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Special Lecture SeriesBiosensors and Instrumentation

Lecture 2: Introduction to Electrochemistry

Electrochemistry BasicsElectrochemistry is the study of electron transfer processes that normally occur at electrode-solution interfaces, in what are termed redox reactions. The term redox reaction is short-hand for reduction-oxidation reaction. A large number of chemical reactions can be regarded as the outcome of a reduction and an oxidation process:

• Reduction: A + e– ⟶ A– (molecule A receives an electron)

• Oxidation: B ⟶ B+ + e– (molecule B loses an electron)Such reactions can be created by mixing molecules A and B, where the electron released by B in the oxidation step is transferred to a nearby molecule A, which undergoes reduction. This is shown schematically in Slide 3.One example of an important electron transfer process in a biological system occurs in the metabolic pathways of living cells. Energy is transferred by oxidation and reduction processes involving hydrogen ions (protons) and ionized iron in either a 3+ (more oxidized) or 2+ (more reduced) state. These reactions can be represented schematically as in slide 4, and can each take place at electrode surfaces as also shown in this slide. Each of these electrode reactions forms what is known as an electrochemical half-cell. If the two electrodes were to be connected by a conducting wire, so that electrons given up in the oxidation of Fe at one electrode are carried forward for the reduction reaction at the other electrode, we would then have a complete electrochemical cell. Other examples of electron transfer reactions occurring at electrodes are shown in slide 5.Redox reactions taking place in a complete electrochemical cell, comprising two isolated half-cells and two solutions of molecules A and B, are shown in Slide 6. A porous membrane prevents direct interaction between molecules A and B. One of the electrodes acts as a source of electrons and the other as a sink. The two electrodes are connected by a conducting wire that acts as a pathway for electrons given up by B to be carried to A. This forms a complete electrochemical cell.

Electrode ReactionsAn electrode reaction is a chemical process involving the transfer of electrons to or from a surface, usually a metal or semiconductor. This may be a cathodic process whereby a species is reduced by the gain of electrons from the electrode, as in the following three examples:

(I) Cu2+ + 2e– ⟶ Cu(II) Fe3+ + e– ⟶ Fe2+

(III) 2H2O + 2e– ⟶ H2 + 2OH–

By convention, the current flowing for a cathodic reaction is a negative quantity, and the electrode assumes a positive potential.

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Alternatively, the charge transfer may be an anodic reaction in which a species is oxidized by the loss of electrons to the electrode, as in the following three examples:

(I) 2H2O – 4e– ⟶ O2 + 4H+

(II) 2Cl– – 2e– ⟶ Cl2

(III) Pb +SO42– – 2e– ⟶ PbSO4

By convention, the current flowing for an anodic process is a positive quantity, and the electrode attains a negative potential. The above examples indicate the possible diversity of electrode reactions. The electroactive species may be organic or inorganic, neutral or charged, a species dissolved in solution, the solvent itself, a film on the electrode surface, and even the electrode material itself. Moreover, the product may be dissolved in solution, a gas, or a new phase on the electrode surface (e.g., growth of an aluminium oxide film on an aluminium electrode).The reduction of a chemical species requires the transfer of an electron from occupied electron energy levels close to the Fermi level of the electrode to an unfilled molecular orbital (MO) of the chemical. Likewise, oxidation requires the transfer of an electron from an occupied MO to an unoccupied level near the Fermi level. These electron transfers, which involve the rapid quantum mechanical tunnelling of electrons between the Fermi level and a molecular orbital, are depicted in Slide 7. The Fermi energy level corresponds to the mean potential energy of the most energetic electrons in the metal. The reference level of zero electron volts shown in slide 7 is the energy of an electron at rest some distance away from the electrode surface. An electron at rest has zero kinetic energy, and if removed from the influence of any kind of electric charge it will have zero potential energy. Electrons inside a metal have negative potential energy – otherwise they would readily ‘fall out’ of the metal. The energy transition required of an electron to jump from the Fermi level to reference zero is known as the work function. The work function values for some metals are given in Slide 8. As shown in slide 9, because different metals exhibit different work functions, they will exhibit different characteristics when used in electrochemical experiments. Based only on thermodynamic reasoning, silver and copper electrodes are more likely to reduce the chemical species whose molecular orbit energies are at the level shown on slide 9. On the other hand a platinum electrode is more likely to oxidize this chemical species than either a gold, copper or silver electrode. If a metal electrode M is dipped into its own metallic salt solution (i.e., a solution containing the corresponding metal ions ) some of the atoms in the solid may dissolve into the solution as ions. Each atom that does this leaves z electrons behind, which results in a negative charge on the electrode and a positive charge (cation) in the solution. The cations in the solution are attracted to the surface of the negatively charged electrode to form what is known as an electrical double layer. Mz+ Ions already in the solution can also attract electrons from the electrode and the resulting neutral M atoms stick to its surface. This leads to the electrode acquiring a positive charge, together with the formation of an electrical double layer formed by negative charges (anions) in the solution attracted to the positively charged electrode. An equilibrium state is reached when the rates of atom escape and capture become equal and the following redox equilibrium is set up:

