§5 Voltammetry 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.

Cd2+ + 2e- Cd 2OH- -2e H2O + 1/2 O2 U外 ∝ i U外- Ud= iR When applied voltage reaches the decomposition voltage of metal ion: (Cd2+) 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, 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 E = Eo + ln CM RT 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） Limiting current A B C D When a microplatinum electrode or dropping mercury electrode is used and no stirring is carried out, concentration polarization takes place soon, following polarogram is obtained

Cd2+ + 2e- +Hg Cd(Hg) (amalgam) 2Hg - 2e- + 2Cl- Hg2Cl2 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 voltage, BC section in the figure Limiting current A B C D Cathode (DME): Cd2+ + 2e- +Hg Cd(Hg) (amalgam) Anode (calomel or pool mercury electrode with a big area): 2Hg - 2e- + 2Cl- Hg2Cl2

U = ESCE -Ede = -Ede( vs. SCE) 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。

（活塞） （螺线管） （金属垫圈）） （聚氨酯） 0.05~ 0.5mm diameter (iii) Easy to remove diffusion layer on mercury drop surface when the drop falls Hg microelectrodes

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

Sample Cells

Knocker, 敲击器，门环

Mn+ + ne- +Hg M(Hg) Ede = Eo + ln RT nF Ce Ca §5-2 Equation of diffusion current A basis of polarographically quantitative analysis On dropping mercury electrode: Mn+ + ne- +Hg M(Hg) Ede = Eo + ln RT nF Ce Ca Where Ce is Mn+ concentration on the electrode surface, Ca is M concentration in amalgam on electrode surface

Concentration polarization around mercury drop Diffusion layer Bulk solution Electrode Diffusion layer Bulk solution Electrode d Concentration polarization around mercury drop

When the applied voltage gets more negative, Ce →0, then 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

K = 607 n D1/2m2/3t1/6 id = 607nD1/2m2/3t1/6C 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 id = 607nD1/2m2/3t1/6C Concentration of electro-active analyte(mmol.L-1) Drop time (sec) Mercury mass flow rate(mg.sec-1) Diffusion coefficient of electroactive analyte in solution(cm2.sec-1) From above equation, we can find that when temperature, matrix solution and capillary characteristic are kept constant, id is proportional to C Average limiting diffusion current denoting average current on mercury drop from drop forming to falling (mA) Number of transferring electrons in electrode reaction(e/mol)

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

Wave height of polarographic wave is determined easier than peak current, so following equation is in more common use

●Calibration curve method As shown in right graph ● i (or h) C hx Cx 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:

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?

A + ne- B §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

0.059 gACAe n gBCBe lg Ede = Eo + Where -id = kACA -i = kA(CA- CAe) Nernst equation is still vivid here: Ede = Eo + 0.059 gACAe n gBCBe lg Where -id = kACA -i = kA(CA- CAe) CAe may be calculated according to above eqs. CAe = -id + i kA

CBe ∝ - i CBe =- K i - i kB Ede = Eo + 0.059 gAkB id- i n gBkA i lg • On the other hand, according Faradaic law, during electrolysis, concentration of reduction production B is proportional to current flow, that is, CBe ∝ - i CBe =- K i Supposed K = 1/ kB - i kB Hence Ede = Eo + 0.059 gAkB id- i n gBkA i lg • = Eo + 0.059 gAkB n gBkA lg 0.059 id - i n i +

0.059 gAkB n gBkA lg E’ = Eo + 0.059 id - i lg n i Ede= E‘ + 令 Ede= E‘ + 0.059 id - i n i lg ( * ) When i = ½ id , log term in above equation is equal to zero, corresponding potential is called halfwave potential E1/2 E1/2 = Eo + 0.059 gAkB n gBkA lg (#) ●E1/2 independent on the concentration ●basis of qualitative analysis

0.059 (id )c - ic lg n ic Ede= E1/2 + 0.059 (id )a - ia n ia Because cathode current is in more common use, equation (*) is rewriting as: For a reduction wave Ede= E1/2 + 0.059 (id )c - ic n ic lg Ede= E1/2 - 0.059 (id )a - ia n ia For an oxidation wave 0.059 (id )c - i n i – (id )a For a complex wave For three types of polarographic waves mentioned above, E1/2 have a same expression as formula(#)

◆ E1/2

Polarographic waves of different concentrations of Cd2+ i(mA) Ede (vs.SCE)V Polarographic waves of different concentrations of Cd2+ [Cd2+] : in 1M KCl solution Why using E1/2 but not Edec as a qualitative analysis basis?

i E E1/2

§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

当接通回路，但未施加外加电压时，滴汞电极与参比电极短路，这时汞滴带正电，溶液中阴离子向电极表面扩散 ≈ + - G 0.1M Null potential point + DME Calomel electrode Corresponding to section cb After voltage applied DME Calomel electrode Corresponding to section ac Before voltage applied 当接通回路，但未施加外加电压时，滴汞电极与参比电极短路，这时汞滴带正电，溶液中阴离子向电极表面扩散

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（迁移） of the sought-for ions in the solution ● 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 The first: O2 +2H+ + 2e- H2O2 ( acidic solution) 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 •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 Diffusion process Electrode reaction Chemical reaction Adsorption process Reactant product

A + ne- → B (electrode 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) B + X → A + Z (chemical reaction) k1 • 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

Total reaction: 2Fe2+ + H2O2 → 2OH- + 2Fe3+ 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 of X and A in solution Limiting catalytic current Rate constant

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

ip and Ep are respectively peak current and peak voltage DME R Pt SCE i ip Ep -U ip and Ep are respectively peak current and peak voltage U is toothed wave voltage(锯齿波电压)

ip = 2.69×105n3/2 D1/2 u 1/2 AC RT 0.028 Ep = E1/2 – 1.1 = E1/2 - nF n 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 Ep = E1/2 – 1.1 = E1/2 - RT nF 0.028 n (25℃) 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 U i 0.0 -5.0 +5.0 ipa ipc DEp E i Cathodal wave Reduction(阴极） Anodic wave Oxidation（阳极） t U Ui Us

The peak potential difference between cathodal peak and anodic peak is DEp = Epa – Epc = 2.22 RT nF = 56.5 n (mV) 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

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+ Al3+ Fe3+(added) Titrated by F- ThF62- AlF6- Titration continued FeF63- （非电活性）

（Dead-stop end point titration） §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 irreversible, curve ABC in the lower left side. Eg. I2 → S2O32-(永停法） i a A B C O

（potentiometric titration with double indicating electrodes) §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。

对于可逆电对，产生同样大小的电流所需要提供的电压小于不可逆电对 a =0 a =1 a=0.5 a>1 ← DE→ 滴定终点可 用作图法求出，也可直接由pH计指针的摆动确定。 I III II IV a 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小于不可逆电对