introduction to electrochemistry 2 by t. hara

Introduction to Electrochemistry 2

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2. Electrochemistry, as a province of academic.

2.1. Overview2.2. Thermodynamics2.3. Interface2.4. Kinetics2.5. Experimental Methods

Recommended TextElectrochemistry Principles, Methods, and Applications

C. M. A. Brett & A. M. O. BrettOXFORD UNIVERSITY PRESS


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2.1. Overview(1) Electrochemistry is a study of redox reaction:

- Reduction [a reactant gains electron(s)]- Oxidation [a reactant loses electron(s)]

(2) Reduction reactions take place heterogeneously at Interfaces between electrodes and electrolyte(s):

- Anode at which oxidation reaction(s) take(s) place.- Cathode at which reduction reaction(s) take(s) place.

(3) Chemical reactions including redox reactions are thermodynamically and kinetically controlled/affected:

- Thermodynamics … Potential difference- Kinetics … Charge and/or mass transfer


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2.1. Overview(1) Electrochemistry is a study of redox reaction:

- Reduction [a reactant gains electron(s)]- Oxidation [a reactant loses electron(s)]

Zn Cu

wire

Salt bridge

Cu(II) sulfate Zn(II) sulfate

electrons

Reduction:Cu2+(aq) + 2e- → Cu(s)

Oxidation:Zn(s) → Zn2+(aq) + 2e-

Total Cell Reaction:Zn(s)+Cu2+(aq) → Zn2+(aq)+Cu(s)


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2.1. Overview(2) Reduction reactions take place heterogeneously at Interfaces between electrodes and electrolyte(s):

- Anode at which oxidation reaction(s) take(s) place.- Cathode at which reduction reaction(s) take(s) place.

Zn2+(aq)

e-

Zn(s)

e-

Cu(s)

Cu2+(aq)


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2.1. Overview(3-a) Chemical reactions including redox reactions are thermodynamically and kinetically controlled/affected:

- Thermodynamics … Potential difference

Cu2+(aq) + 2e- → Cu(s) +0.34 V

Zn2+(aq) + 2e- → Zn(s) -0.76 V

StandardReductionPotential

=1.10 V


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2.1. Overview(3-b) Chemical reactions including redox reactions are thermodynamically and kinetically controlled/affected:

- Kinetics … Charge and/or mass transfer

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e-

Cu(s)

Cu2+(aq)

Electron conduction is fast.Ion conduction is

slow.


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2.2. Thermodynamics“Why is it that some electrochemical reactions proceed spontaneously in one direction?”The cell potential tells us the maximum work (maximum energy) that the cell can supply. This value is ΔG=-nF.

For example, the cell notation, Zn|Zn2+(aq)||Cu2+(aq)|Cu, means we consider the cell reaction as Zn+Cu2+Zn2++Cu. The half-reactions are represented by Cu2++2e-Cu (E0=+0.34 V) and by Zn2++2e-Zn (E0=-0.76 V). Then Ecell=+0.34-(-0.76)=+1.10 V. The corresponding ΔG=-nF value is -212 kJ /mol which is negative, showing that the reaction proceeds spontaneously as written (n is the number of electrons involved in the reaction, and F is Faraday constant, F96500 C/mole).


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2.2. ThermodynamicsNernst equation is given by

Ecell0 is the value of the cell potential when the activities of

reactants equals the concentration of reactants.

The higher the concentration of i-th reactant (ci), the lower the activity coefficient of it (γi). The activity, αi=γici.

When you need to the precise value of Ecell,0, you only have to measure s at different concentrations and extrapolate to zero concentrations. That’s it!


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2.2. ThermodynamicsThe following is a list of standard electrode potentials of common half-reactions in aqueous solution, that is measured relative to the standard hydrogen electrode at 25°C (298 K) with all species at unit activity.

These ions are thermodynamically unstable, eager for electrons, and therefore quite strong oxidizing agents. Reduced forms (metals) are stable; therefore, those metals are valuable as ornaments.