�Mz+

(solution) + ze� $ M(solid)

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This is illustrated in Slide 10. The amount, and polarity of the net charge on an electrode will depend on where the equilibrium lies for this reaction. In slide 10 the overall charge on the electrode is negative, it appears to have a negative potential at equilibrium. At equilibrium a potential difference is established across the electrical double layer at the metal-solution interface. The potential difference (voltage) appearing between the two electrodes of a complete electrochemical cell as shown in slide 11 is given by:

�where φs is the potential of the bulk solution. The graph of the potential would look something like this, we’re assuming that at equilibrium metal M1 takes on a negative charge and M2 takes a positive charge.

It is important to distinguish between the terms ‘potential’ and ‘voltage’. Electronic engineers often use the term ‘applying a voltage’ to a circuit location, when what they are doing is applying a potential difference to this location with respect to a reference ground plane. If EM2 is assigned a reference potential of zero, then EM1 is the electrode potential for electrode M1. The absolute value of an electrode potential cannot be determined – it can only be given as a magnitude with respect to another potential. If the metallic salt solution into which the electrode is immersed is of unit molar concentration, under atmospheric pressure (101.3 kPa) at 25℃ (298K), the equilibrium electrode potential is known as the standard electrode potential.

Standard Reduction PotentialA good example of a practical electrochemical cell (or more precisely a combination of two half-cells) is shown in Slide 12 in the form of the Daniell Cell. This cell consists of a zinc electrode immersed into a zinc sulphate solution as one half-cell, together with a copper electrode immersed in a copper sulphate solution. These two half-cells are electrically connected via a glass tube containing a gel saturated with a sodium chloride solution. This so-called ‘salt bridge’ prevents Cu2+ ions going directly to the zinc electrode to pick up free electrons. This would electrically short-circuit the electrochemical cell. A porous ceramic can

[(EM1 � �s)� (EM2 � �s)] = (EM1 � EM2)

Potential

ϕs

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be used for this purpose instead of the salt bridge. The Gibbs free energy (chemical potential) of the system is related to the emf E (1.1V) of this cell by:

�where n is the number of electrons transferred (n = 2 in this case) and F is the Faraday constant of value 9.65x104 C mol–1. The electrical potential is calculated using:

� (1)The factor (–ΔG0/nF) in this equation is termed the standard reduction potential E0. This is determined at standard temperature and pressure as with the electrode potential mentioned previously. The units in square brackets are the activities/concentrations of the reduced and oxidised forms.The reduction potential (also known as the redox potential or oxidation-reduction potential) is a measure of the tendency of a chemical species to acquire electrons and hence to be reduced. The reduction potential is measured in Volts. Each chemical species has its own intrinsic reduction potential. The more positive the potential, the greater is the affinity for the species to acquire electrons and the greater its tendency to be reduced. Reduction potentials of chemicals in aqueous solutions are determined by measuring the potential difference between an inert sensing electrode (e.g., platinum, gold, graphite) in contact with the solution and a stable reference electrode connected to the solution by a salt bridge. The Standard Hydrogen Electrode (SHE) is the reference from which all standard reduction potentials are determined (see Slide 13). Although hydrogen is not a metal, it can be oxidized to form hydronium ions (protons):

H2 – 2e– ⟷ 2H+

If this reaction is performed under standard conditions the potential is defined to be zero. Standard conditions are defined to be: a temperature of 25℃ (298K); hydrogen gas supplied at a pressure of one atmosphere (101 kPa); 1 mol dm–3 concentration of hydrogen ions (e.g., 1M HCl or 0.5M H2SO4). This half-cell reaction, in turn, defines the zero reference level for the determination of the standard reduction potential of another half-cell system coupled to the standard hydrogen electrode. The standard reduction potential (Eo) is measured under standard conditions (298K, concentrations of 1M for each ion participating in the reaction at a pressure of 1 atmosphere for each gas that is part of the reaction, and metals in their pure state). Standard reduction potentials for some reactions are given in Table 1 at the end of this document.The reactions given in Table 1 are spontaneous in the direction as presented if the standard potential Eo is greater than zero, and are spontaneous in the reverse direction to that presented if the standard potential is less than zero. If an equation is reversed, so that the reactants become the products, the sign of Eo must also be reversed. Thus, from Table 1 we can define the reduction of the ferric ion as follows:

