fibre microelectrode etched to different tip lengths. prepared for each length (Fig. 4). When the fibre was recessed inside the glass, the impedance was tested using a drop of saline in contact with the side o f the electrode, n o t the tip, as shown in Fig. 5. This electrode had an abnormally low impedance, but otherwise the shape of the impedance curve at 60 pm tip was normal. The electrode was still able to transmit a signal with the carbon flush with the glass and even across the glass wall 60 pm back from the tip. Impedance of three-barrelled electrodes Three-barrelled microelectrodes with a carbon fibre in one barrel were prepared. All barrels were stem-filled with 0.9% saline and the impedance tested as for single-barrel microelectrodes. The results of measurements on 4 triple microelectrodes are s h o w n in Fig. 6. These graphs indicate the approximate range of impedances found. For comparison, the range of impedance values of single-barrel microelectrodes from Fig. 2 is shown as a vertical bar at each test frequency. (1) Normal tip test (2) Test with recessed tip tl 9'ass 1-/ | ~.J_ Silver w i r e connection Carbon / t Saline droplet Saline b a t h Glass extends beyond carbonfibre Fig. 5. Method of measuring impedance with (1) carbon fibre tip exposed, and (2) recessed inside glass. lOOM IOM 0 U c Q. _E ~M lOOK 10K IHz I ....... 10Hz I I IOOHz IKHz .... J IOKHz Frequency (Hz) Fig. 6. Impedance--frequency plots for 4 triple-barrel microelectrodes with a carbon fibre in the recording barrel. Vertical bars represent range of values for single-barrel carbon fibre microelectrodes shown in Fig. 2, 43 The effects of different electrolytes in the stem of the microelectrode In order to c o n n e c t the carbon fibre protruding into the stem of the microelectrodes to the preamplifier, a conduct i ng fluid must be used. In early work on single microelectrodes (cf. Fig. 2), m e r c u r y was used, with a bare silver wire dipping into it. In later work, c o n c e n t r a t e d salt ( - 2 M NaC1) solution with a chlorided silver wire for c o n t a c t was used, and in w ork on multibarrel microelectrodes, some electrodes were filled with c o n c e n t r a t e d saline and some with 0.9% saline. A few electrodes filled with dilute saline were mo r e noisy than those filled with c o n c e n t r a t e d saline. We have, however, been unable to show any systematic noise differences between electrodes filled with dilute and c o n c e n t r a t e d saline, and none at all between electrodes filled with m e r c u r y and c o n c e n t r a t e d saline. DISCUSSION The i m p e d a n c e - - f r e q u e n c y plots for carbon fibre microelectrodes of Fig. 2 have a slope of a p p r o x i m a t e l y --1 in t he region 100 Hz to 1 kHz. If the electrodes were acting as pure capacitors, a straight line with a slope of --1 would be ex p ect ed, since for a capacitor, the reactive impedance has a peak value 1 (Z) = 27rfC " log(z) = --1 log(27rfC) . An S-shaped curve rather than a straight line was actually obtained. This can be b etter fitted by an equivalent circuit consisting of a 'leak' resistor in parallel with the capacitor plus a series resistor, as shown in Fig. 7A. The impedance of the circuit in Fig. 7A is given by: z=(R12+ 2R~R2+ R:2)1 (1) where Z = peak value of impedance, a = 1 + (2 RICf) 2. By choosing appropriate values o f RIR2 and C a curve was obtained t hat m at ched the experimental curves. In Fig. 7B, the best fit to the median value of the impedances for single-barrel microelectrodes is shown along with the curve joining the actual median values. It can be seen t hat the c o m p u t e d Curve is a good fit to the median at low and high frequencies, diverging slightly at 10 Hz to 1 kHz. This may be due to a f r e q u e n c y - d e p e n d e n c e of the tip capacitance (Gesteland et al., 1959). However, the c o m p u t e d curve is well within the range of experimental data for all frequencies. In the model R, = 4.5 X 107 fit, R: -8 X 104 gt, C = 4 X 10 -'° F. The phase angle of t he model is given by = tan-l \R1 + R2~ / " 44 A lOOM ~ Range of actual values w ComDutedvalues • Actual median IOM q~ O e"O @ e~ 1M lOOK ;OK L, 1Hz I I I I 10Hz 100Hz 1K Hz 10K Hz Frequency (Hz) B F i g . 