Instrumentation for Electrochemistry. Lecture 4

Transcription

1 1 Instrumentation for Electrochemistry Lecture 4

2 Instrumentation for 2 Electrochemistry Part 1: The electrochemical cell - revision Potentiostats and other circuits Part II: Conductometric sensor instrumentation Electrical Cell-Substrate Impedance Sensing

3 3 What is Electrochemistry? Study of electrochemical reactions? Ox ne ed eduction/oxidation reactions Behind many biological processes Electrochemical sensing modes: Potentiometric Amperometric Conductometric/Impedimetric

4 4 Electrochemical Cell E: eference Electrode CE CE: Counter (or auxiliary) Electrode E WE: Working Electrode WE

5 5 Equivalent Circuit CE s - Solution resistance (CE to E) E ref s u - Uncompensated resistance (E to WE) C ref u ref - eference electrode resistance C dl ct WE

6 6 Equivalent Circuit CE C ref - Parasitic loss in E leads C dl - Electrical double layer capacitance of WE E C ref ref s u ct - WE charge transfer resistance C dl ct WE

7 7 Potentiostat Potentiostats control the potential difference between E and WE e in applied to the input of OA-1 e in OA-1 out E I w CE WE Potential on WE = e in OA-1 sources CE current e out OA-2

8 8 Potentiostat OA-2 is a current follower so eout = iwout Not a practical circuit e in OA-1 out E I w CE WE Only one input potential profile e out OA-2

9 9 Potentiostat e in S OA-1 CE E OA-2 -e wk(vs. ref) = -e in i w WE out OA-3 -i w out

10 10 Potentiostat Feedback OA-2 E C ref f ref u e in in OA-1 s CE ct C dl WE Insert the three-electrode equivalent circuit into the potentiostat circuit

11 11 Alternative Potentiostat 3 e in OA-1 f CE 1 e out 2 E OA-2 4 WE e WE (vs. ref) = e in

12 12 Instrumentation Amplifier Assume 1 = 2 = 3 = V Voltage 1 = V 1 Voltage 2 = V 2 Current in gain: I gain = V 1 V 2 gain V gain V out

13 13 Instrumentation Amplifier No current into op-amp inputs so: V 3 = V 1 I gain V 4 = V 2 These are the inputs for the differential amplifier stage I gain V gain 1 3 V out V

14 14 Instrumentation Amplifier Output voltage: V Becomes: So amplifier gain: A d = 1 2 gain V gain V out

15 15 Instrumentation Amplifier If A d = gain Common mode gain is unity for well matched resistors So CM can be extremely high 3 V 1 V gain V out

16 16 Back to Potentiostats Performance requirements and design considerations Current supply depends on control amplifier OA-1 CE Possible to add current boost amplifier Charging Cdl in transient measurements can require significant I/V levels

17 17 Transient charging WE capacitance Cdl = 10 μf Series resistance S = 100 Ω Charge the double layer capacitance by 1V in 10 5 s What is the CE current and voltage? 1A and 100V!

18 18 Transient esponse Ideal op-amps respond instantly open-loop gain eal op-amps have a low-pass frequency response Gain (db) closed-loop gain The cut-off frequency of this response ( 3dB) determines the speed of response 0 1E00 1E02 1E04 1E06 Frequency (Hz)

19 19 Transient esponse CE The cell also contributes to the transient response C dl and solution resistance contribute to cell time constant τc E C ref ref s u This and the time constant of the C dl ct potentiostat τp determine response WE

20 20 Transient esponse Input Voltage esponse to step function with u This is the true voltage on WE Charging of C dl through u Voltage WE Voltage Time

21 21 u Compensation A fraction f of the current follower output is fed back to input Inputs CE Compensation voltage is then ifout and input is: ewk (vs ref) = ein ifout E WE out True WE potential: etrue = ein ifout iu Adjust f to compensate Adjust potentiometer to set f

22 22 u Measurement Quick and dirty - increase f until oscillation occurs then reduce to 80% Measuring u is preferable One method is current interruption Current i1 Voltage E = i1u Time Time