In contrast, this guy is eager to donate electrons, and therefore a quite strong reducing agent.


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2.2. Thermodynamics

Why do these two guys have different potentials?

The difference is caused from a difference in electronic configurations: the [Co(H2O)6]3+ has a (t2g)4(eg)2 electronic configuration; the [Co(NH3)6]3+ has a (t2g)6(eg)0.

(t2g)4(eg)2 (t2g)6(eg)0

PE


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2.2. Thermodynamics

In electrochemistry, the standard hydrogen electrode (SHE) potential is taken as a reference point.


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2.2. Thermodynamics

In alikaline solution, the potential of hydrogen evolution is going to be more negative.


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2.2. Thermodynamics

In acidic solution, the potential of oxygen evolution is equal to +1.23 V.


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2.2. Thermodynamics

In alkaline solution, the potential of oxygen evolution is going to be less positive.


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*Beyond Thermodynamics“Why is it that electrochemical reactions are restricted by the movement of ions?”The movement of ions is slower than that of electrons.

Ions in electrolyte solutions are solvated. Solvated ions move at different velocities, according to their size and charge.

- Diffusion is due to a concentration gradient. Diffusion occurs for all species.

- Migration is due to electric field effects. Thus, migration affects only charged species.


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*Beyond ThermodynamicsDiffusion is described by Fick's first law:

where Ji is the flux of species i of concentration ci in direction x, and is the concentration gradient. Di is the proportionality factor between flux and concentration gradient, known as the diffusion coefficient. The negative sign arises because the flux of species tends to cancel the concentration gradient.


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*Beyond ThermodynamicsIn the presence of an applied electric field of strength E= (potential gradient),

=

where the second term on the right-hand side represents migration (z: charge, R: ideal gas constant). Opposing this electric force there are three retarding forces: (1) a friction force; (2) an asymmetric; and (3) an electrophoretic effect.


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*Beyond Thermodynamics(1) a friction force:

The larger the size of solvated ion, the bigger the friction force. We consider an isolated ion. The force due to the electric field is F=zeE which is counterbalanced by a viscous force given by Stokes' equation F=6πηrv where η is the solution viscosity, r the radius of the solvated ion and v the velocity vector. The maximum velocity is, therefore v=(zeE)/(6πηr)=μE where μ is the ion mobility, and is the proportionality coefficient between the velocity and electric field strength.


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*Beyond Thermodynamics(2) an asymmetric effect: Because of ion movement the ionic atmosphere becomes distorted such that it is compressed in front of the ion in the direction of movement and extended behind it.

(3) an electrophoretic effect: Ion movement causes motion of solvent molecules associated with ions of the opposite sign. The result is a net flux of solvent molecules in the direction contrary to that of the ion considered.

+E

+

δ-δ+


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2.3. InterfaceThe interfacial region in solution is the region where the value of the electrostatic potential, ф, differs from that in bulk solution. The basic concept was of an ordering of positive or negative charges at the electrode surface and ordering of the

opposite charge and in equal quantity in solution to neutralize the electrode charge (electric double layer is formed).

The models of electric double layer are listed as follows:

(1) Helmholtz model

(2) Stern model


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2.3. Interface(1) Helmholtz model: This model of the interface is comparable

to the classic problem of a parallel-plate capacitor. One plate would be on the metal surface. The other, formed by the ions of opposite charge from solution rigidly linked to the electrode. So xH would be an ionic radius.


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2.3. Interface(2) Stern model: In the model, the compact layer of ions (Helmholtz layer) is followed by a diffuse layer extending into bulk solution. The distribution of species in the diffusion layer with distance from the compact layer obeys Boltzmann’s low. So the thickness of the diffuse layer would be (εrε0kBT/2ciz2e2)1/2 where εr is relative dielectric constant of the solution and ε0 is vacuum permittivity.