Fe3+ + e- ⟶ Fe2+ (+0.771 V vs. SHE)

This informs us that the standard reduction potential (E0) for this reaction is +0.771 Volts, as referenced against the standard hydrogen electrode (SHE), and occurs spontaneously. For the oxidation reaction (hydrolysis) of water, leading to the production of oxygen gas, we have to reverse the relevant reaction given in Table 1:

�G = �nFE

E = ��G0

nF � RTnF ln

⇣[reduced form]

[oxidised form]

⌘= ��G0

nF + RTnF ln

⇣[M

n+]

[M]

⌘

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H2O (l) ⟶ ½O2 (g) + 2e– + 2H+ (aq) (-1.229V vs. SHE)This informs us that the electrolysis of water does not occur spontaneously, but has to be driven by a voltage of at least 1.23 V, applied externally across the electrodes of the electrolysis cell. Multiplying up or dividing down the various quantities throughout a reaction equation does not change the Eo value, because the ratio of the reactant to product concentrations is not changed. For example, doubling up the quantities in the water electrolysis reaction is written as:

2H2O (l) ⟶ O2 (g) + 4e– + 4H+ (aq) (-1.229V vs. SHE)The Eo values given in Table 1 for metal reactions provides the means to judge the relative tendency for a reduction reaction to occur at an electrode made of that metal, compared to that of the reduction of an H+ ion under standard conditions (i.e., at a hydrogen electrode). All of the metals appearing at the top of Table 1 (those having the largest positive E0 values) have high reduction potential - they can be easily reduced and so act as strong oxidizing agents. From Table 1 we can see that silver and copper are better oxidizing agents than Zn2+ or Al3+, for example. On the other hand, the large negative reduction potential (–3.8V) of a calcium electrode makes it very difficult to reduce Ca+ ions to Ca atoms. However, Ca readily loses electrons to act as a reducing agent. In summary, as the reduction potential increases (i.e., its negative value decreases) the tendency of the electrode to behave as a reducing agent decreases. Thus, metals such as calcium (Ca) and potassium (K) act as good reducing agents, whereas metals such as silver (Ag) and gold (Au) are very poor reducing agents.

Example Question: With the aid of Table 1 calculate the emf produced by the Daniell cell shown in Slide 12.Solution: Write down the two half-reactions, with their standard reduction potentials:

Zn2+ + 2e– ⟶ Zn(s) (–0.7618 V) Cu2+ + 2e– ⟶ Cu(s) (+0.3419 V)

One of these reaction equations (along with the sign of its Eo value) must be reversed, because the number of electrons gained in one half-reaction must equal the number of electrons lost in the other half-reaction. Also, the sum of these two half-reactions gives the value of the cell emf, which must have a positive value for an electrochemical (Galvanic) cell because both reactions are spontaneous. The two half-reactions we require are therefore:

Zn(s) ⟶ Zn2+ + 2e– (+0.7618 V) Cu2+ + 2e– ⟶ Cu(s) (+0.3419 V)

Adding these two half-reactions: Zn(s) + Cu2+ ⟶ Zn2+ + Cu(s) (Eocell = 0.7618 + 0.3419 = +1.1037 V)

The emf produced by the Daniell cell is therefore approximately +1.1 V. In practice, the cell emf will depend on temperature and the relative concentrations of reactants and products. If the concentrations of the reactants increase relative to those of the products, the cell reaction becomes more spontaneous and the emf will increase. If the cell is used as a voltage source to drive an external electric current, the reactants will be consumed to form more products, and the emf falls in magnitude.

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The Nernst EquationIn the above example it was noted that the emf of a cell is sensitive to changes in temperature and the relative concentrations of the reactants and products. The Nernst equation provides a quantitative way to determine the shift of an equilibrium potential E away from the standard reduction potential Eo as a result of changes in the temperature and activities (equal to concentrations if dilute solutions) aOx and aR of the oxidized and reduced species, respectively. The Nernst equation can be obtained directly from Equation (1) derived from the calculation of the free energy change of a reversible electrode reaction:

�or

� (2)in which R is the universal gas constant (8.31 J K–1 mol–1), n is the number of electrons involved in the electron transfer process, and F is the Faraday constant (9.648×104 C mol–1). Thus, at T = 298 K for a redox reaction involving a single (n = 1) electron transfer process:

�For reactions at a solid electrode surface, it is convention to take the electrode’s activity as unity (i.e., aR = 1). So, at T = 25℃ for a single (n = 1) electron transfer process at a metal surface acting as the reducing agent the Nernst equation takes the form:

� (3)This assumes that the concentrations of the redox species are low enough to equate chemical activity to concentration [Ox]. If the electrode serves to oxidize the reduced species of a redox couple, then:

� (4)The direction of electron flow for a cell composed of two different ½-cells can be predicted by comparing their redox potentials. A ½-cell that accepts electrons from a standard hydrogen electrode is defined as having a positive redox potential, and a ½-cell that donates electrons to a standard hydrogen electrode is defined as having a negative redox potential. Electrons will flow from the ½-cell having the more negative Eo value to the ½-cell having the less negative (or positive) Eo potential.

