# capter5 voltammetry

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```					§5 Voltammetry
§5-1 Basic principle of polarograpy

Voltammetry

A group of analytical methods based on
determining current flow – voltage curve
during electrolysis

Several types of methods based on
Electrode type
How the potential is applied
How the current is measured.
When applied voltage reaches the
decomposition voltage of metal ion:

Reduction reaction on cathode:

Cd2+ + 2e-             Cd
Oxidation reaction on anode:

2OH- -2e              H2O + 1/2 O2

U外 ∝ i               U外- Ud= iR

Where U外 denotes applied potential,
Ud is decomposition potential, R is
total resistance of electrolysis circuit,   (Cd2+)
i is current through the circuit.
When following conditions are obeyed, U外 – i graph is showed
in following Figure

Lower current density
during electrolysis

No quantitative relationship
between current (or potential)
and concentration of
interested ions
To find the analytical relationship between the current and
the concentration of sought-for ions , following measurements

●MICROPLATINUM ELECTRODE
Or DROPPING MERCURY ELECTRODE
( in most common use)
to insure high current density
● NO STIRRING
to insure enough high concentration difference
between the electrode surface and the solution bulk
Then
RT
E=   Eo   +      ln CM
nF
When the current flowed for only a short period through the
electrode, ion concentration on the surface of the electrode
reduce suddenly. The difference in ion concentrations between
the surface and the bulk solution is equivalent to an
electrochemical cell, which is called concentration
polarization(浓差极化). thus, there is a voltage that is
equivalent to this concentration change called concentration
polarization potential（浓差电势）
C      D

When a microplatinum electrode or dropping mercury
electrode is used and no stirring is carried out,
Limiting current
concentration polarization takes place soon, following
B
polarogram is obtained             A
When applied voltage does not reach reduction voltage of
metal ion, only a little current flow, called residual current
produced by reduction of impurities and charging current,
eg AB in the Figure
Arriving on decomposition voltage,
the electrode reactions occur, the
current rises rapidly with increasing                    C        D

voltage, BC section in the figure

Cathode (DME):                                       Limiting current
Cd2+   +   2e-   +Hg      Cd(Hg)                 B
A
(amalgam)
Anode (calomel or pool mercury
electrode with a big area):
2Hg - 2e- + 2Cl-         Hg2Cl2
When it reaches C point voltage, due to concentration
polarization, the current arrives at a limiting value and
does not rise markedly, called limiting current, consisting of
residual current and diffusion current

极谱波可以用i~ U外表示曲线表示，也可以用i ~ Ede曲线来表示，从下
面的讨论可以看出，二者是基本重合的。

U = ( ESCE -Ede ) + i R

∵ i and R are very little in
polarographic electrolysis

U = ESCE -Ede = -Ede( vs. SCE)
To remove completely influence of iR, three electrode
system is usually used.
Very little oscillation
Polarography

First voltammetric technique
Differs form hydrodynamic
●unstirred (diffusion dominates)
●dropping Hg electrode (DME) is used as a
working electrode
Current varies as drop grows then falls off
In polarographic analysis, supporting electrolyte is
usually added to increase the current-conductivity and
eliminate migration current. Usually relatively higher
concentration of strong electrolytes (alkali metal salts)
serves as supporting electrolyte

(iii) Easy to remove
Hg   microelectrodes layer on mercury
diffusion
drop surface when the
drop falls

（螺线管）

（活塞）

（聚氨酯）

（金属垫圈））
0.05~
0.5mm
diameter
Advantages of DME (compared to planar electrode)
● clean surface generated
● rapid achievement of constant current during drop
growth
● Hg easily oxidized, limited use as anode(E < +0.4V)
● remixing of solution when drop falls to remove previous
2Hg + 2Cl- -2e →Hg2Cl2
diffusion layer
●nonfaradaic residual currents limit detertion to > 10-5
● high-1. overvoltage means even metals with high –Ve E0
mol.L Hg
can be measured without H2 formation
●cumbersome(笨重的,尴尬的) to use(toxic mercury)
●sometimes produce current maxima for unclear
reasons( use maxima suppressor)
Sample Cells
§5-2 Equation of diffusion current A basis of
polarographically quantitative analysis

