页数：110页文件大小：5.20 MB来源： 仪器分析ppt课件
本课件以英文讲解伏安分析法，从电极过程与传质方式出发，介绍极谱法、循环伏安、脉冲伏安与溶出伏安技术的原理、波形特征与典型应用。
§5 Voltammetry§5-1 Basic principle of polarograpy Voltammetry 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-CdOxidation reaction on anode:2OH--2e H2O + 1/2 O2U外∝i Where U外denotes applied potential,Udis decomposition potential, is total resistance of electrolysis circuit,iis current through the circuit.U外-Ud= R(Cd2+)
When following conditions are obeyed, U外–i graph is showedin following Figure Lower current density during electrolysis Adequatelystirring to removeconcentration gradient No quantitative relationship between current (or potential)and concentration ofinterested ions
To find the analytical relationship between the current andthe 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 STIRRIN Gto insure enough high concentration difference between the electrode surface and the solution bulk Then = Eo+ ln CMR Tn
When the current flowed for only short period through theelectrode, ion concentration on the surface of the electrodereduce suddenly. The difference in ion concentrations between the surface and the bulk solution is equivalent to an electro chemical cell, which is calledconcentrationpolarization(浓差极化).thus, there is voltage that is equivalent to this concentration change calledconcentrationpolarization potential（浓差电势）When microplatinum electrode or dropping mercuryelectrode is used and no stirring is carried out,concentration polarization takes place soon, followingpolarogram is obtained Limiting currentABCD
When applied voltage does not reach reduction voltage of metal ion, only little current flow, called residual currentproduced by reduction of impurities and charging current,eg ABin the Figure Limiting currentABCD Arriving on decomposition voltage,the electrode reactions occur, the current rises rapidly with increasingvoltage,BCsection in the figure Cathode (DME):Cd2++ 2e-+Hg Cd(Hg)(amalgam)Anode (calomel or pool mercuryelectrode with big area):2Hg-2e-+ 2Cl-Hg2Cl2
When it reaches point voltage, due to concentrationpolarization, the current arrives at limiting value anddoes 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) + R∵ and are very little inpolarographic electrolysis = ESCE-Ede=-Ede( vs. SCE)To remove completely influence of R, three electrodesystem is usually used.
Very little oscillation
Polarography First voltammetric technique Differs form hydrodynamic
unstirred (diffusion dominates)
dropping Hg electrode (DME) is used as aworking 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）0.05~0.5mmdiameter(iii) Easy to removediffusion layer on mercury drop surface when the drop falls Hg microelectrodes
Advantages of DME (compared to planar electrode)
clean surfacegenerated
rapidachievement of constant current during dropgrowth
remixingof solution when drop falls toremovepreviousdiffusion layer
high Hgovervoltagemeans even metals with high–Ve E0can be measured without H2formation Disadvantages of DME
Hg easilyoxidized, limited use as anode(E < +0.4V)2Hg + 2Cl--2e→Hg2Cl2
non faradaic residual currentslimit detertion to > 10-5mol.L-1.
cumbersome(笨重的,尴尬的)to use(toxic mercury)
sometimes producecurrent maximafor unclearreasons( use maxima suppressor)
Sample Cells
§5-2 Equation of diffusion current basis ofpolarographically quantitative analysis On dropping mercury electrode:Mn++ ne-+Hg M(Hg)Ede= Eo+ lnRTnFCe CaWhere Ceis Mn+concentration on the electrode surface,Cais concentration in amalgam on electrode surface
Diffusion layer Bulk solution Electrode Diffusion layer Bulk solution Electroded Concentration polarizationaround mercury drop
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, thenid= KC Idreaches limiting value proportional to ion concentration in bulk solution, and do not changes withapplied voltage longer
In above equations, is called Ilkovic constant, it is expressed as follows:Ilkovic equation---diffusion current equation = 607nD1/2m2/3t1/6id= 607nD1/2m2/3t1/6CAverage limiting diffusion current denoting average current on mercury drop from drop forming to falling (mA)Number of transferringelectrons in electrodereaction(e/mol)Diffusion coefficient of electro active analyte in solution(cm2.sec-1)Mercury mass flow rate(mg.sec-1)Drop time(sec)Concentration of electro-active analyte(mmol.L-1)From above equation, we can find thatwhentemperature, matrix solution and capillary characteristic are kept constant, idis proportional to
How it works?