Control of Electrode ReactionsElectron transfer reactions at an electrode surface can be controlled by changing the electrical potential of the electrode. We can approach an understanding of this by considering how an electric current can be induced in a metallic conductor. The energy band model of a metal depicts the free electrons partially occupying a band of de-localised energy levels up to the Fermi energy level. If a potential difference (i.e., a voltage) is applied between the ends of a metal wire in an electrical circuit, electrons will move down the induced gradient of energy levels in the metal to produce a current, as shown in Slide 17. The free energies of the filled

E = Eo +RT

nFln

✓aOx

aR

◆

E = Eo

+ 2.303RT

nFlog10

✓aOx

aR

◆

E = Eo

+ 2.3038.31⇥ 298

9.648⇥ 10

4log10

✓aOx

aR

◆⇡ Eo

+ 0.059 log10

✓aOx

aR

◆(V)

E = Eo + 0.059 log10

⇣aOx

1

⌘= Eo + 0.059 log10[Ox]

E = Eo

+ 0.059 log10

✓1

aR

◆= Eo � 0.059 log10[R]

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electron energy states are increased in the metal end connected to the negative battery terminal, and are lowered at the positively biased end. It is important to distinguish between potential energy and electrical potential. The potential, with respect to a reference level, of a metal connected to a negative battery terminal will be lowered because less work will be required to bring a positive charge up to it. On the other hand, the potential energy of its electron energy states will be increased because they are negatively charged, and can facilitate a reduction reaction by raising the energies of electrons at the Fermi energy of the metal to where they can make a transition (usually by tunnelling) into an unoccupied molecular orbital of a chemical species adsorbed or near the metal’s surface. This achieves a reduction reaction. For a positively biased metal, its electronic energy states are lowered, making a reduction process less likely for a given chemical species but improving the chance that an oxidizing reaction can occur. These two possibilities are demonstrated in Slide 18.We will consider a half-cell composed of an electrode immersed in a solution containing a chemical species that exhibits a reversible reaction:

Ox + ne– ⟷ Rwhere n is the number of electrons transferred in the reaction. The electrode is assumed to be an inert metal (e.g., platinum or gold) so that no electron transfer reaction occurs across its surface when immersed in an electrolyte. In other words it performs as an ideal polarized electrode. To simplify our discussion we will also assume that the counter electrode completing the electrochemical cell is of sufficiently large surface area that its current density is very small. This will serve to make this counter electrode non-polarizable, being able to conduct the cell current without changing its potential. This counter electrode could, for example, be platinum foil acting as a standard hydrogen electrode, separated from the first half-cell by a porous glass frit or a membrane. The voltage-current characteristics of the complete electrochemical cell are therefore determined solely by the performance of the first electrode, which we will call the working electrode. Also, the chemical concentrations of Ox and R are low enough that concentrations, rather than chemical activities, can be used in the Nernst equation. If the working electrode potential is adjusted to enable an oxidation reaction where R is oxidised to Ox (R ⟶ Ox + ne–), the associated anodic (oxidation) current density is by convention assigned a positive value. To an external observer a conventional electric current is directed into the electrode. A negative value is given to the current associated with a reduction (cathodic) reaction where Ox is reduced to R (Ox + ne– ⟶ R), and conventional current flows away from the electrode and along the wire. At the condition of dynamic equilibrium the rates of oxidation and reduction are equal. Thus, the oxidation exchange current density IOx and the reduction exchange current density IR density are equal and opposite to give a zero net exchange current density density Io:

IOx + (–IR) = Io = 0 (5)

The magnitude of the exchange currents will each depend on the surface concentrations [Ox]s and [R]s of the electroactive species Ox and R, respectively, and on the electron transfer rate constants kOx and kR:

IOx = nF [Ox]s kOx (6)

IR = nF [R]s kR (7)