On dropping mercury electrode:

Mn+ + ne- +Hg              M(Hg)

RT    Ce
Ede =   Eo   +    ln
nF    Ca
Where Ce is Mn+ concentration on the electrode surface,
Ca is M concentration in amalgam on electrode surface
Electrode
Diffusion layer   Bulk solution

d

Electrode

Concentration polarization
around mercury drop

Diffusion layer   Bulk solution
When the applied voltage exceeds the decomposition voltage,
diffusion-controlled current is expressed as:
i = K(C-Ce)
When the applied voltage gets more negative, Ce →0, then

id = KC

Id reaches a limiting value proportional to ion
concentration C in bulk solution, and do not changes with
applied voltage longer
Ilkovic equation---diffusion current equation
In above equations, K is called Ilkovic constant, it is expressed
as follows:

K = 607 n D1/2m2/3t1/6
Concentration of
id =   607nD1/2m2/3t1/6C                            electro-active
analyte(mmol.L-1)
Drop time
(sec)
Mercury mass flow
Diffusion coefficient
From above equation, we can find that when
rate(mg.sec-1)
of electroactive Number of transferring
Average limiting diffusion
current denoting matrix
temperature,average solution and capillary
analyte in     electrons in electrode
solution(cm 2.sec-1)
current on mercury drop from                  reaction(e/mol)
characteristic are kept constant, id is proportional               to C
drop forming to falling (mA)
How it works?
▲ The applied voltage is gradually increased, typically
by going to a more positive( more negative
decomposing potential)

▲ A small residual current is observed.

▲ When the voltage becomes great enough, reduction
occurs at the analytical electrode causing a current.

▲ The electrode is rapidly saturated so current
production is limited – based on diffusion of the
analyte to the small electrode.
How it works ?

The reduced species alters the surface of the
mercury electrode.

To prevent problems, the mercury surface is
renewed by “ knocking off ” a drop –providing a
fresh surface.

This results in an oscillation of the data as it is
collected.
Polarographically quantitative analytical methods

●Direct comparison method
If t, m, D and n are constant, then we can simplify things by
using a standard.
Then
i dSTD      CSTD

i d UNK     CUNK
Wave height of polarographic wave is determined easier
than peak current, so following equation is in more
common use

h STD     CSTD

h UNK     CUNK
●Calibration curve method
As shown in right graph

●
hx
i (or h)
●

●
●
●
Cx
C
Polarographic working curve

When only one sample is analysized, this method can be
employed.

At first measuring the polarographic wave height hx of
an unknown solution with a volume of V, then a little
amount of the standard solution of concentration CS with
a volume of VS is added and the wave height of the
mixture solution is measured. As we know, following
equations are vivid:
h X  KC X
 VCX  VSCS 
H  K
 VV        

        S   

(以毫米或记录纸格数表示)，而不必测量扩散电流的

Quantitative Analysis

■From Ilkovic equation:
Id = KC
Usually use method of standard Additions(with uL
■Detection Limits: ~ 10-5 ~ 10-6mol.L-1
■Resolution: DE1/2 ≈ 0.2V(not very good)

How do the DL and Resolution be improved?
§5-3 Halfwave potential —polarographic qualitative analysis

下面推导极谱波方程式

A + ne-           B

CAe concentration of A on mercury drop surface
CA concentration of A in bulk solution
CBe concentration of B the electrode surface
if B soluble, CBe concentration of B in the solution near the electrode
if B forms amalgam, then it means B concentration in amalgam
if B is metal element and insoluble in mercury, then it equals to 1
CB equals to zero, the concentration of B in bulk solution
Nernst equation is still vivid here:

0.059    gACAe
Ede   = Eo + n    lg
gBCBe

Where
-id = kACA
-i = kA(CA- CAe)
CAe may be calculated according to above eqs.
-id + i
CAe   =     kA
On the other hand, according Faradaic law, during electrolysis,
concentration of reduction production B is proportional to
current flow, that is,
CBe ∝ - i
Supposed K = 1/ kB   -i
CBe =- K i
kB
Hence
0.059    gAkB id- i
lg
Ede =      Eo   + n       gBkA • i

0.059 gAkB     0.059    id - i
=   Eo   +      lg      +       lg
n     gBkA     n         i
0.059 gAkB
令 E’ =     + n lg g k
Eo
B A
0.059    id - i
Ede= E‘ +        lg         (*)
n         i

When i = ½ id , log term in above equation is equal to zero,
corresponding potential is called halfwave potential E1/2

0.059 gAkB
E1/2 =   Eo   +         lg             (#)
n     gBkA

●E1/2 independent on the concentration
●basis of qualitative analysis
Because cathode current is in more common use, equation (*) is
rewriting as:

0.059    (id )c - ic
Ede= E1/2   + n    lg                  For a reduction wave
ic
0.059    (id )a - ia
Ede= E1/2   -       lg                 For an oxidation wave
n          ia
0.059    (id )c - i
Ede= E1/2   + n    lg                  For a complex wave
i – (id )a

For three types of polarographic waves mentioned above, E1/2
have a same expression as formula(#)
E1/2

◆

◆
Why using E1/2 but not Edec as a qualitative

i(mA)
analysis basis?

Ede (vs.SCE)V
Polarographic waves of different concentrations of Cd2+

[Cd2+] :
in 1M KCl solution
i

E1/2   E
§5-4 Interference currents and their removing methods

● residual current
■ redox reactions of impurities in solution
■ charging of Hg drop

Charging current formation is shown in the figures
next page
+ ++ + +                  - - - - -
After voltage applied             - - - - -   ≈          ≈ + ++ + +     ≈
Before voltage applied
G           G               G

Null potential
DME         当接通回路，但未施加外加电
point
压时，滴汞电极与参比电极短
DME     路，这时汞滴带正电，溶液中
+
+
+
+
阴离子向电极表面扩散
++ + +
Calomel
electrode

Corresponding to section cb
Calomel                                      0.1M
electrode

Corresponding to section ac

(约为10-7A数量级)通过（Why some 10-7A? Please refer to
page 157~158, in the teaching book)， 这已足以引致困难。

● Migration current

In polarographic analysis, you must remove

convection(对流)
migration（迁移） of the sought-for ions in the solution

Why?

Migration current The current produced by static attraction
of the electrode to sought-for ions
它与被分析物质的浓度之间并无 一定的比例关系，故
应予以消除。
How to remove them?

■Hold the solution still(使溶液保持禁止）to
eliminate convection

■Add supporting electrolyte to remove migration
Supporting electrolyte: strong electrolyte, inert
(electro-inactive), with a concentration 100 times
than sought-for ion
●Maximum (or malformed peak )

Shielding
region(具体原因
+       +    请参照教材
-    -     P159)
+     - +
+- - +
+ ++
Measurements removing current maxima
surfactant, eg. 动物胶，聚乙稀醇，羧
甲基纤维素, Triton X-100等, ≤0.01%
● Oxygen wave
试液中的溶解氧在滴汞电极上被还原而产生两个极谱波：

The first:
O2 +2H+ + 2e-       H2O2     ( acidic solution)
O2 + 2H2O +2e-     H2O2 + 2OH- (neutral or basic medium)
E1/2 = -0.05V(vs.SCE)
The second:
H2O2 + 2H+ + 2e-          2H2O (acidic medium)
H2O2 + 2e-      2OH-      (neutral or basic medium)
E1/2 = -0.94V(vs.SCE)
Oxygen wave eliminating methods