The applied voltage is gradually increased, typicallyby going to more positive( more negativedecomposing potential)
small residual current is observed.
When the voltage becomes great enough, reductionoccurs at the analytical electrode causing current.
The electrode is rapidly saturated so current product ion 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 isrenewed by “ knocking off ” drop–providing afresh surface.This results in an oscillation of the data as it iscollected.
Direct comparison method Polarographically quantitative analytical methods If t, m, and are constant, then we can simplify things by using standard.Then
Wave height of polarographic wave is determined easierthan peak current, so following equation is in morecommon use
Calibration curve method
(or h)Chx CxPolarographic working curve As shown in right graph
Standard add it ion method When only one sample is analysized, this method can be employed.At first measuring the polarographic wave height hxofanunknown solutionwith volume of V, then alittleamount of the standard solution of concentration CSwitha volume of VSisaddedand 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 Add it ions(with uLadditions, 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-BC Aeconcentration of on mercury drop surfaceCAconcentration of in bulk solution CBe concentration of the electrode surface if soluble, CBe concentration of in the solution near the electrodeif forms amalgam, then it means concentration in amalgam if is metal element and in soluble in mercury, then it equals to 1CBequals to zero, the concentration of in bulk solution
Nernst equation is still vivid here:Ede= Eo+0.059gAC AengBC Belg Where-id= kACA-i= kA(CA-CAe)CAemay be calculated according to above eqs.CAe=-id+ ik
On the other hand, according Faradaic law, during electrolysis,concentration of reduction product ion is proportional to current flow, that is,CBe∝-iCBe=-KiSupposed = 1/ B-ikBHence Ede= Eo+0.059g AkBid-ing BkAilg•= Eo+0.059g AkBng BkAlg0.059id-in ilg+
E’ = Eo+0.059g AkBng BkAlg令When = ½ id, log term in above equation is equal to zero,corresponding potential is called half wave potential E1/2E1/2= Eo+0.059g AkBng BkAlg
E1/2independent on the concentration
basis of qualitative analysis Ede= E‘+0.059id-in ilg(*)(#)
Because cathode current is in more common use, equation (*) isrewriting as:For reduction wave Ede= E1/2+0.059 (id)c-icniclg Ede= E1/2-0.059 (id)a-ianialg For an oxidation wave Ede= E1/2+0.059 (id)c-ini–(id)alg For complex wave For three types of polarographic waves mentioned above, E1/2have same expression as formula(#)
E1/2
i(mA)Ede(vs.SCE)VPolarographic waves of different concentrations of Cd2+[Cd2+] :in 1M KCl solution Why using E1/2but not Edecas qualitativeanalysis basis?