7. A : equivalent circuit for carbon fibre microelectrode. B: impedance--frequency plot o f m o d e l (solid line) and median values o f actual impedance shown by microelectrodes from Fig. 2. This suggests that the phase shift of high frequencies (1 kHz -- 10 kHz) is different to that of lower frequencies. Thus, if the microelectrodes were used to record nerve spikes and slow waves, the phase relationship of the two would be distorted. The carbon fibre microelectrodes are probably therefore best used only for spike recording. If the network in Fig. 7 is a realisticequivalent circuit for the microelectrode, we m a y ask what are the physical structures responsible for the various circuit components. The capacitance term is almost certainly due to the formation of an electrolytic double layer at the carbon fibre--saline inter- 45 face. With two capacitances in series, the smaller one dominates the impedance, so we can ignore the relatively large capacitance at the interface between the fibre and the fluid in the stem of the microelectrode and concentrate on the capacitance at the tip. For a large number of different waterbased electrolytes and different metals, the capacitance at the interface between electrolyte and conductor is between 0.15 and 0.2 Fm -2 (Bockris and Drazic, 1972). This is because the capacitance is determined mainly by a layer of water molecules at the interface, all orientated such that their dipole m o m e n t s are aligned with the electric field generated by the interface. For a microelectrode with an exposed tip of 25 pm, the surface area of the tip (assuming a flat end) would be 2~rl + ~r 2, i.e. 679 pm 2 if r = 4 pm and 1 = 25 pm. Assuming 0.2 Fm -2 for the double layer, one obtains 1.35 X 10 -l° F for the tip capacitance. This is much less than that observed experimentally, and for t h a t there could be two explanations. Firstly, the surface area of the carbon could be greater than that of the equivalent cylinder, i.e. the carbon contains pores or cracks of some kind. X-ray diffraction and scanning electron microscopy have been used to investigate the fine structure of carbon fibres (Johnson and Tyson, 1969). These studies have shown that fibres may consist of fine fibrils 5--10 nm in width with smaller crevices between them. During manufacture, the fibres are etched to produce a rough surface for better adhesion of epoxy resins. Thus, the actual surface area in electrochemical terms could be several times the nominal one. Secondly, part.of the large capacitance could be due to charge stored on the very thin glass just proximal to the tip. Evidence for this view comes from the observation that differences in exposed tip length (cf. Fig. 3) can only account for a small proportion of the observed difference between different electrodes (cf. Fig. 2), and that when the carbon fibre has been etched back into the glass, the glass wall can still transmit a signal, albeit with a higher impedance (Figs. 4 and 5). In a carbon fibre microelectrode, the glass near the tip will have been stretched to the breaking thickness of the glass at a relatively large diameter. It may well be that the dielectric properties of such thin glass are different to those of glass in bulk, in particular in its ability to adsorb water molecules and thus contribute to the electrolytic capacitance of the microelectrode. Variations in electrode manufacture (such as length of first pull, oven temperature etc.) which affect the dimensions of the tip and in particular the length of carbon with glass collapsed around it, would then account largely for the impedance differences between electrodes. Probably both factors, i.e. increased surface area of the carbon and capacitative coupling through the glass, contribute to the large tip capacitance. The parallel resistance R1 appear to vary between electrodes but not in one electrode with different tip lengths (Figs. 2, 3). It may be that carbon fibres are anisotropic in electrical properties, i.e. that their resistance along the fibre axis is less than the transverse resistance along a radius. Electrodes with different tip lengths would have the same cross-sectional area of fibre exposed and if this was the only important characteristic for R h R1 would 46 be independent of tip length. The final c o m p o n e n t R2 is of great importance since it controls the impedance of the system at frequencies above about 5 kHz. This is a lumped resistance term including resistance of the fluid in the stem of the microelectrode and the resistance of the saline in the bath. The latter can be obtained (Robinson, 1968) by treating the tip of the electrode like a sphere of radius re, surrounded by a thin shell of fluid radius r. Integrating r from re to infinity gives the total resistance Rs. For a tip length 25 pm, the sphere with a equivalent surface area will have a radius re where 47rre2 = 2~rl + ~r 2, let r = 4 pm, 1 = 25/~m. Then re = 14.7 pm. Then: oo Rs = .]f P dr re where p = specific resistivity of saline. Taking p = 70.0 f~cm at 20 ° C (Weast, 1977) we obtain Rs ~ 3800 ~2. Even if re is taken as 8 gm, Rs is only ~ 1 3 , 0 0 0 f~. Thus, this resistance would appear to be too small to