Amperometric biosensors

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Lionel Harmon
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1 Electrochemical biosensors II: Amperometric biosensors Lecture 2

2 Amperometric Sensors: Problem formulation amperometric techniques have some selectivity as every RedOx reaction has it s own characteristic potential E 0, V 2+ + Cu + e Cu 2 Pb + + 2e Pb 2 Tl + + 2e Tl 3 In + + 3e In 2 Cd + + 2e Cd 2 Zn + + 2e Zn

3 Electrode Reactions Current: Faradaic current: current associated with Oxidation/Reduction of species of interest A IC A + e B Capacitive current: charging of double layer de = C dt Other background currents due to presence of other species g p p e.g. oxygen

4 Faradaic current: Electrode Reactions A + ne B ne electrode B A Possible limiting steps: electron transfer mass transport rate of arrival of A = 1/n rate of e-transfer = rate of departure 1 I JA = = naf J B

5 The electrode-solution interface Different activity it next to electrode! Helmholtz layer model Gouy-Chapman model Stern model Graham model = Stern model + IHP

activation Gibbs energy [ ] ν [ ] j = ja jc = νfka Red Fkc Ox Δ / k Be G RT = both

6 The rate of charge transfer Ox + ν e Red First order reaction the rate of reduction: vox = kc [ Ox] the rate of oxidation: = [ Red] vred k a c c [ ] [ Red] j =ν Fk Ox ja =ν Fk a The activation Gibbs energy [ ] ν [ ] j = ja jc = νfka Red Fkc Ox Δ / k Be G RT = both processes involve activation k Be Δ a [ Red] ν [ Ox] j = νfk B e Fk B e G / RT Δ Gc / RT a a c a

7 The Butler-Volmer equation Reduction reaction Ox + ν e Red Δ G = Δ G (0) + FΔ φ transition state t is product like: (0) transition state is reagent like: Δ c G Δ G (0) c =Δ Gc + α FΔφ c Δ c G c (0) cathodic c transfer coefficientc e usually approx. 0.5 Oxidation reaction Red ν e Ox transition state is product like: transition state is reagent like: Δ G (0) c =ΔGc FΔφ Δ G Δ G =ΔG (0) (1 α) FΔφ c c φ c Δ G c (0)

8 The Butler-Volmer equation [ Red] ν [ Ox] j = ν Fk B e e Fk B e e Δ Ga (0)/ RT (1 α ) F Δ φ / RT Δ Gc / RT α FΔ φ / RT a a c a if the cell is balanced (j=0) by an external source, E: j = j = j f =, a c 0 F RT exchange current density a a a Δ a (0)/ (1 ) [ Red] Δ Gc / RT fe [ Ox] j = ν Fk B e e α c c a G RT fe j = ν Fk B e e α now, if a voltage is supplied: The Butler-Volmer equation η = E E ( (1 α) f η α f η j = j0 e e )

9 The Butler-Volmer equation j = j e e ( (1 α ) fη α fη ) 0 The low overpotential limit fη 1, in practice η < 0.01V j = j (1 + (1 α) fη α fη...) j fη 0 0 η j j f 0 Ohm s law The high overpotential limit in practice η 0.12V positive overpotential: ti (1 α) f j = j e η 0 j = negative overpotential: 0 f j0e α η

10 Electrode polarizability non-polarizable electrodes: potential changes only slightly with current, polarizable electrodes: potential ti changes significantly with current reference electrodes are highly non-polarizable η j j f high exchange current is benefitial for low polarizatbility 0

11 Tafel plot a plot of ln(j) vs. overpotential is called Tafel plot

12 Electrode Reactions Mass transport modes: Diffusion: i spontaneous movement due to concentration gradient Convection: transport by gross physical movement, e.g. stirring or flowing the solution, or rotating/vibrating the electrode Migration: movement of charged particles Cxt (, ) zfdc φ ( xt, ) J ( xt, ) = D + C ( xtv, ) ( xt, ) x RT x

13 Mass transport mechanisms Migration (for ions) in response to a gradient of potential J m = zf i ϕ Di[] i i RT x Diffusion in response to a concentration gradient J d = D A [ A] xx Convection in response to pressure gradient Jc = [ ] A v

Concentration polarization concentration

RT E = E + ln c zf 0 0 E = E + ln a = E + ln γ

14 Concentration polarization concentration polarization - phenomena related to consumption of the reactive species on the electrode at zero current: RT RT RT zf zf zf 0 RT E = E + ln c zf 0 0 E = E + ln a = E + ln γ + ln c with current: RT zf 0 E = E + ln c RT c c E E ln η = = zf c

Concentration polarization c RT c η = E E = ln zf c

using Nernst-Einstein equation: D = λ ionic

15 Concentration polarization c RT c η = E E = ln zf c Mass transport t through h the Nernst layer: First Fick s law: c c c c J = D = D x δ c c j = zfj = zfd δ limiting current density j lim = c crtλ zfd = δ zf δ using Nernst-Einstein equation: D = λ ionic conductivity conc. overpotential vs current: RTλ zf 2 2 c RT jδδ η = ln 1 zf zcfd

