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
 Adequately stirring to remove
 concentration gradient



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
are adopted:

  ●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

通常用通入N2 ,H2等 方法消除溶解氧对极谱测定的影
响。
                 (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
 Disadvantages of DME
   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
●Standard addition method

 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   




在进行定量测定时,通常只需测量所得极谱波的波高
(以毫米或记录纸格数表示),而不必测量扩散电流的
绝对值。
            Quantitative Analysis

■From Ilkovic equation:
                       Id = KC
Usually use method of standard Additions(with uL
additions, no volume correction needed)
■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
       (non-faradaic current / non-redox current)


       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
电容电流是由于汞滴表面与溶液间形成的双电层,在与参比电报
连接后,随着汞滴表面的周期性变化而发生的充电现象所引起
的。此电流与滴汞电极的电位有关。
残余电流一般可采用作固的方法予以扣除(见下图)。

对于微量组分(如<10-5M)的测定,虽然注意到所用试剂的纯度并
经过仔细的除氧,但由于电容电流的存在,仍有微量的残余电流
(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。
所以电容电流的存在是提高极谱分析灵敏度的主要障碍。
● 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 )
极大(或畸峰)
在极谱分析中,常常出现 一种特殊现象,即在电解开始后, 电流随
电位的增加而迅速增大到 一个很大的数值,当电位变得更 负时、这
种现象就消失而趋于正 常),这种现象称为极大 或畸峰。


                    Shielding
                    region(具体原因
       +       +    请参照教材
         -    -     P159)
       +     - +
        +- - +
         + ++
Measurements removing current maxima
 Add maximum suppresor, usually
 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
§5-5 Characteristics and disadvantages of
polarographic analysis
 ●advantages
  •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)
●Disadvantages
  • poor sensitivity
  • prewave interference
  • poor resolution, DE1/2 ≥100mV for practical separation
    of two peaks
§5-6 Polarographic Catalytic Wave




                                      Electrode
                                      reaction
  Reactant   Diffusion   Adsorption
                                                  product
             process     process
                                      Chemical
                                      reaction
如果化学反应与电极反应同时发生(平行),而且化学反应为
定速步骤,则该极谱波称为极谱催化波 , 例如,

         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
●Advantages of single-sweep polarography
• 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


由于使用高输入
阻抗的电位计,
所以极谱电流主
要从对电极上通
过,电解回路中
流过的电流很小,
因而工作电极的
电位完全受外加
电压所控制,参
比电极的电位保
持恒定
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

对于不可逆体系,DEp > 56.5/n(mV), ipa / ipc < 1,阴阳
峰电流比值越小,则该电极体系越不可逆
    § 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
自学:掌握脉冲极谱法提高测定灵敏度的原理
§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)
根据溶出过程中阳极电流与离子浓度的线性关系进行定量
Electrodes in stripping voltammetry

●Hung mercury electrode
● glass carbon electrode mercury plating(镀汞膜的玻
璃态石墨电极)

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
 Advantages
• 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-
Fe3+(added)                    Fe3+(added)

                                   Titration
                                   continued

                               ThF62-
                               AlF6-
                               FeF63-
§5-12 双指示电极安培滴定(永停滴定)
(Dead-stop end point titration)

                 下图
Ce4+ + Fe2+ = Ce3+ + Fe3+

●由于外加电压很小,只有可逆电对
才有电流通过

●不可逆电对,电解池中无电流通过,
如左图中1和5

●当0<a<1或a>1时,溶液中分别存
在Fe3+ + e→Fe2+和Ce4+ + e →Ce3+可
逆电对,要使电解回路中产生电流 ,
需要的外加电压很小,当a=0.5,
a=1,5等时,电对的可逆性最高,而
当a=0 或a=1 时,电对为完全不可逆。

●在永停滴定时,外加电压很小,
所以只有可逆电对才有电流产生。
                    Titration curve of dead-stop end
                    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
对于可逆电对,产生同样大
小的电流所需要提供的电压                           IV
                              II
小于不可逆电对
                                           a

				
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