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2.4. KineticsIn order for the consideration electrode reactions, the following five steps must be listed up.

Step 1. Diffusion of the species to where the reaction occurs.

Step 2. Rearrangement of the ionic atmosphere.

Step 3. Reorientation of the solvent dipoles.

Step 4. Alterations in the distances between the central ion and the ligands.

Step 5. Electron transfer.


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2.4. KineticsThe Arrhenius expression relates the activation enthalpy, ΔH*, with the rate constant, k:

k=Aexp[-ΔH*/RT]

A is the pre-exponential factor. If we write the pre-exponential factor, A, as

A=A'exp[ΔS*/R],

then

k=A'exp[-(ΔH*-TΔS*)/RT]=A'exp[-ΔG*/RT]

In an electron transfer reaction, the rearrangement of the ionic atmosphere is a fundamental step, and thus it is useful to include the activation entropy ΔS*.


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2.4. KineticsBy applying a potential to the electrode, we influence the highest occupied electronic level in the electrode (the Fermi level, EF). Electrons are always transferred to and from this level.


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2.4. KineticsFor a reduction we can write

ΔGc*=ΔGc*,o+αcnFE.

In a similar way, for an oxidation

ΔGa*=ΔGa*,o-αanFE

where E is the potential applied to the electrode and α is a measure of the slope of the energy profiles in the transition state zone and, therefore, of barrier symmetry. Values of αc and αa can vary between 0 and 1, but for metals are around 0.5. A value of 0.5 means that the activated complex is exactly halfway between reagents and products on the reaction coordinate, its structure reflecting reagent and product equally. In this simple case of a one-step transfer of n electrons between an oxidant and a reductant, it is easily deduced that (αa+αc) = 1.


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2.4. KineticsWe obtain for a reduction

kc=A'exp[-ΔGc*,o/RT]exp[-αcnFE/RT]

and for an oxidation

ka=A'exp[-ΔGa*,o/RT]exp[αanFE/RT].

These equations can be rewritten in the form

kc=kc,oexp[-αcnF(E-E0)/RT]

and

ka=ka,0exp[αanF(E-E0)/RT].

This is the formulation of electrode kinetics first derived by Butler and Volmer. On changing the potential applied to the electrode, we influence ka and kc in an exponential fashion.


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2.4. KineticsThe observed current for kinetic control of the electrode

reaction is proportional to the difference between the rate of the

oxidation and reduction reactions at the electrode surface and is given by

I = nFA(ka[R]*-kc[O]*)

where A is the electrode area.


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2.4. KineticsI = nFA(ka[R]*-kc[O]*)

Note that kc[O]* and ka[R]* is going to be limited by the transport of species to the electrode. - When all the species that reach it are oxidized or reduced the

current cannot increase further.- Diffusion limits the transport of electroactive species close to

the electrode; the maximum current is known as the diffusion-limited current.


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2.4. KineticsI = nFA(ka[R]*-kc[O]*)

This is affected not only by the electrode reaction itself but also by the transport of species to and from bulk solution. This transport can occur by diffusion, convection, or migration. Normally, conditions are chosen in which migration effects can be neglected, this is the effects of the electrode's electric field are limited to very small distances from the electrode. These conditions correspond to the presence of a large quantity (>0.1M) of an inert electrolyte (supporting electrolyte), which does not interfere in the electrode reaction. Using a high concentration of inert electrolyte, and concentrations of 10-3 м or less of electroactive species, the electrolyte also transports almost all the current in the cell, removing problems of solution resistance and contributions to the total cell potential. In these conditions we need to consider only diffusion and convection.


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2.4. KineticsDiffusion is due to the thermal movement of charged and neutral species in solution, without electric field effects.

Forced convection considerably increases the transport of species. Natural convection, due to thermal gradients, also exists, but conditions where this movement is negligible are generally used.