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In the equilibrium state the concentrations of Ox and R at the electrode surface remain constant with time. There are no concentration gradients of the electroactive reactants Ox and R at the surface of the working electrode, and so the potential of the working electrode will remain steady at the standard potential value E given by the Nernst equation. If a voltage is now applied across the cell so as to raise the working electrode potential to a value ~0.24 V more positive than Eo, for example, a steady state condition can only arise if an anodic (oxidation) current flows so as to change the concentration ratio [Ox]s:[R]s from 1:1 to a situation close to 1000:1. The Nernst equation in fact demands that this be the case. Under steady state conditions, with an electrode potential (E–Eo) = +0.24 V, the oxidized form (Ox) of the redox couple is by far the most dominant species. As first observed by Tafel in 1905, cell currents are often related exponentially to the value of (E–Eo). This implies that the rate constants in equations (6) & (7) depend on the applied potential, and the modern interpretation of this effect is embodied in the Butler-Volmer equation (named after two physical chemists, John Butler of England and Max Volmer of Germany):

(8)

The factor αA is the transfer coefficient for the electron tunnelling process involved in the anodic transfer of an electron from a molecular orbital in an oxidized species to the electrode, and αC is the corresponding transfer coefficient for the cathodic reaction. For simple transfer processes αA + αC = 1, and it is commonly assumed that αA ≈ αC ≈ 0.5. The quantity (E–Eo) is termed the over-potential to define the deviation from the equilibrium potential. Raising the working electrode potential to a value 0.24 V more positive than Eo represents a high positive value for the over-potential. In this case the 2nd term of equation (8) can be neglected to give:

! (9)

If the electrode potential is set to a value 0.24 V more negative than Eo, i.e., (E–Eo) = –0.24 V, steady state conditions will arise through a cathodic current leading to [Ox]s/[R]s = 0.001. The reduced form (R) then becomes the dominant species at the electrode surface. The 2nd term in equation (4) is now the dominant one and the cathodic current density is given by:

! (10)

The total current given by equation (8) is shown in Slide 19, as the sum of the two exponential components of the anodic and cathodic currents given by eqns (9 & 10). It is important to note that the current-potential response shown in Slide 19, based on the Butler-Volmer equation, is valid only for the situation where the electrode reaction is controlled by the charge-transfer kinetics at the electrode surface. No account is made of the rate limiting step which may result from the relatively slow diffusion of an oxidized or reduced electroactive species away from the electrode surface into the bulk electrolyte, or the diffusion of these species to the electrode surface from the bulk electrolyte. Such mass transfer is required in order to maintain the concentration ratio [Ox]s:[R]s dictated by the Nernst equation.

I = Io

exp

✓↵A

nF (E � Eo

)

RT

◆� exp

✓�↵

C

nF (E � Eo

)

RT

◆�

log10(IOx) = log10(Io) +↵AnF

2.3RT(E � Eo

)

log10(IR) = log10(Io)�↵C

nF

2.3RT(E � Eo

)

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Based on the treatment presented by Bard and Faulkner , equation (8) can be modified to take 1

into account the influence of diffusion-controlled mass-transfer:

! (11)

When the electrode reaction is controlled by the diffusion of the electroactive species (mass-transfer controlled) the current has a limiting value Ilim given by:

! (12)

where A is the electrode surface area, D and [C]bulk are the diffusion coefficient and bulk concentration of the limiting electroactive species, respectively, and δ is the distance from the electrode surface into the bulk electrolyte over which the diffusion process is effective (the diffusion layer thickness).

Cyclic VoltammetryThis is the name given to the experimental procedure whereby the potential (relative to a reference electrode) of a working electrode immersed in a solution containing an electroactive species is cycled at a steady rate either side of the equilibrium potential value Eo. The resulting current flowing through the counter electrode is monitored in a quiescent solution. The potential-time waveform has a symmetrical ‘saw-tooth’ profile, with the same positive and negative sweep rates, that can range from a few millivolts up to 100 V s–1. Thus, for example, the potential at any time t for a negative-going voltage sweep is given by:

E(t) = Ei + νtwhere Ei is the initial potential and ν is the linear sweep rate (V s–1). When the potential of the working electrode is more positive than Eo, the electroactive species may become oxidized and produce an anodic current (i.e., electrons passing from the solution to the working electrode). On the return voltage scan, as the potential of the working electrode becomes more negative than Eo, reduction may occur and give rise to a cathodic current. A schematic of such a cyclic voltammogram is shown in Slide 20, and reflects the International Union of Pure and Applied Chemistry (IUPAC) convention that the anodic current is plotted in the upper (positive) half of the potential-current plot, with the cathodic current given in the lower (negative) half. However, in many text books (for example Bard and Faulkner, 2001) and scientific publications (mostly from laboratories in the USA) the IUPAC convention is ignored, so that the cathodic (negative) and anodic (positive) are placed in the upper and lower halves of the plot, respectively!We can understand the basic shape of a voltammogram by rearranging the Nernst equation to form a time-dependent relationship:

!