iEE1/2
§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 form at ion is shown in the figuresnext page
≈+++++-----≈≈+++++-----GGG0.1MNull potential point++++++++DME Calomelelectrode Corresponding to section cb After voltage applied DME Calomelelectrode 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。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 topage 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。残余电流一般可采用作固的方法予以扣除（见下图）。
Migration current In polarographic analysis, you must removeconvection(对流)migration（迁移）of the sought-for ions in the solution Why?Migration current The current produced by static attractionof 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-in active), with concentration 100 timesthan 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。++-----+++++++Shieldingregion(具体原因请参照教材P159)Measurements removing current maxima Add maximum suppresor, usuallysurfactant, 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 ofpolarographic 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 underappropriate 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, an ion ororganic compounds etc thatis electro-active)
Disadvantages•poor sensitivity•prewave interference• poor resolution,DE1/2≥100mVfor practical separation of two peaks
§5-6 Polarographic Catalytic Wave Diffusion process Electrodereaction Chemical reaction Adsorption process Reactantproduct
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-→ (electrode reaction)B + X→ + (chemical reaction)k1• is called catalyst• polarographic current is called catalytic current,i1∝[A]• chemical reaction is its velocity-determining step• must have high over-potential on the electrodeto insure catalytic circle
For example Total reaction: 2Fe2++ H2O2→ 2OH-+ 2Fe3+An other one:MoO52-2H++ 2e→ MoO42-+ H2OMoO42-+ H2O2→ MoO52-+ H2O
When no adsorption exists, catalytic wave and classicalpolarographic wave have same shape, catalytic current is expressed as follows:i1= 0.51n D1/2m2/3t2/3k1/2Cx1/2CA Limiting catalytic current Concentration of and in solution Rate constant
For polarographiccatalyticwave, the current is independent on height of mercury column:i1∝m2/3t2/3∝h2/3h-2/3∝1Difference between catalytic wave and diffusion wave:But for diffusion-controlled currentid∝m2/3t1/6∝h2/3h-1/6∝h1/2Temperature coefficients:1% ~2% / ℃ forid4% ~ 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, some100 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
UDMER PtSC Eiip Ep-Uiipand Epare respectively peak current and peak voltage is toothed wave voltage(锯齿波电压)
For reversible electrode reaction, diffusion current equation of single-sweep polarography is expressed as followsip= 2.69×105n3/2D1/2u1/2ACuis scan rate of voltage(V.s-1), is electrode area (cm2)Relationship between potential at peak Epand half wave potential E1/2Ep= E1/2–1.1 = E1/2-RTnF0.028n(25℃)For reduction wave, Epis-28/n more negative than correspondingE1/2, and for oxidative wave, 28/n more positive than E1/2
Advantages of single-sweep polarography•Sensitivity: DL ~ 10-7mol.L-1, 2-3 magnitude order higherthan classical polarography•More precise, measuring peak height, but not wave height•Simple, rapid•Higher resolution, peak separation of 35 ~ 50m resolved•Little prewave interference, 5s interval time beforescanning•Little oxygen wave interference, in-reversible electrodereaction 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0.0-5.0+5.0ipaipcDEp EiCathodal wave Reduction(阴极）Anodic wave Oxidation（阳极）tUUi Us
The peak potential difference between cathodal peak and anodic peak is DEp= Epa–Epc= 2.22RTn F=56.5n(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
§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 aboutthe 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 titrationwith single indicating electrode, polarographic titration)Amperometric titration:keeping potential constant Potentiometric titration:keeping current constant orat null-current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.
a: analyte is electroactive (able to be reduced on electrode),but the titrant is notb: analyte and titrant are all able to be reduced on the polarelectrode
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-1Using electrode with big area, DL can be down to10-6mol.L-1Back titration can increase upper limit of determination• some electro-in active materials can also be measured using electro-active titrant.
Example Th4+Al3+Fe3+(added)Titrated by F-ThF62-AlF6-Fe3+(added)Titration continued ThF62-AlF6-FeF63-（非电活性）
§5-12双指示电极安培滴定（永停滴定）（Dead-stop end point titration）下图
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5Ce4++ Fe2+= Ce3++ Fe3+
当0
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。
iaABCO Titration curve of dead-stop end point method
With reversible system titratingreversible one, curve ABCE in the leftfigure. Eg. Ce(IV)→Fe3+
With irreversible system titratingreversible one, curve ABCD in the leftfigure, eg. S2O32-→I2
With reversible system titratingirreversible, curve ABC in the lower left side. Eg. I2→ S2O32-(永停法）
§5-13双指示电极电位滴定（potentiometric titration with double indicating electrodes)
potentiometric titration includes two kinds single-indicating electrodedouble-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IIIIIII Va0
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