We consider systems under conditions in which the kinetics of the electrode reaction is sufficiently fast that the control of the electrode process is totally by mass transport. This situation can, in principle, always be achieved if the applied potential is sufficiently positive (oxidation) or negative (reduction).


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2.4. KineticsDiffusion is the natural movement of species in solution, without the effects of the electric field. The rate of diffusion depends on the concentration gradients. Fick's first law expresses this:

,

where J is the flux of species, с/х the concentration gradient in direction x (a plane surface is assumed) and D is the proportionality constant known as the diffusion coefficient.


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2.4. KineticsThe D value in aqueous solution normally varies between 10-5 and 10-6 cm2/s, and can be determined through application of the equations for the current-voltage profiles of the various electrochemical methods.

Alternatively, the Nernst-Einstein (D=kTμ) or Stokes-Einstein relations (D=kT/6πημ) may be used to estimate values of D.


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2.4. KineticsThe variation of concentration with time due to diffusion is described by Fick's second law which, for a one-dimensional system, is

.

The solution of Fick's second law gives also the variation of flux, and the diffusion-limited current, with time, it being important to specify the conditions necessary to define the behavior of the system (boundary conditions).


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2.4. KineticsThe experiment leading to the diffusion-limited current involves application of a potential step at t=0 to an electrode, in a solution containing either oxidized or reduced species, from a value where there is no electrode reaction to the value where all electroactive species that reach the electrode react. This gives rise to a diffusion-limited current whose value varies with time. For a planar electrode, which is uniformly accessible, this is called semi-infinite linear diffusion, and the current is

0

where I=nFAJ, x is the distance from the electrode, and we consider,

for simplicity, an oxidation (anodic current) with c=[R]. If it were a

reduction, a minus sign would be introduced into the above equation.


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2.4. Kinetics


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2.4. KineticsFor small values of t there is a capacitive contribution to the current, due to double layer charging, that has to be subtracted. This contribution arises from the attraction between the electrode and the charges and dipoles in solution, and differs according to the applied potential (Q=CV); a rapid change in applied potential causes a very fast change in the distribution of species on the electrode surface and a large current during up to about 0.1s.


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2.4. KineticsThe concentration gradient tends asymptotically to zero at large distances from the electrode, and the concentration gradient is not linear. However, for reasons of comparison it is useful to speak of a diffusion layer defined in the following way:

0=D

where is the diffusion

layer thickness.


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2.4. KineticsThe diffusion layer results from the extrapolation of the concentration gradient at the electrode surface until the bulk concentration value is attained. This approximation was introduced by Nernst. is frequently related to the mass transfer coefficient kd since when c0=0

d=D/,

kd has the dimensions of a heterogeneous rate constant.

The diffusion layer thickness is expressed as

=( .

The mass transfer coefficient is for c0=0

(.


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2.4. KineticsSo far, the kinetics of

(1) electrode processes

and

(2) mass transport to an electrode

have been discussed.

From now on, these two parts of the electrode process are combined and we see how the relative rates of the kinetics and transport cause the behavior of electrochemical systems to vary.


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2.4. KineticsMass transport to the electrode surface assumes that this occurs solely and always by diffusion (except under forced convection). The mass transfer coefficient kd describes the rate of diffusion within the diffusion layer, and kc and ka are the rate constants of the electrode

reaction for reduction

and oxidation,

respectively.

Thus for the simple

electrode reaction

O+ne-R,


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2.4. Kineticskd,O and kd,R are the mass transfer coefficients of the species О (oxidizing agent) and R (reducing agent). In general these coefficients differ because the diffusion coefficients differ. We already have the Butler-Volmer expressions for the kinetic rate constants:

kc=kc,oexp[-αcnF(E-E0)/RT]

ka=ka,0exp[αanF(E-E0)/RT].

Assume that (c/ t)=0, i.e. steady state, in other words the

rate of transport of electroactive species is equal to the rate of their reaction on the electrode surface (Note that the rate of mass transport is usually lower than that of reactions on the electrode surface.). The steady state also means that the applied potential has a fixed value.