account for R:, which is of the order of 80,000 ~2. (The series resistance of the carbon fibre in the microelectrode can contribute about 50 × 2 5 0 f~, i.e. 12,500 f~ for a 50 mm microelectrode.) This calculation, however, assumes that the resistivity of saline, p, close to the tip of the microelectrode is comparable to t h a t in bulk solution. This is probably not the case, since in the vicinity of the tip, the ions are highly ordered due to the electric field generated by the interface. Thus, the mobility of the charge carriers will be reduced, and the effective resistivity of the solution increased. On this hypothesis, R2 will be a function of tip size, just as will R1 and C. So we may expect all 3 parameters of the model to depend on tip geometry. Recording microelectrodes are usually connected to ultra-high impedance FET probes so that no significant power transmission takes place from electrode to probe. Thus impedance matching is not considered necessary. The reason for making impedance plots for inicroelectrodes is to assess the noise generated by the microelectrode, since this is of a similar order as the signal when recording extracellular nerve spikes. The main noise c o m p o n e n t for metal microelectrodes is the thermal or Johnson noise, given by: ~iEN = x / 4 k T Z r ~ f (2) where ( ~ E N = rms thermal noise voltage over bandwidth 5f, k = Boltzman's constant, T = absolute temperature, Zr = real part of electrode impedance (cf. Gesteland et al., 1959). Assuming t h a t the total noise over a given bandwidth is given by the sum of the rms noise voltages at different frequencies, we can integrate SEN and obtain over a bandwidth b-a: b EN = k 1/2 T v2 .( a Zr 1/2 f - t n df (3) 47 where Zr is given by i Zr= -~-+Rz ) , = 1 + (27rCRlf) 2 in our model (Fig. 6). Eqn. 3 when integrated from a = 10 Hz to b = 10,000 Hz gives EN ~ 5.1 pV rms f r o m 10 Hz to 10,000 Hz. The experimentally measured noise is a b o u t twice this value (10.5 pV), which is a fair agreement, but which could indicate that factors ot her than thermal noise are involved. The experimental noise value for the com pl e t e system of < 2 5 pV peak-to-peak is comparable with good tungsten microelectrodes (Merrill and Ainsworth, 1972). The same equivalent circuit acts as a model for bot h single-barrel and triple-barrel electrodes, and t her e f or e one can e xpe c t (and we have found) similar lownoise recording characteristics in multibarrel electrodes with a carbon fibre recording channel. There seems to be little difference in recording quality or noise between electrodes stem-filled with m er c ur y, or for electrodes filled with concentrated salt solution with a chlorided silver wire, and t herefore the latter should probably be used for reasons of e c o n o m y and safety. In most tests we have f o u n d little difference be t w een electrodes filled with c o n c e n t r a t e d NaC1 solution and dilute (0.9%) NaC1 solution, bu t occasionally dilute saline-filled electrodes have failed to record well, and it might be bet t er to use concentrated saline. On the o t h e r hand, in multibarrel electrodes, concent rat ed saline may crystallize at the t o p of the stem, and if these crystals reach the iontophoresis barrels, chemical or electrical c o n t a m i n a t i o n may occur b e tween barrels. On balance, therefore, we would advise t hat dilute saline should be used in iontophoresis (multibarrel) electrodes, and c o n c e n t r a t e d saline in single electrodes. In conclusion, it would appear that the circuit shown in Fig. 7 is a good model for the carbon fibre electrode in a saline bath with a chlorided silver indifferent electrode. The predicted (thermal) noise from this model at 10 Hz to 10 kHz is a b o u t half the experimentally measured noise of ~ 1 0 . 5 pV rms. This low noise is caused by the very large tip capacitance that is probably due to the porous surface of the carbon fibre at the tip, and also to the anomalous behaviour of the thin glass m e m b r a n e just proximal to the tip. ACKNOWLEDGEMENTS We are most grateful t o Ms. J. A b b o t t and Mrs. I. Sampson for technical help, and to Courtauld, for a generous free sample of 'Grafil' fibres. The integral in eqn. 3 of the Discussion was evaluated by Dr. U. Ehrenmark. REFERENCES Armstrong-James, M. and Millar, J. (1979) Carbon fibre microelectrodes, J. neurosci. Meth., 1: 279--287. 48 Bockris, J.O.'M. and Drazic, D. (1972) Electrochemical Science, Taylor and Francis, London, Barnes and Noble, New York, N.Y. Curtis, D.R. (1964) Microelectrophoresis. In W.L. Nastuk (Ed.), Physical Techniques m Biological Research, Vol. 5, Academic Press, New York. 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