23 23 u Measurement Computer controlled potentiostats may use a small step in potential ( E = 50mV) applied in a non-faradaic potential region Then the only current flowing will be charging C dl through u Current response i(t) = ( E/ u ) e ( t/τ), where τ = u C dl Computer control of E and f along with automated analysis of the current

24 24 Contact esistance If the internal resistance is small, another uncompensated resistance can dominate The resistance of the contact (c) to the working electrode can be ~0.3 Ω If cell current is high the voltage drop is significant. E/CE contact resistances are less important Measure voltage in parallel to get ic

25 25 Feedback Problems The stability of the potentiostat depends on negative feedback If the phase shift in the system is more than 180 we get ve feedback and instability Use of a transimpedance amplifier can also cause problems. Large resistors for high current gain are a problem, as is low u

26 26 Microelectrodes Planar Diffusion Hemispherical Diffusion Commonly referred to as Ultra Micro Electrodes (UME). Usually defined as electrodes with characteristic dimension <20 μm Low current, high current density, small iu drop and reduced ucdl

27 27 Low Current Measurement Micro and Ultra -micro electrodes mean very low currents. na-fa measurements can require large feedback resistance in current follower Shielding for noise and all sorts of stray currents may be essential Time constant of current follower f

28 28 Low Current Measurement Electrometer can replace WE connection of potentiostat Keithley offer a free handbook on low level measurements Low currents do mean that effects of u can usually be discounted

29 29 Galvanostat The galvanostat forces a constant current through a cell Basic concept is a voltage source driving through a resistance cell, I = Ein/ CE Measure the WE voltage at E E ref E WE E in

30 30 Galvanostat Circuits E ref E ref Icell = Ein / E in V = 0 V E in V = Ein Eref = Ewk (vs. ref)

31 31 Potentiostat Based Galvanostat Potentiostat CE E in E E ref WE Icell = -Ein/

32 Instrumentation for 32 Electrochemistry Part 1: The electrochemical cell - revision Potentiostats and other circuits Part II: Conductometric sensor instrumentation Electrical Cell-Substrate Impedance Sensing

33 33 Conductometric Biosensors Detect changes in electrical conductivity resulting from an enzyme reaction Sources of conductivity change Generation of ion groups Separation of Different Charges Ion Migration Change in Association of Ion Particles. Change in Size of Charged Groups. Enzymes Amidases Dehydrogenases & Decarboxylases Esterases Kinases Phosphatases & Sulphatases

34 34 Interdigitated Electrodes Microfabricated metal electrodes in Pt, Ag, Au Enzyme immobilised, by covalent binding in an electro-inactive protein (e.g., albumin) paste or gel, onto electrodes.

35 35 Wheatstone Bridge A Assume Vo = 0 V Then VAD = VAB So I11 = I23 Similarly VDC = VBC So I12 = I24 V S D I 1 3 I 2 1 V o 4 2 B C

36 36 Wheatstone Bridge A Divide the two equations: 3 I 2 I = 3 4 This is a balanced Wheatstone bridge V S D V o 4 2 B C

37 37 Wheatstone Bridge A Voltage across 2 2 V BC = V S 1 2 Voltage across 4 4 V DC = V S 3 4 V S D I 1 3 I 2 1 V o 4 2 B C

38 38 Wheatstone Bridge Vo = VBC VDC 2 4 V o = V S I 2 A I 1 1 Assume 2 = 3 = 4 = Conductance sensor V S D V o B replaces 1 = S = δ 2 1 V o = V S S C S

39 39 Wheatstone Bridge So with 2 = and S = δ V o = V S I 2 A I 1 1 Then rearrange to give: V o = V S 4 2! V S D V o B If δ >> then V o V S 4 4 C S

40 Wheatstone Bridge with 40 Amplification 3 V s V out 4 2 4

41 41 AC Bridge Impedances (Z) rather than Z 1 Z 2 = Z 3 Z 4 Similar equation for balanced circuit V s D Z 3 I 2 A V o I 1 Z 1 B Complex output Z 4 C Z 2

42 Electrochemical 42 Impedance Bridge Measure impedance of cell around OCP Use variable & C to balance bridge ac null detector ac source Potentiometer to null dc cell voltage Separate detection of ac and dc null Limited applications in studying reactions dc null detector Cell

43 43 AC Impedance Potentiostat ac input dc input OA-1 OA-2 E CE f diff. amp. phase angle meter ac voltmeter φ i V WE WE Measure phase and amplitude of the current

44 44 Phase Sensitive Detector System Taken from: Lasia, A. (2013). Determination of Impedances. In Electrochemical Impedance Spectroscopy and its Applications (pp ), Springer, New York.