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2.4. KineticsThe flux of electroactive species, J, is

= kd,O([O]*-[O]

= kd,R([R]-[R]*)

When all О or R that reaches the electrode is reduced or oxidized, we obtain the diffusion-limited cathodic or anodic current densities Jl,C and Jl,a:

,

Since kd=D/δ, we can write

kd,o/kd,R=p=(DO/DR)1/2,


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2.4. KineticsWe can point out extreme cases for this expression:

Let us consider only О present in solution: Jl,a=0 and ka=0. Thus

that is

This result shows that the total flux is due to a transport and a reaction term. When kc>>kd,o then

reaction transport


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2.4. Kineticsand the flux is determined by the transport. On the other hand, when kc<<kd,o

and the kinetics determines the flux.


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2.4. KineticsWe now consider the factors that affect the variation of kc, ka, and kd. The kinetic rate constants depend on the applied potential and on the value of the standard rate constant, k0.

When [O]*=[R]*, then kc=ka=k0.

At the moment we note that there are two extremes of comparison between k0 and kd:

k0 >> kd … reversible system

k0 << kd … irreversible system

The word reversible signifies that the system is at equilibrium at the electrode surface and it is possible to apply the Nernst equation at any potential.


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2.4. Kinetics

k0 >> kd … reversible system

k0 << kd … irreversible system

These are

the variation of current

with applied potential,

voltammograms.


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2.4. KineticsReversible reactions are those where ko>>kd and, at any potential, there is always equilibrium at the electrode surface.

The current is determined only by the electronic energy differences between the electrode and the donor or acceptor species in solution and their rate of supply. Applying the Nernst equation

and given that j/nF=kd,0([0]*-[O]) we have

that is.


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2.4. KineticsSimilarly,

.

Substituting above two equations in the Nernst equation, assuming the electrode is uniformly accessible (I=AJ), we get the steady-state expression

where

=


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2.4. KineticsE1/2 is called the half-wave potential and corresponds to the potential when the current is equal to (Il,a+Il,c)/2.


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2.4. KineticsFor irreversible reactions, ko<<kd, kinetics has an important role, especially for potentials close to Eeq. It is necessary to apply a higher potential than for a reversible reaction in order to overcome the activation barrier and allow reaction to occur. This extra potential is called the overpotential, η. Because of the overpotential only reduction or only oxidation occurs and the voltammogram, or voltammetric curve, is divided into two parts. At the same time it should be stressed that the retarding effect of the kinetics causes a lower slope in the voltammograms than for the reversible case.


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2.4. Kinetics

reversible system irreversible system


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2.4. KineticsThe half-wave potential for reduction or oxidation varies with kd, since there is not equilibrium on the electrode surface. For cathodic and anodic processes respectively we may write

where α is the charge transfer coefficient.


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2.4. KineticsThe electrolyte double layer affects the kinetics of electrode reactions. For charge transfer to occur, electroactive species have to reach at least to the outer Helmholtz plane. Hence, the potential difference available to cause reaction is (фм-ф) and not (фм-фS). Only when ф~фS we can say that the double layer does not affect the electrode kinetics. Additionally, the concentration of electroactive species will be, in general, less at distance xH from the electrode than outside the double layer in bulk solution.

ф

фM

ф

ф

x


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2.5. Experimental MethodsThe electrochemical response to an AC perturbation is very important in impedance techniques. This response cannot be understood without a knowledge of the fundamental principles of AC circuits. We consider the application of a sinusoidal voltage

where Vo is the maximum amplitude and ω the frequency (unit is rad/s) to an electrical circuit that contains combinations of resistances and capacitances which will adequately represent the electrochemical cell. The response is a current, given by

where ϕ is the phase angle between perturbation and response.


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2.5. Experimental MethodsImpedances consist of resistances, reactances (derived from capacitive elements) and inductances. Inductances will not be considered here, as for electrochemical cells, they only arise at very high frequencies (>1 MHz).