This equation can also be written:

! (13)

I = Io

[Ox]

s

(t)

[Ox]bulk

exp

✓↵A

nF (E � Eo)

RT

◆� [R]

s

(t)

[R]bulk

exp

✓�↵

C

nF (E � Eo)

RT

◆�

Ilim =nAFD

�[C]bulk

(Ei

� ⌫t� Eo) =RT

nFln

✓[Ox]

s

(t)

[R]s

(t)

◆

[Ox]s

(t)

[R]s

(t)= exp

nF

RT(E

i

� ⌫t� Eo)

�

Allen J. Bard & Larry R. Faulkner, “Electrochemical methods: fundamentals and applications”, Chapter 3, 1

Wiley, 2001, ISBN 9780471043720.

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This form of the Nernst equation emphasizes that the relative concentrations of the controlling electroactive species at the electrode surface are time-dependent in cyclic voltammetry. The example shown in Slide 20 corresponds to the situation where the electrode interfaces with a solution containing only the oxidized form of an electroactive species. The reduced form (R) is not present in the solution. The electrode potential is initially held at a potential sufficiently more positive than Eo, so that no charge-transfer at the electrode occurs under steady state conditions. As the electrode potential approaches the Eo value, reduction of the oxidized species commences, a reduction current flows and the concentration [Ox]s gets smaller. The reduced species (R) will diffuse away from the electrode and a concentration gradient of (Ox) is also created. Diffusion of (Ox) from the bulk electrolyte to the electrode increases and this leads to an increase of the reduction current. This process continues as the electrode potential gets more negative, until the potential falls below Eo. At this point the surface concentration of (Ox) approaches zero according to equation (9), and mass transport of Ox to the electrode surface attains a maximum rate to produce a peak of the reduction current. Beyond this stage of the negative potential sweep the concentration of (Ox) is depleted and the reduction current approaches the limiting value given by equation (12). On initiation of the reverse potential sweep, the large concentration of the reduced species [R]s at the electrode surface provides favourable conditions for their re-oxidation. As the electrode potential approaches and then rises above Eo the generated concentration gradient of (R) at the electrode causes an increase of the oxidation current, which then passes through a maximum value before falling as the concentration of oxidizable species (R) is depleted. As shown in Slide 20, the peaks of the reduction and oxidation currents occur either side of the standard reduction potential Eo. The height and width of these current peaks depend on the rate at which the potential is cycled, as well as the kinetics of the charge-transfer processes at the electrode surface. Other factors include the rates of desorption of (Ox) and (R) from the electrode surface and their rates of diffusion (mass transfer) between the bulk solution and the electrode. These various contributions are shown schematically in Slide 21. Cyclic voltammograms contain a significant amount of information on the control of electrode reactions. The geometry of the electrode can also influence the shape of a voltammogram. For a large area, flat, electrode, the diffusion (mass-transfer) processes depicted in Slide 21 are restricted to a planar surface over the electrode. A microelectrode protruding from a substrate, on the other hand, will have access to a much larger, hemi-spherical, diffusion surface. Cyclic voltammogramms obtained using micro- or nano-scale electrodes will not exhibit the same level of mass-transfer controlled characteristics as those obtained using large area flat electrodes.

AmperometryThe most common class of biosensor operates as an amperometric device, where measurement is made of the current arising from an electrode reaction involving an electroactive analyte. The choice of electrode material is an important consideration for such devices. In general, as we have seen, when the potential of an electrode is moved from an equilibrium state towards more negative potentials, the chemical species that will be reduced first is the oxidant in the redox couple with the least negative (or more positive) standard reduction potential Eo. Slides 22 and 24 depict the relative situations for inert platinum and gold electrodes immersed in an aqueous solution containing either iron, tin and nickel ions (for Pt) or iron and copper ions (for Au). The approximate locations of the Fermi levels for platinum and gold are based on the work function values given earlier. As the potential of a

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platinum electrode is lowered to less positive potentials, starting at +1 V with respect to the hydrogen electrode reference level, the first species reduced will be Fe3+, since the Eo of the Fe3+/Fe2+ couple is the least negative (i.e., most positive), followed by Sn4+. Finally, the reduction of Ni2+ occurs at a negative potential with respect to SHE. When the potential of an electrode is made progressively more positive, the chemical species that will be oxidized first is the reductant in the redox couple of least positive (or more negative) Eo. Thus, for a gold electrode in an aqueous solution containing Cu and Fe2+, copper will be the first to be oxidized as its potential is made more positive, followed by Fe2+. The associated series of electrode current peaks produced by these electrochemical reactions are shown schematically in slides 23 and 25. The dotted curves in slides 23 and 25 represent the currents that would be observed if the potential had been increased slowly in small incremental steps, rather than as a relatively fast potential ramp.