●Hydrogen wave
polarographic analysis
•Relatively high sensitivity, kinear range: 10-2 ~ 10-4mol.L-1
• Relative error: ±2%, as good as that of spectrophotometry
• Simultaneously determine 4 ~ 5 analytes at one time under
appropriate condition
•A little amount of test sample needed
•rapid analysis
•Excellent reproductivity (通过的电流小，对溶液组成无明显影响)
•Wide application field (metal ion, metal complex, anion or
organic compounds etc that is electro-active)
• poor sensitivity
• prewave interference
• poor resolution, DE1/2 ≥100mV for practical separation
of two peaks
§5-6 Polarographic Catalytic Wave

Electrode
reaction
product
process     process
Chemical
reaction

A + ne- → B (electrode reaction)

k1
B + X → A + Z (chemical reaction)

• A is called catalyst
• polarographic current is called catalytic current, i1∝[A]
• chemical reaction is its velocity-determining step
• X must have high over-potential on the electrode
to insure catalytic circle
For example

Total reaction: 2Fe2+ + H2O2 → 2OH- + 2Fe3+

Another one:
MoO52- 2H+ + 2e → MoO42- + H2O

MoO42- + H2O2 → MoO52- + H2O
When no adsorption exists, catalytic wave and classical
polarographic wave have same shape, catalytic current is
expressed as follows:

i1 = 0.51nF D 1/2 m 2/3 t 2/3 k 1/2 Cx1/2 CA

Concentration
Limiting                Rate         of X and A in
catalytic             constant          solution
current
Difference between catalytic wave and diffusion wave:

For polarographic catalytic wave, the current is independent
on height of mercury column:

i1 ∝ m 2/3t 2/3 ∝ h 2/3 h -2/3 ∝ 1

But for diffusion-controlled current
id ∝ m 2/3t 1/6 ∝ h 2/3 h -1/6 ∝ h1/2
Temperature coefficients:
1% ~2% / ℃ for id
4% ~ 5% and more / ℃ i1

催化氢波（自学）
§5-7 Single-sweep polarography(单扫描极谱法）
(Oscillographic polarography，示波极谱法)

Classical polarography:

■ Slow direct current voltage scanning rate: 0.2V/min, some
100 drops of mercury per scan
■ Big residual current

Single-wseep polarography:
■ Rapid scanning rate: 0.25V/sec, one drop of mercury per scan
■ Little residual current
■ Oscillographic polarograph
U

i
R
i
ip
Pt
SCE

Ep
DME
-U

ip and Ep are respectively peak current and peak voltage
U is toothed wave voltage(锯齿波电压)
For reversible electrode reaction, diffusion current equation
of single-sweep polarography is expressed as follows

ip = 2.69×105n3/2 D1/2 u 1/2 AC

u is scan rate of voltage(V.s-1), A is electrode area (cm2)
Relationship between potential at peak Ep and halfwave
potential E1/2
RT          0.028
Ep = E1/2 – 1.1    = E1/2 -                  (25℃)
nF            n

For reduction wave, Ep is -28/n mV more negative than corresponding
E1/2, and for oxidative wave, 28/n mV more positive than E1/2
• Sensitivity: DL ~ 10-7mol.L-1, 2-3 magnitude order higher
than classical polarography
• More precise, measuring peak height, but not wave
height
• Simple, rapid
• Higher resolution, peak separation of 35 ~ 50mV resolved
• Little prewave interference, 5s interval time before
scanning
• Little oxygen wave interference, in-reversible electrode
reaction shows very weak or even no wave
BACK

Back
● Cyclic voltammetry

■ 施加等腰三角形脉冲电压
■ 循环伏安法与示波极谱法具有同样形式的峰电流和峰
电位方程式

+5.0
Cathodal wave
U                            Reduction(阴极）
Us                                       ipc
i   0.0

Ui                                ipa
-5.0                         Anodic wave
Oxidation（阳极）
DEp
t                                           E
The peak potential difference between cathodal peak and
anodic peak is
RT = 56.5
DEp = Epa – Epc = 2.22                  (mV)
nF       n