16 Potential step experiment O + ne R Experiment: potential is increased stepwise to some value, only O is initially present. in a planar geometry: CO( x, t) = CO( b) 1 erf C CO ( b ) = x 4Dt O x 4Dt O C CO ( b J () t = D i() t = nfad ) O Cottrell equation x 4Dt O Cottrell equation

17 Potential step experiment At a spherical electrode the situation is different as the diffusion equation will have another term: 2 Cxt (, ) C 2 C = D 2 t + r r r O( ) O( ) i () t = nfad C b C b O + nfado 4Dt r O Time independent term This leads to unique transport properties of microelectrodes (due to their small radius)

18 Chronoamperometry The potential is stepped to E 2 >E p, current is monitored as a function of time current decay due to mass transfer limitation limiting value: i = ½ nfad C ox δ

19 Potential sweep experiments Current raise, dominated by the drop in C0(0,t) Current drop, dominated by the increase in d. On microelectrodes we expect sigmoidal chape

20 Potential sweep experiment In the case of stirring, the distance d is maintained; The voltammogram will be sigmoidal in the case of stirring In aqueous solution distance d is typically 10-50µm for electrode rotation and µm for solution stirring

21 Linear Sweep Voltammetry (LSW) Linearly varied potential is applied between working electrode and reference electrode while current is monitored. I p ~[Ox] Background current I p

22 Kinetic and Catalytic Effects usually, there is another chemical reaction coupled to the electron transfer consumption of reduced product forward backward slow Voltammogram of ferrocene w.glucose +GOX backward fast regeneration of the oxidized reagent w. glucose

23 Amperometric Sensors amperometric techniques have some selectivity as every RedOx reaction has it s own characteristic potential however the selectivity is limited unless modified electrodes are used Differential pulse p polarogram for a mixture of six cations

24 Amperometric Biosensors First Generation oxygen electrode based sensors Second Generation mediator based sensors Third Generation directly coupled enzyme electrodes

25 Possible glucose detection schemes 3rd generation schemes 1st generation schemes 2nd generation schemes

26 oxygen electrode based sensors Clark s electrode O-rings Ag anode Electrolyte gel Pt catode Teflon membrane Glucose oxidase on nylon net Cellophane membrane

28 Measuring oxygen: E=-0.7V Problems: fairly high potential (interference is probable), oxygen needs to be controlled and replenished (e.g. By oxygen generating reaction or by pumping oxygen containing buffer) Measuring hydrogen peroxide: E=+0.65V Problem: still fairly high potential (interference from e.g. ascorbic y g p ( g asid)

29 Mediator Based Sensors Oxygen is substituted with another oxidizing agent (electron transfer agent) Iron ions or complexes are most common mediators Fc

30 Free Fe3+ are subject to hydrolysis and precipitation

32 Good Mediator Rapid reaction with enzyme Fast electron transfer kinetics Low overpotential Independent of ph Stable in Ox and R forms Doesn t react with oxygen Non toxic

33 Fc derivatives

34 Various mediators (natural and artificial)

35 How it works... Fc+glucose+GOD Fc+glucose In real biosensors both GOD and Fc are immobilised

36 Directly Coupled Enzyme Generally, the enzyme might denature on the electrode surface; electron transfer reaction might be slow Thus, the surface has to be modified... Enzymes can be directly wired to the electrode using organic conducting salts (e.g.ttf/tcnq) or redox polymers Enzymes can be modified to facilitate electron transfer and attachement

37 Possible glucose detection schemes

38 Design example: Glucose sensor Aim: for use by patient at home (should be simple, reliable and cheap) Performance: blood glucose range mm; precision 3-8%; test time 30s; life time 6 month. Selective element: Glucose Oxidase inexpensive, stable over long period Transducer: Amperometric (GOD+Fc) cheap, reliable, easy read-out with LCD. Immobilisation: i covalent bonding for long life (graphite foil coated with Fc, GOD immobilised)

39 ExacTech Glucose Sensor

40 Problems Atkins 25.16a. The transfer coefficient of a certain electrode in contact with M 3+ and M 4+ in aqueous solution at 25 C is The current density is found to be 55.0 ma cm -2 when the overvoltage is 125 mv. What is the overvoltage required for a current density of 75 ma cm -2? Atkins 25.20a Estimate the limiting current density at an electrode in which the concentration of Ag + ions is 2.5 mmol dm -3 at 25 C. The thickness of the Nernst diffusion layer is 0.40 mm. The ionic conductivity of Ag + at infinite dilution and 25 C is 6.19 ms m 2 mol -1. Atkins 25.26a What is the effective resistance at 25 C of an electrode interface when the overpotential is small? Evaluate itfor10cm (a) Pt,H + =7-4 2 H + 2 H,(j 0 7.9x10 A/cm ), (b) Hg,H 2 H (j 0 =7.9x10-13 A/cm 2 ) electrodes.

Lecture 3. Electrochemical Sensing.

Lecture 3. Electrochemical Sensing. Lecture 3 Potential-Controlled Techniques in Electrochemical Sensing. Enzymatic Electrodes. Cyclic voltammetry The most widely used technique for acquiring quantitative information about e/chemical reaction