Three-Electrode SystemThe overall chemical reaction taking place in an electrochemical cell consists of the net effect of two half-cell reactions. Most electrochemical experiments or devices (e.g., sensors) are concerned with electron transfer reactions that occur at only one of the electrodes – namely the working electrode. An experimental cell could therefore consist of the working electrode (also termed the indicator or sensing electrode) coupled with a counter electrode that also functions as the reference electrode. The working electrode’s potential would be monitored or controlled with respect to this reference electrode, and the current response monitored as described above. However, it is preferable to use the three-electrode system of Slide 26Here the working electrode (WE) defines the electrode-electrolyte interface under study. It should behave as a chemically inert and ideal polarized electrode (no current flows over the potential range of interest when interfaced with a pure liquid). The reference electrode (RE) maintains a constant reference potential by operating as a non-polarizable electrode, a situation obtained by ensuring that negligible current flows through it. The purpose of the counter electrode (CE) is to supply the current required by the working electrode without in any way limiting or influencing the measured response of the electrode reaction. To achieve this it should have a large surface area so that it can pass the cell current without changing its own potential. The feedback circuit with the operational amplifier drives the current between the working and counter electrode, while ensuring that none passes through the reference electrode circuit. This maintains stability of the reference potential.

Reference ElectrodesThe role of a reference electrode is to provide a fixed potential, which does not vary, during a potentiometric experiment (Slide 28). In most cases it will be necessary to relate the potential of the reference electrode to other voltage scales, for example to the standard hydrogen electrode (S.H.E.) - the agreed standard for thermodynamic calculations. However, an S.H.E. is not a particularly convenient electrode for routine use - and is potentially hazardous because it uses flowing hydrogen. Therefore, in practice, other secondary reference electrodes are used. The concept of a reference electrode can be understood in terms of a complete electrochemical cell being composed of two ½-cells (slides 28-29). The total cell potential is the difference between the electrode potentials of these two ½-cells. If we can make one of the electrode potentials to be of a fixed and unchanging value, then the potential of the cell will only depend on the electrode reaction occurring at the other electrode (often referred to as the indicator or working electrode).

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An essential feature, therefore, of a reference electrode is that it should provide a stable and reproducible electrode potential, and be relatively insensitive to changes in temperature. Compared to the S.H.E. it must also be easy to make and safe to use. In potentiometric experiments the potential between the indicator (working) electrode and the reference electrode is controlled by a potentiostat, and as the reference half cells maintains a fixed potential, any change in applied potential to the cell appears directly across the working electrode-solution interface. The reference electrode serves the dual purpose of providing a thermodynamic reference and also isolates the working electrode to be the electrode-solution interface under electrochemical examination. In practice, however, any measuring device must draw current to perform the measurement. A good reference electrode should therefore be able to maintain a constant potential even if a few microamperes are passed through its surface. We say that the reference electrode should not be substantially polarised during the experiment or sensing operation. Ideally, it should be non-polarisable.

The Silver-Silver Chloride Reference ElectrodeThe most common and simplest reference system is the silver-silver chloride reference electrode (Slide 30). This generally consists of a cylindrical glass tube containing a 4 Molar solution of KCl saturated with AgCl. The lower end is sealed with a porous ceramic frit which allows the slow passage of the internal filling solution and forms the liquid junction with the external test solution. Dipping into the filling solution is a silver wire coated with a layer of silver chloride (it is chloridised) which is joined to a low-noise cable which connects to the measuring system. In electrochemical terms, the half-cell can be represented by:

Ag / AgCl(Saturated) & KCl(Saturated),and the electrode reaction is:

AgCl(solid) + e– ⟷ Ag(solid) + Cl– with a standard reduction potential of +0.22233 V (cf. S.H.E.).

Double Junction Reference ElectrodesOne problem with reference electrodes is that, in order to ensure a stable voltage, it is necessary to maintain a steady flow of electrolyte through the porous frit. Thus there is a gradual contamination of the test solution with electrolyte ions. This can cause problems when using ion-selective electrodes to measure low levels of K, Cl, or Ag, or when these elements may cause interference problems. In order to overcome this difficulty the double junction reference electrode was developed. The silver-silver chloride cell thus forms the inner element inserted into an outer tube containing a different electrolyte, which is then in contact with the outer test solution through a second porous frit. The outer filling solution is said to form a salt bridge between the inner reference system and the test solution, and is chosen so that it does not contaminate the test solution with any ions which would affect the analysis.