§ 5-8 Squar-wave polarography

U
自 学

●掌握方波极谱法提高极谱分析测定灵敏度的原理
● 方波极谱法有何特点？
●应用方波极谱时应注意那些问题？
§5-9 Pulse polarography

脉冲极谱法是在方波极谱法的基础上发展起来的，施加
电压的方式也与方波极谱基本类似，即在线性扫描直流
电压的基础上施加一个脉冲电压。不同的是方波极谱中
方波电压是连续施加的，而脉冲电压是不连续的，即当
汞滴增长到一定时间时，提供一个电压脉冲。这种方式
可以显著地降低电容电流，从而提高测定的灵敏度、选
择性。

脉冲极谱法有两种类型：
█差示脉冲极谱法：线性扫描电压+脉冲电压
灵敏度最高，波形与方波极谱相似，测定峰值电流

█常规脉冲极谱法：振幅随时间增加的脉冲电压
波形与经典极谱波相似

§5-10 Stripping voltammetry

溶出伏安法也称为反向溶出极谱法，这种方法是使被测定
的物质，在适当的条件下电 解一定的时间，然后改变电
极的电位，使富集在该电极上的物质重新溶出，根据溶出
过程中所得到的伏安曲线来进行定量分析。
（沉积过程）
（溶出过程）

Electrodes in stripping voltammetry

●Hung mercury electrode
● glass carbon electrode mercury plating(镀汞膜的玻

Problems
■ Compared with other polarographic methods, how about
the sensitivity of sripping voltammetry?
■ what advantages do hung mercury electrode and mercury
membrane electrode have ?
§5-11 单指示电极安培滴定（Amperometric titration
with single indicating electrode, polarographic titration)

伏安滴定法是应用伏安曲线的原理来确定化学计量点
的容量分析方法。如果在滴定时观察电流的变化来确
定化学计量点,就称为电流滴定或安培滴定.如果通过
观察电位的变化来确定化学计量点,则成为电位滴定.
Amperometric titration: keeping potential constant
Potentiometric titration: keeping current constant or
at null-current
a: analyte is electroactive (able to be reduced on electrode),
but the titrant is not
b: analyte and titrant are all able to be reduced on the polar
electrode
Electrodes
Reference electrode: calomel electrode,
mercury pool electrode
Working electrode: dropping mercury electrode,
solid microelectrode
• Solid microelectrode can be used
• wide linear range. 0.1 ~ 10-4mol.L-1
Using a electrode with a big area, DL can be down to
10-6 mol.L-1
Back titration can increase upper limit of determination
• some electro-inactive materials can also be measured
using electro-active titrant.
Example

Th4+                           ThF62-
（非电活性）
3+          Titrated by F-
Al                             AlF6-

Titration
continued

ThF62-
AlF6-
FeF63-
§5-12 双指示电极安培滴定（永停滴定）

下图
Ce4+ + Fe2+ = Ce3+ + Fe3+

●由于外加电压很小，只有可逆电对

●不可逆电对，电解池中无电流通过，

●当0<a<1或a>1时，溶液中分别存

a=1,5等时，电对的可逆性最高，而

●在永停滴定时，外加电压很小，

point method

●With reversible system titrating
reversible one, curve ABCE in the left
figure. Eg. Ce(IV)→Fe3+
● With irreversible system titrating
reversible one, curve ABCD in the left
figure, eg. S2O32- →I2
● With reversible system titrating
i                    irreversible, curve ABC in the lower
C
left side. Eg. I2 → S2O32-(永停法）
A
B

O           a
§5- 13 双指示电极电位滴定
（potentiometric titration with double indicating electrodes)

●potentiometric titration includes two kinds
single-indicating electrode
double-indicating electrode

●双指示电极电位滴定(恒电流)和双指示电极电流滴定(恒电
位)相似。区别在于，后者保持电位恒定，观察电流的变化，前者则保持
电流恒定，而观察电极电位的变化。
a =0             a =1
← DE→   ← DE→
滴定终点可 用作图法求出，
也可直接由pH计指针的摆
a=0.5      a>1
动确定。

I           III
0<a<1          a>1

II

a

```
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