45 45 Frequency esponse Analyser cos e(s) Generator sin Im(S) Input signal Taken from: Lasia, A. (2013). Determination of Impedances. In Electrochemical Impedance Spectroscopy and its Applications (pp ), Springer, New York.

46 ECIS - Electrical Cell Impedance 46 Sensing Monitor cell culture Gold electrodes in culture chamber Apply AC signal and measure Z ECIS Electrode 1MΩ Lock in Amplifier 1V AC source Counter Electrode IMPEDANCE

47 47 ECIS - Cell Sensing Low current, 1 V/1 MΩ = 1 μa Non-invasive measurement Z = j/ωc measure at different frequencies Extract morphological information C

48 48 ECIS - Cell Model Cell membrane Model Cell capacitance Cm = r r h r h r: radius h: gap height ρ: resistivity of medium B - Barrier resistance between cells

49 49 ECIS Outputs 78!9.("##1 :;<$("##1 :'$("##1 Cell Inoculation

50 50 Stem Cell Measurements Bagnaninchi, P. O., & Drummond, N. eal-time label-free monitoring of adipose-derived stem cell differentiation with electric cell-substrate impedance sensing PNAS, 108(16), (2011)

51 51 Wound Healing Assay W. Gamal, et al., eal-time quantitative monitoring of hipsc-based model of macular degeneration on Electric Cell-substrate Impedance Sensing microelectrodes, Biosens Bioelectron, vol. 71, pp , 2015.

52 52 Lock-In Amplifier ECIS uses a lock in amplifier Useful in many other AC measurements, such as EIS ECIS Electrode 1MΩ Lock in Amplifier 1V AC source Counter Electrode IMPEDANCE

53 53 Lock-In Amplifier Noise spectrum concentrated at low frequencies But so is the signal Signal shifted to 1 khz ~10 Hz Signal Bandwidth

54 54 Lock-In Amplifier Shift signal out to higher frequencies Approach: Modulate input signal at high frequency examples: optical chopper wheel, frequency modulation Detect only at modulation frequency Noise at all other frequencies averages to zero Use demodulator and low-pass filter

55 55 Lock-In Amplifier Demodulate input signal with mixer Low pass filter to remove noise Lock-In Amplifier Input Mixer Buffer Output Phase sensitive detection eference Low Pass Filter Tune reference to phase of input

56 56 Let s do the Maths! Sensor output - slow signal VS(t) Modulate at frequency f (ω = 2πf) LIA reference signal: V sig = V s (t) cos(!t) V ref = A cos(!t ) Fixed amplitude A, same freq, ω and variable phase φ Multiply together: V sig V ref = V S (t) cos(!t)a cos(!t )

57 57 More Maths Demodulated signal: V sig V ref = 1 /2AV S (t) cos 1 /2AV S (t) cos(2!t ) What if there s noise in the original? V sig = V s (t) cos(!t)n(t) Demodulation with noise: V sig V ref = 1 /2AV S (t) cos 1 /2AV S (t) cos(2!t )n(t) cos(!t ) Noise is removed (or greatly reduced)

58 58 Dual Phase Lock In Amplifier Modulated Input Mixer Buffer L.P.F In-phase eference Mixer Buffer Out-of-phase 90 o Phase Shift L.P.F

59 ECIS Lock-In 59 Amplifier Output

60 60 Key Points I Introduced an equivalent circuit for a threeelectrode electrochemical cell Potentiostats control the potential on a working electrode & measure current Introduced the instrumentation amplifier Looked at microelectrodes and low current measurement

61 61 Key Points II evision of the Wheatstone bridge for conductometric sensors Looked at instrumentation for impedimetric sensors Introduced ECIS and through that the concept of the lock-in amplifier