Liquid Junction PotentialsThe standard voltage given by a reference electrode is only correct if there is no additional voltage supplied by a liquid junction potential formed at the porous plug between the filling solution and the external test solution. Liquid junction potentials can appear whenever two dissimilar electrolytes come into contact. At this junction, a potential difference will develop as a result of the tendency of the smaller and faster ions to move across the boundary more

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quickly than those of lower mobility. These potentials are difficult to reproduce, tend to be unstable, and are seldom known with any accuracy. Steps should therefore be taken to minimise them, the main point is to avoid multiple junctions if possible.

Ion Selective ElectrodesIon-selective electrodes are designed to respond selectively to one particular ion – hopefully to the exclusion of other ion types. They contain a thin membrane capable of only allowing the desired ion to diffuse through it, or to bind to it. They are potentiometric devices characterised by the Nernst Equation. Basically, the potential of the ion selective electrode, as measured against an appropriate reference electrode, is proportional to the logarithm of the activity (concentration) of the ion being tested. This process does not involve a redox reaction.The pH electrode is the most well known and simplest example, and can be used to illustrate the basic principles of ISEs. The standard pH electrode measures the concentration of hydrogen ions and hence the degree of acidity of a solution (pH is defined as the negative logarithm of the hydrogen ion concentration - so pH = 4 indicates a concentration of 1×10–4 moles per litre). We remind ourselves again that the term ‘concentration’ should really be replaced by activity or effective concentration. This is an important factor in ISE measurements. An essential component of a pH electrode is a glass membrane which binds hydrogen ions, but no other ionic species. When the electrode is immersed in a test solution containing hydrogen ions, these external ions diffuse into the hydrated glass gel surface of the membrane, and displace sodium ions which then diffuse across the membrane to produce an equilibrium potential. The potential difference that is created across the glass membrane is proportional to the number of hydrogen ions in the external solution. Because of the need for equilibrium conditions there is very little current flow and so this potential difference can only be measured relative to a separate and stable reference system, which is also in contact with the test solution but is unaffected by it. This reference is usually a silver-silver chloride electrode. A high input-impedance millivolt meter is used to measure this potential difference.

Errors in pH MeasurementsStandards: pH measurements cannot be more accurate than the standards (± 0.01).Junction potential: If ionic strengths differ between analyte and the standard buffer, the junction potential will differ and result in an error of ± 0.01.Junction Potential Drift: Caused by slow changes in [KCl] and [AgCl] - re-calibrate!Sodium Error: At very low [H+], the electrode responds to Na+ and the apparent pH is lower than the true pH.Acid Error: At high [H+], the measured pH is higher than actual pH Equilibration Time: Takes ~30s to minutes for electrode to equilibrate with solution.Hydration of Glass Membrane: A dry membrane will not respond to H+ correctly.Temperature: Calibration needs to be done at same temperature as measurements.Cleaning: Contaminates on probe will cause reading to drift until properly cleaned or equilibrated with analyte solution.

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Table 1: Standard reduction potentials for some common half-cell reactions. (P. Vanysek, CRC Handbook of Chemistry and Physics, 87th Ed., Boca Raton, 2007)

½-Cell Reaction Standard Potential Eo (Volts)

F2 + 2H+ + 2e- ⟷ 2HF +3.053

Au3+ + 3e- ⟷ Au +1.498

O2 + 4H+ + 4e- ⟷ 2H2O +1.229

Br2 + 2e- ⟷ 2Br- +1.066

Ag+ + e- ⟷ Ag +0.7996

Fe3+ + e- ⟷ Fe2+ +0.771

Cu+ + e- ⟷ Cu +0.521

Cu2+ + 2e- ⟷ Cu +0.3419

Hg2Cl2 + 2e- ⟷ 2Hg + 2Cl- +0.26808

AgCl + e- ⟷ Ag + Cl- +0.22233

- - - - - - - - - - - - - - - - - - - - - - - - - - - - H2 - 2e- ⟷ 2H+ 0.0000 - - - - - - - - - - - - - - - - - - - - - - - - - - - -

CO2 + 2H+ + 2e- ⟷ HCOOH -0.199

PbSO4 + 2e- ⟷ Pb + SO42- -0.3588

Fe2+ + 2e- ⟷ Fe -0.447

Cr3+ + 3e- ⟷ Cr -0.744

Zn2+ + 2e- ⟷ Zn -0.7618

2H2O + 2e- ⟷ H2 + 2OH- -0.8277

Al3+ + 3e- ⟷ Al -1.662

K+ + e- ⟷ K -2.931

Ca+ + e- ⟷ Ca -3.80