In the case of a pure resistance, R, Ohm's law V=IR leads to

and ϕ=0. There is no phase difference between potential and current.


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2.5. Experimental MethodsFor a pure capacitor

=

We see that ф=π/2, that is the current lags behind the potential by π/2. Хс=(ωC)-l is known as the reactance (measured in ohms).


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2.5. Experimental MethodsGiven the different phase angles of resistances and reactances described above, representation in two dimensions is useful.


59

2.5. Experimental MethodsOn the x-axis the phase angle is zero; on rotating anticlockwise about the origin the phase angle increases; pure reactances are represented on the у -axis. The distance from the origin corresponds to the amplitude. This is precisely what is done with complex numbers as represented vectorially in the complex plane: here the real axis is for resistances and the imaginary axis for reactances. The current is always on the real axis. Thus it becomes necessary to multiply reactances by -i.

-iX

R

Z

ф


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2.5. Experimental MethodsWe exemplify the use of vectors in the complex plane with a resistance and capacitance in series. The total potential difference is the sum of the potential differences across the two elements. From Kirchhoff's law the currents have to be equal, that is I=IR=IC.

The differences in potential are proportional to R and Xc respectively. Their representation as vectors in the complex plane is …


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2.5. Experimental Methods


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2.5. Experimental MethodsThe vectorial sum of - iXc and of R gives the impedance Z. As a vector, the impedance is Z=R-iXc. The magnitude of the impedance is |Z|=(R2+Xc2)1/2, and the phase angle is

Often the in-phase component

of the impedance is referred to

as Z’ and the out-of-phase

component, i.e. at π/2, is called Z",

that is Z=Z'+iZ". Thus for this

case Z'=R, Z"=-Xc. This is a vertical

line in the complex plane impedance

plot, since Z' is constant but Z" varies with frequency.


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2.5. Experimental MethodsFor CR parallel circuit, the total current is the sum of the two parts, the potential difference across the two components being equal:

We need to calculate the vectorial sum of the currents. Thus1/2 -1/2 .

The magnitude of the impedance is -1/2

and the phase angle is , which is equal to the CR series combination.


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So, 1/Z=1/R+iωC, Z=R/(1+iωCR). This is easily separated into real and imaginary parts via multiplication by (1-iωCR). Thus

, , .

This is a semicircle in the complex plane of radius R/2 and

maximum value of |Z| defined by ωCR=1.


65



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2.5. Experimental Methods2.5.1. Impedance methodsThese methods involve the application of a small perturbation, whereas in the methods based on linear sweep or potential

step the system is perturbed far from equilibrium. This small imposed perturbation can be of applied potential, or of applied current rate. The small perturbation brings advantages: it is possible to use limiting forms of equations, which are normally linear (e.g. the first term in the expansion of exponentials).


67

2.5. Experimental Methods2.5.1. Impedance methodsThe response to the applied perturbation, which is generally sinusoidal, can differ in phase and amplitude from the applied signal. Measurement of the phase difference and the amplitude (i.e. the impedance) permits analysis of the electrode process in relation to contributions from diffusion, kinetics, double layer, coupled homogeneous reactions, etc. There are important applications in studies of corrosion, membranes, ionic solids, solid electrolytes, conducting polymers, and liquid/liquid

interfaces.


68

2.5. Experimental Methods2.5.1. Impedance methodsComparison is usually made between the electrochemical cell and an equivalent electrical circuit that contains combinations of resistances and capacitances (inductances are only important for very high perturbation frequencies, > 1 MHz). There is a component representing transport by diffusion, a component representing kinetics (purely resistive), and another representing the double layer capacity, this for a simple electrode process. Another strategy is to choose a model for the reaction mechanism and kinetic parameters, derive the impedance expression, and compare with experiment. Given that impedance measurements at different frequencies can, in principle, furnish all the information about the electrochemical system.


69

2.5. Experimental Methods2.5.1. Impedance methodsThe impedance is the proportionality factor between potential and current; if these have different phases then we can divide the impedance into a resistive part, R where the voltage and current are in phase, and a reactive part, Xc=l/ωC, where the phase difference between current and voltage is 90°.


70

2.5. Experimental Methods2.5.1. Impedance methodsAny electrochemical cell can be represented in terms of an equivalent electrical circuit that comprises a combination of resistances and capacitances (inductances only for very high frequencies). This circuit should contain at the very least components to represent:

• the double layer: a pure capacitor of capacity Cd

• the impedance of the faradaic process Zf

• the un-compensated resistance, RΩ, which is, usually, the solution resistance between working and reference electrodes.


71

2.5. Experimental Methods2.5.1. Impedance methods• the double layer: a pure capacitor of capacity, Cd

• the impedance of the faradaic process, Zf

• the un-compensated resistance, RΩ, which is, usually, the solution resistance between working and reference electrodes.


72

2.5. Experimental Methods2.5.1. Impedance methods

Impedance of the faradaic process, Zf

Resitance to charge transfer, Rct and,

Impedance that measures the difficulty of mass transport of the electroactive species, Warburg impedance, Zw.


73

2.5. Experimental Methods2.5.1. Impedance methods

For kinetically favored reactions Rct0 and Zw predominates.

For difficult reactions Rct and Rct predominates.


74

2.5. Experimental Methods2.5.1. Impedance methods<Plot of the impedance in the complex plane>

The low-frequency limit is a straight line, which extrapolated to the real axis gives an intercept. The line corresponds to a reaction controlled solely by diffusion, and the impedance is the Warburg impedance, the phase angle being π/4.


75

2.5. Experimental Methods2.5.1. Impedance methods<Plot of the impedance in the complex plane>

At the high-frequency limit the control is purely kinetic, and RCT>>Zw. The electrical analogy is an CR parallel combination..


76

2.5. Experimental Methods2.5.1. Cyclic voltammetry and linear sweep technique

Cathodic current

Anodic current

Cyclic voltammogram

Linear sweep

Perfectly

reversible


77

2.5. Experimental Methods2.5.1. Cyclic voltammetry and linear sweep technique These techniques are potential sweep methods. They consist in the application of a continuously time-varying potential to the working electrode. This results in the occurrence of oxidation or reduction reactions of electroactive species in solution (faradaic reactions) and a capacitive current due to double layer charging. The total current is Itot=IF+IC=IF+Cd(dE/dt). Thus IF and I: this means that the capacitive current must be subtracted in order to obtain accurate values of rate constants (usually IC decays to zero within <0.1 ms only when an appropriate measuring system with a small CR time constant is used).


78

2.5. Experimental Methods2.5.1. Cyclic voltammetry and linear sweep technique These techniques are potential sweep methods. They consist in the application of a continuously time-varying potential to the working electrode. This results in the occurrence of oxidation or reduction reactions of electroactive species in solution (faradaic reactions) and a capacitive current due to double layer charging. The total current is Itot=IF+IC=IF+Cd(dE/dt). Thus IF and I: this means that the capacitive current must be subtracted in order to obtain accurate values of rate constants. Usually IC decays to zero within <0.1 ms (but only when an appropriate measuring system with a small CR time constant is used). Note that where R is the solution resistance, RΩ, and C is the double layer capacitance, Cd.


79

2.5. Experimental Methods2.5.1. Cyclic voltammetry and linear sweep technique The observed current is different from that in the steady state (dc/dt=0). Its principal use has been to diagnose mechanisms of electrochemical reactions, for the identification of species present in solution and for the semiquantitative analysis of reaction rates. Although some improvements can be shown recently, it is basically difficult to determine kinetic parameters accurately from these experimental results.

introduction to electrochemistry 2 by t. hara

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reduction reactions

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aq zn2

cell potential

aq e zns e cus cu2